Organic Optoelectronics

Photoelectronic Conversion Materials, Physics and Devices

Edited by Xinping Zhang, Baoquan Sun and Fujun Zhang

www.mdpi.com/journal/crystals

## **Organic Optoelectronics: Photoelectronic Conversion Materials, Physics and Devices**

## **Organic Optoelectronics: Photoelectronic Conversion Materials, Physics and Devices**

Editors

**Xinping Zhang Baoquan Sun Fujun Zhang**

MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin

*Editors* Xinping Zhang Beijing University of Technology China

Baoquan Sun Soochow University China

Fujun Zhang Beijing Jiaotong University China

*Editorial Office* MDPI St. Alban-Anlage 66 4052 Basel, Switzerland

This is a reprint of articles from the Special Issue published online in the open access journal *Crystals* (ISSN 2073-4352) (available at: https://www.mdpi.com/journal/crystals/special issues/ organic optoelectronics).

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## **Contents**

## **Preface to "Organic Optoelectronics: Photoelectronic Conversion Materials, Physics and Devices"**

Organic optoelectronics is a broad topic involving research interests in a wide range of fields. Physics, materials, structures, and devices based on molecular semiconductors can all be classified into this topic. Another classification may be made by considering light emitting, light harvesting, light conversion or detection processes, where examining how light interacts with semiconductor molecules is the main criterium. This Special Issue intends to make a collection of the most recent progresses in organic optoelectronics.

In order to focus the topics of this Special Issue on the most active fields, we have chosen a title covering photoelectronic conversion materials, physics, and devices. Research articles have been collected in relevance to the light-emitting performance of organic or hybrid semiconductors, photovoltaic or photodetection devices, micro-cavity and random lasers, and structural or morphological or crystallization properties of semiconductor molecules influencing the photoelectronic processes.

> **Xinping Zhang, Baoquan Sun , and Fujun Zhang** *Editors*

## *Article* **A Theoretical Model of Quasicrystal Resonators: A Guided Optimization Approach**

**Libin Cui 1, Anwer Hayat 1, Linzheng Lv 2, Zhiyang Xu 1 and Tianrui Zhai 1,\***

**Abstract:** Fibonacci-spaced defect resonators were analytically investigated by cavity coupling, which exhibited a series of well-defined optical modes in fractals. The analytic model can be used to predict the output performance of microcavity lasers based on Fibonacci-spaced defect resonators, such as the mode number, resonant frequency, and Q factor. All results obtained by the analytical solution are in good consistency with that obtained by the finite-difference time-domain method. The simulation result shows that the Q factor of the resonant modes would increase dramatically with the appearance of narrower optical modes. The proposed theoretical model can be used to inversely design high performance polymer lasers based on the Fibonacci-spaced defect resonators.

**Keywords:** quasicrystal resonator; analytic model; cavity coupling

**Citation:** Cui, L.; Hayat, A.; Lv, L.; Xu, Z.; Zhai, T. A Theoretical Model of Quasicrystal Resonators: A Guided Optimization Approach. *Crystals* **2021**, *11*, 749. https://doi.org/ 10.3390/cryst11070749

Academic Editor: Valentina Domenici

Received: 12 May 2021 Accepted: 23 June 2021 Published: 26 June 2021

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

**Copyright:** © 2021 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**

The discovery of quasicrystals in condensed matter has revolutionized solid-state physics [1–3]. During the last few decades, photonic quasicrystals have been extensively discussed and studied [4–9]. Quasiperiodic structures are natural intermediate cases between periodicity and randomness, which provide more optical design possibilities and richness in the engineering performance of the optical devices. The design of optical devices based on the quasiperiodic structures can achieve a better performance than periodic ones for some specific optical applications, which opens new avenues in the quest for high performance optical devices [10–16].

One-dimensional (1D) optical quasicrystal lattices composed of multilayer stacks have two different dielectrics of permittivity, ε1 and ε2, arranged in deterministic generation rule, which exhibit long-range order but lack of translational symmetry. All these structures exhibit self-similar properties.

In the case of 1D optical quasicrystals the quasicrystalline long-range order results in a pseudogap similar to the bandgap of photonic crystals, while the lack of periodicity in the quasicrystal results in critically localized optical modes similar to the localization in the random systems; in other words, it can be considered as a defect effect. This leads to the appearance of allowed optical modes inside the forbidden 1D pseudogap. The optical modes exhibit fractal self-similar patterns in the transmission spectra that stem from the self-similarity of the underlying structure [17–19]. High Q-factor resonators can be attained due to the splitting and sharpness of the previous modes from the well-defined self-similar feature [20]. Moreover, the progressive fragmentation of the frequency spectrum gives rise to a series of optical modes, which means that in the limit of a large sample size their spectra become singular continuous, which provide many additional Bragg resonances for feedback, leading to a multicolor laser at arbitrarily chosen frequencies within the gain bandwidth [21,22].

The optical modes inside quasicrystals are confined in space but decay weakly rather than exponentially [23–25], which leads to the crosstalk between modes in the energy spectra and it is difficult to realize single-mode control. This is commonly referred to as the "non-resonant" case [4,5,26]. Resonant quasiperiodic multi-quantum-well stacks were proposed [27–29], which show a shorter emission lifetime and higher photoluminescence emission intensity than that in non-resonant conditions.

How are resonator properties such as wavelength, number of modes and output controlled by the quasiperiodicity? Many important concepts that are related to crystals, such as band structure, Bloch theorem, Brillouin zone, etc., are invalid in quasicrystals. The optical behavior of 1D optical quasicrystal lattices can be investigated numerically using the transfer matrix method [26,30–32] and the plane wave method [33]. However, the numerical solutions are not intuitive.

In this paper, we proposed a resonant Fibonacci-spaced multiple-defect-cavity structures, which exhibits properties of self-similar optical modes with a series of well-separated peaks. At the resonant condition, the system is resonant and strongly coupled. When there is an increase in the generation order, very narrow optical modes would appear and the Q factor of the resonant modes would increase exponentially with mode splitting. We developed a general theoretical model of the 1D quasicrystal resonator based on the coupled mode theory. The mode splitting, number and frequency of the resonant modes were explained qualitatively by an analytical solution. The theoretical model is completely consistent with the finite difference time domain (FDTD) simulation. We also demonstrate the inverse design of 1D Fibonacci-spaced resonators for the desired wavelength and amplitude of optical modes which can realize the broad color gamut laser display.

#### **2. Theoretical Analysis**

#### *2.1. Theoretical Model of 1D Fibonacci-Spaced Defect Resonators*

One dimensional resonant Fibonacci quasicrystals systems based on multiple defect cavities with two different interdefect distances satisfy the Fibonacci-chain rule between the long and short interdefect distances, as shown in Figure 1. The separations between the defect cavities are denoted by short(*S*) and long(*L*), respectively. The Fibonacci chain (*LSLLSLSL* ... ) follows the construction rule that the next complete sequence is the present sequence plus the previous sequence, marking the first sequence as S and the second as L.

**Figure 1.** Scheme of 1D Fibonacci-spaced defect resonators. The PPV layers are inserted in the period stacks of SiO2/TiO2 structures, in which the PPV acts as both the defect cavity and the gain medium.

In the defect cavity, light is confined in a small volume, which enhances light–matter interactions and favors the laser behavior. The high-Q resonance and wavelength size of defect cavity make it extremely suitable for creating the coupled microcavity arrays. The widths of the interdefect cavity were determined from the resonant Bragg conditions, specifying the constructive interference of the waves reflected from the multiple defect cavities at the excitonic resonance.

The resonant electric field of each defect microcavity could enter into the other's field with a coupling constant *κ*. Similarly, the amount of the coupling can be defined by taking the overlap integral of the modes from the electric field as it enters into the other's field with a coupling strength. We have developed our theoretical model based on the coupled-wave theory. When the coupling effect between the cavities is ignored, there will be one resonant mode in the above system under the resonant condition. The field amplitude in the microcavity evolves over time as *exp*(−*iωt*), therefore, the dynamic equations for resonance amplitudes can be written as: *da dt* = −*iωa*, where *a* is the field amplitude in the microcavity, and *ω* is the resonant frequency [34]. Let us consider the cavity mode coupling effect between the cavities, as shown in Figure 1. We ignore the coupling between the non-adjacent cavities. According to the coupled-wave theory, the dynamic equations for the *n*th resonant cavity can be written in the following form [35]:

$$\frac{da\_{\rm II}}{dt} = -i\omega\_{\rm n}a\_{\rm n} + i\kappa\_{\rm n-1}a\_{\rm n-1} + i\kappa\_{\rm n+1}a\_{\rm n+1} \tag{1}$$

where *an* is the mode amplitude of the nth resonator, *κn*−1 *n* and *κn*+1 *n* present the coupling coefficients of the modes *n* − 1 and *n* + 1 coupled to the mode *n*, respectively. The Fourier transform of *an* is

$$a\_{\rm ll}(t) = \int A\_{\rm l}(\omega) \exp(-i\omega t) d\omega \tag{2}$$

Inserting the value of Equation (2) into Equation (1) and considering all *N* resonators, after solving, the coupling equations in the frequency domain for the given system can be expressed as:

$$
\begin{bmatrix}
\omega\_1 - \omega\_0 & -\kappa\_{21} & 0 & \cdots & 0 \\
\cdots & \cdots & \cdots & \cdots & \cdots & \cdots \\
0 & 0 & \cdots & \omega\_{N-1} - \omega\_0 & -\kappa\_{NN-1} \\
0 & 0 & \cdots & -\kappa\_{N-1N} & \omega\_N - \omega\_0
\end{bmatrix}
\begin{bmatrix}
A\_1 \\
A\_2 \\
\cdots \\
A\_{N-1} \\
A\_N
\end{bmatrix} = 0
\tag{3}
$$

where *A*1, *A*2 ··· *AN* are the complex amplitude of the *N* resonant cavities and *ω*0 is the unperturbed Bragg frequency. Therefore, the above equations will lead a nonzero solutions when the determinant of the coefficient of equations *DN* equals zero. Considering the coupling coefficient between the two cavities is irrelevant to the direction of coupling. In the two opposite directions, we suppose *κij* = *κji* = *κi*, *DN* can be expressed as:

$$D\_{N} = \begin{vmatrix} \omega\_{1} - \omega\_{0} & -\kappa\_{1} & 0 & \cdots & 0 \\ -\kappa\_{1} & \omega\_{2} - \omega\_{0} & -\kappa\_{2} & \cdots & 0 \\ \cdots & \cdots & \cdots & \cdots & \cdots & \cdots \\ 0 & 0 & \cdots & \omega\_{N-1} - \omega\_{0} & -\kappa\_{N-1} \\ 0 & 0 & \cdots & -\kappa\_{N-1} & \omega\_{N} - \omega\_{0} \end{vmatrix} = 0 \tag{4}$$

According to Equation (4), we construct the coupling matrix as follows:

$$\mathbf{C}\_{N} = \begin{vmatrix} 0 & \kappa\_1 & 0 & \dots & 0 \\ \kappa\_1 & 0 & \kappa\_2 & \dots & 0 \\ \dots & \dots & \dots & \dots & \dots & \dots \\ 0 & 0 & \dots & 0 & \kappa\_{N-1} \\ 0 & 0 & \dots & \kappa\_{N-1} & 0 \end{vmatrix} \tag{5}$$

Equation (5) implies that diagonal elements are zero because the mode of the one cavity is not coupled to itself for the off diagonal elements *κij* = 0, except *j* = *i* ± 1, because coupling between the non-adjacent cavities should not be considered.

By comparing Equation (4) and Equation (5), we can obtain *DN* = |(*ω* − *ω*0)*E* − *CN*|, where *E* is the unit matrix. Therefore, *ω* − *ω*0 is the eigenvalue of *CN*. As described in Equation (5), *CN* is a real symmetric matrix, (*CN*) *T* = *CN*. For *N* we can obtain the eigenvalue *ω*1 − *ω*0, *ω*2 − *ω*0 ... *ωN* − *ω*0 from the symmetry of *CN*. It can be further proved by the matrix theory that these *N* eigenvalues are different. (The detailed derivation process is described in Appendix A). Thus, the cavity coupled modes split into the *N* resonance modes.

Based on the well-known matrix theory, we can obtain the resonance frequencies for the *N* defect microcavities arranged following the Fibonacci sequence as described in Figure 1. The coupling coefficients between the cavities with short and long separations are denoted by *κS* and *κL*, respectively. Therefore, Equation (4) can be written as:

$$D\_{N} = \begin{vmatrix} \omega\_{1} - \omega\_{0} & -\kappa\_{L} & 0 & \cdots & 0 \\ -\kappa\_{L} & \omega\_{2} - \omega\_{0} & -\kappa\_{S} & \cdots & 0 \\ \cdots & \cdots & \cdots & \cdots & \cdots & \cdots \\ 0 & 0 & \cdots & \omega\_{N-1} - \omega\_{0} & -\kappa\_{N-1} \\ 0 & 0 & \cdots & -\kappa\_{N-1} & \omega\_{N} - \omega\_{0} \end{vmatrix} = 0 \tag{6}$$

After solving the linear equations, the resonant frequencies can be obtained. *DN* can be expressed as the following recursive relation (See Appendix B for detailed derivation). Note that *κN*−1 depends on the parity of *N*.

$$D\_N = (\omega - \omega\_0)D\_{N-1} - \kappa\_{N-1}^2 D\_{N-2} \tag{7}$$

Once we know both *D*2 and *D*3, *DN* can be extracted step by step using Equation (7).

#### *2.2. Analytical Results and Discussion*

We can figure out all the resultant resonant frequencies from the solution of Equation (6) and some results are described in Table 1.

**Table 1.** The frequencies of the coupled defect mode for *N* = 1, 2, 3, 5, respectively.

We noticed in the analytical solution that the resonant frequencies are distributed symmetrically about *ω*0 and can be evaluated from the coupling coefficient *κS* and *κL*. If *κS* = *κL*, it is referred to a as periodic defect cavities chain, which has been studied in our previous work [36]. Similarly, the Fibonacci-spaced defect resonators exhibit unusual properties, which are very different from those of periodic and random systems, as we can see in Figure 2a, where we plot the evolution of resonant modes as generation order increase, which show self-similar properties of typical Cantor sets.

It could be proved by the matrix theory there exist a limit value for the maximum and minimum resonant frequencies in the above analytical solution. This means that in a limited spectral region the spectra are highly fragmented. For large generation order, the line width of the resonant modes decreases dramatically, which results in resonators with high Q-factors.

**Figure 2.** (**a**) Comparison of resonant frequencies of the Fibonacci-spaced defect resonators obtained from the theoretical model developed (the red line) and the simulation using FDTD (the black line) with different generation order for *κS* = 0.42, *κL* = 0.27. The results agree well, and the discrepancies are expected to vanish if the first and last coupling coefficients are modified due to external losses. (**b**) Q factor increases exponentially with mode splitting.

Due to their highly fragmented frequency spectra, a Fibonacci-spaced chain of defect cavities offers more resonant frequencies than periodic ones in a given frequency range for a given system length, which provides a higher degree of design and tuning flexibility. The analytical solution of the proposed theoretical model can be used to customize high performance microcavity resonators and it can be made via inverse design. The theoretical mode can also be extended to predict the characteristics of 2D quasiperiodic structures.

#### **3. Simulation and Validation**

To validate the theoretical analysis, we compare the theoretical results to the FDTD simulations. In the simulation, the refractive indices of SiO2 and TiO2 were chosen as 1.54 and 2.5, respectively, which were measured by a spectroscopic ellipsometer (ESNano, Ellitop). The thickness of the SiO2/TiO2 layer was 90/70 nm. The refractive index and the thickness of the MDMO-PPV (defect/gain layer) were about 1.67 and 94 nm, respectively. The important parameters were optimized by FDTD, so that the photonic band gap overlapped almost completely with the emission spectrum of MEMO-PPV, and the unperturbed defect mode frequency is exactly at the center of band-gap of the 1D photonic structure.

We found an excellent agreement in the resonant frequencies by comparing the results of the analytical model based on the coupling mode effect with FDTD simulation, as shown in Figure 2a. The deviations between the theory and the simulation are from the coupling of two cavities on both sides to the outside world. We expect this discrepancy vanish if the external losses are modified in the first and last coupling coefficients.

It can be observed from Figure 2a that every mode of any hierarchy will split into submodes to form the Cantor spectrum. In the third hierarchy there are three modes: the mode on the both sides will further split into submode for the global structure, and the middle mode will also split in the same manner for next stage. Thus, it turns out that the Fibonacci-spaced defect resonators have a perfect self-similar spectrum. The Q factor of the resonant modes would increase exponentially with the appearance of narrower optical modes, as shown in Figure 2b. Considering only the resonant modes in the center of the band, the Q value increases from 480 for *N* = 1 to 23,960 for *N* = 13, where the size of the device increases from 1.694 to 5.862 μm.

#### **4. Inverse Design of Laser Resonators Based on the Fibonacci-Spaced Defect Resonators**

Some features of the regular quasicrystals are not required for the operation of microcavity lasers. According to the analytical model, the regular quasicrystals can be modified to be an ideal resonator for microcavity lasers. For example, the mode splitting provides a simple, flexible and versatile approach for the design of high performance resonators [36–40]. It would allow us to engineer the behavior of the cavity mode simply by tailoring the separation and size of the defects. Here, the ratio *α* = *L S* is arbitrary. For *L* = *S* the structure becomes periodic and for *τ* equal to the golden mean 1.618, it becomes the canonical Fibonacci chain [41]. The simulation results show that Δ*ω*, which refers to frequency detuning from *ω*0 due to coupling, decreases exponentially with increasing the ratio *α*, as shown in Figure 3.

**Figure 3.** The relation between Δ*ω* and *α* for *N* = 3, 5, 8. The dotted line indicates the positions on the curve at *τ* = 1.618.

According the relation between Δ*ω* and *α* and the analytical solutions mentioned above, we can optimize 1D quasicrystal resonators to obtain target optical modes at arbitrary positions in a broad spectral range.

In this section, we have studied inverse design of the 1D quasicrystals resonators to obtain desired laser emission, as shown in Figure 4. By adjusting the separation of the defects in above model, the optical modes can be fine-tuned across a broad-spectrum range, as shown in Figure 4a. Organic polymers have broad emission spectrum, which demonstrates excellent features in flexible spectrum modulation. It has been reported [42,43] that the intensity of the band-gap modes can be adjusted by controlling the phase shift of both reflecting facets. In Figure 4b, we have demonstrated the effect on the intensity of optical modes in the band-gap by changing the number of boundary layers. Based on the analytic model, the number of optical modes can be predicted, which corresponds to the number of defects, as shown in Figure 4c. The wavelength and intensity of the output emissions are calculated as points located in the CIE chromaticity diagram in Figure 4d. Thus, the CIE chromaticity demonstrates the output of the laser with broad color gamut.

Note that there is a slight difference between the resonant frequency of Fibonaccispaced defect resonators obtained from the theoretical model and that obtained from FDTD, especially for high generation orders. It can be attributed to the fact that the coupling between non-adjacent cavities is not considered in the proposed method. Even so, the developed analytical model can be extended to a more general case of aperiodic plasmonic systems, which provides a simple and efficient route towards designing real systems with flexible, multispectral optical responses. It opens a new avenue in the quest for high performance optical devices.

**Figure 4.** (**a**) Modes splitting for *N* = 3 with *τ* = 3, 1.5, 1.43. (**b**) Intensity of optical modes for different boundary layers. (**c**) The number of optical modes for different number of defects. (**d**) Schematic diagram of the emission spectra for the R, G and B components.

#### **5. Conclusions**

In conclusion, we have presented 1D quasicrystal resonators which exhibit progressive fragmentation of the frequency spectrum as generation order increases and gives rise to quasicontinuous but well-defined optical modes in the limit of large sample size. The analytical solution of the proposed theoretical model provides precise control on singleor multifrequency across a broad spectral range, which can be used in the polymer laserbased display with broad color gamut and also can meet the operating requirements of high-resolution spectroscopy.

**Author Contributions:** Conceptualization, L.C. and T.Z.; Methodology, L.C. and L.L.; Validation, L.C. and T.Z.; Formal Analysis, L.C. and L.L.; Investigation, L.C. and Z.X.; Writing—Original Draft Preparation, L.C.; Writing—Review and Editing, L.C., A.H., and T.Z.; Supervision, T.Z.; Project Administration, T.Z.; Funding Acquisition, T.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** Beijing Natural Science Foundation (Z180015); National Natural Science Foundation of China (61822501).

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data sharing not available.

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

#### **Appendix A**

In the first step, keeping in view the concept of matrix theory, if *CN* is a real symmetric matrix, it can be deduced that *CN* has *N* real eigenvalues. In the second step, if we have *DN* = (*ω* − *ω*0)*E* − *CN* = *dij* , then the cofactor of *dN*1 can be arranged in the following form:

$$\begin{array}{c|cccc} & -\kappa\_1 & 0 & \cdots & 0 & 0 \\ & \omega - \omega\_0 & -\kappa\_2 & \cdots & 0 & 0 \\ & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots \\ & 0 & 0 & \cdots & -\kappa\_{N-2} & 0 \\ 0 & 0 & \cdots & \omega - \omega\_0 & -\kappa\_{N-1} \end{array} \qquad = (-1)^{N-1} \kappa\_1 \kappa\_2 \cdots \kappa\_{N-1} \neq 0 \tag{A1}$$

Thus, the rank of *DN* is greater than or equal to 1, that is *R*(*DN*) ≥ *N* − 1. On the other hand, *R*(*DN*) ≤ *N* − 1 because *ω* − *ω*0 is the eigenvalue of *CN*. Therefore, we can obtain *R*(*DN*) = *N* − 1 for any eigenvalue of *CN*. From *R*(*DN*) = *N* − 1, we can derive that *N* real eigenvalues of *CN* are different. In summary, it can be concluded that *CN* has *N* different real eigenvalues.

#### **Appendix B**

*DN* is the determinant of tridiagonal matrix in Equation (6). It can be written as:

$$D\_{N} = \begin{vmatrix} \omega - \omega\_{0} & -\kappa\_{L} & 0 & \cdots & 0 \\ & -\kappa\_{L} & \omega - \omega\_{0} & -\kappa\_{S} & \cdots & 0 \\ & \ddots & \ddots & \ddots & \ddots & \ddots \\ & 0 & 0 & \cdots & \omega - \omega\_{0} & -\kappa\_{N-1} \\ & 0 & 0 & \cdots & -\kappa\_{N-1} & \omega - \omega\_{0} \end{vmatrix} = $$

$$\begin{vmatrix} \omega - \omega\_{0} & -\kappa\_{L} & 0 & \cdots & 0 \\ -\kappa\_{L} & \omega - \omega\_{0} & -\kappa\_{S} & \cdots & 0 \\ \cdots & \cdots & \cdots & \cdots & \cdots & \cdots \\ 0 & 0 & \cdots & \omega - \omega\_{0} & -\kappa\_{N-2} \\ 0 & 0 & \cdots & -\kappa\_{N-2} & \omega - \omega\_{0} \end{vmatrix} \tag{A2}$$

$$\begin{vmatrix} \omega - \omega\_{0} & -\kappa\_{L} & 0 & \cdots & 0 \\ -\kappa\_{L} & \omega - \omega\_{0} & -\kappa\_{S} & \cdots & 0 \\ \cdots & \cdots & \cdots & \cdots & \cdots & \cdots \\ 0 & 0 & \cdots & \cdots & \cdots & \cdots \end{vmatrix} \tag{A3}$$

$$\begin{vmatrix} \omega - \kappa\_{N-1} & \omega - \omega\_{0} & -\kappa\_{N-2} & \cdots & 0 \\ 0 & 0 & \cdots & \cdots & \cdots & \cdots & \cdots \\ 0 & 0 & \cdots & \cdots & -\kappa\_{N-3} & \omega - \omega\_{0} \end{vmatrix}\_{N-2}$$

Thus, from Equation (A2), *DN* can be expressed as the following recursive relation:

$$D\_N = (\omega - \omega\_0)D\_{N-1} - \kappa\_{N-1}^2 D\_{N-2}$$

where *DN*−1 and *DN*−2 are the determinant of the bottom-right (*N* − 1) × (*N* − 1) and (*N* − 2) × (*N* − 2) submatrix of *DN* respectively.

#### **References**

### *Article* **Vortex Laser Based on a Plasmonic Ring Cavity**

**Xingyuan Wang 1,\*, Xiaoyong Hu 2,\* and Tianrui Zhai 3,\***

**Abstract:** The orbital angular momentum (OAM) of the structure light is viewed as a candidate for enhancing the capacity of information processing. Microring has advantages in realizing the compact lasers required for on-chip applications. However, as the clockwise and counterclockwise whispering gallery modes (WGM) appear simultaneously, the emitted light from the normal microring does not possess net OAM. Here, we propose an OAM laser based on the standing-wave WGMs containing clockwise and counterclockwise WGM components. Due to the inhomogeneous intensity distribution of the standing-wave WGM, the single-mode lasing for the OAM light can be realized. Besides, the OAM of the emitted light can be designed on demand. The principle and properties of the proposed laser are demonstrated by numerical simulations. This work paves the way for exploring a single-mode OAM laser based on the plasmonic standing-wave WGMs at the microscale, which can be served as a basic building block for on-chip optical devices.

**Keywords:** micro-nano photonics devices; optical microcavity; micro-nano vortex laser; orbital angular momentum; plasmonic devices

#### **1. Introduction**

After the knowledge about the linear momentum and spin angular momentum of light, a breakthrough is the recognition of the orbital angular momentum (OAM) of light [1]. The OAM is a completely new degree of freedom. In theory, the OAM light provides infinite orthogonal modes. As a result, the OAM states can greatly expand the information capacity, which has directed attention to applications for optical communication [2] and quantum information [3]. Since the first demonstration of a laser in 1960 [4], various lasers have been investigated, such as the plasmonic nanolaser [5], the random laser [6–8], the photonic crystal nanocavity laser [9], and the exciton-polariton laser [10], and so forth. Advances in nano-technology make it possible to manipulate the light on a chip [11–15]. Because the generation of micro-scale OAM light is of great significance to on-chip applications, it has received extensive attention.

Optical vortex beams with helical phase front carry OAM. In order to obtain OAM light, one can modulate the wave front of a coherent light. The wave-front modulations are mostly based on changing the optical path difference, employing a geometry phase, or controlling diffraction on demand with suitable optical elements, such as spiral phase plates, lens, Pancharatnam–Berry phase elements, and holograph [16–23] and so forth. In addition, the direct generation of OAM light within the laser cavity has been developed, to the great attention of researchers [24–34]. Microring has advantages in realizing compact lasers. However, the conventional microring cavity supports the standing-wave WGM with the same weight of clockwise (CW) and counterclockwise (CCW) components, resulting in a net zero OAM of the emitted light. In order to obtain emitted light with OAM, much attention is paid to breaking the rotation symmetry between the two counter-propagating

**Citation:** Wang, X.; Hu, X.; Zhai, T. Vortex Laser Based on a Plasmonic Ring Cavity. *Crystals* **2021**, *11*, 901. https://doi.org/10.3390/ cryst11080901

Academic Editor: Anna Paola Caricato

Received: 19 June 2021 Accepted: 29 July 2021 Published: 31 July 2021

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

**Copyright:** © 2021 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/).

WGMs in the ring cavity. For instance, the OAM laser can be made based on the travelingwave WGM at the non-Hermitian exceptional point of a ring cavity [34]. Despite these impressive advances, designing controllable single-mode OAM lasers at the microscale are still challenging.

Here, we propose a vector OAM laser based on the plasmonic standing-wave WGMs. In this framework, the OAM light is constructed by modulating the scattered waves from the standing-wave WGM in the plasmonic ring cavity, and the desired single-mode lasing can be achieved.

#### **2. Principle and Results**

Figure 1a shows the schematic of an OAM laser. The ring cavity is a coaxial cylindrical structure with a silver–InGaAsP–silver geometry. The bottom of the cavity is encapsulated by silver, so only the upper face of the ring is reserved as the port of the OAM-light emission. This microcavity supports plasmonic mode, for which the electric field component with polarization along the radial direction in the cavity plane (x-y plane) is dominant. We construct the OAM light based on the standing-wave WGMs. For the standing wave, the oscillations between two adjacent nodes are in phase, while the oscillations on the opposite sides of a node are in anti-phase, that is, there is a *π* phase jump at each node. However, the OAM light beam possesses helical phase fronts. In order to obtain OAM light, we introduce tiny effective-refractive-index perturbations at discrete positions along the azimuthal direction of the InGaAsP ring (the effective-refractive-index perturbations are in the region with *r*inner ≤ *r* ≤ *r*outer and 0 ≤ *z* ≤ *h*InGaAsP, where *r*inner, *r*outer and *h*InGaAsP are the inner radius, outer radius, and height of the InGaAsP ring, respectively). The tiny effective-refractive-index perturbations will couple the standing-wave WGM to the OAM mode by extracting the phase of the standing wave and shifting it to the phase of the OAM mode. In detail, we introduce 2*m* effective-refractive-index perturbations at discrete parts in the ring. Each individual section of the effective-refractive-index perturbations has an angular width Δ*θ* = *π*/2*m* along the azimuthal direction of the ring. The azimuthal coordinates at the centrals of these 2*m* sections are *θ*1(*n*) = *πn*/*m* (*n* = 1, 2, 3, . . . , 2*m*), respectively. For convenience, we define these 2*m* sections of the ring as region 1, and define other parts of the ring as region 2 (region 2 of the ring also consists of 2*m* sections, where each individual section has an angular width Δ*θ*, and the azimuthal coordinates at the centrals of these sections are *θ*2(*n*) = *πn*/*m* + Δ*θ* (*n* = 1, 2, 3, . . . , 2*m*), respectively). In this framework, the standing-wave WGM with azimuthal mode number *l* = *m* can be coupled to the desired OAM light. The effective refractive indexes in the ring (*r*inner ≤ *r* ≤ *r*outer, 0 ≤ *z* ≤ *h*InGaAsP) along the azimuthal direction (*θ*) are

$$n\_G = $$

$$\begin{cases} \begin{array}{ll} n\_{\text{InGaAs}} + \delta + \delta i + \delta e^{i\phi\_{\text{n}}}, & \theta\_{1}(n) - \frac{\Lambda\theta}{2} \le \theta \le \theta\_{1}(n) + \frac{\Lambda\theta}{2}(n = 1, 3, 5 \dots 2m - 1) \\\ n\_{\text{InGaAs}} + \delta + \delta i + \delta e^{i(\phi\_{\text{n}} + \pi)}, & \theta\_{1}(n) - \frac{\Lambda\theta}{2} \le \theta \le \theta\_{1}(n) + \frac{\Lambda\theta}{2}(n = 2, 4, 6 \dots 2m) \\\ n\_{\text{InGaAs}} + n^{\circ}i, & \theta\_{2}(n) - \frac{\Lambda\theta}{2} \le \theta \le \theta\_{2}(n) + \frac{\Lambda\theta}{2}(n = 1, 2, 3 \dots 2m) \end{array} \tag{1}$$

where the tiny perturbations δ*eiφn* and δ*ei*(*φn*+*π*) will couple the standing-wave WGMs with *l* = *m* into the desired OAM light. Because the oscillations of the standing-wave WGMs jump a *π* phase at each amplitude node, a *π* is needed in the term δ*ei*(*φn*+*π*). *φn* = *qnπ*/*m* (*n* = 1, 2, 3, . . . , 2*m*). The OAM carried by the emitted light is related to *q* (*q* = 0, ±1, ±2, . . .). The *φn* and *φn* + *π* can be controlled by tuning the real and imaginary part of the perturbation terms. Researchers have explored some methods to modulate the effective dielectric constant or effective refractive index [34,35]. The loss *n i* can be used to suppress the lasing of the competing modes. It is worth noting that the δ + δ*i* is not required. However, in order to facilitate the practical effective refractive index modulations, δ + δ*i* is used in our theoretical model. In this case, δ + δ*i* + δ*eiφn* and δ + δ*i* + δ*ei*(*φn*+*π*) (δ > 0) can be achieved without resorting to gain and negative real parts. In this paper, we adopt the following definition: the material corresponds to loss material when the imaginary part of the refractive index of the material is positive.

**Figure 1.** The cavity mode and the emitted mode of the OAM laser for *l* = 11. (**a**) Schematic of an OAM laser. The *z* = 0 is at the bottom of the InGaAsP ring, and the (*x* = 0, *y* = 0) is at the center of the ring. (**b1**)–(**g1**), mode 1 inside the cavity [(**b1**)–(**d1**)] and the corresponding emission mode [(**e1**)–(**g1**)]. (**b2**)–(**g2**). Mode 2 inside the cavity [(**b2**)–(**d2**)] and the corresponding emission mode [(**e2**)–(**g2**)]. (**b1**),(**b2**), the intensity distributions |*Er*|/*E*0 of the radial component of the electric field inside the cavity (the |*Er*|/*E*0 and the phase of *Er* in the area marked by rectangular box is also presented in the enlarged figures). (**c1**),(**c2**), the intensity distributions |*Eθ* |/*E*0 of the azimuthal component of the electric field inside the cavity (the |*Eθ* |/*E*0 and the phase of *Eθ* in the area marked by rectangular box is also presented in the enlarged figures). (**d1**),(**d2**), the intensity distributions |*Ez*|/*E*0 of the *z* -component of the electric field inside the cavity (the |*Ez*|/*E*0 and the phase of *Ez* in the area marked by rectangular box is also presented in the enlarged figures). (**b1**)–(**d1**), (**b2**)–(**d2**) are the mode properties at *z* = *h*InGaAsP/2. (**e1**)–(**g1**), (**e2**)–(**g2**) are in the cross section (the radius of the area is 5000 nm) of the emission modes at 2 μm above the upper surface of the cavity. *E*0 is the maximum of the |*Er* | in the (**b1**). The green lines in the enlarged figures are the boundaries of different sections. The *q* = 2 is used. The eigenfrequencies of the two modes are 1.9999 × 1014 + *i*6.25 × 1011 Hz and 2.0031 × 1014 + *i*9.45 × 1011 Hz, respectively. These results are calculated by the Comsol Multiphysics.

Now, we carry out 3D full wave simulations (via the commercial software COMSOL Multiphysics) to demonstrate the OAM laser. We take a standing-wave WGM with *l* = 11 in the microcavity as an example. The effective-refractive-index perturbations in region 1 consist of 2*m* discrete sections with an angular width Δ*θ* = *π*/2*m*, where *m* = 11. The azimuthal coordinate at the center of each section of region 1 is *θ*1(*n*) = *nπ*/11, where *n* = 1, 2, 3, . . . , 22. Then, the effective refractive indexes in the ring are

*nG* = ⎧ ⎨ ⎩ *n*InGaAsP + 0.006 + 0.006*i* + 0.006*eiφn* , *nπ* 11 − Δ*θ* 2 ≤ *θ* ≤ *nπ* 11 + Δ*θ* 2 (*n* = 1, 3, 5 . . . 21) *n*InGaAsP + 0.006 + 0.006*i* + 0.006*ei*(*φn*+*π*), *nπ* 11 − Δ*θ* 2 ≤ *θ* ≤ *nπ* 11 + Δ*θ* 2 (*n* = 2, 4, 6 . . . 22) *n*InGaAsP + *n i*, *nπ* 11 + Δ*θ* 2 ≤ *θ* ≤ *nπ* 11 + 3Δ*θ* 2 (*n* = 1, 2, 3 . . . 22) (2)

> where *φn* = *qnπ*/11, *n*InGaAsP = 3.34, and *n* = 0.012. In the simulations, we consider the condition that the silver is at a low temperature, and use the refractive index

*n*Ag = 0.0014 + 10.9741*i* at 4.5 K [5], which has low metal loss. In this paper, we adopt the following definition: the mode corresponds to loss mode when the imaginary part of the eigenfrequency of the mode is positive. The inner radius, width and height of the InGaAsP ring are 620 nm, 50 nm and 200 nm, respectively.

Figure 1 presents the details of the standing waves in the cavity and the emitted modes for *l* = 11. Here, the laser cavity with *q* = 2 is taken as an example, and the z-direction mode number and radial mode number of the cavity mode are fixed. The |*Er*|, |*Ez*|, and |*Eθ* | show obvious nodes along the azimuthal direction of the ring [Figure 1(b1)–(d1),(b2)–(d2)], which is the typical character of the standing wave modes. Besides, the standing-wave nature of the cavity modes is further confirmed by the phases of *Er*, *Ez*, and *Eθ* of the cavity modes (the last figures of the Figure 1(b1)–(d1),(b2)–(d2)). Because the cavity mode is coupled into the emitted OAM light by the tiny perturbations in region 1, mode 1 and mode 2 with different distributions in the cavity exhibit distinct emission characteristics. For mode 1, the azimuthal antinodes of *Er* (the dominant component of the electric field) match the sections of region 1 (Figure 1(b1),(d1)). Besides, the phase of the *Er* of mode 1 in each individual section of region 1 is the same, and the *Er* of mode 1 has a phase difference *π* between adjacent sections of region 1 (Figure 1(b1)). Thus, mode 1 is coupled to the desired OAM mode as shown by Figure 1(e1)–(g1), in which the *Er*, *Ez* and *Eθ* all show phase characteristics of the OAM light. For mode 2, only the azimuthal antinodes of *Eθ* match the sections of region 1 (Figure 1(c2)), while the azimuthal antinodes of *Er* and *Ez* match the sections of region 2 [Figure 1(b2),(d2)]. Besides, the *Er*, *Eθ*, and *Ez* of mode 2 in each individual section of region 1 all simultaneously contain mode oscillations with opposite phases. Thus, the emission from mode 2 to the OAM mode is suppressed as shown in Figure 1(e2)–(g2) (the intensity of mode 1 and mode 2 in the cavity is nearly the same. However, compared with the bright color of the emitted light from mode 1 (Figure 1(e1)–(g1)), the emitted light from mode 2 (Figure 1(e2)–(g2)) shows a nearly dark color, indicating the suppression of the emitted light from mode 2.) This property will help suppress unwanted components in the emitted light.

Figure 2 shows that the OAM of the emitted light can be tuned by tuning the tiny modulation of the effective refractive index (tuning *q* in the *φn*). The emission modes for *q* = 1, 2, and 3 are presented in the first, second and third row of Figure 2, respectively. It can be found that the phase repeats one, two, and three times from 0 to 2*π* upon one full circle around the center of the emitted light beam for *q* = 1, 2, and 3, respectively, which means the OAM can be designed on demand.

Now, we show that this OAM laser can naturally ensure the single-mode operation of desired mode. Here, we make a comparison between the modes with the same field distribution in the vertical cross section of the bend waveguide of the microring but with different field distributions in the azimuthal direction. For the standing-wave WGM, one mode (mode 1) of the pair of modes with *l* = *m* is mainly confined in region 1, and the other mode (mode 2) is mainly confined in region 2. In addition, the cavity modes with *l* -= *m* all have nearly the same distribution weight in two regions. Thus, the desired mode 1 experiences the lower loss from region 2 than other modes, that is, enhancing the loss in region 2 can relatively suppress the lasing of other competing modes. In order to demonstrate this principle, we conduct the 3D full-wave simulations. We take the laser cavity with *q* = 2 and *m* = 11 as an example. Figure 3a shows the ratios of the volume integral of |*E*| 2 confined in region 1 to the volume integral of |*E*| 2 confined in region 2. Obviously, the electric fields of the desired mode 1 are mainly confined in region 1 (Γ1/Γ2 ∼ 4.2). In contrast, the electric fields of mode 2 are mainly confined in region 2 (Γ1/Γ2 ∼ 1/4.2). For other WGMs (for instance the mode pair with *l* = 10 and mode pair with *l* = 12.), electric fields are nearly equally distributed in region 1 and region 2 (Γ1/Γ2 ∼ 1). Thus, as the loss in region 2 increases, the quality factor of mode 1 (red line in Figure 3b) decreases slower than other modes (blue line and black lines in Figure 3b). As a result, the single-mode lasing of the desired mode will be benefited when the perturbation loss of region 2 is relatively large. It is worth noting that the OAM natures of the emission mode will not change as the loss in region 2 increases as shown in Figure 3c.

**Figure 2.** Tuning the OAM of the emitted light. The first row [(**a1**)–(**c1**)], second row [(**a2**)–(**c2**)], and third row [(**a3**)–(**c3**)] of the figure present the simulation results of the modes for *q* = 1, 2 and 3, respectively. These results are in the cross section (the radius of the area is 5000 nm) of the emission modes at 2 μm above the upper surface of the cavity. It is worth noting that the corresponding modes inside the cavity (mode 1) have nearly the same field intensity.

**Figure 3.** Suppressing the lasing of the competing modes. (**a**) The *n* dependence of the ratios of the volume integral of |*E*| 2 confined in the region 1 to the volume integral of |*E*| 2 confined in region 2, which is calculated as Γ1/Γ2 = ˝ Region 1|*E*| 2 *dv*/ ˝ Region 2|*E*| 2 *dv*. Here, *n* is the modulation in Equation (2). (**b**) The quality factors of the modes as a function of the *n* . (**c**) The intensity (|*Er*|/*E*0, |*Eθ* |/*E*0, and |*Ez*|/*E*0) and phase distributions of the emission mode at P1 and P2 of the (**a**). The (**c**) are in the cross section (the radius of the area is 5000 nm) of the emission mode at 2 μm above the upper surface of the cavity. In this example, *q* = 2 and *m* = 11. The red lines correspond to the desired mode 1 with *l* = 11, the blue lines correspond to mode 2 with *l* = 11, the black lines correspond to the modes with *l* = 10, and 12.

*nG* =

Finally, we investigate the switch of the OAM of the emitted light. In order to control the OAM of the emitted light, we modulate the effective refractive index of region 1 to couple one standing-wave WGM (mode 1) to an OAM mode, and modulate the effective refractive index of region 2 to couple the other standing-wave WGM (mode 2) to the other OAM mode. Then, the losses of region 1 and region 2 are used to select the lasing mode between mode 1 and mode 2. Here, the effective refractive indexes in the ring are

$$\begin{cases} \begin{array}{ll} \begin{array}{ll} n\_{\text{InCaAsP}} + \eta\_{1i}i + \delta + \delta i + \delta e^{i\phi\_{n}^{\dagger}} , \quad \theta\_{1}(n) - \frac{\Lambda\theta}{2} \leq \theta \leq \theta\_{1}(n) + \frac{\Lambda\theta}{2}(n = 1, 3, 5 \dots 2m - 1) \\\ n\_{\text{InCaAsP}} + \eta\_{1i}i + \delta + \delta i + \delta e^{i(\phi\_{n}^{\dagger} + \pi)} , \quad \theta\_{1}(n) - \frac{\Lambda\theta}{2} \leq \theta \leq \theta\_{1}(n) + \frac{\Lambda\theta}{2}(n = 2, 4, 6 \dots 2m) \\\ n\_{\text{InCaAsP}} + \eta\_{2i}i + \delta + \delta i + \delta e^{i\phi\_{n}^{2}} , \quad \theta\_{2}(n) - \frac{\Lambda\theta}{2} \leq \theta \leq \theta\_{2}(n) + \frac{\Lambda\theta}{2}(n = 1, 3, 5 \dots 2m - 1) \\\ n\_{\text{InCaAsP}} + \eta\_{2i}i + \delta + \delta i + \delta e^{i(\phi\_{n}^{2} + \pi)} , \quad \theta\_{2}(n) - \frac{\Lambda\theta}{2} \leq \theta \leq \theta\_{2}(n) + \frac{\Lambda\theta}{2}(n = 2, 4, 6 \dots 2m) \end{array} \tag{3}$$

where Δ*θ* = *π*/2*m*, *θ*1(*n*) = *πn*/*m* (*n* = 1, 2, 3, ..., 2*m*), *θ*2(*n*) = *πn*/*m*+Δ*θ* (*n* = 1, 2, 3, ..., 2*m*), *φ*1 *n* = *q*1*nπ*/*m* (*n* = 1, 2, 3, ..., 2*m*), *φ*2 *n* = *q*2*nπ*/*m* (*n* = 1, 2, 3, ..., 2*m*). The electric field |*E*| of mode 1 and mode 2 are mainly localized in region 1 and region 2, respectively. Thus, the lasing of mode 1 or mode 2 can be selectively suppressed by tuning the additional material loss (*η*1*i*) in region 1 and the additional material loss (*η*2*i*) in region 2, which enables the switch of the emission mode between two different OAM modes. Now, we present the results of the 3D full-wave simulation. In our example, we used the parameters *m* = 11, δ = 0.006, *q*1 = 2, *q*2 = 3. We assume that the parameters (*η*1, *η*2) are tuned from (*η*1 = 0, *η*2 = 0.006) to (*η*1 = 0.006, *η*2 = 0). The gain of the InGaAsP can be achieved when being pumped. The homogeneous pumping gain of the InGaAsP ring is mimicked by adding an additional background imaginary part Δ*i* (Δ < 0) to the effective refractive index of the InGaAsP ring. It is worth noting that we do not consider the effect of the specific gain spectrum of the gain material for the sake of simplicity. Figure 4a shows that the loss of mode 1 is compensated for before the loss of mode 2 with the increase of the homogeneous pumping gain of the InGaAsP for (*η*1 = 0, *η*2 = 0.006). Thus, mode 1 will be the lasing mode. In this case, the phases of *Er*, *Ez* and *Eθ* of the emitted lasing beam all repeat two times from 0 to 2*π* upon one full circle around the center of the emitted light beam (Figure 4c). After tuning the system parameters (*η*1, *η*2) from (*η*1 = 0, *η*2 = 0.006) to (*η*1 = 0.006, *η*2 = 0), the loss of mode 2 is compensated before the loss of mode 1 with the increase of the homogeneous pumping gain of the InGaAsP as shown by Figure 4b. Thus, the lasing mode switches from mode 1 to mode 2. In this case, the emitted lasing beam is switched to the other OAM mode as shown in Figure 4d, in which the phases of the *Er*, *Ez* and *Eθ* all repeat three times from 0 to 2*π* upon one full circle around the center of the emitted light.

16

**Figure 4.** Switching the OAM carried by the emitted light. (**a**), (**b**), The homogeneous background gain dependence of the imaginary part of the eigenfrequencies of modes for the system with parameters (*η*1 = 0, *η*2 = 0.006) (**a**), and (*η*1 = 0.006, *η*2 = 0) (**b**). (**c**) The emitted lasing beam corresponding to P0 in (**a**). (**d**) The emitted lasing beam corresponding to P0 in (**b**). The phases of the emission modes in (**c**) and (**d**) are in the cross section (the radius of the area is 5000 nm) of the emission mode at 2 μm above the upper surface of the cavity.

#### **3. Conclusions**

In this paper, we propose a mechanism for constructing OAM light by modulating the scattered waves from the standing-wave WGM in the plasmonic ring cavity. Within this framework, the single-mode lasing can be realized. Moreover, the OAM of the emitted light can be designed on demand. This work provides a mechanism for exploring a single-mode OAM laser with tunable OAM at the microscale.

**Author Contributions:** Conceptualization, X.W.; writing—original draft, X.W.; writing—review and editing, X.W., X.H. and T.Z.; supervision, X.W., X.H. and T.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China (Grant Nos. 61822501, and 11734001), and the Beijing Natural Science Foundation (Grant No. Z180015).

**Data Availability Statement:** The data presented in this study are available within the article.

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

#### **References**

## *Article* **High-Performance Flexible Transparent Electrodes Fabricated via Laser Nano-Welding of Silver Nanowires**

**Tao Wang 1,†, Yinzhou Yan 2,\*,†, Liye Zhu 2, Qian Li 2, Jing He 2, Xiaoxia Zhang 1, Xi Li 2, Xiaohua Zhang 2, Yongman Pan 2 and Yue Wang 1**

**Abstract:** Silver nanowires (Ag-NWs), which possess a high aspect ratio with superior electrical conductivity and transmittance, show great promise as flexible transparent electrodes (FTEs) for future electronics. Unfortunately, the fabrication of Ag-NW conductive networks with low conductivity and high transmittance is a major challenge due to the ohmic contact resistance between Ag-NWs. Here we report a facile method of fabricating high-performance Ag-NW electrodes on flexible substrates. A 532 nm nanosecond pulsed laser is employed to nano-weld the Ag-NW junctions through the energy confinement caused by localized surface plasmon resonance, reducing the sheet resistance and connecting the junctions with the substrate. Additionally, the thermal effect of the pulsed laser on organic substrates can be ignored due to the low energy input and high transparency of the substrate. The fabricated FTEs demonstrate a high transmittance (up to 85.9%) in the visible band, a low sheet resistance of 11.3 Ω/sq, high flexibility and strong durability. The applications of FTEs to 2D materials and LEDs are also explored. The present work points toward a promising new method for fabricating high-performance FTEs for future wearable electronic and optoelectronic devices.

**Keywords:** flexible transparent electrodes; silver nanowires; laser nano-welding; organic electronics

#### **1. Introduction**

High-performance flexible transparent electrodes (FTEs) with outstanding mechanical and optical properties facilitate the rapid development of wearable electronics and optoelectronics [1]. Compared with rigid materials such as silicon and silica, elastic substrates make the devices foldable, twistable, compressible, and stretchable without compromising stability and reliability, allowing for a wide range of applications, including flexible electronic displays, organic light-emitting diodes (OLEDs), solar cells, and electronic skins [2–5]. FTEs are critical components in the above-mentioned wearable devices to ensure a high-efficiency power supply with low energy consumption. Moreover, the excellent optical transmittance would replace indium tin oxide (ITO) for next-generation, highly flexible optoelectronic applications, overcoming the drawbacks of time-consuming synthesis, indium requirement, and fragility during stretching and bending. In recent decades, numerous efforts have been made to develop alternative FTEs, including graphene [6–8], nanowires [9–12], carbon nanotubes (CNTs) [13–15], and PEDOT:PSS [16–18].

Silver nanowires (Ag-NWs) have attracted considerable attention as FTE materials owing to their good electrical conductivity, high transparency in the visible band, excellent ductility, and facile fabrication process [19]. In particular, the conductive networks formed by ultralong metallic nanofibers have shown promise for application to FTEs because of their superior optical, electrical, and mechanical properties [20,21]. A variety of electronic

**Citation:** Wang, T.; Yan, Y.; Zhu, L.; Li, Q.; He, J.; Zhang, X.; Li, X.; Zhang, X.; Pan, Y.; Wang, Y. High-Performance Flexible Transparent Electrodes Fabricated via Laser Nano-Welding of Silver Nanowires. *Crystals* **2021**, *11*, 996. https:// doi.org/10.3390/cryst11080996

Academic Editor: Giancarlo Salviati

Received: 7 August 2021 Accepted: 18 August 2021 Published: 21 August 2021

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

**Copyright:** © 2021 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/).

components with Ag-NW FTEs were fabricated in previous studies, including flexible and transparent antennas [22], wireless circuits [23], transistors [24], and sensors [25], demonstrating the potential applications in wearable devices. However, the contact resistance between Ag-NWs and adhesion to the organic substrates have presented two major challenges for high-performance FTEs. Methods for the improvement of contact resistances have been sophisticatedly presented in previous works. Thermal annealing has received the most attention due to its facile fabrication process and high welding quality. However, thermal annealing requires an oxygen-free environment due to the high chemical reactivity of Ag-NWs at high temperature. Moreover, thermal annealing is not suitable for the flexible organic substrates due to the low melting temperature of organic materials. Consequently, a low-temperature thermal annealing (below 200 ◦C) was developed [26]. Other physical welding methods employing force, electricity, light, etc. were also developed to realize Ag-NW network welding without significant thermal effects for FTEs [27–35]. Although high-pressure welding optimized the conductivity of the Ag-NW FTEs down to 8.4 Ω/sq, the substrates and other layers could be destroyed [27]. To solve this problem, Liu et al. proposed a capillary-force-induced cold-welding technique in which the moisture-treated Ag-NWs exhibited a significant reduction in sheet resistance (~37 Ω/sq) due to the giant capillary forces exerted between Ag-NWs [28]. Unfortunately, the poor adhesion of Ag-NWs on the substrate has not been improved. Another method that has been used is electric welding; it is based on the high contact resistance at the junction of Ag-NWs, where Joule heating caused by the application of bias voltages results in localized melting, welding the Ag-NWs [29]. The main drawback of this method is the non-homogeneous current distribution due to the complex Ag-NW network, which proved unsuitable for large-area welding. Hong et al. achieved Ag-NW nano-welding by electron-beam irradiation, which provided sufficient energy to melt the Ag-NWs [30]. However, the required vacuum chamber and the high-cost instrument limited the method for industrial applications. Compared with electron beams, light is an ideal energy source to induce the nano-welding of Ag-NWs. Liang et al. employed ultraviolet A (UVA) light irradiation for Ag-NW nano-welding, reducing the sheet resistance by three orders of magnitude (down to 25 Ω/sq) with a good transparency (97%) [31]. The femtosecond pulsed laser (fs-pulsed laser) was also used to irradiate Ag-NWs, where the excited localized surface plasmon resonances (LSPRs) at the gaps between Ag-NWs generated a considerable enhancement of electric field strength, inducing local melting for nano-welding. Meanwhile, the polyethylene glycol terephthalate (PET) substrate was not damaged during the laser irradiation. The obtained sheet resistance and optical transmittance by fs-pulsed nano-welding were 16.1 Ω/sq and 91%, respectively [32]. Although nanosecond pulsed lasers (ns-pulsed lasers) were also tested for the nano-welding of Ag-NWs [33], most of the laser-irradiation methods were only suitable for inorganic and limited organic substrates with high melting temperatures and stiffnesses (glass, silica, PET, PVA), owing to the requirement of thermal endurance from laser energy input. Generally, the most used highly flexible and bio-compatible organic materials (e.g., polydimethylsiloxane, PDMS), possess low melting points and stiffnesses. Therefore, a nano-welding technique for junction-localized energy confinement that will not deteriorate the substrate is still lacking. In addition, the adhesion of Ag-NW networks to the organic substrate also needs to be resolved by jointing Ag-NWs with the substrate gently [9,10].

In this work, we developed a facile technique for fabricating high-performance FTEs via ns-pulsed laser nano-welding of Ag-NWs on organic substrates, creating Ag-NWs/PMMA/PDMS sandwich structures. LSPR-induced laser energy confinement at the junctions between the Ag-NWs was employed to generate a high temperature for nano-welding in order to reduce contact resistances while dramatically boosting the electrical conductivity of the Ag-NWs. Meanwhile, the Ag-NW networks were jointed with the organic substrate for good adhesive strength. The ns-pulsed laser energy for nanowelding was low enough to avoid thermal damage to the organic substrates completely. The fabricated FTEs in this work demonstrated superior mechanical, electrical, and optical

properties. The compatibility of FTEs with 2D materials and traditional LEDs was also explored for the design of flexible optoelectronic devices in the future.

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

A schematic of the procedure for fabricating Ag-NW FTEs is illustrated in Figure 1a. The glass substrates (2 cm × 2 cm) were first cleaned ultrasonically in acetone, isopropanol, and deionized water, successively, for 5 min. The polymethyl methacrylate (PMMA) solution in toluene (purchased from Shanghai Kexinda Polymer Materials Co., Ltd., Shanghai, China) was spin-coated onto the glass substrate at 8000 rpm for 40 s to achieve a thickness of ~10 μm, then cured in ambient atmospheric for 10 s. Then, the PMMA film was treated with plasma (YZD08-5C, 80 W, Saiaote Technology Co. Ltd., Wuhu, China) for 30 s to achieve a hydrophilic surface, beneficial for both uniform spreading and the prevention of agglomeration during Ag-NW suspension deposition. The Ag-NWs (purchased from Nanjing XFNANO Co., Ltd., Nanjing, China), with a mean length of ~100 μm and diameter of 30.0 ± 5.0 nm, diluted in isopropyl alcohol (IPA) for various concentrations (0.3–0.7 mg/mL), were sprayed onto the PMMA surfaces. To minimize the coffee-ring effect on Ag-NWs deposition, 3M low-adhesion tapes were employed to confine the suspension flow within a specific region. The homogeneous Ag-NWs were therefore formed after the suspension was dried. The densities of Ag-NWs on PMMA films were controlled by two synthesis parameters: the concentration of the Ag-NWs suspension (0.3–0.7 mg/mL) and the number of spraying layers (5–20 layers). Afterwards, the Ag-NWs/PMMA film was irradiated by a 532 nm ns-pulsed laser (Spectra-Physics, LAB-190-30H, 10 ns, 27 Hz) under ambient conditions at room temperature, achieving Ag-NW nano-welding and jointing with the PMMA substrate. It should be noted that the highly transparent PMMA with respect to 532 nm (95%) and the short pulse duration minimized the thermal damage on the substrate within the irradiation time of 50 s. The oxidation of Ag-NWs during laser irradiation was also negligible. The PDMS Sylgard 184 (purchased from Dow corning Co., Ltd., Midland, MI, USA) was mixed and stirred with the curing agent at the ratio of 10:1 by weight to obtain the PDMS colloidal solution. The fabricated Ag-NWs/PMMA film was then flipped over on the spinner. The PDMS solution was spin-coated onto the bottom side of the Ag-NWs/PMMA film at a rotation speed of 5000 rpm for 30 s. The PDMS film was baked at 120 ◦C for 2 min on a plate heater in a vacuum chamber for solidification and bubble removal. The Ag-NWs/PMMA/PDMS film was therefore obtained, where the thickness of the PDMS film was ~20 μm. It should be noted that the PDMS film provided an outstandingly flexible substrate for the FTEs, and the plasma-treated PMMA film served as a buffer layer for high adhesion of Ag-NWs and PDMS in the sandwich structure, as shown in Figure 1b. Figure 1c demonstrates the optical and mechanical performance of the Ag-NWs/PMMA/PDMS FTEs. In addition, the MoS2 monolayer (purchased from Shenzhen Six-Carbon Technology, Shenzhen, China), grown on an *n*-type Si substrate with a 300 nm-thick SiO2 film, was also employed for future experiments.

The sheet resistances were measured using the four-point probe method (Suzhou Jingge Electronic Co., Ltd., ST2258C, Suzhou, China), in which the mean values of sheet resistances from six random points of the FTEs were calculated. The optical transmittances of the FTEs were obtained by a UV-VIS spectrophotometer (Shimadzu, UV-3600, Kyoto, Japan). The morphologies of the Ag-NWs in the FTEs were captured by optical microscopy (Olympus BX-51, Tokyo, Japan), scanning electron microscopy (Hitachi, SU8220, Tokyo, Japan), and transmission electron microscopy (FEI, Tecnai G2-20-S-TWIN, Lausanne, Switzerland). The film thickness was acquired by a profilometer (Veeco Dektak-XT, Bruker, Billerica, MA, USA). The gate-voltage applied to the MoS2 was supplied by a DC power supply (Beijing leading Hongzhi Electronic Technology Co., Ltd., XD1715A-120, Beijing, China). The photoluminescence spectra were analyzed by a SmartRaman confocal-micron-Raman system (developed by Institute of Semiconductors, CAS, Beijing, China) with a 10x/*NA*0.25 objective lens (Olympus, MPlan N, Tokyo, Japan) under the backscattering geometry, which was coupled with a Horiba LabRam iHR550 spectrometer (Kyoto, Japan) with a 100 lines/mm grating and a CCD detector. The excitation CW laser wavelength was 633 nm (HNL 100-EC-PS, 25.8 μW, Changchun New Industries Technology Co., Ltd., Changchun, China). The electrical power supply and current measurement for LEDs were provided by a source meter (Keithley 4200-SCS, Tektronix, Beaverton, OR, USA).

**Figure 1.** Fabrication of Ag-NWs/PMMA/PDMS FTEs. (**a**) Schematic of synthesis procedure. (**b**) Cross-section schematic of the FTEs. (**c**) Mechanical and optical properties of the FTEs.

The numerical simulation was performed using the finite element algorithm method in the COMSOL Multiphysics (licensed by COMSOL Co., Ltd., Stockholm, Sweden) software package. A 2D cross-sectional model was developed to calculate the electric fields regulated at the cross-junctions and gaps between Ag-NWs. The Ag-NW diameter was 30 nm, and the relative permittivity was −9.3751 + 0.83203*i* according to Drude's model. The ambient environment was set as air. For the analysis of electric field enhancement, a plane wave with a wavelength of 532 nm was incident onto the Ag-NWs. Perfectly matched layers were applied as the boundary conditions.

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

#### *3.1. Morphology of Laser Nano-Welded Ag-NWs*

The morphologies of Ag-NWs nano-welded via various laser fluences are shown in Figure 2. The as-deposited Ag-NWs were randomly distributed on the PMMA film, forming a conductive network, as shown in Figure 2a. The close-up view in Figure 2b further demonstrates the cross junctions of the Ag-NWs before laser nano-welding. The contacts between Ag-NWs and with the PMMA substrate were ascribed to van der Waals forces. The fluence threshold for laser nano-welding was ~10.0 mJ/cm2, by which the cross junctions were melted slightly and connected after resolidification. The melting phenomenon became obvious with the laser fluence increasing to 17.4 mJ/cm2. It can be clearly seen in Figure 2c–e that only the cross junctions were melted during laser irradiation whereas the other parts of Ag-NWs were not affected, indicating the laser-

induced thermal effect was confined to the contact points. When the laser fluence was greater than 27.9 mJ/cm2, the Ag-NWs sustained thermal damage. The high molten volumes and surface tensile effect broke the Ag-NWs, as shown in Figure 2f. Figure 2g,h further exhibits the welded points before and after laser irradiation, providing strong evidence of Ag-NW melting at the cross junction. To further optimize the laser nanowelding parameters, the effects of laser fluence and irradiation time on sheet resistance were studied, as shown in Figure 2i. The sheet resistance of as-deposited Ag-NWs was 110 Ω/sq and dramatically reduced via laser nano-welding within tens of seconds. The increased laser fluence and irradiation time both lowered the sheet resistance. It can also be seen that the sheet resistances were close to constants dominated by laser fluences as the irradiation time exceeded 50 s. The irradiation time of 50 s was therefore chosen as the optimal parameter to avoid oxidation of the Ag-NWs and thermal damages on the organic substrate. It should be noted that the high sheet resistance with a laser fluence of 37.9 mJ/cm2 at an irradiation time of 50 s was due to the deterioration of the Ag-NWs, as shown in Figure 2f. Hence, the laser fluence was set to 27.9 mJ/cm2 with an irradiation of 50 s for the lowest sheet resistance down to 11.3 Ω/sq, whereby the thermal effect on organic substrates was also negligible.

**Figure 2.** Morphologies and electrical properties of Ag-NWs/PMMA/PMMA FTEs via ns-pulsed laser nano-welding under various process parameters. (**a**) SEM images. (**b**) Close-up view of as-deposited Ag-NWs before nano-welding. (**c**–**f**) Laser nano-welding of Ag-NWs under laser fluence of (**c**) 10.0 mJ/cm2, (**d**) 17.4 mJ/cm2, (**e**) 27.9 mJ/cm2, and (**f**) 37.9 mJ/cm2 at irradiation time of 50 s. (**g**,**h**) TEM images of (**g**) as-deposited and (**h**) laser nano-welded Ag-NWs. (**i**) Evolution of sheet resistance with laser fluence and irradiation time.

#### *3.2. Mechanism of Laser Nano-Welding of Ag-NWs on PMMA*

To further study the mechanism of laser nano-welding of the Ag-NWs on organic substrates, a numerical simulation of laser interaction with Ag-NWs was performed. Two typical structures of as-deposited Ag-NWs were considered, as illustrated in Figure 3a,b, including cross-junction and head-to-head configurations. It is well-acknowledged that the LSPRs in the vicinity of Ag-NWs can be excited by light with a wavelength of ~50 nm, by which the electromagnetic (EM) fields are significantly enhanced and localized around the Ag-NWs. Meanwhile, the Joule heating caused by ohmic energy loss resulted in melting for the nano-welding of Ag-NWs [36–39]. The electric fields in the two structures are shown in Figure 3c,d. It can be clearly observed that the electrical intensities were boosted in the gaps between Ag-NWs, where the enhancement ratios were 573.4 and 2193.2 for cross-junction and head-to-head structures, respectively. As a result, these regions were first melted under laser irradiation and connected, realizing Ag-NW welding. The electrical intensities far from these gaps were extremely low, preventing the deterioration of Ag-NWs. The numerical simulation was in agreement with the experimental results, revealing the mechanism of laser nano-welding of the Ag-NWs. Furthermore, selective nano-welding was conducive to Ag-NW network jointing with the PMMA. Owing to its low melting point (~200 ◦C), the PMMA film can be melted due to the high temperature at the Ag-NW welding regions, and the Ag-NW network was partially embedded into the organic film for good adhesion. To validate the hypothesis, a 3M low-adhesion tape was employed to press and remove the Ag-NWs from the FTEs, as shown in Figure 3e,f. The adhesion between Ag-NWs and PMMA was significantly strengthened after laser nano-welding, as shown by the slight reduction of Ag-NW quantity under removal cycles of over 100. This confirmed the jointing of the Ag-NW network and PMMA substrate by laser irradiation.

#### *3.3. Synthesis Optimization of Ag-NWs/PMMA/PDMS FTEs*

The criteria for high-quality FTEs consist of electrical conductivity and transmittance. The ideal FTEs should possess high conductivity, good transmittance, and durable flexibility. The transmittance was generally reduced as conductivity increased due to light scattering and absorption by the high concentration of Ag-NWs. Therefore, the balance between conductivity and transmittance should be maintained by optimizing the density of Ag-NWs on the PMMA film. The multiple-spraying strategy was therefore employed to control the density by two parameters, that is, the concentration of the Ag-NWs suspension and the number of spraying layers. To obtain a stable sheet resistance, the number of spraying layers was greater than five. Figure 4 shows the sheet resistances and transmittances of Ag-NWs/PMMA/PDMS FTEs under different suspension concentrations and spraying layers after laser nano-welding with 28.9 mJ/cm2 for 50 s. In Figure 4a–e, it can be clearly seen that the sheet resistance and transmittance were both decreased as the concentration and number of spraying layers increased. For the low concentration of 0.3 mg/mL, the sheet resistance was dramatically reduced when the number of spraying layers was eight, and then kept constant. Furthermore, the transmittance was linearly reduced from 89.9% to 63.4% as the number of spraying layers and concentration increased. The higher concentration could reduce the number of spraying layers down to five for the lowest sheet resistances. To evaluate the optimal performance in optical and electrical properties, the figure of merit (*FoM*) was employed as follows [40]:

$$FoM = \frac{T^{10}}{R\_{sl}}\tag{1}$$

where *T* is the transmittance at 550 nm and *Rsh* is the sheet resistance of the FTEs. The optimal *FoM*s under various suspension concentrations were extracted and are plotted in Figure 4f. The suspension concentration of 0.5 mg/mL with five spraying layers was selected for the highest *FoM*, where the transmittance was 85.9% and the sheet resistance was 11.3 Ω/sq. The performance was comparable with that obtained in previous works [27–35].

The advantages of the technique developed in this work are its facile fabrication method and the low cost of FTE synthesis.

**Figure 3.** Numerical simulation of laser nano-welding of Ag-NWs and validation of Ag-NWs jointing with PMMA substrates. (**a**) Cross junction. (**b**) Head-to-head configurations for simulation. (**c**,**d**) Electric field distributions and intensities (**c**) near the cross junction between Ag-NWs and (**d**) near the gap of head-to-head Ag-NWs. (**e**,**f**) Removal experiments using 3M low-adhesion tapes for (**e**) as-deposited and (**f**) laser nano-welded Ag-NWs on PMMA film.

**Figure 4.** Evolution of transmittance and sheet resistance of Ag-NWs/PMMA/PDMS FTEs with the number of spraying layers using Ag-NW suspension concentrations of (**a**) 0.3 mg/mL, (**b**) 0.4 mg/mL, (**c**) 0.5 mg/mL, (**d**) 0.6 mg/mL, and (**e**) 0.7 mg/mL, as well as the calculated *FoM*s. (**f**) Optimization from various suspension concentration and spraying layer parameter sets.

#### *3.4. Durability of Ag-NWs/PMMA/PDMS FTEs*

Figure 5a shows the transmittance spectra of PDMS, PMMA, and Ag-NWs/PMMA/ PDMS FTEs in the visible band. Although the Ag-NWs slightly reduced the transmittance, the flat spectrum in the visible band indicated good transparency without wavelength selection, as shown in Figure 1c. The flexibility of Ag-NWs/PMMA/PDMS FTEs was examined by the fold-bending test. The fold-bending-induced strain (*ε*) was 75.6%, which was estimated by [41]

$$
\varepsilon = \frac{t}{2R} \times 100\% \tag{2}
$$

where *t* is the thickness of the FTE and *R* is the bending radius, which were 31.0 μm and 20.5 μm measured by the profilometer, respectively. Figure 5b shows the sheet resistance maintained for up to 100 cycles of fold-bending with high strain, and then increased due to the fatigue of Ag-NWs. In addition, the adhesion of Ag-NWs on the organic substrate was also investigated. The above-mentioned discussion indicates that the Ag-NW network was jointed onto the PMMA film during laser nano-welding, whereby the adhesion between Ag-NWs and substrate was significantly strengthened since the Ag-NWs were partially embedded in the PMMA film. The 3M low-adhesion tape was thereby used to carry out the Ag-NW adhesion test by pressing it onto the film and peeling it off. Figure 5c indicates that the sheet resistance could be kept constant for the peeling-off process for up to 110 cycles, confirming the good adhesion of Ag-NWs on the PMMA/PDMS film via laser nano-welding. Figure 5d exhibited the stability of the Ag-NWs/PMMA/PDMS FTEs in ambient atmospheric at room temperature, where the sheet resistances were constant for 1 month. The excellent durability, flexibility, adhesion, and period stability recommend the laser nano-welded Ag-NWs/PMMA/PDMS FTEs for wide application in future wearable devices.

#### *3.5. Applications of Ag-NWs/PMMA/PDMS Films as High-Performance FTEs*

To demonstrate the performance of Ag-NWs/PMMA/PDMS FTEs, two typical configurations of wearable devices were employed and fabricated as shown in Figure 6. The applications of 2D materials in flexible electronic/optoelectronic components have been well-acknowledged [42]. For vertical device structures, FTEs became important for 2D material wearable designs. Figure 6a shows the typical sandwich structure for gatecontrolled MoS2 luminescence, in which an Ag-NWs/PMMA/PDMS FTE covered an MoS2 monolayer, which was deposited on a 300 nm-thick SiO2 isolayer oxidized from an *n*+-Si substrate. The PMDS side was contacted with the MoS2 monolayer for applying the gate voltage, *U*, from the Ag-NW network to the *n*+-Si substrate. The generated electric field, *E*, was estimated by *E* = *U*/*d*, where *d* is the combined thickness of the PMMA, the PDMS, the MoS2 monolayer, and the SiO2 isolayer. The luminescence of the MoS2 monolayer is regulated by the gate voltage due to the interaction of excitons with charge carriers via the phase-space filling effect [43,44]. This optoelectronic property can be used to realize electro-optical modulators operating in the visible band. Owing to the high transparency and conductivity of Ag-NWs/PMMA/PDMS FTEs, the phenomenon was achieved by in-situ PL measurement, as shown in Figure 6b. The PL intensity from the MoS2 monolayer was significantly enhanced as the gate-voltage-induced electric field increased. The PL enhancement ratio was from 203.8% to 239.7% under the electric field intensity of 10.0–29.7 kV/cm, as demonstrated in Figure 6c, confirming the compatibility of Ag-NWs/PMMA/PDMS FTEs with 2D materials for electro-optical applications.

**Figure 5.** Durability of Ag-NWs/PMMA/PDMS FTEs. (**a**) Transmittance spectra in the visible band. (**b**–**d**) Durability tests for (**b**) flexibility, (**c**) adhesion, and (**d**) period stability.

The Ag-NWs/PMMA/PDMS films can also be used as facile, high-performance conductive tapes for conventional electronic components, where the good ohmic contacts with the footprints can be achieved by van der Waals and static electrical forces instead of by soldering. Figure 6d shows the *I–V* characteristics of a commercial surface-mounted LED with rigid metal electrodes and FTEs, respectively. It can be clearly seen that the ohmic contacts between FTEs and LED footprints were achieved. The increased opening voltage threshold of the LED from 1.7 V to 1.8 V was attributed to the inserted resistance of the FTEs. However, the *I–V* curve using FTEs was very similar to that of rigid metal electrodes. The photographs of luminescence from the LEDs with various electrodes under different bias voltages are shown Figure 6e. Although the inserted resistance slightly reduced the efficiency of the LED, the luminescence behaviors suggested the superiority of FTEs over conventional metal electrodes in future flexible electronic devices.

**Figure 6.** Applications of Ag-NWs/PMMA/PDMS FTEs. (**a**) Sandwich structure for gate-controlled PL emission from MoS2 monolayer. (**b**) PL spectra of MoS2 monolayer under various gate-voltage-induced electric field strengths. (**c**) Evaluation of PL enhancement ratio with electric field strength. (**d**) *I–V* curves of commercial LEDs with rigid metal electrodes and FTEs, where the insets demonstrate the experimental setups. (**e**) Photographs of luminescence from the LEDs under various bias voltages through different electrodes.

#### **4. Conclusions**

In this work, high-performance Ag-NWs/PMMA/PDMS FTEs were fabricated by the nanosecond pulsed laser nano-welding of Ag-NWs on PMMA/PDMS flexible substrates. Compared with previous fabrication techniques, laser nano-welding provided a facile and time-saving approach to improve Ag-NW network formation and adhesion onto the flexible organic substrates. The stimulated localized surface plasmon resonances confined the incident laser energy into the cross junctions and gaps between Ag-NWs for selective melting. The Ag-NWs were therefore welded for resistance reduction and jointed with the PMMA film with high adhesive strength. The fabricated FTEs demonstrated a high transmittance of 85.9% in the visible band and a low sheet resistance of 11.3 Ω/sq, attributable to the small absorption cross section and high conductivity of the nano-welded Ag-NWs. The superior durability, high flexibility, strong adhesion, and period stability tolerance commended the FTEs for practical wearable applications, in pursuit of which two typical components in 2D material luminescence devices and LEDs were explored. The gate voltages for high electric fields for regulating the PL emission from an MoS2 monolayer was determined. The FTEs were also confirmed to be suitable for conventional electronic devices (i.e., LEDs), as a flexible-type electrode for wearable designs to replace rigid metal ones, since soldering between the FTEs and component footprints for ohmic contacts was avoided. The present work points a path forward in the development of high-performance FTEs for next-generation flexible electronic/optoelectronic devices with outstanding optical transmittance, high conductivity, and good durability.

**Author Contributions:** Conceptualization, Y.Y.; methodology, Y.Y. and T.W.; software, T.W. and J.H.; validation, T.W. and Y.Y.; formal analysis, T.W. and Y.Y.; investigation, T.W., Y.Y. and Y.W.; data curation, L.Z., Q.L., X.Z. (Xiaoxia Zhang), X.L., X.Z. (Xiaohua Zhang), and Y.P.; writing original draft preparation, T.W.; writing—review and editing, Y.Y.; supervision, Y.Y. and Y.W.; project administration, Y.Y.; funding acquisition, Y.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China, grant number 12074019 and Key Program of Science and Technology Development Project of Beijing Municipal Education Commission, grant number KZ202110005002.

**Data Availability Statement:** The data presented in this study are available from the corresponding author.

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

#### **References**

## *Article* **Mobility of Small Molecules in Solid Polymer Film for** π**-Stacked Crystallization**

**Yue Liu and Xinping Zhang \***

Institute of Information Photonics Technology, Beijing University of Technology, Beijing 100124, China<EMAIL_ADDRESS>
**\*** Correspondence<EMAIL_ADDRESS>
**Abstract:** Crystallization or π-stacked aggregation of small molecules is an extensively observed phenomenon which favors charge transport along the crystal axis and is important for the design of organic optoelectronic devices. Such a process has been reported for *N*,*N* -Bis(1-ethylpropyl)-3,4,9,10 perylenebis(dicarboximide) (EPPTC). However, the π-stacking mechanism requires solution–air or solution–solid interfaces. The crystallization or aggregation of molecules doped in solid films is generally thought to be impossible, since the solid environment surrounding the small molecules does not allow them to aggregate together into π-stacked crystals. In this work, we demonstrate that the movement of the EPPTC molecules becomes possible in a solid polymer film when it is heated to above the glass transition temperature of the polymer. Thus, crystal particles can be produced as a doped matrix in a thin solid film. The crystallization process is found to be strongly dependent on the annealing temperature and the annealing time. Both the microscopic and spectroscopic evaluations verify such discoveries and characterize the related properties of these crystals.

**Keywords:** small molecules; crystallization; moving in solid film; glass transition temperature; annealing temperature; annealing time

#### **1. Introduction**

Crystallization of organic molecules through π-stacking is an important approach to improve the charge transport performance in semiconductors and achieve high-efficiency optoelectronic devices [1–3]. Different forms of crystalline materials or structures have been reported to produce organic semiconductors with much-improved optical and electronic properties [4–7]. Various techniques have been employed to produce organic molecular structures with oriented aggregation and ordered distribution [8,9]. Thermal annealing is a convenient and efficient approach to realizing such molecular rearrangement or surface modification processes [10–16]. The precondition for such crystalline aggregation is the planar molecular structure, and this can generally be satisfied in small molecules, which allow face-to-face aggregation between one another.

Perylene and its derivatives have high electron mobility, which makes them promising candidates for organic photovoltaic and transistor devices [6,7,17,18]. Due to the planar structures of the perylene molecules, they can easily aggregate into one-dimensional crystals at the solution–solid, vapor–solid, and solution–air interfaces, as well as at those between different solvents [1,3,17,19]. However, such a crystallization process has not been observed within solids. In this work, we report the crystallization of perylene molecules in the solid thin film of polymers, where the polymer needs to be annealed to its glass transition temperature so that the solid film becomes sufficiently softened and flexibilized to allow the motion of the doped small molecules. The corresponding mechanisms are revealed not only by the microscopic and spectroscopic properties, but also by the annealing temperature- and annealing time-dependence of the crystallization process. Blending small molecules with polymers is an important approach to construct efficient optoelectronic devices based on heterojunctions. New charge transfer complexes [20–22] can be thus

**Citation:** Liu, Y.; Zhang, X. Mobility of Small Molecules in Solid Polymer Film for π-Stacked Crystallization. *Crystals* **2021**, *11*, 1022. https:// doi.org/10.3390/cryst11091022

Academic Editor: Emilio Parisini

Received: 1 August 2021 Accepted: 23 August 2021 Published: 25 August 2021

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

**Copyright:** © 2021 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/).

produced and utilized to investigate new photophysics and to develop new photovoltaic devices.

Figure 1 shows the basic principles for the formation of the EPPTC crystals inside a solid film of polymer chains. In Figure 1a, we illustrate a matrix of small molecules of perylene (*N*,*N* -Bis(1-ethylpropyl)-3,4,9,10-perylenebis(dicarboximide) (EPPTC)) doped in a solid film, which are distributed randomly without any orientational arrangement. In our approach, we used polymethyl methacrylate (PMMA) to supply the polymeric solid film. Owing to the planar molecular shape, π-stacking between the EPPTC molecules becomes possible, provided that channels are supplied for the EPPTC molecules to move across the PMMA molecular chains.

**Figure 1.** (**a**) Distribution of the EPPTC molecules in the solid film of PMMA molecular chains. (**b**) Crystallization of EPPTC small molecules due to their motion across the annealing-flexibilized PMMA molecular chains.

The crossing channel can be produced by heating the solid polymer film to the glass transition temperature, which is 100–120 ◦C. Therefore, 120 ◦C was measured as the threshold temperature for the crystallization process of EPPTC in PMMA film. The softened PMMA molecular chains allow the small molecules to move across the solid film and become aggregated, forming π-stacked crystals after the cooling down of the whole sample, as shown in Figure 1b. Apparently, the crystals are roughly in fusiform shapes, which are distributed randomly in their orientations and sizes. It is also understood that the length and thickness of the crystals are dependent on the annealing temperature and annealing time. Furthermore, since the glass transition has a threshold temperature, the formation of

the crystal particles in the solid polymer film also has a threshold temperature, which is found to be about 120 ◦C. Below this temperature, the crystallization process illustrated in Figure 1b is found to not be possible even with a long time of annealing.

#### **2. Annealing-Aided Crystallization of Small Molecules in Polymeric Solids**

#### *2.1. Annealing Temperature Dependence*

In the experiments, we first prepared solutions of EPPTC and PMMA in chloroform with a concentration of 10 mg/mL and 15 mg/mL, respectively. A mixture solution was prepared by mixing the above two solutions with a volume-to-volume ratio of 1:1. A blend film was then prepared by spin-coating the mixture solution onto a glass substrate with a speed of 2000 rpm for 30 s. Multiple samples were prepared under the same conditions so that comparison could be made between different annealing processes.

For the annealing, we employed five temperatures: 30, 60, 90, 120, and 150 ◦C. However, for annealing temperatures below 120 ◦C, nearly no changes were observed either in the microscopic or in the spectroscopic response of the sample. This is clearly because the glass transition temperature was not reached. In Figure 2, we present only the scanning electron microscope (SEM, JEOL, Tokyo, Japan) and atomic force microscope (AFM, Witec GmbH, Ulm, Germany) images of the samples annealed at 120 and 150 ◦C. The SEM and AFM images of the sample annealed at 120 ◦C are shown in Figure 2a,b, respectively. Since the annealing temperature is already above the threshold for glass transition, crystal particles with very small sizes and very low densities can be observed in both images. The mean diameter of the crystal particles is roughly 140 nm. We need to note that the annealing time was 10 min and the size and density of the crystal particles may be increased by extending the annealing time. Thus, it is verified that the glass transition temperature is the threshold for the crystallization of EPPTC molecules, where the softened PMMA molecular chains allow the movement of the EPPTC molecules and their aggregation through π-stacking.

**Figure 2.** SEM (**a**,**c**) and AFM (**b**,**d**) images for the samples annealed at 120 (**a**,**b**) and 150 ◦C (**c**,**d**).

When the annealing temperature was increased to 150 ◦C, for the same annealing time of 10 min, the crystal length and thickness were increased dramatically, as shown by the SEM and AFM images in Figure 2c,d, respectively. Using a rough evaluation, the crystals have a mean length of about 900 nm and a width of 160 nm. Meanwhile, the height of the crystals was also increased slightly from about 36 to 40 nm. Furthermore, the density of the crystal particles was more obviously increased. According to Figure 2c,d, the number of crystal particles was increased by a factor of five, corresponding to an increase in the total number of crystal particles from about 6 to 30. This implies convincingly that above the glass transition temperature the PMMA molecules become more flexible and allow the strong aggregation of the EPPTC molecules into crystals.

It is also understood that the crystal particles formed by molecular aggregation through π-stacking greatly influence the spectroscopic properties of the small molecules. Figure 3a shows the absorption spectra at different annealing temperatures, and Figure 3b,c show the normalized data in Figure 3a and the PL spectra of the blend film, respectively, for different annealing temperatures. As the temperature was increased from 30 to 120 ◦C, where the annealing time was 10 min, a weak feature appeared at about 474 nm and the relative intensity at 530 nm was reduced, as shown in Figure 3b. However, when the temperature was increased to 150 ◦C, which exceeds the glass transition temperature, the spectral feature became obvious at 473 nm (dashed upward arrow in black) and the peak at about 530 nm suddenly became a valley in the absorption spectrum (dashed downward arrow), as shown in Figure 3b. Furthermore, the absorption spectrum peak at about 542 nm appeared in a sudden manner (dashed upward arrow in red). All of these changes highlighted by dashed arrows resulted from the aggregation of the EPPTC molecules in the softened PMMA film, or from the crystallization through π-stacking of the EPPTC molecules.

**Figure 3.** (**a**) Absorption spectra measured at different annealing temperatures. (**b**) Normalized absorption spectra in (**a**). (**c**) Normalized PL spectra measured at different annealing temperatures. (**d**) Fluorescence lifetime at 612 (blue triangle in (**c**)) and 668 nm (red triangle in (**c**)) for the sample annealing at 150 ◦C for 10 min.

Figure 3c shows the PL spectra annealed at 30, 60, 90, 120, and 150 ◦C for 10 min, where all spectra have been normalized. Obviously, with an annealing temperature lower than 120 ◦C, there is little change in the PL spectra. However, when the annealing temperature exceeds 150 ◦C, the PL spectrum changed dramatically: the main peak shifts from about 630 nm to 612 nm (blue triangle) and a new peak appears at about 668 nm (red triangle). According to our previous work [17], the emission at 612 nm corresponds mainly to the intrinsic molecular emission from EPPTC and that at 668 nm mainly to the crystal phase emission. Figure 3d shows the measurements of the emission dynamics at 612 and 668 nm using green and red circles, respectively. At 612 nm, the emission lifetime is in the range of 1~2.5 ns. However, the lifetime extends to about 6 ns at 668 nm, which can be identified as the lifetime of the emission from EPPTC crystal phase. Therefore, the spectroscopic response confirms the crystallization of the EPPTC molecules doped in the PMMA solid film when the sample is annealed at a temperature above the glass transition threshold. It needs to be noted that since the glass transition temperature is different for different polymers and for polymers with different molecular weights, the annealing strategy should be modified for different polymer materials.

#### *2.2. Annealing Time Dependence*

At a temperature above the glass transition threshold of PMMA, it takes time for the EPPTC molecules to become aggregated into crystal particles. Figure 4 shows the SEM images of the sample annealed at 150 ◦C for different times. Before annealing, no crystal particles can be observed in Figure 4a, implying that no crystallization process took place before annealing. Crystal particles can be resolved in Figure 4b for an annealing time of 30 s, although they are small and appear with a low density. For an annealing time longer than 1 min, EPPTC crystal particles can be observed clearly on the surface of the PMMA film. Figure 4c–f show the SEM images for annealing times of 1, 2, 5, and 10 min, respectively. Obviously, both the size and density of the EPPTC crystal particles increase dramatically with increased annealing time. The crystal particles can be clearly resolved only for an annealing time longer than 2 min, and the morphology of the surface of the solid film remains nearly constant when the sample is annealed for more than 5 min. The mean width and length of the crystals are roughly the same as those demonstrated in Figure 2c,d. It is also clearly observable in Figure 4 that the crystals are distributed randomly with random orientations, and that each particle contains inhomogeneous structures, implying that the crystal particles are not single crystals.

Figure 5 shows the spectroscopic characterization of the EPPTC-doped PMMA thin film sample, which was annealed at 150 ◦C for different times. Figure 5a,b show the directly measured and normalized absorption spectra, respectively. The main absorption peak at about 490 nm did not change its spectral position during the whole process. At least four other new features can be observed with increased annealing time, as highlighted by the dashed arrows in Figure 5b. The absorption peak around 473 nm was enhanced with increased annealing time, while that at about 530 nm is reduced and a new peak appeared at 542 nm; these features are similarly observed in Figure 3b. However, the most obvious difference between Figures 3b and 5b is the spectral peak at about 578 nm, which was observed clearly when the annealing time was longer than 1 min. Therefore, this is the more typical absorption spectrum of the crystal phase.

**Figure 4.** SEM images at an annealing temperature of 150 ◦C for (**a**) 0, (**b**), 0.5, (**c**) 1, (**d**) 2, (**e**) 5, and (**f**) 10 min.

As has been discussed with regard to Figure 3c, the PL spectrum becomes separated into two components for an annealing temperature of 150 ◦C. This is again observed in Figure 5c where the annealing time is longer than 1 min, which agrees with the observation of the time-dependent absorption in Figure 5b. The spectral feature peaked at a longer wavelength of 668 nm; this resulted from the crystal phase emission, as highlighted by the dashed arrow in Figure 5c. The difference between the crystal phase emission and the intrinsic molecular emission lies not only in their spectral positions but also in their lifetimes. This is shown in Figure 5d, where we demonstrate the PL dynamics at 612 and 668 nm for different annealing times. Clearly, the emission from the crystal phase at 668 nm is much longer than that from the intrinsic emission from EPPTC molecules.

From Figure 5d, we can also observe that the longest emission lifetime corresponds to an annealing time of 30 s at 150 ◦C, and that emission lifetime reduces with increased annealing time. For an annealing time longer than 1 minute, the decay dynamics of the emission remain nearly constant. This implies that there exists an intermediate state for the formation of the crystal phase with less quenching of the photoluminescence due to intermolecular interactions. However, after 10 min of annealing, the intrinsic EPPTC emission is much quenched due to the intermolecular interaction in the crystal phase; therefore, emission lifetimes at 612 and 668 nm are both reduced. The lifetime values become fixed after the equilibrium of the crystallization process is reached at a specified annealing temperature for a sufficiently long annealing time. We can also identify clearly from Figure 5d that the emission lifetime at 668 nm is much longer than that at

612 nm, implying long-lived crystal phase emissions, as compared with the intrinsic EPPTC molecular emissions, verifying the formation of the π-stacked crystals.

**Figure 5.** Absorption (**a**,**b**) and PL (**c**) spectra of the blend film annealed at 150 ◦C for different annealing times. (**b**) A normalized replot of (**a**). (**d**) Emission decay dynamics at 668 nm for different annealing times of 0.5, 1, 2, 5, 10 min and a comparison with that at 612 nm for an annealing time of 10 min.

#### **3. Conclusions**

We have demonstrated in this experimental work that it is possible for small molecular semiconductors to move and aggregate into crystal phases in a solid film of polymers, as long as the polymer film is softened and flexibilized, e.g., through heating it to its glass transition temperature. We verified such mechanisms using EPPTC molecules doped in a PMMA thin film. Both the microscopic and spectroscopic evaluations justified the validness of the proposed mechanisms and characterized the properties of the crystalized materials/structures. We can thus conclude that heterojunctions based on blends of small molecules and polymers can be constructed and modified by a low-temperature annealing process after production of the solid film, which simplifies the preparation and enables high-quality thin-film devices to be produced. Therefore, this strategy is important for the design and realization of organic optoelectronic devices based on blend materials or heterojunction structures.

**Author Contributions:** Conceptualization, X.Z.; Formal analysis, X.Z.; Funding acquisition, X.Z.; Investigation, Y.L. and X.Z.; Methodology, X.Z.; Project administration, X.Z.; Resources, X.Z.; Supervision, X.Z.; Writing—original draft, X.Z.; Writing—review & editing, X.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China, grant number 61735002 and 12074020 and by Beijing Municipal Education Commission, grant number KZ202010005002. The APC was funded by National Science Foundation of China.

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors acknowledge the National Natural Science Foundation of China (61735002, 12074020) and Beijing Municipal Education Commission (KZ202010005002) for their support.

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

#### **References**

## *Article* **Two-Dimensional Crystalline Gridding Networks of Hybrid Halide Perovskite for Random Lasing**

**Jingyun Hu 1, Haibin Xue 2 and Xinping Zhang 1,\***

**\*** Correspondence<EMAIL_ADDRESS>
**Abstract:** We report fabrication of large-scale homogeneous crystallization of CH3NH3PbBr3 (MAPbBr3) in the patterned substrate by a two-dimensional (2D) grating. This achieves high-quality optotelectronic structures on local sites in the micron scales and a homogeneous thin-film device in a centimeter scale, proposing a convenient technique to overcome the challenge for producing largearea thin-film devices with high quality by spin-coating. Through matching the concentration of the MAPbBr3/DMF solutions with the periods of the patterning structures, we found an optimized size of the patterning channels for a specified solution concentration (e.g., channel width of 5 μm for a concentration of 0.14 mg/mL). Such a design is also an excellent scheme for random lasing, since the crystalline periodic networks of MAPbBr3 grids are multi-crystalline constructions, and supply strong light-scattering interfaces. Using the random lasing performance, we can also justify the crystallization qualities and reveal the responsible mechanisms. This is important for the design of large-scale optoelectronic devices based on thin-film hybrid halide perovskites.

**Keywords:** two-dimensional patterning; periodical grids; hybrid halide perovskites; random lasing; large-scale thin-film networks

#### **1. Introduction**

Organic-inorganic hybrid halide perovskites are a group of promising semiconductor materials for high-efficiency optoelectronic devices [1–6]. Light-emitting [7–9] and photovoltaic [10–12] diodes, as well as lasing devices [13–17], have been reported on extensively. Although single- or multi-crystals have been synthesized in large scales at high quality [18–22] and have been applied for various purposes, thin-film devices [23–26] are more attractive in the construction of devices that are integratable into micro- or nano-scale systems. However, the conventional spin-coating method may encounter problems with the homogeneity of the produced film, in particular for large-scale fabrication. This is not only because of the dewetting of the solution on the conventional substrates, but also due to the quick crystallization of the molecules in random scales and random distributions.

Patterning the substrate with designed micro- or nano-structures and optimized microscopic dimensions may not only modify its surface-energy properties, but also control the molecular crystallization process by dividing the large-area surface into periodic/nonperiodic localized sites. This is an ideal strategy to achieve large-area thin films with high qualities precisely controllable on each local site. Such a strategy applies not only to hybrid halide perovskites [27] but also to any other organic/inorganic semiconductors [28,29] or even biomolecules [30] with strong aggregation performance. The corresponding designs also simultaneously facilitate new functions, including micro- /nano-cavity effects, local-field confinement, output coupling control, optical waveguides, and interface structural optimization or metasurface incorporation [31]. We have recently reported controllable crystallization of the hybrid halide perovskites into grating lines with

**Citation:** Hu, J.; Xue, H.; Zhang, X. Two-Dimensional Crystalline Gridding Networks of Hybrid Halide Perovskite for Random Lasing. *Crystals* **2021**, *11*, 1114. https:// doi.org/10.3390/cryst11091114

Academic Editor: Luisa De Marco

Received: 17 August 2021 Accepted: 11 September 2021 Published: 13 September 2021

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

**Copyright:** © 2021 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/).

continuous distribution over a large length scale [27], which provides an effective approach to overcome the above-mentioned challenge for producing high-quality MAPbBr3 crystal stripe gratings with controllable performance.

In this work, we report fabrication of large-area thin films into two dimensions, which enabled strong confinement of the molecules into more localized sites, and thus higher-quality crystallization. An optimized matching was found between the solution concentration and the patterning periods, with a duty cycle of about 50%. The random lasing performance was investigated to characterize the fabricated 2D structures and to verify the responsible mechanisms. Thus, we achieved thin-film CH3NH3PbBr3 (MAPbBr3) with a homogeneous area in the scale of cm2 and locally high-quality crystalline structures in sizes of microns.

#### **2. The Network of Squarely Gridded Thin Film of MAPbBr3**

The preparation method is illustrated in Figure 1 for the gridding network of the MAPbBr3 thin film. First, a two-dimensional (2D) grating was produced by photolithography, where a positive photoresist S1805 was employed, so that the grating consists of periodically distributed square cylinders on a glass substrate, as shown in Figure 1a. Using different masks, we have fabricated gratings with different periods of 10, 20, and 50 μm. Then, the solution of MAPbBr3 in DMF with different concentrations was spin-coated onto the top surface of the grating. In the last stage, the sample was heated to 90 ◦C for about 60 s. Figure 1c,d shows the microscopic characterization of the template photoresist grating by 3D profiler and the finalized MAPbBr3 grating by a fluorescence optical microscope, respectively. They illustrate clearly high-quality 2D gratings of square cylinders with steep edges and homogeneous 2D grids of crystallized MAPbBr3. Since Figure 1 is used to interpret the preparation procedures, we did not present detailed parameters of the structures in Figure 1c,d. We have also found that for a concentration of 0.14 mg/mL, the gridding network surrounding the cylinders can be filled completely and homogeneously, as illustrated in Figure 1b. Higher concentrations led to inhomogeneity and connection between neighboring locations, while concentrations that were too low led to incomplete fill of the grating grooves.

**Figure 1.** (**a**,**b**): Schematic illustration of the fabrication of gridded MAPbBr3 crystalline film by filling the void space in the 2D PR grating through spin-coating the MAPbBr3/DMF solution. (**c**) 3D topological image of the template PR grating prepared by photolithography. (**d**) Optical microscopic image of the fabricated 2D crystalline grid of MAPbBr3 under illumination by UV light.

Figure 2 shows the microscopic measurements on the practically fabricated structures. Figure 2a–c show the 3D topological mapping of the photoresist grating structures for a period of 50, 20, and 10 μm by a 3D profiler, which verify excellent distribution and homogeneity performance of these grating structures. Although it is not specified in the figures for the clarity of the demonstration, according to the 3D topological measurements, the modulation depth of the gratings or the square cylinder height is about 1 μm for all of the samples. We have also carried out fabrication experiments for a larger grating period of 100 μm and smaller periods than 2 μm to optimize the structural parameters. However, we did not find much difference between the fabrication using 50 and 100 μm. In contrast, for grating periods smaller than 2 μm we did not achieve satisfying crystalline structures of MAPbBr3 on the patterned substrates. Therefore, we include in this work our fabrication and investigation of the patterned MAPbBr3 thin film by three typical periods of 10, 20, and 50 μm.

**Figure 2.** 3D topological images (**a**–**c**) and optical microscope images (**d**–**f**) of the template PR grating and the finished crystalline MAPbBr3 grid for periods of 50 μm, 20 μm, and 10 μm, respectively. The scale bars denote a same length scale of 80 μm.

Figure 2d–f show the fluorescence microscope images of the fabricated MAPbBr3 thin film on patterned substrates with photoresist gratings of different periods. For a grating period of 50 μm, due to the large width and large volume of the grating grooves, there are two opposite effects during the crystallization processes. On one hand, a large amount of MAPbBr3 was confined completely into the grating grooves, which favors good crystallization performance inside the large volumes. On the other hand, due to the low concentration of the solution, the materials confined in the grating groove during the spin-coating process are limited; the large volume inside the grating grooves allows more freedom and more time for MAPbBr3 to get crystallized; these factors reduce the quality and homogeneity of the crystals, as can be confirmed by Figure 2d. We can observe that all of the MAPbBr3 are confined to the grooves with very clear edges, however, defects are distributed randomly and extensively in the crystal networks, which can be identified by the dark textures on the bright green background.

Similar effects can still be observed in Figure 2e, where the grating period was reduced to 20 μm. More continuous crystals may be observed in Figure 2e than in Figure 2d, in particular in the space surrounding the photoresist square cylinders, as highlighted by dashed red squares. In contrast, when the grating period is reduced to 10 μm, the continuity and homogeneity of the crystal grid becomes much improved, as can be seen in Figure 2f. The whole network can be observed as a whole crystalline MAPbBr3 film with "black

holes" punched by the photoresist square cylinders. The significantly reduced space in the grooves of the grating with a period of 10 μm enables complete filling by MAPbBr3 and high-quality crystallization with continuous connection over the whole grating structure. It is also understandable that breaks may be observed over the large-scale solid structure, as can be verified by the dark defects in Figure 2f. It is thus an indication that for a given solution concentration there exists an optimized channel width for the crystallization of MAPbBr3 in the 2D-distributed grating grooves. For a concentration of 0.14 mg/mL of MAPbBr3 in DMF, the grating period of 10 μm with a rough 50% duty cycle is found to be the best design for producing continuous crystalline structures.

Figure 3a–c show the scanning electron microscope (SEM) images for the samples patterned with a period of 10, 20, and 50 μm, respectively. Figure 3d shows the X-ray diffraction (XRD) spectra for these three samples. According to the SEM images, the sample patterned by the 10-μm grating exhibits the best surface quality among the three samples. Looking at the XRD spectra in Figure 3d at 2θ = 15◦ in the inset of Figure 3d, we can find that the sample with a 10-μm has the strongest diffraction, the narrowest spectrum, and the smallest diffraction angle. This also implies the best crystalline quality among these three samples. Therefore, the experimental results in Figure 3 again confirmed our analysis above (Figure 2).

**Figure 3.** (**a**) SEM image for the patterned structure with a period of 10 μm and an enlarged view of a local area. (**b**,**c**) SEM images for the structures with a patterning period of 20 and 50 μm, respectively. (**d**) XRD spectra measured on the three kinds of structures patterned at different periods. Inset: an enlarged view of the spectra.

#### **3. Optical Spectroscopic Performance of the Gridded Crystalline Film**

*3.1. Absorption and Photoluminescence*

Figure 4a,b show the absorption and emission spectra of the fabricated grating structures, respectively, where the three measured spectra correspond to the samples in Figure 2d–f. According to Figure 4a, the absorption spectra of the patterned structures with different periods are peaked nearly the same at about 525 nm with a bandwidth of about 20 nm at FWHM. However, the three spectra have different contrasts, or they have different background intensity for wavelengths longer than 550 nm. Such background results mainly from the scattering of light by the patterned MAPbBr3. It is understandable by looking at the microscopic images in Figure 2, where the structures have 50 and 20 μm patterning, that they also have more inhomogeneity or defect structures than with 10 μm patterning. Meanwhile, the absorption by the 50 μm grating patterned structures has a broader absorption spectrum due to more defects or inhomogeneity than those with 20 and 10-μm patterning.

**Figure 4.** Absorption (**a**) and PL (**b**) spectra of the crystalline MAPbBr3 film gridded at different periods. In (**b**), the bandwidth of each PL spectrum at FWHM is listed.

The PL spectra in Figure 4b are all peaked at about 533 nm, which have nearly the same spectral shape. Nevertheless, they still have slight differences in the bandwidth at FWHM, which is 20.39, 22.47, and 20.75 nm for the grating periods of 10, 20, and 50 μm. Although we did not observe a monotonic variation of the bandwidth when increasing the grating period, we can still identify a narrow emission spectrum at a grating period of 10 μm, implying more homogeneous crystallization of MAPbBr3, which can be further confirmed by the random lasing properties.

#### *3.2. Random Lasing*

Figure 5 shows the random lasing performance of the 2D patterned structures at different periods, where Figure 5a,a', Figure 5b,b' and Figure 5c,c' correspond to the grating periods of 50, 20, and 10 μm. In the measurements, a femtosecond laser with a pulse length of 150 fs, a repetition rate of 1 kHz, and a center wavelength of about 400 nm was used as the pump. A spectrometer with a sub-1 nm resolution was positioned in front of the sample and used to measure the emission spectrum. Figure 5a shows the emission spectrum measured at different pump fluence for the sample with a grating period of 50 μm. An obvious random lasing peak occurs as the pump fluence exceeds 48 μJ/cm2, which increases dramatically with the increasing of the pump fluence. The peak intensity as a function of pump fluence is plotted in Figure 5a', where two stages can be observed, implying a clear threshold effect of the random lasing performance. Using linear fitting to the measurement data to these two stages, we can resolve a threshold pump fluence lower than 50 μJ/cm2. Similar measurements and analysis are made for the sample with a patterning period of 20 μm, as shown in Figure 5b,b'. However, a higher pumpfluence threshold can be justified for Λ = 20 μm, which is roughly 60 μJ/cm2. This can be understood by considering the lower density of defects or higher crystallization quality,

as compared with Λ = 50 μm, where the light-scattering strength has been reduced and consequently the optical gain mechanisms were weakened. Similar effects apply further to the case of Λ = 10 μm, as shown in Figure 5c,c', where random lasing spectrum can be clearly observed when the pump fluence is increased to about 70 μJ/cm2. This aligns well with the observation of the most homogeneous crystallization structures for Λ = 10 μm. All of the experimental results in Figure 5 have shown clear threshold effects and two-stage variations of the emission intensity with pump fluence, indicating excellent random-lasing performance for all of the samples. In particular, the random lasing performance supplies a further verification of the crystallization qualities at different pattering periods.

**Figure 5.** Random lasing performance (emission spectra and lasing threshold) of the MAPbBr3 crystalline gridding at different periods: (**a**) Λ = 50 μm; (**b**) Λ = 20 μm; (**c**) Λ = 10 μm. (**a'**–**c'**) Emission intensity at about 550 nm as a function of the pump fluence, corresponding to (**a**–**c**), respectively.

A more convincing analysis is the comparison of the lasing bandwidth. To make this comparison more objective, we need to isolate the random lasing spectrum from the emission spectrum. This can be done using the mathematics below:

$$\mathbf{I}\_{\rm RL}(\lambda) = \mathbf{I}(\lambda) - \mathbf{I}\_0(\lambda) \times \mathbf{I}(\mathbf{535 nm}) / \mathbf{I}\_0(\mathbf{535 nm}) \mathbf{0}$$

where IRL(λ) is the pure random lasing spectrum, I(λ) is the directly measured emission spectrum, I0(λ) is the background fluorescence spectrum at the lowest pump fluence below the threshold for random lasing, and I(535 nm) and I0(535 nm) are the intensities of the corresponding spectra at 535 nm, which is outside the spectral range of random lasing.

Figure 6 shows the extracted pure random lasing spectra for patterning periods of 50, 20, and 10 μm. There is observed a slight redshift of the peak wavelength (λ0) of the lasing spectrum with increasing the pattering period. However, we did not observe a monotonic variation of the lasing bandwidth, where we have a full bandwidth at half maximum of 6.42, 7.07, and 4.98 nm for the patterning periods of Λ = 50, 20, and 10 μm, respectively. Nevertheless, for Λ = 10 μm, we achieved the narrowest lasing emission spectrum. This verifies again that the structures with a period of 10 μm have the best crystallization quality and the highest homogeneity, so that the lasing spectrum has a narrowest bandwidth of 4.98 nm.

**Figure 6.** Comparison between the bandwidth of the random lasing spectra measured on the patterned MAPbBr3 crystalline film at different gridding periods.

#### **4. Conclusions**

We achieved locally high-quality and large-scale homogeneous crystalline networks of MAPbBr3. This overcomes the challenge of producing large-area thin film devices of hybrid halide perovskites with high quality by spin-coating. At a specific concentration of MAPbBr3 in DMF, the optimized crystal networks were produced in a 2D grating with a period of 10 μm. Random lasing was achieved for all of the two-dimensionally gridded MAPbBr3 crystals with a period of Λ = 10, 20, and 50 μm. However, the lowest lasing threshold was measured for Λ = 50 μm and the narrowest lasing bandwidth was obtained at Λ = 10 μm. The underlying mechanism is that the strong scattering of light by high density of defects with rough interfaces enables the lowest lasing threshold at Λ = 50 μm, while the most homogeneous crystal structures allow random lasing with the narrowest bandwidth at Λ = 10 μm. These discoveries are important for the design of optoelectronic devices based on large-scale MAPbBr3 crystalline films with high quality and high homogeneity.

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

**Funding:** This research was funded by National Natural Science Foundation of China, grant number 61735002, 12074020 and by Beijing Municipal Commission of Education, grant number KZ202010005002. The APC was funded by Beijing Municipal Commission of Education.

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

#### **References**

## *Article* **Photodetector Based on CsPbBr3/Cs4PbBr6 Composite Nanocrystals with High Detectivity**

**Yue Han, Rong Wen \*, Feng Zhang, Linlin Shi, Wenyan Wang, Ting Ji, Guohui Li, Yuying Hao, Lin Feng \* and Yanxia Cui**

> College of Physics and Optoelectronics, Key Laboratory of Advanced Transducers and Intelligent Control System of Ministry of Education, Key Laboratory of Interface Science and Engineering in Advanced Materials of Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China<EMAIL_ADDRESS>(Y.H<EMAIL_ADDRESS>(F.Z<EMAIL_ADDRESS>(L.S<EMAIL_ADDRESS>(W.W.);

><EMAIL_ADDRESS>(T.J<EMAIL_ADDRESS>(G.L<EMAIL_ADDRESS>(Y.H<EMAIL_ADDRESS>(Y.C.) **\*** Correspondence<EMAIL_ADDRESS>(R.W<EMAIL_ADDRESS>(L.F.)

> **Abstract:** High-quality, all-inorganic CsPbBr3/Cs4PbBr6 composite perovskite nanocrystals (NCs) were obtained with all-solution-processing at room temperature, and a photodetector (PD) with high detectivity was realized based on CsPbBr3/Cs4PbBr6 NCs. The detectivity (*D\**) of the proposed PD is 4.24 × 1012 Jones under 532 nm illumination, which is among the highest levels for PDs based on all-inorganic perovskite NCs. In addition, a high linear dynamic range (LDR) of 115 dB under 1 V bias was also realized. Furthermore, the underlying mechanism for the enhanced performance of the proposed PD was discussed. Our work might promote the preparation of high-performance PDs based on dual-phase all-inorganic perovskite nanocrystals.

> **Keywords:** all-inorganic lead halide perovskite; CsPbBr3; Cs4PbBr6; perovskite nanocrystals; photodetector

#### **1. Introduction**

All-inorganic lead halide perovskites have shown excellent photoelectrical properties with high absorption coefficients, wide spectra, high carrier mobility values, and long charge diffusion lengths. Because of these advantages, they are widely used in PDs [1–4], solar cells [5–8], lasers [9–11], light-emitting diodes [12–14], and so on. In addition, compared with the organic–inorganic hybrid perovskite, all-inorganic lead halide perovskites have higher chemical stability to the environment because there are no organic ions in them. Among many kinds of all-inorganic lead halide perovskites, CsPbBr3 NCs demonstrate strong competitiveness for their excellent photoelectric characteristics, such as adjustable photoluminescence (PL) with narrow full-width at half maximum (FWHM) in visible light, an easy preparation process for their devices, and small size which causes a quantum size effect. Moreover, the CsPbBr3 NCs can be stored in air for 30 days with no obvious decrease in their photoelectric performance [15]. Some research on optoelectronic devices based on CsPbBr3 NCs has been conducted. For example, Li et al. reported an interesting recyclable dissolution–recrystallization phenomenon of CsPbBr3 NCs and its application on the room temperature self-healing of compact and smooth carrier channels for PDs with *D\** of 6.1 × 1010 Jones [16]. Zeng et al. demonstrated a high-performance self-actuation PD, for which CsPbBr3 NCs were synthesized using room temperature saturation recrystallization, and the NC films were prepared by a centrifugal casting method. Compared with the dripcoating method, the photocurrent of the device increased three-fold, and the optimized device had a high on/off ratio (>105) [15]. However, the *D\** of these all-inorganic perovskite NC PDs is not high enough. Generally, the detectivity can be improved by increasing the bright current and suppressing the dark current. Additionally, improving the quality of nanocrystalline films to reduce defect states is vital for the suppression of the dark current.

**Citation:** Han, Y.; Wen, R.; Zhang, F.; Shi, L.; Wang, W.; Ji, T.; Li, G.; Hao, Y.; Feng, L.; Cui, Y. Photodetector Based on CsPbBr3/Cs4PbBr6 Composite Nanocrystals with High Detectivity. *Crystals* **2021**, *11*, 1287. https:// doi.org/10.3390/cryst11111287

Academic Editor: Luisa De Marco

Received: 4 October 2021 Accepted: 21 October 2021 Published: 24 October 2021

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

**Copyright:** © 2021 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/).

Quan et al. have found that embedding CsPbBr3 NCs in the Cs4PbBr6 matrix can prevent the agglomeration of CsPbBr3 NCs [17]. This means that the presence of Cs4PbBr6 NCs could improve the quality of NC films. Thus, we prepared CsPbBr3/Cs4PbBr6 composite NCs by controlling the proportion of PbBr2 in the synthesis process. Cs4PbBr6 is an indirect band gap semiconductor with a wide band gap (3.8 eV) [18], and Cs4PbBr6 NC is a zerodimensional material, which absorbs light yet does not emit it [19]. This non-luminous property can effectively reduce radiation recombination. In addition, it has been proved that the presence of Cs4PbBr6 will enhance the absorption of the dual-phase perovskite NCs in the UV spectrum [17,20,21]. This is helpful for improving the detection performance of the PD in the UV spectrum.

Taking the above-mentioned issues into account, the saturation recrystallization method was utilized to synthesize the dual-phase NCs at room temperature. The dualphase NC film was spin-coated on the customized substrate and Au electrode. Moreover, the planar metal-semiconductor-metal (MSM) PDs based on CsPbBr3/Cs4PbBr6 composite NCs were realized. The proposed PD exhibited a high *D\** of 4.24 × 1012 Jones, with an LDR of 115 dB under 1 V bias. To explain the improvement of *D\**, the role of Cs4PbBr6 NCs was investigated. Our work might provide a guidance for developing a high-performance PD based on CsPbBr3/Cs4PbBr6 perovskite NCs.

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

*Materials:* Cesium bromide (CsBr, 99.5%), lead bromide (PbBr2, 99.0%), Oleic acid (OA, 85%) and oleylamine (OAm, 80–90%) were purchased from Aladdin. Toluene (AR) was purchased from Beijing Chemical Works. All these chemicals were used as received.