#### **2. Materials and Methods**

The schematic device processing started with the deposition of 500 nm thermally grown SiO2 on a RCA cleaned Si wafer as an isolation layer. For the bottom electrode, a 20 nm Ti adhesion layer with a Pt layer of 60 nm thickness was deposited by a DC sputtering system. Then an AlN switching layer of 10 nm thickness was deposited at room temperature in a mixed Ar and N2 ambient atmosphere using DC sputtering at a working pressure of 7.6 mTorr. Prior to patterning the top electrode, a 7 and 10 nm thick WNx diffusion barrier layer was deposited by DC sputtering at room temperature by maintaining the flow rate of Ar and N2 at 24 sccm and 12 sccm, respectively. Subsequently, an 80 nm thick Cu layer was deposited as the top electrode using DC sputtering at room temperature to complete the stacked device structure. Both the barrier and the Cu top electrode were patterned using a circular metal shadow mask to a diameter of 120 μm. The electrical DC and pulse characteristics were performed with the Agilent B1500/B1530 semiconductor parameter analyzer. The Cu top electrode was always biased with DC and pulse signals, while the Pt bottom electrode was grounded in the electrical measurement setup. The structural information of the device was taken by using a JOEL JEM-2010 transmission electron microscope (TEM).

#### **3. Results and Discussion**

Figure 1a depicts the schematic layout of the proposed Cu/WNx/AlN/Pt CBRAM device. The cross-sectional TEM image of the device shown in Figure 1b clearly indicates the

multiple layers in the stacked structure. The device switches from a high-resistance pristine state to a low-resistance state called the forming process. The forming behavior of without barrier layer (WOBL) and with barrier layer (WBL) devices shown in Figure 1c confirms a larger leakage current with low forming voltage in WOBL devices due to the diffusion of copper into the switching layer during top electrode deposition [33,34]. The insertion of the WNx barrier layer, which prevents copper diffusion, reduces the leakage current and increases the forming voltage. The result shows with a thicker WNx barrier layer (10 nm), forming voltage increases undesirably and during resistive switching operation, it shows volatile operation. Hence, a WBL device with a barrier layer thickness of 7 nm was compared with the WOBL device for further investigation. The forming voltage distribution for 10 devices is shown in Figure 1d. The average forming voltage of the WOBL device is 1.2 V, whereas it is 2.5 V for the WBL device. The device-to-device variation of Vforming is larger in the case of the WOBL device and is mainly due to uneven spatial copper diffusion into the AlN switching layer.

**Figure 1.** (**a**) Schematic structure of the Pt/AlN/WN/Cu RRAM device. (**b**) The TEM cross-sectional image of the device. (**c**) The forming characteristics of WOBL and WBL devices. (**d**) Forming voltage distribution for memristor without/with barrier layer for 10 devices.

Figure 2a,b show the typical DC current-voltage characteristics of the WOBL and WBL devices. Both devices exhibit bipolar switching behavior with a positive bias sweep of 1.2 V at a compliance current (CC) of 1 mA for set operation and a negative sweep of −0.8 V for reset operation, respectively. From the measured 100 DC switching cycles, we observed that the WOBL device shows larger cycle-to-cycle variation in HRS/LRS compared to the WBL device. Without the barrier layer, multiple incomplete conductive paths are formed by the diffusion of copper into the AlN layer during the forming process, which subsequently causes variation in set/reset switching cycles. The device-to-device and cycle-to-cycle on/off resistance distribution is plotted in Figure 2c,d with each device tested for 30 DC cycles. The on-state resistance, LRS, of WOBL devices is significantly lower compared to WBL devices. This indicates filament formation through a large amount of Cu ion migration. The WOBL devices show the worst-case coefficient of variances (σ/μ) of 167% and 33% for HRS and LRS, respectively. In the case of the WBL, the variations improved significantly to 38% and 18%, respectively. This result confirms the switching stability with the insertion of the barrier layer. The resistance at LRS increases with the increase

of temperature, which confirms the metallic nature of the conductive filament shown in Figure 2f. From the resistance-temperature plot, the temperature resistance coefficient is calculated by using Equation (1) [35]:

$$R(T) = R\_0[1 + \alpha(T - T\_0)]\tag{1}$$

where *R*0 is the resistance at temperature *T*0 and α is the temperature coefficient of resistance. The estimated α = 0.003 confirms the formation of a Cu filament during the on state.

**Figure 2.** Typical DC I-V characteristics for 100 cycles; (**a**) without barrier layer; (**b**) with barrier layer (7 nm); and (**c**) with barrier layer (10 nm). The statistical distribution of LRS and HRS for memristor; (**d**) without barrier layer; (**e**) with barrier layer; and (**f**) temperature-dependent resistance in LRS.

The conduction mechanism of the Cu/WNx/AlN/Pt CBRAM cell was investigated by analyzing the ln(I)~ln(V) graph in different regions as shown in Figure 3. The I-V curve between 0 and 0.25 V with a slope of 1.2 is well-fitted with the ionic conduction Equation (2) given by [36,37]:

$$
\ln(j) \propto \ln(V) - \left(\ln T + a/T\right) \tag{2}
$$

where *J*, *V*, *a*, and *T* are current density, bias voltage, constant, and temperature. This equation explains that ionic conduction occurs due to the oxidation of electrochemically active metal Cu into Cu ions and then the migration of Cu ions to the Pt bottom electrode with the application of positive bias to the top Cu electrode. The Cu ions are reduced at the bottom Pt electrode and the metallic conductive filaments grow from the bottom electrode to the top electrode, making the connection between the electrodes. As the applied bias voltage increases, the diameter of the filament becomes thicker, resulting in higher slopes of 2.1 and 3.7 between 0.25 to 0.58 V and 0.58 to 0.65 V, respectively. Due to the presence of the WNx barrier layer, there is a gradual increment in slope. During biasing from 0.55 to 0 V, the current plot fitted well with the ohmic conduction mechanism which can be expressed by Equation (3):

$$
\ln(j) \propto \ln(V) - a/T \tag{3}
$$

where *J*, *V*, *a*, and *T* are current density, bias voltage, constant, and temperature. The current conduction from 0 to −0.47 V follows Ohm's law as −0.47 V was not sufficient to rapture

the Cu filament. During reset operation with bias, from −0.48 to −0.74 V, there is a slope of −2.2 which indicates the breaking of the Cu filament, while from −0.74 to 0 V there is a positive slope of 1.3, showing the drift of Cu ions from the filament side to the Cu electrode. Similar conduction mechanisms were demonstrated using an Ag-based conductive bridge random access memory system in a prior study [36].

**Figure 3.** Conduction mechanism of WBL device in; (**a**) set operation HRS region from 0 to 0.65 V; (**b**) LRS region from 0.55 to 0 V, (**c**,**e**) reset operation from 0 to −0.47 V and from −0.47 to −0.74 V (**d**) reset operation HRS region from 0.74 to 0 V.

The schematic of the resistive switching mechanism for WOBL and WBL CBRAM devices is depicted in Figure 4, explaining switching stability. Because there is no barrier layer between the Cu atoms and the AlN switching layer, more Cu atoms diffuse into the AlN switching layer for the WOBL device than the WBL sample in the pristine state, as shown in Figure 4a,b. During positive bias, Cu ionization begins at the top electrode and progresses towards the Pt electrode, where it is reduced back to Cu atoms to form the conductive bridge in the CBRAM device. After the complete formation of the conductive path between the electrodes, the device switches to the LRS state. The WOBL layer inherits multiple incomplete conductive filaments with one or a few complete conductive filaments. During the reset process, the electrochemical dissolution of the filament happens, and the Cu ions drift back to the top electrode. The switching variability in the WOBL device is illustrated by taking two competing filamentary paths into account. Assuming the CF1 is an initially formed conductive path which undergoes continuous structural change with several set-reset switching cycles. The gap formed in the filament during the reset event is g1. The selected conductive path will be CF1 only if g1 < g2. The CF2 conductive path undergoes minimal structural change as very little current flows. After several set-reset cycles, the CF2 becomes the selected conductive path with g2 < g1, which leads to a new LRS/HRS value. The change in conductive path is the main source of switching instability, and it is more pronounced with the presence of multiple incomplete conductive filaments. The presence of the WNx barrier layer limits the diffusion of Cu atoms into the switching

layer, preventing the occurrence of multiple conductive paths as shown in Figure 4c. The lower number of filamentary paths improves switching stability, which is an important requirement for synaptic devices.

**Figure 4.** Schematic of (**a**) WOBL and WBL devices in a pristine state. Set and reset the switching mechanism of (**b**) WOBL and (**c**) WBL devices.

The endurance plots for both devices are shown in Figure 5a,b for 500 DC cycles. The HRS/LRS were evaluated at a read voltage of 0.2 V. The WBL device has shown a stable and consistent memory window as compared to the WOBL device. To further evaluate the nonvolatile operation of RRAM, the data retention characteristic behavior at HRS/LRS was evaluated at room temperature (RT) as well as the elevated temperature of 120 ◦C as displayed in Figure 5c,d. Both WOBL and WBL devices exhibited high retention of 104 s at RT. Nonetheless, at 120 ◦C, the HRS of the WOBL device degrades after 103 s due to temperature-assisted metal diffusion into the switching layer.

The gradual conductance switching rather than abrupt switching upon application of a pulse is an important requirement for the memristive device to behave as an artificial synapse in neuromorphic hardware. To evaluate the synaptic characteristics of the WBL device, 50 identical positive pulses of 0.8 V/1 μs for potentiation and 50 similar negative pulses of −0.8 V/1 μs for depression were applied to the device as shown in Figure 6a. The conductance increased gradually from 400 to 800 μS during the potentiation period, and similar progressive decrementing behavior was observed during the depression period. Figure 6b shows the normalized potentiation/depression curves from which the nonlinearity factor can be calculated by using the following Equations (4)–(6) [38]:

$$G\_P = B\{1 - e^{\left(\frac{P}{A}\right)}\} + G\_{\text{min}} \tag{4}$$

$$G\_D = -B\left\{1 - e^{\left(\frac{P - P\_{\text{max}}}{A}\right)}\right\} + G\_{\text{max}}\tag{5}$$

$$B = \frac{G\_{\text{max}} - G\_{\text{min}}}{1 - e^{\frac{-P\_{\text{max}}}{A}}} \tag{6}$$

where *G*, *G*max, *G*min, and *P*max denote the conductance, maximum conductance, minimum conductance, and maximum number of pulses, respectively.

**Figure 5. DC** endurance behavior of (**a**) WOBL and (**b**) WBL devices. Data retention characteristics of WOBL and WBL devices were measured at (**c**) room temperature and (**d**) 120 ◦C.

The non-linearities calculated for potentiation and depression are 2.2 and 3.5, respectively. Figure 6c displays the long-term potentiation/depression (LTP/LTD) for 30 epochs. When switching between successive pulses, the device displays smooth and monotonic transitions of conductance, which is desirable for enhancing neuromorphic systems' learning accuracy. The LTP/LTD characteristics of the device are suitable for pattern recognition applications of the neural network. The neurons transmit signals through the synapse, and the learning algorithm is used to update the weight value of the synaptic device. The WBL device shows a multilevel conductance state with better linearity and could achieve pattern recognition accuracy quickly. The above results confirm the AlN CBRAM with WNx barrier layer is a potential synaptic device for neuromorphic computing.

**Figure 6.** (**a**) Synaptic potentiation/depression characteristics measured by applying 50 identical 0.8 V/1 μs potentiation pulses and 50 identical −0.8 V/1 μs depression pulses. (**b**) Normalized conductance with nonlinearity measurement. (**c**) Thirty repeated potentiation/depression cycles of the WBL device.

#### **4. Conclusions**

In this study, we have demonstrated improved switching stability and excellent data retention along with highly linear 30 epoch LTP/LTD synaptic functions by inserting the WNx barrier layer in the AlN memristor. The result could be attributed to the insertion of a 7 nm thick WNx barrier layer, which prevents the formation of multiple conductive bridges by limiting the diffusion of Cu into the switching layer. The cycle-to-cycle and device-to-device switching uniformity improved substantially by regulating Cu migration in the host layer. The CBRAM device demonstrated longer DC endurance for 500 cycles and stable data retention for 103 s at 120 ◦C. The ohmic and ionic conduction mechanisms of the non-volatile CBRAM cell during set/reset operation were explained by fitting the current transport in the switching layer. Finally, the repeated LTP and LTD synaptic functions with a fixed pulse scheme are demonstrated.

**Author Contributions:** Conceptualization, S.K.M. and C.-H.W.; writing and data curation, S.K.M. and K.P.K.R.; fabrication and measurements, S.K.M., P.B.; formal analysis, review, and investigation, C.-H.W. and Y.K.; project administration, P.-T.L., P.B. and K.-M.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Ministry of Science and Technology under the contract MOST 109-2221-E-216-002.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

## *Article* **An Analysis of Some Properties and the Use of the Twist Map for the Finite Frenkel–Kontorova Model**

**Wolfgang Quapp 1,\* and Josep Maria Bofill 2,3**

	- 3 Institut de Química Teórica i Computacional, Universitat de Barcelona, (IQTCUB), Martí i Franqués, 1, 08028 Barcelona, Spain
	- **\*** Correspondence<EMAIL_ADDRESS>or<EMAIL_ADDRESS>
**Abstract:** We discuss the twist map, with a special interest in its use for the finite Frenkel–Kontorova model. We explain the meaning of the tensile force in some proposed models. We demonstrate that the application of the twist map for the finite FK model is not correct, because the procedure ignores the necessary boundary conditions.

**Keywords:** Frenkel–Kontorova model; average distance; finite chain; tensile force; twist map

#### **1. Introduction**

The Frenkel–Kontorova model (FK) was proposed in 1938 to discuss dislocations in a chain of particles [1]. In the last century, many aspects of solid-state physics have been discussed using the FK model as an example. One divides a set of particles into a one-dimensional subsystem of interacting elements and a remainder as a substrate. The latter acts on the extracted subsystem by a potential. Of special interest may be electronic applications [2–7] for Wigner electrons or Josephson junctions. Further models are chargedensity wave conductors [8–10], charge transport in solids and on crystal surfaces [11], magnetic or ferro- and antiferromagnetic domain walls [12], magnetic superlattices [13], superconductivity [14,15], and vortex matter [16–18], to name a few.

The FK model for a chain of *N* particles (called atoms) at positions *ui* on an axis has the energy [1,19]

$$\mathcal{U}I(\mathbf{u}) = \sum\_{i=1}^{N} \lambda \, V(u\_i) + \sum\_{i=1}^{N-1} \frac{k}{2} (u\_{i+1} - u\_i - a\_o)^2 \,. \tag{1}$$

The substrate potential function is the usual one

$$V(u\_i) = 1 - \cos\left(\frac{2\,\pi}{a\_s}u\_i\right).$$

The parameter *as* is the period of this potential, and *λ* is its amplitude. The second term is the spring term for the nearest neighbor forces between the atoms. Parameter *k* is its amount. The equilibrium distance, *ao*, of the chain would hold without the potential *V*, thus for *λ* = 0. Usually, the two periods *ao* and *as* are different [20].

Sometimes the equilibrium distance, *ao*, of the chain is missing [21–23]. At first, one has to assume that *ao* = 0 is used. One treats the FK model as a different one with the pure harmonic potential of the spring forces between the nearest neighbors but often with an additional linear tensile force of amount *μ*

$$\sum\_{i=1}^{N-1} \left[ \frac{k}{2} (u\_{i+1} - u\_i)^2 - \mu \left( u\_{i+1} - u\_i \right) \right]. \tag{2}$$

**Citation:** Quapp, W.; Bofill, J.M. An Analysis of Some Properties and the Use of the Twist Map for the Finite Frenkel–Kontorova Model. *Electronics* **2022**, *11*, 3295. https:// doi.org/10.3390/electronics11203295

Academic Editor: Lucas Lamata

Received: 20 September 2022 Accepted: 10 October 2022 Published: 13 October 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Note that the alternating tensile force of form (2) reduces to two summands

$$-\mu \left( \mu\_N - \mu\_1 \right) \ .$$

If *μ* = 0, then putting all *ui* = 0 (or putting all *ui* = *n as* with an integer *n*) gives zero energy [24–26]. This is the global minimum, but it is a trivial one. If one starts with any finite chain with no zero distances between the atoms, and if one uses the values of the parameters of ref. [21] for *λ* ≤ *k*, and *μ* = 0, then a minimization would return this trivial result.

In Appendix A, we remark that for *λ k*, further stationary states can exist for *ao* = 0 and for *μ* = 0. However, these states are not global minima.

The paper mainly discusses the application of the twist map on a finite FK chain. In Section 2, we recall the formulas for an equilibrium structure, and we argue against using these formulas to apply the twist map. In Section 3, we explain the meaning of the tensile force. In Sections 4 and 5, we discuss the boundary conditions of a finite FK chain and explain with examples the incorrect results of the twist map. Further small points are the energy of the FK chain and the putative problem of the irrational relations of the two periodicities of the FK model. Some aspects of our treatments include connections to an infinite FK chain [21].

#### **2. Equations for Stationary States**

At first, it seems that the gap of form (2) does not matter, because for the minimum search for the inner atoms, *ui*, holds an equation, where the *ao* disappears

$$\frac{\partial \mathcal{U}(\mathbf{u})}{\partial u\_{i}} = \frac{2\pi\lambda}{a\_{\rm s}}\text{sin}\left(\frac{2\,\pi u\_{i}}{a\_{\rm s}}\right) + k[2\,u\_{i} - u\_{i+1} - u\_{i-1}] = 0, \; i = 2, \ldots, N - 1. \tag{3}$$

Note that the linear tensile force with amount *μ* also disappears [27]. However, the *ao* as well as the *μ* do not disappear at all; they emerge in the two boundary equations for the first and the last atom of the chain, *u*1 and *uN* [19,28]

$$\frac{\partial \mathcal{U}(\mathbf{u})}{\partial u\_1} = \frac{2\pi\lambda}{a\_\text{s}} \text{sin}\left(\frac{2\,\pi u\_1}{a\_\text{s}}\right) - k[u\_2 - u\_1 - a\_o] + \mu = 0\tag{4}$$

and

$$\frac{\partial \mathcal{U}(\mathbf{u})}{\partial u\_N} = \frac{2\pi\lambda}{a\_s} \text{sin}\left(\frac{2\,\pi u\_N}{a\_s}\right) + k[u\_N - u\_{N-1} - a\_o] - \mu = 0 \,\text{J} \tag{5}$$

Equations (3)–(5), for all atoms *i* = 1, ... *N*, form a system of coupled equations, where we have to include the boundary conditions Equations (4) and (5). To select a single 'solution' of one or a small number of them will usually not give a correct stationary state of the FK chain.

In contrast to this simple remark, many researchers propose to use the 'twist map', which successively calculates one *ui*+1 if the former *ui* and *ui*−1 are known—an assumption that we cannot make. If one does not know the solution, one also does not know the location of the two special atoms at the start of the map [19]. In real calculations, the twist map is started at an arbitrary pair of two points in a finite region [21]. Of course, to start the twist map at arbitrary point pairs (see the M*i* in Figure 1 of ref. [21]) provides nice pictures, including the excursion to chaos. We claim that many calculations of twist maps do not use the correct initial values; for example, see Example 1 and Section 6 below.

**Example 1.** *A simple example is a chain with N = 3 atoms, with the parameters as* = 2 *π, k* = 2.5*, λ* = 1*, and ao* = 2*as*/3*. The equilibrium structures of a minimum are obtained by the NMinimize procedure of Mathematica 13.0, starting with a chain with ui* = *ao* (*i* − 1) *for i* = 1, .., 3*, as shown on the left of Figure 1.*

**Figure 1.** (**Left**): Minimum solution for an FK chain with *N* = 3 atoms. (**Right**): With an arbitrary start of *u*1 = 0, we obtain *u*2 = *a*0 = 2*as*/3, and we obtain with Equation (3) the shown point *u*3. However, the structure is not a minimum, see text. Note that the atoms are shifted on the site-up potential to help the imagination.

Using the twist map of Equations (4) and (3) starting at an arbitrary point, for example, with *u*1 = 0, we obtain with Equation (4) *u*2 = *a*0 = 2*as*/3, and we obtain with Equation (3) the structure on the right hand side of Figure 1. It does not look like a minimum. The left minimum has an energy of 2.756 units, but this special twist map 'solution' has an energy of 2.826 units. Its gradient (0, 0, 0.118)*T* is not a zero vector.

The reason for the deviation of the gradient from zero is that the third Equation (5) for *i* = *N* = 3 is not fulfilled for the obtained *u*3. Only when one begins with *u*1 of a stationary structure is the third equation fulfilled. Further arguments to understand the result are given in ref. [19]. We conclude with the following theorem.

**Theorem 1.** *Using the twist map at an arbitrary start point is useless. In the general case, it will not provide a stationary structure of the FK chain. The reason is that Equation (5) is not fulfilled, in the general case. This is not restricted to the N* = 3 *chain.*

The twist map fulfills the demand of equilibrium only from step to step. Only when the start pair belongs to the correct minimum do the results (under numerical problems, see below) build a correct minimum structure. In the system, one can fulfill some equations with false values, which vice versa compensate—however, one cannot assume that the other equations obtain the correct solution.

#### **3. A Remark on the Length of the Chain**

We treat the energy of the chain structure (1). When the spring distance of the chain, *ao*, and the period of the site-up potential, *as*, are equal, and if *μ* = 0, or if *a*0 = 0 and *μ*/*k* = *as*, or if *a*0 + *μ*/*k* = *as*, then an equilibrium chain exists in its ground state with all particles at the bottom of the site-up potential, with energy zero for every particle, and thus with zero energy for the chain in its ground state. (This case was originally treated [1] for an infinite chain.)

In any other case, an infinite chain needs an infinite energy in the sum, which is impossible. Strangely, the authors of ref. [29] stated that ". . . one does not hope that the sum of the energies converges." Nevertheless, they worked with the divergent sum. Tong et al. [30] treated a finite segment of the infinite incommensurate FK chain without the boundary conditions. Without further explanation, the problem was circumscribed by the word 'formal sum' [31,32].

A way out, avoiding the infinite energy of an infinite chain, was proposed [33] by dividing the energy of the chain by *N*, the number of atoms. So, one has a finite energy per atom [34,35], and one can apply the optimization per atom at *ui*, discussed in Section 2 [36].

#### **4. The Meaning of the Tensile Force**

If *λ* = 0, we see with Equations (4) and (5) that the equilibrium separation of the chain becomes

$$a\_0 + \mu/k \,. \tag{6}$$

In addition, if one uses the ansatz of form (2) with *a*0 = 0, then the value of the tensile force divided by the value of the spring force, *μ*/*k*, becomes the placeholder of the *a*0 in the original FK model. One can put [37,38]

$$l\_o = \mu/k \quad \rightarrow \quad \text{new} \quad a\_o \text{ .}$$

The meaning of the tensile force in (2) is to include an equilibrium separation of the chain, *lo* for *a*0. One can ask why one needs the tensile force.

On the other hand, one can ask for the action of the tensile force, if its amount *μ* increases. It has the form

> −*μ* **f** *T* **u**

with the special form of the force vector

$$\mathbf{f}^T = (-1, 0, \dots, 0, 1)\dots$$

At *μ* = 0, we may be in an original minimum (with *a*0 = 0 or not). Increasing the amount of *μ*, we can optimize another minimum. The curve, which describes the consecutive series of minima, is a Newton trajectory; it was named the curve of the force-displaced stationary points [19,39–44]. Newton trajectories connect stationary points of an index difference of one [45] on the original potential energy surface. It is a quite interesting property that the special form of the **f** vector acts as a change in the orginal distance, *a*0, of the atoms of the FK chain, see value (6), and not only as the tilding of the potential of the first and the last atom of the chain. The FK chain is similar to an accordion. If one pulls the ends, all of the bellows relax. Newton trajectories with force **f** can be used to calculate many kinds of solitones of the FK chain and, thus, intermediate minima of the potential energy surface and saddle points with an increasing index [3,6,19,46–48].

#### **5. The Meaning of the Free Boundary Conditions**

Now, we discuss the boundary conditions (BCs). If one has free BCs, then we cannot start with an arbitrary 'left' BC, because the minimization will probably result in different BC in the end. So, the steps of an arbitrary twist map start in a nebula. The developments by some researchers [21,49–51] (to name a few), which use the twist map, ignore that the chain will find another minimum structure at the boundary, in comparison to an arbitrary twist map result [19].

Of course, if one starts the twist map with the correct *u*1, *u*2 of a minimum structure or of another stationary state of the FK chain, then one can regain this stationary structure with the result of the twist map, at least for the first section of the structure; see the example below. However, we do not know where the stationary structure of an FK chain begins if the BCs are free.

**Example 2.** *The example is again the chain with parameters as* = 2*π, k* = 2.5*, λ* = 1*, and ao* = 2*as*/3*, for N = 3, 4, 8–10, 20, 47, 74, 99, 500, 1000, and N* = 5000 *atoms. The equilibrium structures, probably minima, are obtained by the NMinimize procedure of Mathematica 13.0 starting with a chain with ui* = *ao* (*i* − 1) *for i* = 1, ... , *N. The first atom of the chain at u*1 *changes its place with N, as well as the average distance*

$$
\vec{u} = \frac{\mu\_N - \mu\_1}{N - 1} \; \prime \tag{7}
$$

*see Table 1. The numbers in Table 1 are rational numbers, because they are the result of a computer calculation. We do not know whether the character of the limit for N to* ∞ *is rational or irrational. The two values possibly converge for large N against defined values around u*1 *= 0.369 and ao. However, we do not know the exact limit of a.*˜

**Table 1.** Position of the first atom of a minimum of an FK chain and its average distance.

We show in Figure 2 a minimum of an FK chain with *N* = 500 atoms. The central region represents the winding number, the ratio 2/3 of *ao*/*as*; however, the two boundary regions show the large influence of the free BCs. A swing in at the left boundary needs ≈50 atoms, and an analogous transient process needs ≈50 atoms at the right boundary. One could imagine that an infinite chain with the 2/3 ratio could be represented by the central piece of Figure 2. However, a cut anywhere relaxes the strain at the border [20], and the shown boundary pattern will emerge again. It also holds for *N* = 1000 and *N* = 5000, where we obtain similar pictures.

The structures of the FK chain at the reported minima are mirror symmetrical up to a length of *N* = 46; see the left panel of Figure 1. Beginning with *N* = 47, the symmetry is broken, and the different form at the two boundaries emerges, as in Figure 2.

**Figure 2.** Minimum solution for a fixed *ao*, see text. FK chain with *N* = 500 atoms, with the first 66 atoms on the left and the last 66 atoms on the right. The center is an enlarged piece with the regular pattern representing the rational relation to *as* sorting three atoms in two wells.

In Figure 3, we show the corresponding twist map representation of the first 66 atoms for *N* = 500. There, we used the map Φ*i* = *ui*(mod *as*) for the minimization result. Consecutive pairs of atoms are shown, (Φ*i*, Φ*i*+1), (Φ*i*+1, Φ*i*+2), (Φ*i*+2, Φ*i*+3), ... and so on. The dashed triangle is the start set of points, and the red triangle shows the periodic stable cycle of the central region of the FK chain. The swing in at the left boundary of the chain is the path from the dashed to the red triangle. Note that the points of the inner cycle form a kind of a unit cell defined by the used winding number, 2/3, but they are not free of tension. This is demonstrated by the relaxation at the boundaries.

**Figure 3.** Twist map representation of the first 66 atoms of a long chain. The dashed line is the start triangle of points, and the red line is the quasi-stable cycle of three atoms in one cell of two troughs, as in the central region of Figure 2. (The calculation was a minimization.)

#### **6. The Twist Map for a Finite FK Chain**

In the right side of Figure 4, we depict the result of the twist map used with the two correct initial points, *u*1 = 0.369 and *u*2 = 4.701, of the optimized structure. The calculation was performed with Mathematica 13.0 with the usual accuracy. The result fits the true structure up to *N* ≈ 300 atoms. Then, the twist map 'breaks out', and at *N* = 353 the former right BC appears. Its way out emerges by numerical effects, which can accumulate over the consecutive iterations.

**Figure 4.** (**Left**): FK chain, optimized minimum with *N* = 500 atoms. (**Right**): The result of the twist map with the two points of the minimum, *u*1 and *u*2, at the start. It repeats the left BC; however, it 'finishes' at *N* = 353 with a right BC; then, the calculation is reflected.

The twist map must include the handling of the tension of the central quasi-unit cells. The *N* = 4 minimum shown on the left of Figure 5, with a *u*1 value of 0.117, is two times 'shorter' than the putative unit cell of 4*π*/3, see Table 1. The distances of the minimized structure also change from atom to atom in the central part. It only looks like a unit cell. In reality, a unit cell does not exist.

The result for an infinite chain [21] does not hold here, where one has a unit cell if *ao*/*as* is a rational number. There is no period of the kind

$$u\_{i+3} = u\_i + \mathcal{D}a\_s \quad \text{but it holds} \quad u\_{i+3} = u\_i + \mathcal{D}a\_s + \varepsilon\_{i+3}$$

with variable values of  *i*. The smallest  *i* we find at the central region of the chain with 244 ≈ 2 × 10−11.

The fact that even the twist map calculation by Equation (3) finds (though at a false place) a correct upper boundary structure, as the direct optimization does, is very interesting. One has to consider that the quasi-perfect cyclic behavior in the central region is not the behavior of a limit cycle, in contrast to the propositions of ref. [36].

**Figure 5.** (**Left**): FK chain minimum for *N* = 4 atoms; it is not the unit cell of Figure 2, center; however, it is shorter, see Table 1. (**Right**) The result of a twist map calculation with the two points, *u*1 = 0 and *u*2 = 2*as*/3, of a putative unit cell at the start. It does not result in the quasi-unit cells of Figure 2.

Next, we show a twist map calculation in the right panel of Figure 5 and in Figure 6. The start is the putative unit cell with *u*1 = 0 and *u*2 = 4 *π*/3. However, the twist map does not find the structure of consecutive unit cells. It finds that the 3-cycle of Figures 2 and 3 rotates and does not form a correct stable cycle, at least not for three atoms. See the twist map representation in Figure 6.

**Figure 6.** Twist map representation of a twist map calculation with *u*1 = 0 and *u*2 = 4*π*/3. The dashed line represents the start sequence of points.

#### **7. The Disappearence of Incommensurabilities**

For a given length of a finite FK chain with *N* atoms for *λ* = 0,

$$L\_o = \left(N - 1\right)a\_{o\nu}$$

one can determine an integer *M* such that the chain of length *Lo* covers up *M* troughs of the site potential. If *λ* is set correctly, the FK chain will fit into the *M* troughs forming a structure of a minimum with an average separation *a*˜, with Equation (7). It holds independently of whether the numbers, *Lo*, *ao*, *a*˜, and *as*, are rational or irrational. One can cite ref. [52] ". . . a finite chain on a periodic substrate will always be locked because of its free ends." The relation of *N* to *M* is in every case a commensurable ratio between two integers [53]; see Example 3.

**Example 3.** *We treat an example of a chain with a putative 'irrational' winding number [54] of ao* = 0.873*as and the other parameters as* = 2*π, k* = 2.5*, and λ* = 1*, for N* = 500*. The equilibrium structure, probably a minimum, is obtained by the NMinimize procedure of Mathematica starting with a chain with ui* = *ao* (*i* − 1) *for i* = 1, ... , *N. Figure 7 shows the structure and the corresponding twist map representation.*

**Figure 7.** (**Left**): Optimized FK chain minimum for *N* = 500 atoms with winding number 0.873. (**Right**): Twist map representation of the result. The dashed line is the start sequence of nine points plus the first step of the next cycle. It is a quasi-cyclic result.

The structure seems not to be very erratic. The twist map shows a quasi-cycle of nine points. However, the winding number 0.873 is not fully irrational.

#### **8. Remark on the Aubry Transformation of a Finite Chain**

There should be a value *λC*, where a qualitative change in the behavior of the infinite FK chain occurs [21,55,56]. For a finite chain, there is no such value. If *λ* > 0, and *k* > 0, then the action of the site-up potential will fix the chain in a minimum, if we start a minimization for the 'relaxed' chain with distances *a*0; see Section 7.

The putative Aubry-phase transition demonstrated by Figure 6 in ref. [54] is an incorrect interpretation. The first eigenvalue of the second derivatives of the potential of the chain is the frequency for a collective movement of the chain. For an unpinned chain, it has to be zero; thus, the potential has to be flat. However, in the example used in [54], the

first eigenvalue is greater than zero. Thus, the potential is a minimum in both treated cases, *λ* > *λC* and *λ* < *λC*, and the chain is pinned. Of course, the pinning is small if the *λ* is small. The chain can collectively vibrate; however, it cannot move.

For the interpretation of the experiment [57] with *N* = 1–5 atoms, we assume that the reported effect is for other reasons.

#### **9. Discussion**

We understand the long history of the twist map in the following way:

For a finite FK chain, the parameter *a*0 is given; however, the localization of the minimum is unknown. We do not know the values of *u*1, *uN*, and *a*˜. Thus, we cannot start the twist map.

To salvage this nevertheless, one assumes a limit *l* of the average separation and starts with this *l* anywhere with assumed points *u*1 and *u*2 for the initial values. One postulates that every arbitrary pair of the start values is possible.

It is clear that the result is not helpful for an original finite FK chain, see Figure 1.

We note that many researchers have treated finite chains [9,33,35,54,57–65] (to name a few); however, they use a useless contrast of rational with irrational numbers in the finite FK model.

In a positive contrast, the treatment in [66] sorts the FK chain in a 'commensurable' way into the site-up potential.

#### **10. Conclusions**

We are surprised by researchers' attention to the twist map in the field of the FK model. For a finite FK chain, the twist map theory can only be a supplement; otherwise, important physics conclusions of the model are lost.

**Author Contributions:** Conceptualization, W.Q. and J.M.B.; software, W.Q.; validation, J.M.B.; writing—original draft preparation, W.Q.; writing—review and editing, J.M.B.; funding acquisition, J.M.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Spanish Ministerio de Economıa y Competitividad, Project No. PID2019-109518GB-I00, and the Spanish Structures of Excellence Maria de Maeztu program through Grant MDM-2017-0767.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** All structure data of FK chains, and Mathematica files are available by e-mail from W.Q.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript:

#### **Appendix A**

For *k* = 0 and *μ* = 0, the FK model shortens to the pure site-up potential without spring forces. Any arbitrary distribution of the atoms at the bottom of the siteup potential is possible.

For *λ λc* > *k* > 0 in the FK model, further minimum structures are possible under *a*0 = 0, aside from the zero solution discussed in Section 1. *λc* depicts a critical value. Note that every small *k* > 0 prevents the length of the FK chain from becoming too large.

In Figure A1, we depict a case for *N* = 8, *λ* = 10, *k* = 1, and *μ* = 0. The structure has two 'slightly stretched' springs, three 'stretched' springs, and two 'overstretched' springs, which are possible because of the much smaller *k* parameter. Note that most of the atoms are not at the minima of the site-up potential, as claimed for large *λ* [34].

**Figure A1.** A nonzero FK minimum to potential (2).

#### **References**

## *Review* **Recent Progress of Non-Cadmium and Organic Quantum Dots for Optoelectronic Applications with a Focus on Photodetector Devices**

**Hasan Shabbir and Marek Wojnicki \***

Faculty of Non–Ferrous Metals, AGH University of Science and Technology, Mickiewicza Ave. 30, 30-059 Krakow, Poland<EMAIL_ADDRESS>
**\*** Correspondence<EMAIL_ADDRESS>
**Abstract:** Quantum dots (QDs) are zero-dimensional (0D) nanomaterials with charge confinement in all directions that significantly impact various applications. Metal-free organic quantum dots have fascinating properties such as size-dependent bandgap tunability, good optical absorption coefficient, tunability of absorption and emission wavelength, and low-cost synthesis. Due to the extremely small scale of the materials, these characteristics originated from the quantum confinement of electrons. This review will briefly discuss the use of QDs in solar cells and quantum dots lasers, followed by a more in-depth discussion of QD application in photodetectors. Various types of metallic materials, such as lead sulfide and indium arsenide, as well as nonmetallic materials, such as graphene and carbon nanotubes, will be discussed, along with the detection mechanism.

**Keywords:** quantum dot; confinement; tunable photoexcitation; solar cell; quantum dot laser; carbon dot; quantum dots photodetector

#### **1. Nanomaterials**

Nanomaterials have garnered much attention in recent years due to their fascinating and distinctive characteristics that surpass the limitations of bulk materials. Any substance with at least one dimension under 100 nm can be categorized as a nanomaterial [1,2]. Materials with all dimensions larger than nanoscale are called 3D materials or bulk materials, while researchers use a few classifications based on the dimensions of nanomaterials. If two dimensions are larger than the nanoscale, they are called 2D nanomaterials, e.g., quantum wells and nanolayers, a heterostructure composed of two barrier layers sandwiching a single thin well layer. This layer, which contains electrons and holes, is just about 100 Å thick; as a result, the electrons and holes start behaving like waves. In practice, standing waves in a direction perpendicular to the layers correspond to the permissible states in this structure. The system is quantized because only specific waves are standing waves. Many quantum mechanical processes can be observed and controlled in thin quantum well layered semiconductor structures. Modern epitaxial crystal growth techniques can produce them with great precision.

If one dimension of a material is in the nanoscale range and two dimensions are larger than nanoscale, it is categorized as a 1D nanomaterial, e.g., nanorods and nanowires [3,4]. 1D nanomaterials are used in solid-state electronics and as diagnostic tools in medical sciences. They can conduct at the level of one degree of freedom. This enables the utilization of nanowires in applications where electrical conduction is required [5].

If all dimensions of a material are smaller than 10 nm, it is called a 0D material, e.g., nanoparticles and quantum dots (QDs).

As the size limits approach the zero dimension and the region becomes extremely confined, it is also referred to as a dot. QDs are produced when material sizes become smaller and smaller in each dimension, which causes them to behave like groups of atoms

**Citation:** Shabbir, H.; Wojnicki, M. Recent Progress of Non-Cadmium and Organic Quantum Dots for Optoelectronic Applications with a Focus on Photodetector Devices. *Electronics* **2023**, *12*, 1327. https:// doi.org/10.3390/electronics12061327

Academic Editor: Lucas Lamata

Received: 30 January 2023 Revised: 3 March 2023 Accepted: 6 March 2023 Published: 10 March 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

and exhibit fascinating features. The electron–hole pair is also produced by some energy input, such as UV radiation, and the pair is kept together by Coulombic forces [6]. QDs' size ranges from 2 to 10 nm, or between 10 and 50 atoms, and they have 100 to 1000 electrons. Almost all material systems, including metal, insulators, and semiconductors, exhibit size-dependent electrical or optical characteristics in the quantum size domain. Due to its fundamental and technological significance, the semiconductor's energy band gap alteration is the most appealing [7]. The materials for the next generation of flat panel displays, photovoltaic, and optoelectronic devices are semiconductors with extensively tunable energy band gaps [8].

Quantum dots (QDs) are tiny semiconductor particles that can be utilized in photodetectors and other applications. They are typically only a few nanometers in size. QDs can be employed as a light-sensitive substance, also referred to as a photoconductive substance, in a photodetector. One example of a photodetector using QDs is a QD infrared photodetector (QDIP) [9,10]. QDIPs use a layer of QDs as the active material, which absorbs the incoming infrared light and generates an electrical current [11]. It has been demonstrated that they have good stability, quick response times, and high sensitivity.

Another example is a QD-based ultraviolet photodetector. The photoactive material employed in the detector is QDs, and it has a high sensitivity and quick response time for detecting UV light [12,13]. Figure 1 shows the different types of materials based on dimensions.

A third example is a QD-based hybrid photodetector, which combines the benefits of QDs and conventional semiconductor materials, such as silicon [14,15]. These devices combine silicon and QDs to produce a sensitive and effective photodetector. Overall, due to their distinct optical and electrical characteristics and their potential to enhance the performance of these devices, quantum dots are a promising material for use in photodetectors [16].

Although the discovery of QDs is familiar due to the toxic nature of initially observed QDs such as cadmium, their application is limited [17]. The semiconductor quantum dots used to make quantum dots (QDs) photodetectors include cadmium sulfide (CdS), lead sulfide (PbS), indium arsenide (InAs), and organic quantum dots [18]. Due to their distinct optical and electrical characteristics, these QDs have potential applications in photodetector sensors. The most extensively researched QD material for photodetector sensors is cadmium sulfide (CdS) [19]. They can efficiently convert light into an electrical signal due

to their high quantum yield and absorption coefficient, allowing them to absorb much light. These characteristics make CdS QDs ideal for ultraviolet and infrared photodetectors [20].

Nevertheless, CdS have many disadvantages. Cadmium is a poisonous heavy metal that can cause serious health issues if inhaled, and proper precautions are needed to dispose of devices made up of cadmium. Quantum dots based on CdS are not biodegradable and can affect the ecosystem [21]. CdS are also more expensive than other quantum dot materials, so researchers are working on different QD materials useful for photodetection applications [22].

The second most commonly used QDs for photodetection applications are lead sulfide (PbS) QDs. They are especially beneficial for infrared photodetectors because they feature a band gap that makes them sensitive to infrared light [23]. Quantum dots made of indium arsenide (InAs), which have a high near-infrared absorption coefficient and are, therefore, particularly effective for near-infrared photodetectors, are another potential material for use in photodetector sensors [24,25]. Overall, the wavelength range of the light that needs to be detected and the specific specifications of the device will determine which QD material is best [26].

This review is focused on non-cadmium nanomaterials for electronic applications. As light-emitting diodes also work with the mechanism of electron–hole recombination, QDs also have potential applications in this area [27]. In terms of applications, quantum dots are used in various fields, including electronics, biomedicine, and renewable energy. For example, quantum dots can be used in electronics to make highly efficient solar cells, LED lights, and other devices. In biomedicine, quantum dots are used as imaging agents to study cells and tissues in the body [28]. In renewable energy technologies, quantum dots are used to produce hydrogen fuel from water using sunlight [29].

#### **2. Optical and Electrical Properties of Quantum Dots**

There are different energies for the electrons in quantum dots. When QDs absorb energy above their band gap, an exciton (electron–hole pair) is created. The electron and hole pair is confined if the diameter of the nanomaterial is smaller than its exciton Bohr radius, often known as the average physical distance between the electron and hole [30]. This electron and hole pair confinement is called the quantum confinement effect, which causes a discrete packet of energy and cannot be considered continuous [31,32]. One of the fascinating phenomena that QDs exhibit is photoluminescence. In this phenomenon, QDs absorb higher-energy photons and release low-energy photons. The electron moves into an excited state upon absorption. When it recombines with a pair, it emits lower energy light. This process takes place in femtoseconds [33].

Photoluminescence generally depends not on the type of materials but on the size [34]. As the quantum dot size decreases, the band gap of the quantum dot increases, causing the emission wavelength to shift toward a lower wavelength, and this is known as the blue shift, which is emission in the visible range. However, the emission can also occur in other regions of the electromagnetic spectrum, such as ultraviolet or infrared. QDs have exciting optical properties such as better photostability, high molar extinction, and high quantum yield (ratio of photons emitted vs. photons absorbed). QDs can be observed using confocal microscopy, fluorescence spectroscopy, total internal reflection microscopy, etc. [35,36].

QDs also have fascinating electrical properties, such as when sufficient energy is absorbed by the QD electron excited from the valence band to the conduction band while leaving the hole (empty state) in the valence band. This hole can be considered a positive mobile charge in the valence band. QDs possess a discrete energy state like an electron of a single atom [37]. Typically, a photon can only form one exciton and excite one electron across the band gap of fluorescent materials, with extra energy being lost as heat. However, multiple exciton generation is possible in QDs, which can be produced simultaneously, increasing the efficiency with which the nanocrystals convert energy [38].

Quantum yield measures the efficiency with which a system converts absorbed light into a different form of energy, such as heat or electricity. In the case of quantum dots, it refers to the efficiency with which the dots convert absorbed light into emitted light [39,40].

The equation for quantum yield is typically expressed as the ratio of the number of photons emitted by the quantum dots to the number of photons absorbed by the dots. This ratio can be expressed as follows:

$$\text{Quantum yield} = \frac{\text{Number of photons emitted}}{\text{Number of photons absorbed}}$$

The quantum yield plays an important role in the properties of QDs. The confinement behaviors produced by QDs' core/shell structures are closely connected to the core and shell materials [41]. For instance, the electron–hole pair is confined within the core when the energy band gap of the shell material is more significant than that of the core material, and when the energy band gap of core materials is more significant, the electron–hole pair is confined in the shell [42]. QDs, like carbon quantum dots, are extremely sensitive to the presence of extra charges, such as electrons or holes, on their surfaces and in their environment, which can change the photoluminescence and absorption wavelength of QDs. The functional group present on the surface of carbon quantum dots can absorb and trap the photon, which can change the emission wavelength of carbon QDs [43]. Due to these fascinating properties, quantum dots are used in many applications, such as solar cells [44], lasers [45], and photodetectors [46].

#### **3. Quantum Dot Lasers**

Semiconductor spherical nanocrystals (colloidal quantum dots), monolayers, and nanowires have found usage in the laser industry. CDs offer wide electromagnetic spectrum emissions from infrared to the visible range due to their size tunability, optical transition, and solution processibility. Compared to conventional semiconductors, QDbased semiconductors are easier to manipulate in size and shape [47,48]. Due to the unique absorption and emission properties of QDs, it is possible to produce lasing from a single exciton. A QD laser provides even spacing, low threshold amplification, and continuous wave operation. The shell absorbs the energy and acts as an antenna when the core–shell QDs are excited by photons having energies above the energy band gap. These QD outpace Auger recombination, so the threshold for lasing operation decreases [45].

#### **4. Quantum Dots for Solar Cells**

For more than two decades, semiconductor quantum dots (QDs) have attracted much attention due to the optoelectronic properties based on zero dimensions. Through the QD band energy level, colloidal quantum dots and self-assembled quantum dots improve the photogeneration of carriers for photovoltaic applications [49]. By expanding the range of photoexcitation, theoretically, it is possible to achieve maximum thermodynamic efficiency although the mechanism of carrier transport and carrier collection also contribute to its efficiency. Self-assembled and colloidal quantum dots are the two most-used types of QDs in solar cell applications [50]. The growth of solar cell wafers is also crucial for their efficiency, including surface passivation and well-controlled heterointerface [51].

Future risks include rising temperatures caused by global warming, shrinking fossil fuel supplies, and ever-increasing energy needs, which will require scientists and researchers to continuously work on developing efficient and affordable renewable energy alternatives [52]. Sunlight, which is abundantly available worldwide and can be converted into electricity or other forms of energy without polluting the environment, is one of the most commonly used renewable energy sources. Photovoltaic systems are based on converting sunlight into electricity, another valuable form of energy [53]. Photovoltaic device usage to produce electrical energy has increased, but obstacles still need to be overcome before these devices can significantly contribute to satisfying the world's energy needs [54].

Generally, there are three types of solar cells: traditionally, silicon-based monocrystalline and polycrystalline solar cells have been used [55]. The second type is thin-film solar cells, which are less expensive due to the low cost of absorbing material compared to silicon. These include copper gallium indium diselenide, cadmium telluride, and organic solar panels [56]. The third type, perovskite solar cells, uses hybrid organic–inorganic materials as the light-harvesting active layer. Perovskite materials, such as all-inorganic cesium lead halides and methylammonium lead halides, are cheap and straightforward to manufacture. Carrier mobility, doping density, trap density, and diffusion length in films are crucial factors that affect the performance of photovoltaic devices [57].

Junwei Yang et al. [58] reported synthesizing CdTe core QD-based solar cells. They used the aqueous route to synthesize QDs. CdTe core QDs were first synthesized and then deposited on a TiO2 photoanode. An increase in absorption spectrum is observed for CdTe core QDs compared to CdTe cells. The power conversion efficiency of QD-based solar cells is increased up to 22% compared to CdTe/CdS plain solar cells. The suppressed charge recombination is also confirmed in QD-based solar cells. The authors also reported that thickness plays an important role in quantum efficiency. With optimization of CdSexS1-x shell thickness, about 7.24% conversion efficiency can be achieved, while Jun Du reported that Zn–Cu–In–Se alloyed QDs increase the absorption efficiency when deposited on TiO2 film electrode, and reported conversion efficiency up to 11.66% [44].

#### **5. Nanomaterials for Photodetection**

Nanomaterials have properties that are suitable for photodetection, especially twodimensional nanomaterials Two-dimensional (2D) materials have emerged as promising candidates for photodetectors due to their unique electrical and optical properties. In particular, their ultra-thin structure allows for efficient light absorption and carrier transport, leading to high sensitivity and fast response times. Two examples of 2D materials that are commonly used for photodetectors are:

Graphene is a single layer of carbon atoms arranged in a honeycomb lattice. It has excellent electrical conductivity and high carrier mobility, which makes it an attractive material for photodetectors [59]. When light is absorbed by graphene, it generates electron– hole pairs, which the graphene's high carrier mobility can efficiently collect. Graphene photodetectors have shown high responsivity and fast response times, making them useful for optical communications and imaging applications, while graphene hybrid composite materials with metallic nanomaterials and inorganic nanomaterials can increase photosensitivity [60].

Transition metal dichalcogenides (TMDs): TMDs are a family of 2D materials consisting of a transition metal atom sandwiched between two chalcogen atoms. They have a direct bandgap, which allows for efficient light absorption and emission [61]. TMDs have shown high sensitivity to light in the visible and near-infrared regions, making them useful for applications such as biomedical imaging and environmental monitoring. In addition, TMDs can be easily integrated with other electronic components, making them promising for on-chip optoelectronics [62]. 2D materials have shown great potential for photodetector applications due to their unique electrical and optical properties. Graphene and TMDs are just two examples of 2D materials that are being actively researched for their photodetection capabilities. As research in this area continues, it is likely that even more promising 2D materials will be discovered and developed for photodetector applications.

Infrared light detection is essential for biological sensing, spectroscopy, and in-depth 3D imaging. At the same time, semiconductors such as silicon, Cds, HgCdTe, and HgS are used for photodetectors. However, these materials have a few drawbacks, such as toxicity, low responsivity, and high cost of fabrication. The imaging performance of the quantum well photodetector, which is comparable to that of the mercury cadmium telluride (HgCdTe) detector, has recently attracted a lot of interest [63].

Following progress in the nanomaterials industry, it has been found that they have some advantages for photodetection over conventional materials, and the most-used nanomaterials are quantum well.

Quantum well infrared photodetectors (QWIP) absorb electrons through electronic intersubband polariton in a quantum well [64]. To be used for infrared detection, the energy difference between the first and second quantized states of the quantum well infrared photodetector's quantum wells must match the energy of the incoming infrared photons. III-V direct band gap semiconductor gallium arsenide (GaAs) is usually used to make QWIPs [65].

Therefore, research is also being carried out to create high-performance photodetectors using these nanomaterials. This review article focuses on quantum dot photodetectors [66]. They have been used in applications such as gas sensors and medical images, etc. Quantum well infrared detectors also have some limitations, such as the intersubband transition in the conduction band due to infrared photon polarization not being allowed in quantum wells [67,68]. This limitation can be overcome by using grating. However, they have a few more drawbacks, such as higher dark current, low quantum yield, lower responsivity, and detection level, and require cryogenic temperature to operate, so these limitations can be fulfilled by quantum dot photodetectors that have similar properties to quantum wells and also have some advantages due to the confinement of electrons in three dimensions [69]. QDs have reduced dependence on temperature for carrier transport, and carrier lifetime is also 10–100 times longer, which means that the electron remains excited for a more extended period, which causes a reduction in the dark current and increases sensitivity. QD-based detectors can absorb normal incident light without grating [70].

Similar to a quantum well, a quantum dot exhibits detection through the confinementinduced intraband photoexcitation of electrons. A photocurrent is generated by attracting the electrons in the collector with an electric field generated by the applied bias.

Colloidal QDs are low-cost materials, due to solution-based fabrication into semiconductor wafers and tunable band gap material, that are used as light emitters in flat panel displays. QDs are a cheap alternative to III–V group-based materials for imaging and sensing [71]. Research is being already carried out to make it possible to place QDs in a complementary metal–oxide–semiconductor (CMOS) circuit and increase the responsivity of QDs while decreasing the low noise equivalent power. If QDs can emit electrons across a wide range of the electromagnetic spectrum, they will be more practically efficient [72].

Infrared detectors are mainly categorized based on the material used for detection. Some of these are already extensively used in industry, including direct band gap semiconductor alloys such as HgCdTe and InSb, majority carrier Type-I superlattices, e.g., GaAs/AlGaAs QWIPs, and extrinsic semiconductors, e.g., Si: Ga, Ge: Hg. The fourth type is silicon Schottky barriers such as PtSi, and IrS. At the same time, the other two types include high-temperature superconductors and QD-based photodetectors, e.g., InAs/GaAsbased detectors [73,74]. The QD-based photodetector will be discussed in this review. Examples of quantum dots for photodetection are given below.

#### **6. Lead(II) Sulfide (PbS) Quantum Dots**

Lead(II) sulfide (PbS) QDs are special semiconductors with distinctive optoelectronic characteristics. Their strong absorption coefficient and band gap of 0.35 eV make them suitable for photovoltaic, photoconductor, and light-emitting diode applications [75,76]. PbS quantum dots are advantageous for sensing and imaging applications because they also have a high quantum yield and a narrow emission spectrum. Furthermore, their band gap can be modified by varying the quantum dot size, enabling further improvement of their optoelectronic characteristics [60,77].

One of these characteristics is their high absorption coefficient, which enables effective light absorption over a broad range of wavelengths. This is because PbS quantum dots have a significant quantum confinement effect, which confines the electrons to a limited area and causes them to have a high absorption coefficient [78].

The high responsivity of PbS quantum dots is a crucial characteristic that makes them effective as photodetectors which means more transformation of absorbed photons into an electrical signal [59,79]. Due to their high electron–hole recombination rate and rapid electron mobility, PbS quantum dots have a high responsiveness that enables the effective conversion of absorbed photons into electrical current. PbS quantum dots are also ideally suited for applications with high sensitivity and low noise because of their excellent signalto-noise ratio and low dark current [80,81]. Therefore, lead sulfide (PbS) quantum dots (QDs) are considered potential material options for next-generation light, affordable, and flexible photodetectors due to their wide tunable band gaps, high absorption coefficients, and simple solution synthesis methods.

Alberto Maulu et al. synthesized PbS QDs and then modified their surface properties by using 3-mercaptopropionic acid (MPA) and tetrabutylammonium iodide (TBAI) [82]. It was observed that modification with this ligand significantly alters the properties of QDs. MPA-based QDs showed a decrease in dark current and low noise ratio, which causes the enhancement of detective and photosensitivity compared to TBAI-based QDs. MPA-modified QDs have functional group (Pb–OH bonds), while TBAI has a functional group (Pb–I bond), which is the primary reason for the Pb enhancement properties.

QDs used the trap sensitization method to show photoconductivity, increasing the responsivity but decreasing the response time for low optical power. At medium power incidents, light, when traps are filled with both types of photodetector, shows similar types of properties.

Urvashi Bothra et al. investigated the effect of ligands on PbS properties. They showed that a PbX2 [X = I, Br])-based photodetector decreases the trap density compared to a PbS-based device, which increases the performance of (PbS) PbX2-based devices [83].

Jin Beom Kwon et al. fabricated short-wave infrared (SWIR) photodetectors based on PbS QDs [84]. These infrared photodetectors minimize the harmful effect caused by the low wavelength band of SWIR. They fabricated a PbS photodetector with an absorbance peak at 1410 nm and used poly(3-hexylthiophene) (P3HT) as a conductive polymer with PbS QDs. Measurements were made on the properties of the synthesized PbS QDs, and the current– voltage (I–V) features of the PbS SWIR photodetectors. The maximal responsiveness of the PbS SWIR photodetector with P3HT optimization was found to be 2.26 times greater than that of the PbS SWIR photodetector without P3HT. Moreover, the former demonstrated a reduced operating voltage due to the high hole mobility and an adequate highest occupied molecular orbital level of P3HT. Figure 2 shows the I–V characteristics of the PbS-based photodetector.

**Figure 2.** I–V characteristics of (**a**) PbS SWIR photodetector without P3HT polymer and (**b**) PbS SWIR photodetector with P3HT polymer [84].

To compare their performance, they measured the I–V characteristics and responsiveness of the manufactured PbS SWIR photodetectors. The electron–hole pairs produced in the photoactive layer of the PbS SWIR photodetectors were removed from the electrodes by an external electric field when exposed to IR light. When the IR light source was turned off, the dark current was measured, and the light current was measured when the light source was turned on. The output power of the IR light source was 1 W/m2, and the voltage sweep range was between −5 V and 5 V. The highest current difference between the dark current and light current and responsivity was recorded at −5 V in the case of the PbS SWIR photodetector without a P3HT layer. The largest current difference was 23.72 mA, and when this was divided by the input voltage, the corresponding responsivity was calculated as 2635.6 A/W. The PbS SWIR photodetector with a P3HT layer exhibited the best properties when applying 20 mg/mL of P3HT. The greatest current difference was confirmed to be 5891.1 A/W, which is 2.26 times greater than SWIRs, and the maximum current difference was 53.02 mA at −5V.

The drawbacks of current single-layer PbS-QDs photodetectors include excessive dark currents, slow light responses, and poor on–off ratios. It has been demonstrated that combining high-conducting graphene with organic materials and metal nanoparticles to create hybrid PbS-QDs devices can increase photoresponsivity. However, these hybrid devices bring other problems, and Zhenwei Ren et al. [80] synthesized the bilayer QDs device, which can be easily integrated into a flexible polyimide substrate. It increases the responsivity, signal-to-noise ratio, linear dynamic, and detection.

Moreover, this improvement in the device's properties is attributable to QDs' significant role. For example, the QDs junction accelerates carrier separation when the light is on. When the light is off, the QDs support the recombination of accumulated carriers in two films via the interface. Junction control is more dominant than trap control, which is the main determining factor in single-layer devices. They fabricated the bilayer photodetector using tetrabutylammonium iodide (TBAI)- and 1,2-ethanedithiol (EDT)-treated QDs. They compared it with a single-layer detector and observed that the bilayer photodetector enhanced optoelectronic properties. The bilayer PbS- TBAI/PbS-EDT devices have higher light current and detection efficiency, while the responsivity of PbS- TBAI/PbS-EDT is comparable to PbS-EDT devices due to the very close photocurrent.

It can be concluded that surface functional chemistry and modification of PbS with ligands improve the performance, and hybrid structure with modifications from different ligands can also improve the performance.

#### **7. Indium Arsenide (InAs) Quantum Dots**

Indium arsenide (InAs) quantum dots (QDs) are also potential materials for photodetector sensors due to their distinct optical and electrical characteristics. These QDs are especially beneficial for NIR photodetectors due to their high near-infrared (NIR) absorption coefficient [85]. NIR imaging is one possible use for InAs QD-based photodetectors. Due to InAs QDs' band gap, developing highly sensitive NIR imaging systems with them is possible. These gadgets are used in telecommunications for sensing, night vision, and medical imaging [86]. Deep-tissue imaging, optical communication, and covert illumination are just a few of the optoelectronics and biomedical uses for indium arsenide quantum dots, which typically emit in the near-infrared spectrum. Systems with bigger optical band gaps have yet to be produced, despite theory suggesting that further quantum confinement through size reduction could enable visible light emission.

NIR spectroscopy is another use for InAs QD-based photodetectors. Due to the NIR light detection capability, highly sensitive NIR spectroscopy devices can be made [87]. Additionally, the development of optoelectronic devices such as solar cells, LEDs, and lasers has utilized InAs QD-based photodetectors. These devices can increase the efficiency of solar cells and other optoelectronic devices by effectively converting light into electrical energy. Applications for these devices include bio-photonics, environmental monitoring, and chemical sensing [88,89].

Overall, because of their distinct optical and electrical characteristics, as well as their capacity to detect NIR light, InAs QDs have the potential to be utilized in a variety of photodetector applications. They might find use in spectroscopy, optoelectronic devices, and NIR imaging [90]. InAs quantum dots (QDs) might have a different band gap depending on their size and shape. Due to quantum confinement, the band gap of InAs QDs is typically between 0.35 and 0.4 eV, which is lower than that of bulk InAs (0.36 eV) [91], which is shown in Figure 3.

**Figure 3.** Photoluminescence spectra of In(Zn)As/ZnSe/ZnS QDs synthesized with different amounts of stearic acid (SA) ligand relative to the initial zinc precursor under UV illumination (Reproduced from [92], with permission from ACS Publications).

A low-temperature nanocluster synthesis technique was used by Daryl Darwan et al. to create highly luminous, visible-light-emitting In(Zn)As/ZnSe/ZnS QDs [92]. Each QD has an ultra-confined In(Zn)As nanocluster and emits light with a high photoluminescence quantum efficiency of 58% at tunable wavelengths between 538 and 640 nm. Theoretical calculations support the hypothesis that In(Zn)As nanoclusters are responsible for the infrared to visible spectral shift. This suggests that optical tuning in the visible region is also possible by utilizing confined semiconductor systems with a wide range of applications. The schematic is shown in Figure 4. Using an ultra-confinement technique, they were able to extend the spectrum coverage of InAs-based QDs into the visible range.

#### **8. Organic Materials Based on Quantum Dots**

Organic materials, such as polymers or small organic compounds, are used to create organic quantum dots (OQDs), a particular kind of quantum dot. Due to their special optical and electronic characteristics, they could be used in photodetector sensors. Organic photovoltaics is one potential use for OQD-based photodetectors (OPVs) [93,94]. The active layer in OPVs, which transform light into electrical energy, can be made of OQDs. OQDs may absorb various wavelengths, which can enhance the efficiency of OPVs. They could also be used to make solar cells that are less expensive than ordinary inorganic solar cells. OQD-based photodetectors can also be used in flexible and wearable gadgets. OQDs offer

thin, bendable, and solution-processable advantages, making them ideal for application in bendable and flexible products such as flexible screens and wearable technology [95].

Devices for sensing and bioimaging have also been created using OQDs. OQDs have the potential to be used in biosensing and biomedical imaging, as well as optical imaging. They are advantageous in these applications because of their high quantum yield, strong stability, and great sensitivity [96]. OQDs are a promising material for photodetector sensors overall because of their distinct optical and electronic characteristics and their potential for usage in a variety of applications, including solar cells, flexible and wearable devices, and bio-imaging and sensing equipment [97].

#### **9. Carbon-Based Materials for Photodetection**

Carbon materials, such as carbon nanotubes, graphene, and fullerenes, are used to synthesize carbon-based quantum dots (CQDs), a particular kind of quantum dot. Due to their extraordinary optical and electronic characteristics, they could be used in photodetector sensors [98].

The photodetection of diverse wavelength ranges is one potential use for CQD-based photodetectors. It has been demonstrated that carbon-based quantum dots have a broad absorption spectrum, making them appropriate for use in photodetectors that must detect a variety of wavelengths [99]. They are, therefore, very beneficial for multi-spectral imaging and sensing. High-speed optoelectronics is a further possible use for CQD-based photodetectors. Because of their rapid response times, carbon-based quantum dots can be used in high-speed optoelectronic systems, including optical communications and high-speed data transfer [100]. Devices enabling sensing and bioimaging have also been made with CQDs. The unique optical and electrical characteristics of carbon-based quantum dots make them suitable for biosensing and bioimaging applications, including in vivo imaging. They are helpful in various applications due to their high quantum yield, outstanding stability, and great sensitivity [101]. CQDs are a promising material for photodetector sensors overall because of their distinctive optical and electronic properties and their potential to be employed in a variety of applications, including multi-spectral imaging and sensing, high-speed optoelectronics, and bio-imaging and sensing devices [102].

Both graphene quantum dots (GQD) and carbon dots (CD) are being studied for potential application in photodetector sensors. Small, carbon-based nanoparticles known as CDs have been shown to exhibit robust fluorescence characteristics [103]. On the other hand, GQDs, which are small graphene flakes, have been discovered recently to have fluorescence characteristics similar to those of CDs, with the added advantage of being more stable and simpler to functionalize. CDs and GQDs are promising candidates for photodetector sensors due to their efficiency at absorbing light and transforming it into an electrical signal [104].CDs' performance is negatively influenced by their inefficient near-infrared (NIR-I and NIR-II) excitation and emission. By resolving this, CDs can be utilized for in vivo bioimaging.

#### **10. Graphene Quantum Dots (GQDs)**

There may be applications for graphene quantum dots (GQDs), tiny graphene sheets, in photodetector sensors. Their unique electrical and optical features make them suitable for sensing technologies. GQDs have been found to possess strong fluorescence properties, effectively absorbing light and turning it into an electrical signal [105]. GQDs are extremely stable and may be functionalized with various chemical groups, enabling precise control over their optical and electrical characteristics. They are beneficial for sensing applications requiring specificity and sensitivity [106].

Graphene, in particular, is a 2D monolayer of sp2 hybrid carbon. At the Dirac point, graphene's conduction band meets with its valence band. This causes a linear dispersion relationship, making it a zero-band gap semiconductor with zero density of electronic states and an incredibly high room temperature carrier mobility [107]. The broad spectrum response and quick response of graphene are perfect photoelectric qualities due to its zeroband gap semiconducting nature. Although graphene quantum dots have lesser absorption and responsiveness, researchers are primarily focusing on hybridizing graphene with high-absorption materials to enhance photodetection capability like quantum dots [108].

GQDs are also ideally suited for photodetectors and other optoelectronic devices due to their outstanding charge transfer characteristics. Different photodetector designs, including p–n junction, Schottky, and photoconductive ones, can incorporate GQDs [109]. They are helpful for various sensing applications because they can detect a wide range of wavelengths, from visible to infrared.

Molahalli Vandana et al. fabricated a UV-based photodetector by utilizing graphene QDs with polypyrrole polymer [110]. They used two different amounts of graphene, 20 and 40 mL in polypyrrole, labeled as PGC2 and PGC4, while single graphene QDs (GQDs) were also utilized. The active layer of ITO electrode was illuminated with UV light of 265 and 355 nm for about 200 s. The graphene QDs are an excellent light absorber and electron donor to increase the carrier concentration. Figure 4 compares the photocurrent of GQDs, PGC2, and PGC4.

**Figure 4.** Comparison between the photocurrents of three photodetector devices under illumination [110].

PGC2 and PGC4 show responsivity of about 0.33 μA/W and 0.36 μA/W and corresponding photocurrent of 2.65 μA and 2.9 μA when illuminated at wavelength 265 nm, while a responsivity of 1.93 and 2.33 μA/W and photocurrent of 15.5 μA and 18.7 μA was observed for PGC2 and PGC4 when illuminated with UV light of 355 nm. Based on the results, which show that the PGC4 photodiode had the highest 18.7μA photocurrent, it can be concluded that the quantum dots in the polymer boosted electron mobility due to the high electrical properties of the nanocomposite.

#### **11. Carbon Dots**

Carbon QDs are nanomaterials made of carbon, similar to substances such as nanodiamonds, fullerenes, carbon nanotubes, graphene, and graphene oxide. Small, water-soluble carbon nanoparticles known as carbon dots (CDs) have been shown to have potential uses in photodetector sensors [111]. CDs are a desirable material for use in sensing technologies due to their distinctive electrical and optical characteristics. Strong fluorescence qualities have been discovered in them, making them efficient at absorbing light and transforming it into an electrical signal [112]. CDs' high quantum yield and outstanding stability have been found to make them appropriate for use in photodetectors [113]. The precise control of their optical and electrical properties is made possible by their simplicity in synthesis and functionalization. As a result, they are advantageous for sensing applications that demand

specificity and sensitivity [114]. CDs' superior charge transport characteristics have also been discovered, making them suitable for photodetectors and other optoelectronic devices. Many photodetector designs, including p–n junction, Schottky, and photoconductive ones, can incorporate CDs [115]. They are helpful for various sensing applications because they can detect a wide range of wavelengths, from visible to infrared. Additionally, CDs are nontoxic and biocompatible, which makes them advantageous in medicinal applications such as cancer therapy and bioimaging. Additionally, CDs can be functionalized with different biomolecules to enable the detection of certain biomolecules and biological activities [116].

They have gained attention due to their environmentally friendliness, chemical stability, and good conductivity, making them useful in various fields such as biomedical and biotechnological research, solar cells, light-emitting devices, imaging, electrochemical studies, and electrochemiluminescence studies [117]. Carbon dots are a class of nanoparticles composed mainly of carbon and oxygen, while some amino and carboxyl functional groups are also present on the surface [118]. These nanodots have unique optical, electrical, and chemical properties that make them highly versatile and helpful in various applications. Some of the critical properties of carbon dots include: Size: Carbon dots are nanoparticles with diameters ranging from 1 to 10 nanometers. Their small size allows them to display unique properties and quantum confinement effects, which are helpful for a number of applications. These properties make carbon dots valuable for various applications, including sensors, catalysts, and energy storage and conversion. Luminescence: Carbon dots can emit light, making them useful for applications such as biosensors and imaging [119]. Chemical stability: Carbon dots are highly stable in many different chemical environments, including basic and acidic conditions. Their stability makes them useful for sensing and imaging applications. Conductivity: Since CDs have excellent electrical conductivity, carbon dots can be used in photovoltaic and energy storage applications [120]. Biocompatibility: Due to their non-toxicity and biocompatibility, carbon dots can be used in biological systems without damaging healthy cells. Surface functionalization: The surface of carbon dots can be modified with different chemical groups, enabling them to be useful for specific purposes [121]. Optical properties: Carbon dots can absorb light in the ultraviolet and near-infrared parts of the spectrum, making them useful for specific applications. For example, their strong absorbance in these spectrum regions can be utilized in solar cells to absorb and convert sunlight into electricity and in LED lighting to provide energy-efficient and long-lasting light sources [122]. CDs can emit light when excited by an external energy source, such as electricity or heat. The emission wavelength, or the specific range of wavelengths that the light emitted by CDs falls within, can be manipulated by changing the size and composition of the CDs. This can be achieved by using different starting materials or synthesis methods while synthesizing CDs. Solubility: Since they are highly soluble in a wide range of solvents, including water, carbon dots are simple to handle and incorporate into different systems [123]. High surface area: The small size of carbon dots results in a high surface area, which makes them ideal for applications such as catalysis and drug delivery [123].

One crucial property of CDs is their ability to emit light when excited by light, also known as photoluminescence. The photophysical responses of CDs, including their light absorption and emission, are influenced by the isolated network of sp2 carbon bonds in their structure [123]. In contrast, extended networks of carbon bonds, as found in carbon nanotubes, graphite, and graphene, do not interact with light as strongly. This may be due to the rapid recombination of photogenerated electrons and holes without the emission of radiation. CDs typically absorb light over a broad range of wavelengths [124]. They can absorb light over a wide range of wavelengths, but the specific wavelength at which they emit light is determined by the population of a particular energy level or "domain" and the surface properties of the quantum dots. This phenomenon, known as excitationdependent emission, is a characteristic of CDs arising from these nanomaterials' surface state. Essentially, the surface of the quantum dots plays a crucial role in determining

the specific wavelength at which they will emit light when excited by an external energy source [125].

Carbon dots have a high absorption coefficient, which implies they can absorb a lot of light, in addition to their fluorescence and quenching qualities. Due to their ability to transform light into energy that may be utilized to treat a range of medical problems, they are valuable in phototherapy applications [126].

K. Sarkar et al. [127] show the use of carbon dots (CDs) synthesized from Carica Papaya through a facile synthesis method as a potential broadband photodetector in a hybrid (organic–inorganic) heterostructure with a silicon wafer. The engineered CDs' maximum detectivity and responsivity are around1AW−1 and 2 × 1012 Jones, respectively. The device structure ensures a promising photodetector technology comparable to silicon process technology through a cheap and simple fabrication process. Additional optimization effort and defect engineering can speed up switching.

Sergii Kalytchuk et al. demonstrated the synthesis of purple-emissive CDs utilizing folic acid as the only precursor in a simple and reproducible process [128]. The CDs have a high photoluminescence quantum yield of 54.6% and emit light at a wavelength of 390 nm, which is independent of the excitation wavelength and integrates the emission color spectrum of intensely glowing carbon dots to purple. They employed CDs to increase the silicon photodetector's UV range sensitivity. It was found that the photoresponsivity of the silicon photodetector in the UV range of 0.8 to 2.5 mA/W was enhanced by 203.8% with CDs' integration.

Di Li et al. [129], by modifying the surface of CDs with functional groups of sulfoxide/carbonyl, changed the optical band gap of CDs. They proposed a mechanism for improved NIR emission, which can be seen in Figure 5. The CDs have a layered structure, and the outer layers have bonding sites. The interaction between the S = O/C = O functional group and layers increased surface oxidation, which caused the reduction in the lowest unoccupied orbital (LUMO). As a result, these functional groups disrupt CDs' organized structure. Due to the increased surface oxidation, the LUMO orbitals are lower in the outer layers compared to the inner layers and cause the NIR emission of CDs.

**Figure 5.** Non-treated CDs (left column) and CDs modified with S = O/C = O rich molecules (right column). The red (oxygen atom) and green double-bonded balls represent the C = O/S = O rich molecule (Reproduced from [129], with permission from John Wiley & Sons, Inc.).

#### **12. Future Prospects and Conclusions**

Several optoelectronics applications that have been utilized as a result of advancements in nanomaterial synthesis were covered in this study. Researchers have used QDs in various

devices, including solar cells, lasers, and photodetectors. Quantum dots act differently from bulk materials in light emission and absorption due to the quantum confinement effect, which is favorable for laser and solar panel applications. This review briefly discussed different optoelectronic devices based on QDs.

QDs in photodetectors have a bright future, with the possibility of increased performance, reduced costs, and new applications. Future quantum dot photodetectors are expected to have several benefits over current photodetectors. They could, for instance, offer greater sensitivity, faster response times, and lower noise levels. Since they can be tailored to absorb light over a broad range of wavelengths by altering their size and composition, they are also anticipated to be more flexible.

Factors contributing to the usefulness of QDs as compared to a traditional photodetector that is discussed in this review include:

PbS quantum dots have a high electron–hole recombination rate and rapid electron mobility, which increases the responsivity and improves the efficiency of the conversion of photons into electric current. PbS quantum dots' properties can also be modified with ligand reactions. Bilayer PbS quantum dots with different modification ligands, tetrabutylammonium iodide (TBAI), and 1,2-ethanedithiol (EDT) devices have higher light currents and detections.

This review study also discusses indium arsenide (InAs) quantum dots (QDs). It was shown that due to their high infrared absorption coefficient, they make good photodetectors in the region of infrared detection. They are helpful for imaging at infrared wavelengths as well.

This review discusses organic quantum dots such as graphene, particularly carbon quantum dots. CDs' particular electrical and optical properties make them desirable materials for sensing technologies. They have been shown to possess strong fluorescence properties, effectively absorbing light and converting it into an electrical signal. Their ease of synthesis and functionalization allows precise control of their optical and electrical properties. They are, therefore, beneficial for photodetectors that require specificity and sensitivity.

**Author Contributions:** Conceptualization, H.S.; writing—original draft preparation, H.S.; data curation, H.S.; writing—review and editing, H.S. and M.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received financial support from the AGH University of Science and Technology.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** Author declares no conflict of interest.

#### **References**

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## *Article* **Rational Distributed Bragg Reflector Design for Improving Performance of Flip-Chip Micro-LEDs**

**Yuechang Sun, Lang Shi, Peng Du, Xiaoyu Zhao and Shengjun Zhou \***

Center for Photonics and Semiconductors, School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, China

**\*** Correspondence<EMAIL_ADDRESS>Tel.: +86-027-5085-3293

**Abstract:** The distributed Bragg reflector (DBR) has been widely used in flip-chip micro light-emitting diodes (micro-LEDs) because of its high reflectivity. However, the conventional double-stack DBR has a strong angular dependence and a narrow reflective bandwidth. Here, we propose a wide reflected angle Ti3O5/SiO2 DBR (WRA-DBR) for AlGaInP-based red and GaN-based green/blue flip-chip micro-LEDs (RGB flip-chip micro-LEDs) to overcome the drawbacks of the double-stack DBR. The WRA-DBR consisting of six sub-DBRs has high reflectivity within the visible light wavelength region at an incident angle of light ranging from 0◦ to 60◦. Furthermore, the influence of the WRA-DBR and double-stack DBR on performances of RGB flip-chip micro-LEDs is numerically investigated based on the finite-difference time-domain method. Owing to higher reflectivity and less angular dependence of the WRA-DBR, the RGB flip-chip micro-LEDs with the WRA-DBR have a stronger electric field intensity in the top side in comparison with RGB flip-chip micro-LEDs with the double-stack DBR, which indicates that more photons can be extracted from micro-LEDs with the WRA-DBR.

**Keywords:** distributed Bragg reflector; flip-chip; micro-LED; FDTD

**Citation:** Sun, Y.; Shi, L.; Du, P.; Zhao, X.; Zhou, S. Rational Distributed Bragg Reflector Design for Improving Performance of Flip-Chip Micro-LEDs. *Electronics* **2022**, *11*, 3030. https://doi.org/10.3390/ electronics11193030

Academic Editor: Lucas Lamata

Received: 3 September 2022 Accepted: 20 September 2022 Published: 23 September 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

#### **1. Introduction**

Micro light-emitting diodes (micro-LEDs) have been highlighted as a promising candidate for the realization of next-generation display panels with high dynamic range (HDR) and high resolution because of their numerous advantages such as high luminance, outstanding power efficiency, fast response time, stability, long lifetime, and wide color gamut [1–9]. The full-color micro-LED display panels can be realized by a combination of efficient red, green, and blue micro-LEDs (RGB micro-LEDs) [10–13]. However, to realize the above applications, the external quantum efficiency (EQE) of RGB micro-LEDs should be further improved. A number of methods applied to broad-area LEDs for improving the efficiency could also be applied to micro-LEDs, such as flip-chip technology [6,14–20], surface roughening [21,22], chip shaping [23–25], and patterned sapphire substrate (PSS) [26–29]. Among these methods, flip-chip technology is widely used in micro-LEDs due to its advantage in light extraction efficiency (LEE), heat dissipation, and current spreading.

It is well known that the light generated in the multiple quantum wells (MQWs) active region emits in all directions. In flip-chip micro-LEDs, we expect that light emits to air mainly from the top substrates. However, a myriad of light generated in MQWs travels downward, which does not make any contributions to the LEE. A bottom reflector plays an essential role in improving the LEE by reflecting the light back into the top substrates. The distributed Bragg reflector (DBR) has been extensively used as the bottom reflector owing to its high reflectivity in a specific wavelength region [30–32]. A typical DBR is made by stacking low refractive index dielectric layers (e.g., SiO2) and high refractive index dielectric layers (e.g., TiO2 and Ti3O5), exhibiting a low absorption in the visible light region. Five pairs of TiO2/SiO2 single-stack DBR designed for GaN-based green LEDs exhibited that the reflective bandwidth with a high reflectivity (>80%) was larger than

100 nm [31]. A double-stack DBR optimized for two different central wavelengths was designed to provide a higher reflectivity and a larger reflective bandwidth in comparison with a single-stack DBR [33]. Nevertheless, the double-stack DBR still shows severe angular dependence, which hinders further improvement of LEE in flip-chip micro-LEDs. A fullangle DBR composed of 14 sub-DBRs optimized for central wavelength in blue, green, and red wavelength regions exhibited a wide reflective bandwidth and alleviated the angular dependence [34]. However, the reflective bandwidth of the full-angle DBR is limited in the blue and green light wavelength region, which is not suitable for red micro-LEDs. Therefore, to improve the performance of the RGB flip-chip micro-LEDs, a DBR with wider reflective bandwidth covering the whole visible light wavelength region and less angular dependence is required.

To overcome the above-mentioned drawbacks of the DBRs, we propose a wide reflected angle Ti3O5/SiO2 DBR (WRA-DBR). The WRA-DBR is composed of six sub-DBRs optimized for different central wavelengths ranging from the blue light wavelength region to the red light wavelength region. The WRA-DBR has a superior reflectivity within the whole visible light region and exhibits less angular dependence. The average reflectivity of the WRA-DBR at a normal incident angle of light within the wavelength region from 400 nm to 700 nm can reach up to 99.73%. Furthermore, the average reflectivity of the WRA-DBR is up to 97.93% when the incident angle of light is 60◦. Compared to conventional double-stack DBR, the WRA-DBR exhibits a wider reflective bandwidth and alleviates the angular dependence. To further evaluate the effect of the WRA-DBR on the optical performance of RGB micro-LEDs, a simulation was carried out by using finite difference time domain (FDTD) method. The result demonstrates that the WRA-DBR can act as a potential candidate for realizing high-efficiency RGB flip-chip micro-LEDs.

#### **2. Model and Methods**

The DBR, based on the thin-film interference effect, is an array of multilayer stacks composed of two kinds of dielectric layers with high and low refractive indices. The dielectric layer thickness can be calculated by the following formula [35]:

$$m\_1 \ t\_1 = n\_2 \ t\_2 = \lambda / 4\_\prime \tag{1}$$

where the *n*1 and *n*2 are refractive indices of the high refractive layer and the low refractive layer, respectively, the *t*1 and *t*2 are thicknesses of the high refractive layer and the low refractive layer, respectively, and *λ* is the central wavelength.

Figure 1a shows the schematic illustration of the single-stack DBR. The single-stack DBR consists of *N* periods of layer 1 and layer 2. The refractive indices of layer 1 and layer 2 are *n*1 and *n*2, respectively. The thicknesses of layer 1 and layer 2 are *t*1 and *t*2, respectively. We consider the refractive indices of the incident medium and the substrate are *n*0 and *n*3, respectively. The reflection coefficient and reflectivity of the single-stack DBR can be calculated based on the transfer matrix method (TMM). From the TMM, the total transfer matrix *M* can be calculated according to the following equation [36,37]:

$$\mathbf{M} = \begin{pmatrix} M\_{11} & M\_{12} \\ M\_{21} & M\_{22} \end{pmatrix} = \mathbf{D}\_0^{-1} \left[ \mathbf{D}\_1 \mathbf{P}\_1 \mathbf{D}\_1^{-1} \mathbf{D}\_2 \mathbf{P}\_2 \mathbf{D}\_2^{-1} \right]^N \mathbf{D}\_3 \tag{2}$$

the reflection coefficient can be expressed as

$$r = \frac{M\_{21}}{M\_{11}}.\tag{3}$$

the dynamical matrix for the medium α can be expressed as [36,37]

$$\mathbf{D}\_{\boldsymbol{\alpha}} = \begin{cases} \begin{pmatrix} 1 & 1 \\ n\_{\boldsymbol{\alpha}} \cos \theta\_{\boldsymbol{\alpha}} & -n\_{\boldsymbol{\alpha}} \cos \theta\_{\boldsymbol{\alpha}} \end{pmatrix} \text{for TE wave} \\ \begin{pmatrix} \cos \theta\_{\boldsymbol{\alpha}} & \cos \theta\_{\boldsymbol{\alpha}} \\ n\_{\boldsymbol{\alpha}} & -n\_{\boldsymbol{\alpha}} \end{pmatrix} \text{for TM wave} \end{cases}, \boldsymbol{\alpha} = \boldsymbol{0}, \ 1, \ 2 \text{ and } 3 \tag{4}$$

the propagation matrix is given by

$$P\_{\mathfrak{a}} = \begin{pmatrix} \exp(i\phi\_{\mathfrak{a}}) & 0 \\ 0 & \exp(-i\phi\_{\mathfrak{a}}) \end{pmatrix}, \mathfrak{a} = 1, \, 2 \tag{5}$$

and

$$\phi\_{\alpha} = \frac{2\pi}{\lambda} n\_{\alpha} t\_{\alpha} \cos \theta\_{\alpha\nu} \text{ a} = 1,2 \tag{6}$$

where *λ* is the wavelength of incident light, and *θα* is the incident angle of light in the dielectric layer calculated by Snell's law of refraction:

$$n\_0 \sin \theta\_0 = n\_1 \sin \theta\_1 = n\_2 \sin \theta\_2 = n\_3 \sin \theta\_3 \tag{7}$$

**Figure 1.** (**a**) Schematic illustration of a single-stack DBR consisting of N periods of layer 1 and layer 2. (**b**) Schematic illustration of DBR consisting of several sub-DBRs. Ni (i = 1, 2, 3 ... ) is the periods of the sub-DBRs.

Then, the reflectivity of the single-stack DBR can be calculated by the following equation:

$$R = r^2 \tag{8}$$

Figure 1b shows the schematic illustration of the DBR consisting of several single-stack DBRs (sub-DBRs). Ni (i = 1, 2, 3 ... ) is the periods of the sub-DBRs. The total transfer matrix of the DBR is

$$\mathbf{M} = \begin{pmatrix} M\_{11} & M\_{12} \\ M\_{21} & M\_{22} \end{pmatrix} = \mathbf{D}\_0^{-1} \left[ \mathbf{D}\_1 \mathbf{P}\_1 \mathbf{D}\_1^{-1} \mathbf{D}\_2 \mathbf{P}\_2 \mathbf{D}\_2^{-1} \right]^{N\mathbf{1}} \cdot \cdots \cdot \left[ \mathbf{D}\_1 \mathbf{P}\_1 \mathbf{D}\_1^{-1} \mathbf{D}\_2 \mathbf{P}\_2 \mathbf{D}\_2^{-1} \right]^{N\mathbf{\tilde{u}}} \mathbf{D}\_3 \tag{9}$$

Then, the reflectivity of the DBR can be calculated from the above-mentioned equations.

#### **3. Results and Discussion**

Based on TMM, we investigate the angular dependence and reflective bandwidth of the double-stack Ti3O5/SiO2 DBR. The double-stack Ti3O5/SiO2 DBR is designed and modeled by TFCalc software. The double-stack DBR consists of two sub-DBRs, which are composed of 12 periods of Ti3O5/SiO2. The refractive indices of Ti3O5 and SiO2 in the simulation are fixed at 2.37 and 1.46, respectively. The central wavelengths of the two sub-DBRs are optimized for 465 nm and 630 nm, respectively. Therefore, the thicknesses of Ti3O5/SiO2 dielectric layers are 48.97 nm/79.68 nm and 66.34 nm/108.00 nm, respectively.

Figure 2a shows the schematic illustration of the double-stack DBR structure. Figure 2b shows the reflectance spectra of the double-stack DBR. The electroluminescent (EL) spectra of red, green, and blue micro-LEDs are also shown in Figure 2b. The peak wavelengths of red, green, and blue micro-LEDs are 630 nm, 520 nm, and 465 nm, respectively. It is clearly seen in Figure 2b that the reflectivity of the double-stack DBR is high within the whole visible light region when the incident angle of light is 0◦. However, as the incident angle increases, the reflective bands exhibit a blueshift and the reflectivity decreases sharply in blue and green light wavelength regions. This result indicates that the double-stack DBR has a strong angular dependence.

**Figure 2.** (**a**) Schematic illustration of double-stack DBR structure. (**b**) Reflectance spectra of the double-stack DBR as a function of incident angle.

To suppress the sharp decrease in the reflectivity in blue and green light wavelength regions, DBR III is designed by inserting a sub-DBR stack into the double-stack DBR. The inserted sub-DBR is optimized for a central wavelength at 520 nm, and the thickness of Ti3O5/SiO2 of the inserted sub-DBR is 55.81 nm/90.82 nm. The total periods of DBR III are the same as that of double-stack DBR, which means that DBR III is composed of 24 periods of Ti3O5/SiO2. Therefore, each sub-DBR of DBR III is made of eight periods of Ti3O5/SiO2. Figure 3b shows the reflectance spectra of DBR III as a function of incident angle of light. After adding a sub-DBR, the sharp decrease of reflectivity of the double-stack DBR in the blue and green light wavelength region is alleviated, revealing that the added sub-DBR can broaden the reflective bandwidth. However, the reflectivity of DBR III in the red light wavelength region at a large incident angle of light remains relatively low.

**Figure 3.** (**a**) Schematic illustration of DBR III structure. (**b**) Reflectance spectra of the DBR III as a function of incident angle.

To further improve the reflectivity of the DBR in the red light wavelength region, DBR IV with a combination of DBR III and another sub-DBR optimized for the central wavelength at 650 nm is designed, and the thickness of Ti3O5/SiO2 of the inserted sub-DBR is 68.45 nm/111.38 nm. Each sub-DBR of DBR IV is composed of six periods of Ti3O5/SiO2. Figure 4a shows the schematic illustration of the DBR IV structure. Figure 4b shows the reflectance of DBR IV. As shown in Figure 4b, the reflectivity is high when the incident angle of light is below 40◦. However, the reflectivity of DBR IV at a large incident angle of light is not greatly improved in comparison with DBR III. To further enhance the performance of DBR IV, we investigate the influence of the sub-DBR optimized for different central wavelengths on the reflectivity. Figure 4c shows the reflectance spectra of DBR IV with the added sub-DBR optimized for different central wavelengths when the incident angle of light is 60◦. The average reflectivity increases as the central wavelength of the sub-DBR increases from 650 nm to 730 nm. When the central wavelength of the inserted sub-DBR is 730 nm, the average reflectivity of DBR IV is larger than 90%. Therefore, we adopted the inserted sub-DBR optimized for the central wavelength at 730 nm.

**Figure 4.** (**a**) Schematic illustration of DBR IV structure; (**b**) reflectance spectra of the DBR IV as a function of incident angle; (**c**) reflectance spectra of DBR IV with an added sub-DBR optimized for different central wavelengths at an incident angle of 60◦.

To overcome the drawbacks outlined above, the WRA-DBR structure with a combination of DBR IV and another two sub-DBRs is designed. The thicknesses of Ti3O5/SiO2 of the two sub-DBRs are 46.34 nm/75.39 nm and 78.98 nm/128.51 nm, respectively. Meanwhile, the central wavelengths of sub-DBRs and number of periods of Ti3O5/SiO2 in the WRA-DBR are 440 nm/4 periods, 465 nm/4 periods, 520 nm/4 periods, 630 nm/5 periods, 730 nm/3 periods, and 750 nm/4 periods, respectively. Figure 5a shows the schematic of the WRA-DBR structure. Figure 5b shows the reflectance spectra of the WRA-DBR at different incident angles of light. Among all the mentioned DBRs, the WRA-DBR possesses the widest reflective bandwidth. It should be mentioned that the average reflectivity of the WRA-DBR at a normal incident angle of light is 99.73% within the wavelength region from 400 nm to 700 nm. The reflectivity of the WRA-DBR can reach up to 97.93% within the wavelength region from 400 nm to 700 nm when the incident angle of light is 60◦, indicating that the WRA-DBR has alleviated the angular dependence.

We investigate the influence of the double-stack DBR and the WRA-DBR on the performance of RGB flip-chip micro-LEDs using the finite-difference time-domain (FDTD) method. Figure 6 shows the simulation models of the RGB flip-chip micro-LEDs with the double-stack DBR and the WRA-DBR. The optical parameters and the thicknesses of each layer of the RGB flip-chip micro-LEDs are shown in Table 1. The AlGaInP-based red micro-LED consists of ITO, p-GaP, p-AlInP, MQWs, n-AlGaInP, and n-GaAs. The GaN-based green and blue micro-LEDs are composed of ITO, p-GaN, MQWs, and n-GaN. The sidewalls of the RGB micro-LEDs are inclined and the inclination angle is 70◦ [38]. For simplicity, the metal electrode layer of the micro-LEDs is neglected. Considering the memory of the computer and computing time, the size of micro-LEDs is set to be 8 μm × 8 μm. The

perfect matched layer (PML) is used to avoid the reflected electromagnetic wave at the boundary of the micro-LEDs. A 9 × 9 dipole source array is placed in the MQWs as a light source, and the space between dipoles is set to 0.8 μm. The emission wavelengths of the dipole sources in the RGB micro-LEDs are 630 nm, 520 nm, and 465 nm, respectively. A cross-sectional discrete Fourier transform (DFT) monitor is used to obtain the electric field distribution and a transmission box monitor is used to calculate the LEEs. Figure 7a–f show the electric field distributions of RGB flip-chip micro-LEDs with the double-stack DBR and WRA-DBR. In Figure 7a–f, region I is the bottom external space of micro-LEDs and region II is the top external space of the micro-LEDs. According to the electric field distributions shown in Figure 7a–f, it can be observed that there exists a weaker electric field intensity in the WRA-DBR in comparison with the electric field intensity in the double-stack DBR, indicating that the WRA-DBR has a higher reflectivity than the double-stack DBR. Therefore, more photons will be reflected upward to region II. Furthermore, compared to RGB flip-chip micro-LEDs with a double-stack DBR, stronger electric field intensity exists in the air of region II outside the RGB flip-chip micro-LEDs with the WRA-DBR, implying that the photons are more likely to be extracted from RGB flip-chip micro-LEDs with the WRA-DBR. Moreover, the LEEs of each face of the RGB micro-LEDs with the double-stack DBR and WRA-DBR are shown in Figure 7g–i. In Figure 7g, the LEEs of blue micro-LEDs with the double-stack DBR and blue micro-LEDs with the WRA-DBR are almost same. The reason for the similar LEEs in the blue micro-LEDs with the double-stack DBR and WRA-DBR is that the double-stack DBR and WRA-DBR both perform well in the blue light region. From the results of Figures 7h and 7i, it can be observed that green and red micro-LEDs with the WRA-DBR exhibit higher LEEs than green and red micro-LEDs with the double-stack DBR.

**Figure 5.** (**a**) Schematic illustration of the WRA-DBR structure. (**b**) Reflectance spectra of the WRA-DBR as a function of incident angle.

**Figure 6.** Simulation model of (**a**) blue/green micro-LED with double-stack DBR, (**b**) blue/green micro-LED with WRA-DBR, (**c**) red micro-LED with double-stack DBR, (**d**) red micro-LED with WRA-DBR.

**Figure 7.** Simulated electric field distributions for a cross section of micro-LEDs: (**a**) blue, (**b**) green, (**c**) red micro-LEDs with double-stack DBR; (**d**) blue, (**e**) green, (**f**) red micro-LEDs with WRA-DBR. LEEs of each face (top and sidewalls) of (**g**) blue, (**h**) green, (**i**) red micro-LEDs with double-stack DBR and WRA-DBR.

#### **4. Conclusions**

In summary, we have designed a WRA-DBR consisting of six sub-DBRs with high reflectivity and less angular dependence within the visible light wavelength region. The average reflectivity of the WRA-DBR at a normal incident angle of light can reach up to 99.73% in the wavelength range of 400 nm to 700 nm. Moreover, the average reflectivity of the WRA-DBR is up to 97.93% when the incident angle of light is 60◦, revealing that the WRA-DBR has less angular dependence. Furthermore, we investigate the influence of the double-stack DBR and WRA-DBR on the performance of RGB flip-chip micro-LEDs using the FDTD method. Compared to RGB flip-chip micro-LEDs with the double-stack DBR, stronger electric field intensity is found in the air outside the substrates of RGB flip-chip micro-LEDs with the WRA-DBR, indicating that the WRA-DBR can significantly improve the performance of RGB flip-chip micro-LEDs. Our work demonstrates the promising potential of the WRA-DBR for realization of high-efficiency RGB flip-chip micro-LEDs.

**Author Contributions:** Conceptualization, S.Z.; methodology, Y.S., X.Z. and S.Z.; validation, Y.S. and L.S.; formal analysis, Y.S., L.S. and P.D.; investigation, Y.S., L.S. and S.Z.; data curation, Y.S. and L.S.; writing—original draft preparation, Y.S.; writing—review and editing, S.Z.; visualization, Y.S.; supervision, S.Z.; project administration, S.Z.; funding acquisition, S.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (52075394) and the National Key R & D Program of China (2021YFB3600200). The authors also acknowledge valuable support from the National Youth Talent Support Program.

**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request.

**Acknowledgments:** The authors also acknowledge valuable support from the National Youth Talent Support Program.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

## *Review* **Hybrid Quantum Dot as Promising Tools for Theranostic Application in Cancer**

**Javed Ahmad 1,\* , Anuj Garg 2 , Gulam Mustafa 3 , Mohammad Zaki Ahmad 1 , Mohammed Aslam 4 and Awanish Mishra 5**

**Abstract:** Cancer is one of the leading causes of death worldwide. In the last few decades, cancer treatment has come a long way, but multidrug resistance (MDR) in cancer still has low survival rates. It means that much research is required for an accurate diagnosis and effective therapy. The new era of cancer research could include theranostic approaches and targeted delivery of chemotherapeutic agents utilizing the nanoparticulate system. Recently, there has been much interest gained among researchers for carbon-based and graphene-based quantum dots due to their higher biocompatibility and ease of biofunctionalization compared to conventional heavy metal quantum dots. Moreover, these quantum dots have various interesting utilities, including bioimaging, biosensing, quantum dots-mediated drug delivery, and their role in photodynamic therapy (PDT) and photothermal therapy (PTT). The current review highlighted the utility of hybrid quantum dots as a theranostic system in different cancers and discussed the various bio-molecules conjugated hybrid quantum dots investigated for diagnostic/therapeutic applications in cancer. The influence of conjugation of different biomolecules, such as folic acid, PEG, etc., with hybrid quantum dots on their biopharmaceutical attributes (such as aqueous solubility, tumor penetrability, stability of loaded therapeutics in the tumor microenvironment), delivery of drugs specifically to tumor tissues, and its therapeutic outcome in different cancer has also been discussed.

**Keywords:** hybrid quantum dots; cancer; bioimaging; theranostic; photodynamic therapy; photothermal therapy

#### **1. Introduction**

Cancer is the leading cause of death worldwide, accounting for nearly 10 million deaths in 2020 [1]. The correct diagnosis is crucial for accurate and effective treatment because all tumors need specific treatments such as surgery, radiotherapy, and chemotherapy. Novel therapeutic interventions and early diagnosis of cancer are major concerns for scientists, physicians, and healthcare professionals. In the last few decades, nanotechnology has been at the forefront of most cutting-edge research in many fields, such as medicine, diagnostics, bioimaging, and other biomedical applications [2]. Among the delivery approach of medicines in different cancers, various nanoparticles (NPs) are the most exploited carrier system for drug delivery in different cancer [3,4]. These carrier systems have different structures and dimensions, which may vary in size range from 1 to 100 nm, particularly for drug delivery in cancer. This gives them different physical and chemical properties that can be exploited for various purposes in cancer. The specific physicochemical properties of nanomaterials are exploited for focused ultrasonic heating therapy [5–7], radiofrequency (RF) ablation [8–10], magnetic fluid hyperthermia [11–13], and magnetic

**Citation:** Ahmad, J.; Garg, A.; Mustafa, G.; Ahmad, M.Z.; Aslam, M.; Mishra, A. Hybrid Quantum Dot as Promising Tools for Theranostic Application in Cancer. *Electronics* **2023**, *12*, 972. https://doi.org/ 10.3390/electronics12040972

Academic Editors: Lucas Lamata and Enzo Pasquale Scilingo

Received: 31 December 2022 Revised: 7 February 2023 Accepted: 8 February 2023 Published: 15 February 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

particle imaging [14,15] in cancer. NPs are widely exploited for bioimaging [16], drug delivery systems [17], therapeutic agents for photodynamic therapy (PDT) [18], photothermal therapy (PTT) [19], regenerative medicine [20], and smart biomaterials [21]. Furthermore, metallic NPs, especially gold [22], silver [23], platinum [24], and palladium [25], are the most investigated biocompatible NPs, for the diagnosis and treatment of cancer. Along with imaging agents to treat a wide range of diseases, including different carcinomas, the delivery of synthetic drugs, therapeutic peptides, and genes has raised interest in the theranostic approach, which can be simultaneously utilized for both diagnosis and treatment through a single system. Different nanomaterials have high penetrating efficiency to biological membranes, good biocompatibility, and can perform multiple functions due to their small size and ability to functionalization. This makes the utilization of nanomaterials a good candidate for theranostic application in different cancers [26].

Quantum dots (QDs) are a very small nanoparticulate system of organic (such as carbon-QDs, graphene-QDs) and inorganic nature (such as zinc sulfide–QDs, cadmium telluride-QDs, cadmium selenide-QDs) and vary in size ranges from 2 to 10 nm [27]. The small nano dimension is helpful to impart specific optical (high brightness, high quantum yield, high extinction coefficient, intermittent fluorescence signals, high stability against photobleaching) [28] and electronic properties that are exploited in different biomedical applications [27–29]. Its nanocrystal is distinguished by an energy band gap, required to excite an electron from one electronic band, i.e., a lower energy level, into another band, i.e., a higher energy level. Because they are so small, these nanocarrier systems of semiconductor origin can easily move electrons to a higher energy state, even when they are exposed to UV light. These properties of QDs are used in the diagnosis and treatment of various diseases, including cancer. This excitation scheme ultimately creates an electronhole pair known as an exciton. The exciton gives off energy in the form of a fluorescent photon when it goes back to its ground state [30]. The 2–10 nm sized semiconducting nanocrystal started to act like the bulk Bohr exciton radius, and the particle's electrical and optical properties changed [31]. The inverse relationship between nanocrystal size and energy band gap is well-documented and understood. The inverse property says that as the size of the nanocrystal decreases, the energy band gap increases, and the corresponding excitation/emission wavelengths decrease. The size of the particle can be changed to change the color of the light that the QDs give off when they are exposed to UV light. By adjusting the particle size and size distribution of the QDs, a wide absorbance range with highly symmetric and narrow emission spectra can be achieved [32]. The different types of QDs are prepared by the bottom-up approach, which involves the assembling of their precursor in the molecular state into nanocrystals [33]. The promising techniques for the preparation of QDs are categorized into four basic approaches, which include biotemplate-based synthesis, colloidal synthesis, biogenic synthesis, and electrochemical assembly [27,33]. These methods for the preparation of QDs are illustrated in Figure 1.

**Figure 1.** Schematic illustration of commonly used preparation approaches for QDs: (**A**) Colloidal synthesis approach. (**B**) Biotemplate-based synthesis approach. (**C**) Electrochemical assembly approach. (**D**) Biogenic synthesis approach. Reproduced from Abdellatif et al. [27], Dove Medical Press, 2022.

Carbon nanomaterials (specifically carbon nanotubes, carbon dots, graphene, and graphene derivatives) and other nanomaterials of organic and inorganic origin are popular for their extraordinary composition and excellent inherent properties for diverse applications such as fluorescent, fingerprinting, photocatalysis, electromagnetic shielding, and electric applications [3,34]. These nanomaterials have also made a pragmatic intervention in the field of biomedical engineering, contributing to research in tissue engineering, drug delivery, biosensing, bioimaging, and cancer theranostic [35]. It is functionalized with QDs as a hybrid nanoparticulate system called hybrid QDs, which have very small dimensions and theranostic utility in cancer. These hybrid systems are utilized to deliver drugs of synthetic/natural/biological origin and act as an imaging agent simultaneously, which are likely to increase their accumulation, specifically in the cancerous or tumor tissue. Thus, these versatile nanoparticulate systems as hybrid QDs have very wide utility in cancer detection/imaging and site-specific delivery of different types of therapeutics to the cancerous tissues (Illustrated in Figure 2).

**Figure 2.** Illustration highlighting the utility of hybrid QDs as cancer theranostics for various applications.

The low drug efficacy in cancer may increase by improving the EPR (enhanced permeability and retention) effect and overcoming the tumor heterogeneity challenges through designing targeted hybrid QDs of a stealth nature [36]. RBC-camouflaged, light-responsive, carbon-based porous particles may be helpful in targeting and penetrating tumor tissues. Protein- and RBC membrane-targeted nanosponges improve targeting and circulation half-life. Porous carbon/silica and graphene QDs as hybrid systems are photoresponsive and tumor-penetrating drug carrier systems for theranostic application [37]. Cyclodextrins (CDs) are natural, water-soluble cyclic oligosaccharides with hydrophilic exteriors and hydrophobic interiors that are known for their utility in drug delivery applications. Their primary and secondary hydroxyl groups on the outside are easy to modify, and their lipophilic inner cavities can be filled with lipophilic moiety by the formation of an inclusion complex. These types of carriers are utilized to improve the aqueous solubility of water-insoluble therapeutics/imaging agents and serve as a promising carrier or drug delivery system in cancer management through hybridization with QDs for theranostic application due to the presence of numerous hydroxyl groups on their surface [38].

The present manuscript provides a detailed discussion and recent advancements in QDs for their utilization to improve the efficacy of loaded therapeutics and imaging applications in the effective management of cancer. It provided a discussion on hybrid quantum dots as a cancer theranostics and emphasized the recent research development (mainly in the last 5 years) in the area of cancer theranostics utilizing hybrid quantum dots.

#### **2. Significance of Hybrid Quantum Dot as Cancer Theranostics**

The significance of the theranostic approach in cancer treatment may utilize the simultaneous delivery of chemotherapeutics and photolytic agents for deep tumor penetration, which effectively damages and inhibits the tumor when treated with single irradiation. It may be utilized for tracking of progress of cancer therapy using incorporated imaging agents [39]. Hybrid QDs have been widely explored for their theranostic application in different types of cancers. However, toxicity issues of QDs due to their composition (heavy or inorganic materials) and nature (ROS generation and strong surface responses) raised concern for their modification/functionalization for biomedical applications. Hence, strategies have been conceptualized to minimize their toxicity and improve their biocompatibility through hybridization/functionalization with other moieties (such as polymers, lipids, polysaccharides, proteins, etc.), providing efficient accumulation in tumor tissues in addition to preventing their accumulation in healthy tissues [40,41]. Biological molecules are attached to QDs using hydrophilic surfactant shells with reactive groups such as COOH, NH2, or SH. Attachments are made using different methods, such as adsorption, covalent bonding, electrostatic interaction, etc. [39–41]. It has been reported to be conjugated with a wide range of biological molecules, including biotin [42], folic acid [43,44], antibodies [45], and peptides [46]. Silanization, which coats QDs with silica, is a good covalent coating method for hydroxyl-rich material surfaces. Silanization makes ligand molecules strongly cross-linked and chemically stable. The end terminal groups of the silane shell can expose thiol, phosphonate, or methyl terminal ends for subsequent QD coating and also make the material more biocompatible. Silanization is favored because it is less toxic than other ligands [47]. Silica shell thickness could control QD light responsiveness. The silica-coated QDs were modified with amino, carboxyl, and epoxy groups and stabilized with PEG segments to assess their applicability. These modified QDs efficiently conjugated with antibodies and were used as fluorescent labels in immunoassay detection [48]. An in vivo study has shown that emissive Si-QDs biodegrade quickly and produce non-toxic silicic acid that may be eliminated by urine [49].

The perspectives of hybrid QDs for their utility in cancer diagnosis/imaging and delivery of payload specifically to tumor tissues are discussed in the subsequent section.

#### *2.1. Perspectives of QDs for Diagnostic/Imaging Utility*

QDs in drug delivery may be utilized as therapeutic/imaging cargo that has photothermal and photodynamic features, making them excellent for bioimaging. Many clinically used photosensitizers (PSs) are not tumor-targeted; hence, they are treated with spatially controlled irradiation. After phototherapies, PS can increase reactive oxygen species (ROS) formation in healthy cells; hence, light exposure should be avoided to reduce skin photosensitivity. The hybrid QDs possess low toxicity and good biocompatibility, coupled with stable photoluminescence (PL), and therefore these are ideal candidates for both in vitro and in vivo bioimaging [40,41]. QDs by themselves are not as efficient as molecular PSs, but QDs can be used as antennae to improve light harvesting and energy transfer to molecular PSs because they absorb much light. NPs are commonly utilized for bioimaging, but their toxicity limits their utility. Because fluorescence imaging is very sensitive and has a good temporal and spatial resolution, hybrid QDs are a good choice for sensing and imaging cell targets. Hybrid QDs are chemically inert, dissolve well in water, are photostable, have a relationship between their optoelectronic properties and their shape and size, have fluorescence resonance energy transfer, high stability in physiological conditions, specific accumulation at target sites, are easy to modify on the surface [50], and have a high absorption coefficient because of hybridized C–C bonds. Therefore, these are good phototherapy chromophores.

Carbon QDs (C-QDs) synthesized and dispersed with excellent fluorescence, photostability, photobleaching resistance, and simple coupling with biological species [51]. C-QDs can carry Ce6 and generate ROS. Using a 639 nm laser, water splitting produced oxygen and hydrogen in vivo. Increased oxygen yielded 1O2 to improve PDT. C-QDs with specific