Microcavity lasers based on whispering-gallery mode (WGM), possessing small size and strong optical confinement, have been attracting great interest in fundamental research and for practical applications [1–4]. Compared to the laser wavelength, the size of the microcavity is usually large enough to cause multimode lasing, resulting in a noisy spectrum, which severely degrades the performance of microlasers in applications such as optical communication and ultrasensitive optical sensors [5,6]. Coupled microcavity configuration is a compact and effective method to purify and regulate the laser spectra of microcavities. For example, a single-mode laser can be realized, based on the Vernier effect, in two coupled cavities with slightly different sizes [6–11]. Non-Hermitian optical systems, which have emerged recently, for lasers are, in essence, open and non-conservative systems. This means the most common gains and losses of physical quantities can be distributed differently with artificial purposes in such coupled microcavities [12]. In particular, if the optical microcavity is tuned to the exceptional point (EP) [13], where the resonance frequencies of the coupled modes coalesce both in their real and imaginary parts and become degenerate, some unique phenomena appear, such as parity–time (PT) symmetry breaking [14–18], chiral modes [19], and enhanced perturbation at higher-order EPs [20,21]. Therefore, this principle provides an alternative approach to modulate the laser spectrum by controlling the gain and loss elements. By managing the gain and loss distribution for the

coupled modes in microcavities, some studies have successfully achieved single-mode lasing in WGM microcavities [22–24].

One of the key points in such coupled microcavity systems is the flexible method for controlling the system parameters, for example, the coupling strength between the coupled laser modes. The coupling strength can be regulated by controlling the gap between different microcavities, which is predetermined for the desired modes in the fabrication process, or precisely controlled by the nano-positioning stages in real-time experiments [14,25]. However, these mechanisms all lack efficiency and flexibility, and are sensitive to external noise sources, such as acoustic waves. Moreover, the coupled cavities fabricated on chip have the fixed coupling gaps. They need a reliable and flexible means for controlling the coupling strengths on chip. Optofluidic devices can integrate some functional fluids into optical or photonics devices [26,27]. Such fluids usually have high transmittance and tunable optical properties, e.g., the refractive index [28,29]. Because the optofluidic devices have a good compatibility with aqueous media, they are widely used in biology and medical science [30–34]. Therefore, optofluidic devices have found great potential in on-chip microlaser systems for their highly integrated level and, more importantly, the microlaser cavity is given a liquid environment, which provides an additional means for tuning the microlaser.

In this study, solid-state dye-doped polymer microdisks are fabricated and integrated with a microfluidic channel, in order to investigate the mechanism and characteristics of the microdisk laser in aqueous media. Some phenomena, such as single-frequency laser and mode splitting in the coupled microcavities, were studied theoretically and experimentally in aqueous media for the first time. We observe that the resonance detuning of mode splitting is affected by changes in the gap between two coupled microdisks. Mode splitting and single-mode lasing in the laser spectrum can also be modulated by changing the refractive indices of the aqueous media and the position of the pump light. In addition, the aqueous media not only have a spectral modulation function but also a mode purification ability because they decrease the refractive index difference between the cavity and the background media, which eliminates some high-order WGM with larger reflection angles at the cavity surface. The results presented in this paper show that optofluidic microlasers possess potential for several promising applications, such as tunable single-mode lasers on chip and bio-photonic sensors.

#### **2. Coupled-Mode Analysis**

The coupled-mode theory could be applied to analyze such a coupled-microdisk laser system. We assume the two coupled modes in two respective cavities have amplitudes *a* and *b*. Considering the sinusoidally varying fields in the time domain, *e*−*i*ω*nt* , *a* and *b* obey the coupled differential equation [20]:

$$i\frac{d}{dt}\begin{pmatrix} a \\ b \end{pmatrix} = \begin{pmatrix} i g\_a & \kappa \\ \kappa & i g\_b \end{pmatrix} \begin{pmatrix} a \\ b \end{pmatrix} \tag{1}$$

where *ga* and *gb* represent the gain (*g* > 0) or loss (*g* < 0) for modes *a* and *b*, respectively. κ denotes the coupling strength between the two microcavities. It leads to an eigenvalue problem: *H*0*Vn* = ω*nVn*, where the eigenvalue ω*n* and eigenvector *Vn* satisfy *Vn e*−*i*ω*nt* = (*a*, *b*) T, and the Hamiltonian *H*0 of the system is

$$H0 = \left(\begin{array}{cc} i\text{g}\_a & \kappa \\ \kappa & i\text{g}\_b \end{array}\right) \tag{2}$$

To determine the eigenfrequency, we solve the equation det(*H*0 – ω*nI*) = 0 (where *I* is the identity matrix), which results in two eigenfrequencies:

$$
\omega\_{\pm} = \frac{i(g\_a + g\_b)}{2} \pm \sqrt{\kappa^2 - \frac{\left(g\_a - g\_b\right)^2}{4}},\tag{3}
$$

The difference between the two eigenfrequencies is

$$
\Delta\omega \equiv \omega\_{+} - \omega\_{-} = 2\sqrt{\kappa^2 - \left(\mathcal{g}\_a - \mathcal{g}\_b\right)^2 / 4},\tag{4}
$$

where Δ*g*˜ = (*ga* − *gb*)/2κ is the normalization gain difference between the two modes. If the two modes experience the same gain or loss, i.e., Δ*g*˜ = 0, the frequency difference equals 2κ, which is the well-known mode-splitting effect, as shown in Figure 1a. However, the two modes have different gains or losses in more general situations. In particular, such frequency difference changes into a purely imaginary number when Δ*g*˜ > 1. In this case, the difference between the two eigenfrequencies no longer shows two different resonance wavelengths in the spectrum, but instead, introduces two modes with different growth or decay rates, which often indicate different net gains in a laser system. Moreover, at the threshold where Δ*g*˜ = 1 two eigenfrequencies coalesce to a single one, with ω = *i*(*ga* + *gb*)/2.

**Figure 1.** (**a**) Real and imaginary parts of Δω/2κ as a function of Δ*g*˜. The difference between the eigenfrequencies changes from purely real to purely imaginary at Δ*g*˜= 0. (**b**) Coupling coefficient *K* as a function of refractive index under different gaps.

The coupling strength κ could be related to the coupling coefficient *K*; defined in the coupling between two parallel waveguides:

$$\kappa = \frac{\text{Kcl}\_{eff}}{n\_{eff}2\pi\text{R}'} \tag{5}$$

where *Le*ff and *ne*ff are the effective interaction length and effective index of the cavity modes, respectively, and *R* is the radius of the microdisk. The coupling coefficient *K*; can be expressed by the overlap integral between the two coupling modes:

$$K = -\frac{i\omega}{4} \int\_{-\infty}^{+\infty} \int\_{-\infty}^{+\infty} (n\_0^2 - n^2) E\_{\mathbf{a}} \bullet E\_{\mathbf{b}} dx dy,\tag{6}$$

where *Ea* and *Eb* are the normalized field distributions in the two respective cavities, and *n*0 and *n* are the refractive indices for the microcavities and the background medium, respectively. The coupling strength *K* in Equation (6) can be calculated numerically, and the relationships between the coupling strength *K* and refractive index *n* under different gaps are shown in Figure 1b. *K* grows with an increase in *n*, or with a decrease in the coupling gap. Because the increased *n* reduces the difference of the refractive indices between the microdisk and background medium, more of the optical field will leak into the coupling gap. This results in an improvement in the overlap between the optical fields in two microdisks, and accordingly increases the value of *K*. Similarly, a smaller coupling gap also improves the overlap of the optical fields and provides greater coupling strength.

#### **3. Optofluidic Microdisk Lasers**

#### *3.1. Fabrication of the Optofluidic Microdisk Device and Experimental Setup*

The experimental setup of the optofluidic microcavity laser is shown in Figure 2a. The optofluidic microdisk device consists of a microfluidic channel and solid-state dye-doped polymer microdisks as shown in Figure 2b,c. Rhodamine B dye (RhB, CAS: 81-88-9, J&K Scientific Ltd., Beijing, China)-doped SU-8 photoresist (SU-8 2002, MicroChem Corp. MA, USA) in a ratio of 1.5 mg:1 mL was used as gain media and mixed by a magnetic stirrer for 2 h. During stirring, attention should be paid to shading the photoresist, in order to avoid quality deterioration. A 2.4 μm active layer of the gain media was then deposited by a spin coater (Specialty Coating Systems Inc., Indianapolis, USA) onto a silicon wafer with a 2 μm thick thermal oxide layer. The geometric shapes of the single and coupled microdisks were pre-designed on the chromium mask, and the gap between each pair of coupled microdisks was increased from 0.2 to 1 μm, and 0.1 μm for each pair. Therefore, the solid-state dye-doped polymer microdisk arrays were fabricated via single-mask standard lithography (Karl Suss MJB 3 Mask Aligner, SUSS MicroTec SE, Garching, Germany). The geometric sizes of the microdisks were measured via scanning electron microscopy (SEM), as shown in Figure 2c and Figure S1 (details can be found in the Supplementary Materials).

**Figure 2.** (**a**) Experimental setup schematic of the optofluidic microcavity laser. (**b**) 3-D schematic of the optofluidic microdisk device. (**c**) Scanning electron microscope (SEM) image of typical coupled microdisks. The scale bar is 10 μm.

The optofluidic microdisk device consists of a microfluidic channel device and solid-state dye-doped polymer microdisks (details can be found in Supplementary Materials). This microfluidic channel is a device that combines a clean glass slide and patterned polydimethylsiloxane (PDMS) leaf. The fabrication process of the optofluidic microdisk device is described in Figure S2 (in Supplementary Materials). The shape of the glass mold was spliced with glass sheets, and the convex structure is shown as in Figure S2a. After the PDMS leaf was formed from the glass mold, the inlet and outlet holes were punched by a needle. The solid-state dye-doped polymer microdisks were sandwiched between the microfluidic channel (PDMS leaf) and a glass slide, as shown in Figure S2d,e. Finally, an optofluidic microdisk device, consisting of a microfluidic channel and solid-state dye-doped polymer microdisks, was fabricated, as shown in Figure 2b and Figure S2e.

The laser spectra were measured using the experimental setup as shown in Figure 2a. The pump laser was a picosecond pulse laser (532 nm, PL2143A, EKSPLA, Vilnius, Lithuanian), and the pulse duration of the pump laser was 30 ps, with a repetition rate of 10 Hz. A monochromator (Acton SpectraPro 2750, Princeton Instruments, NJ, USA) was employed to collect the laser spectra. The spectra were measured by a monochromator with a 1200 grooves/mm grating and the spectral resolution was 0.01 nm. The size of the pump laser was controlled via tunable beam-shaping optics (BSO), and the pump laser energy was adjusted by a variable attenuator (VA). Firstly, the laser beam spot was coupled into the microscope

system and further focused to nearly 50 μm under a 20× objective lens. Through the microscope with a camera, the pump position of the laser beam spot was able to be marked on a screen. The microcavity sample was then moved to the pump position using a 3-D stage. The output laser passed through a Glan–Taylor prism (GTP) and was collected by an optical multi-channel fiber bundle (core diameter 400 μm). The GTP was used as the polarization controller. The laser light was then coupled into the input slit (30 μm) of a monochromator (f = 0.75 m) and detected by an electron-multiplying charged coupled device (EMCCD, DV401A, Andor iDus, OX, UK). Finally, the laser spectra were recorded by a computer.

#### *3.2. Modulation of the Microdisk Laser in Aqueous Media*

A single microdisk was firstly investigated and the appearance of the microdisk sample was measured via SEM, as shown in Figure 3a. In this case, the diameter of the microdisk was set to 20.34 μm and the thickness was 2.4 μm, as measured using scanning electron microscopy (SEM) and a surface profiler, respectively. Compared to air cladding, the microdisk surrounded by water represents a much clearer spectrum. The water environment decreases the refractive index (RI) difference between the microdisk and the background media, where high-order WGMs with larger reflection angles at the cavity surface suffer from degradation of *Q* (quality) values and larger radiation losses. Therefore, they have a higher laser threshold and only fundamental-order WGMs with high *Q* values will exist in the laser spectra, which are shown in Figure 3b. The free spectral range (FSR) of this microdisk was 3.81 nm, agreeing well with the FSR calculated from *FSR* = λ2/(2π*Rne*ff) ≈ 3.87 nm, where λ = 615 nm, *ne*ff = 1.53, and *R* = 10.17 μm were the lasing wavelength, effective refractive index of the microdisk, and radius of the microdisk, respectively. The laser spectra were relatively clear in a water environment, which was conducive to sensing, single-frequency lasers, and other applications. Figure 3c,d show the simulation results of the electric field distribution of a single microdisk using the finite element method (FEM). To reduce consumption of computer memory, we divided the full 3-D model into two 2-D models, as shown in the top view and side view in Figure 3c,d, respectively. The refractive index of the microdisk in the simulation shown in Figure 3c was obtained by calculating the effective index of the three-layer planar waveguide of water-SU8-SiO2. As shown in Figure 3d, the electric field distribution in the cross section of the microdisk was calculated using an axially symmetric model [35]. All the simulation regions for the two 2-D models were surrounded by the perfect matching layer (PML) to avoid reflecting from the boundary. The microdisk was immersed in water, and the polarization of the fundamental-order-radial modes was transverse electric (TE) polarization.

**Figure 3.** (**a**) SEM image of the microdisk. The scale bar is 10 μm. (**b**) Laser spectra of a microdisk dipped in water. The free spectral range (FSR) was 3.81 nm. (**c**) and (**d**) Field distributions of whispering-gallery modes (WGMs) in fundamental-order-radial mode with transverse electric (TE) polarization in the top view and side view. The direction indicated by the red arrow was the direction of electric field propagation. Finite element method (FEM) simulations were performed with the same parameters for the experimental data.

The long-term stability of the microdisk laser was determined by pumping the microdisk every 20 s over a period of 1800 s, with the laser spectra being collected simultaneously. As shown in Figure 4a,b, the laser wavelength maintained the same position during this period. The standard deviation of the curve in Figure 4b is 5.84 pm, which is much smaller than the resolution of the monochromator (0.01 nm). These results indicate that an optofluidic microdisk laser does not have a large wavelength shift over a long term and that the system stability is good enough for our next experiments.

**Figure 4.** (**a**) Laser spectra of optofluidic microdisk laser at different times. (**b**) Measured wavelengths of the lasers as a function of time. Standard deviation was 5.84 pm. (**c**) Laser spectra shifts when the refractive index of the DMSO solution is slightly increased. (**d**) Mean wavelength shifts of the lasers as a function of the refractive indices of DMSO solutions. Violet dots and pink line represent the experimental data and FEM simulation data, respectively. Insert: fundamental-order-radial mode with TE polarization.

The spectral modulation of the optofluidic microdisk laser can be achieved by changing the refractive index of the external environment, similar to the method for measuring the bulk refractive index sensitivity (*S*) of a sensor. Because this is an optofluidic device, it is essential to first characterize the sensitivity according to the changes in the refractive index of the solvent on the sensing surface [36]. In Figure 4c,d, the optofluidic microdisk laser was tested by flowing progressively higher concentrations of dimethyl sulfoxide (DMSO, CAS: 67-68-5, Lingfeng Chemical Reagent Co. Ltd., Shanghai, China) solutions over the sensing surface. The DMSO was diluted with deionized water (DI water) into concentrations of 2%, 4%, 6%, 8%, and 10%. The refractive indices of the DMSO solutions were proportional to the volume ratios of the DMSO (details can be found in Supplementary Materials) [37]. Prior to use, the DI water and DMSO–water mixtures were kept at room temperature for a longer period, to minimize temperature-induced spectrum changes. A redshift of the wavelength in response to an increasing refractive index of the solution was observed from the laser spectra measurement and can be explained by *m*λ = 2π*ne*ff *R* (see details in Supplementary Materials) [38]. *Sexp* and *Ssim* represent the *S* from the experiment and from the FEM simulation, respectively. *Sexp* was obtained by directly measuring the wavelength shift, which was 18.14 nm/RIU. The process of detecting the *S* of the microdisk was also simulated using FEM, based on a 2-D axisymmetric model. Results show that the *Ssim* of the fundamental and second-order radial modes with TE polarization were 18.12 and 28.90 nm/RIU, respectively, and that the *Ssim* of the fundamental and second-order radial modes with transverse magnetic (TM) polarization were 22.98 and 37.65 nm/RIU,

respectively. When the GTP was used to observe the experiment, the polarization state of the output laser was determined to be TE polarization. Therefore, the *S* of the measured microdisk was determined to be fundamental-order-radial mode with TE polarization.

#### *3.3. Mode Splitting from the Coupled-Microdisk Laser in Aqueous Media*

The method of purifying and adjusting the microcavity laser spectrum using the coupled microcavity structure is compact and effective. Normally, a typical WGM propagates along a spherical equatorial plane, whose evanescent field component allows interaction with the surrounding environment. Therefore, when two WGM microcavities are close to each other, their WGMs can be evanescently coupled and form mode splitting [31]. A large array of dye-doped polymer microlasers can be fabricated in parallel via a single step of deep-ultraviolet (DUV) lithography [39]. The coupled microdisks were investigated by immersing in water. At this time, the two modes experience the same gain or loss (*ga* = *gb*), and the frequency difference equals 2κ. Using the gap between the coupled microdisk of 0.3 μm, the diameters of these two coupled microdisks were 19.71 and 19.63 μm, and their SEM image is plotted in Figure 5a. Under evenly pumping schemes, as shown in the insert of Figure 5b, the mode splitting of the laser spectrum can be observed. Δλ represents the distance between two laser peaks under mode splitting and is 0.183 nm in this case. Figure 5c shows the field distributions of WGMs with the fundamental-order-radial mode in a symmetric coupled-microdisk system. The wavelengths of the supermodes are 620.619 and 620.437 nm, respectively. Δλ of the FEM simulation is 0.182 nm, which is very close to the experimental result of 0.183 nm. Different gaps between coupled microdisks were investigated under the same pumping conditions. Because the optical field decays exponentially outside the microdisk, the coupling strengths κ between the two cavities will decrease. Δλ will also decrease, which is shown in Figure 5d. The experimental data and FEM simulation results were well-fitted by the exponential function. As the gap exceeded 0.6 μm, the coupling strengths *K* of the supermodes became weak and the Δλ value stayed at a level of no more than a few dozen nanometers. Because of the limited resolution of the monochromator, narrower mode splitting cannot be observed in experiments.

**Figure 5.** (**a**) SEM image of the coupled microdisks. Gap between two microdisks is approximately 0.3 μm. Scale baris 10μm. (**b**) Laser spectra of coupledmicrodisks with 0.3μm gap. Δλdenotes the distance between two peaks of mode splitting. Insert: schematic of evenly pumping schemes. (**c**) Field distributions ofWGMs

with fundamental-order-radial mode. (**d**) Δλ of the experimental results and FEM simulations as a function of the gap. Purple dots represent the experimentally detected data; cerulean dots and red curves refer to the FEM simulation results and exponential fitting, respectively. FEM simulations were performed with the same parameters for the experimental data.

Furthermore, when we change the refractive index of the aqueous medium *n*, it will also affect the coupling strengths of the supermodes *K*. Here, we used coupled microdisks with a gap of 0.4 μm. As shown in Figure 6a, when the refractive index of the DMSO solution was changed, the resonance detuning of the mode splitting was affected. Figure 6b shows that Δλ of the experimental data was increased, which agreed well with the results of the FEM simulation. The increased background refractive index *n* will extract a greater part of the optical field into the coupling gap, leading to enhanced coupling strength and a larger difference in resonance frequencies of the coupled modes. The coupling coefficient *K* is as a function of *ne*ff, which is given in Equation (5), and the experimental phenomenon is consistent with the FEM results in Figure 1b.

**Figure 6.** (**a**) Mode splitting in a coupled-microdisk resonator laser with resonance detuning. (**b**) Δλ of the experimental data and FEM simulation, shown as a function of refractive index. Pink dots represent the experimentally detected data, while the green curves represent the FEM simulation results. FEM simulations were performed using the same parameters for the experimental data.

In order to increase the difference in the gains/losses between the two microcavities, we used selective pumping schemes in which we changed the position of the pump beam spot gradually from the left side of the coupled microdisks to the right side by 8 μm per step. Figure 6 demonstrates the laser spectra of coupled microdisks with a 0.3 μm gap, with the coupled microdisks immersed in water. We focused on the wavelengths of the spectra from 612 to 615 nm, which are marked in red in Figure 7a,c. The laser spectra in Figure 7a,c correspond to the pump positions plotted in Figure 7b,d. The laser emerged when one of the coupled microdisks was pumped, and the splitting mode arose when the coupled microdisks were evenly pumped. When the pump beam spot gradually moved to the other side of the coupled microdisks, the splitting mode disappeared, and the laser finally vanished. This result is due to the selective pumping process, which changed the gain/loss status between the two coupled microdisks. The modulation gain branches of various supermodes will lead to a switchable single-frequency laser or mode splitting [9]. When only one of the coupled microdisks is pumped, the eigenfrequencies difference will become purely imaginary because in this case Δ*g*˜ is large enough that the value under the square root in Equation (4) is smaller than zero. This will lead to the emission of a single-mode laser when the other laser modes are also below the threshold. Under even pumping, the gain difference between the two microcavities is very small and Δω is real, so it shows doublet peaks in the laser spectrum, i.e., mode splitting.

**Figure 7.** Laser spectra from different positions of the pump beam spot. (**a**) and (**c**) spectra during the moving of the pump laser from left to right. (**b**) and (**d**) schematics of the position of the pump beam spot.

#### *3.4. Single-Frequency Lasing from the Coupled Microdisk in Aqueous Media*

Because of their high beam quality and spectral purity, lasers with a single-frequency laser emission feature are indispensable to many scientific and industrial applications, such as laser spectroscopy, laser metrology, and biomolecular sensing [5,6,39]. Normally, WGM lasers are usually multimode because of the lack of mode selection [9,40]. Methods such as microcavity size reduction, Vernier effect, and PT symmetry effect of coupled microcavities are possible strategies to realize single-frequency laser [9,14,40–42]. These methods need to control the gap size or thermal modulation of the two microcavities in order to control the coupling strength between them, which often requires a complex implementation system and results in low accuracy.

The results of the previous section indicate that selective pumping schemes would change the spectrum of the coupled microdisks. In order to overcome the major drawback of a single-microcavity resonator laser, which essentially involves multimode laser emission, we used selective pumping schemes in a coupled-microdisk system, in order to realize a single-frequency laser emission. The coupled-microdisk resonator was dipped in water. In this case, the gap of the coupled microdisks was 0.5 μm. The position of the pump laser was "left pumping", and the simulated mode field of the single-frequency laser is plotted in the inserts of Figure 8b. In the range 580–610 nm (much larger than one FSR and covers the tuning range of RhB in the ethanol solvent), only one laser peak has been collected by the spectrometer. Therefore, it is determined to be a single-frequency laser. The single-frequency laser spectra of the coupled microdisks at different pumping intensities are plotted in Figure 8a. The central wavelength of the single-frequency laser was 594.39 nm. When the pump laser energy was below the threshold, the spectrum was actually the fluorescence, which increases slowly with the pump energy. Moreover, the fluorescence efficiency of the gain media was very low. When the pump laser energy was higher than the laser threshold, the laser intensity will increase with the pump energy with a higher slope efficiency. On the curve in Figure 8b, there is a sudden change point (laser threshold) between the fluorescence and laser as the pump energy increases. The corresponding laser threshold curve shows that the laser threshold was 83.88 μJ/mm2, as shown in Figure 8b. Selective breaking of PT symmetry can systematically improve the effective amplification of single-mode operation [23].

**Figure 8.** (**a**) Single-frequency emissions of the coupled microdisks under different pump energies. Insert: the energy of the pump laser. (**b**) Lasing intensity as a function of the pump energy intensity extracted from (**a**). Lasing threshold is approximately 0.60 μW (84.88 μJ/mm2) in a water environment. Insert: the position of the pump laser and the mode field of the single-frequency laser.

An interesting phenomenon was observed when we changed the surrounding refractive index of the single-frequency laser. Another coupled-microdisk resonator was dipped in water under left pumping, with the gap at 0.6 μm. As shown in Figure 9a, the wavelength of the original single-frequency laser was 606.994 nm. With the increase in the liquid refractive index, the wavelength of the single-frequency laser gradually shifted to longer wavelengths, and the intensity decreased. Another hopped laser mode occurred at 603.131 nm. If the liquid refractive index is further increased, the original laser will disappear and only one laser peak can be seen in the spectrum. Figure 9c shows that *ln*(*Ihopped*/*Ioriginal*) changed linearly with the liquid refractive index. Here, *Ioriginal* and *Ihopped* are the light intensity of the original laser line and the hopped laser line, respectively. The hopped laser mode resulted from the slightly asymmetric structure of the coupled microdisks, which responded slightly differently to the change in the surrounding refractive index [30]. Therefore, the wavelength shifts of the coupled-microdisk resonances did not shift synchronously. Furthermore, the slight change of refractive index will also change the coupling efficiency of two coupled microdisks. As shown in Figure 9b,c, the wavelength shift sensitivities (*Soriginal* and *Shopped*) were 14.04 and 14.65 nm/RIU, respectively, and the sensitivity of the intensity change (*SI*) was 149.87 RIU−1. Considering standard deviation (σ = 10 a.u.) of the background signal intensity as the lowest detectable lasing intensity, the detection limit of *SI* was 5.34 × 10−5 RIU, based on the equation in a previous article [30]. The resolution of the monochromator can reach 0.01 nm. The detection limits of *Soriginal* and *Shopped* were 7.12 × 10−4 and 6.83 × 10−4 RIU, respectively. These results indicate that *SI* was 13 times more sensitive compared with *Soriginal* and *Shopped*. Because of the Vernier effect, the coupling of the WGMs in the two resonators can produce a large amplification sensitivity. It was noted that the attenuation of light intensity was due to the bleaching of dye, caused by long-time laser pumping. The relative intensities of the original and hopped laser peaks were not affected.

**Figure 9.** (**a**) Single-frequency emissions of the coupled-microdisk resonator laser. (**b**) Wavelength shifts of single-frequency lasers as a function of refractive index. (**c**) Intensity ratio [*ln*(*Ihopped*/*Ioriginal*)] of the two lasing modes, as a function of refractive index. Insert: spectra at the two refractive indices values are given.

#### **4. Conclusions**

In this study, the spectral characteristics of coupled microdisks in aqueous media were examined. The spectral characteristics and modulation mechanism of mode splitting and single-frequency lasers from coupled microdisks were investigated. The resonance detuning of mode splitting was studied by changing the gap between two microdisks, the refractive index of the aqueous media, and the position of the pump laser, namely, selective pumping schemes. The variation of the single-frequency laser was studied by changing the intensity of the pump light and the refractive index of the aqueous media. For single-frequency lasers, the sensitivity can be amplified by changing the light intensity for sensing. The results of this study will help to deepen the understanding of the spectral characteristics and the modulation mechanism of microcavity lasers. Such optofluidic microcavity lasers have broad application prospects in tunable single-mode on-chip lasers and biosensors.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2079-4991/9/10/1439/s1, Figure S1. 3-D schematic of the solid-state dye-doped polymer microdisks. Figure S2. 3-D schematic diagram shows the fabrication process of the optofluidic microdisk device.

**Author Contributions:** X.W. originally conceived the idea. Z.G., C.Z. and L.C. fabricated the devices. Z.G., S.L. and J.H. finished the experiment. Z.G., H.W. and X.W. wrote the manuscript. Z.G. and Y.Z. carried out SEM measurements. Z.G. and H.W. carried out the COMSOL Multiphysics. All authors discussed the progress of the research and reviewed the manuscript.

**Funding:** This research was funded by Special Project of National Key Technology R & D Program of the Ministry of Science and Technology of China, grant number 2016YFC0201401; Shanghai Science and Technology Committee Grant, grant number 18JC1411500; National Natural Science Foundation of China (NSFC), grant number 61805112; National Key Basic Research Program of China (Program 973), grant number 2015CB352006; Natural Science Foundation of Jiangsu Province, grant number BK20181003.

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

#### **References**

© 2019 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 (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Guided Mode Resonance Sensors with Optimized Figure of Merit**

#### **Yi Zhou, Bowen Wang, Zhihe Guo and Xiang Wu \***

Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Department of Optical Science and Engineering, Shanghai Engineering Research Center of Ultra Precision Optical Manufacturing, Fudan University, Shanghai 200433, China<EMAIL_ADDRESS>(Y.Z<EMAIL_ADDRESS>(B.W<EMAIL_ADDRESS>(Z.G.)

**\*** Correspondence<EMAIL_ADDRESS>
Received: 6 May 2019; Accepted: 22 May 2019; Published: 1 June 2019

**Abstract:** The guided mode resonance (GMR) effect is widely used in biosensing due to its advantages of narrow linewidth and high efficiency. However, the optimization of a figure of merit (FOM) has not been considered for most GMR sensors. Aimed at obtaining a higher FOM of GMR sensors, we proposed an effective design method for the optimization of FOM. Combining the analytical model and numerical simulations, the FOM of "grating–waveguide" GMR sensors for the wavelength and angular shift detection schemes were investigated systematically. In contrast with previously reported values, higher FOM values were obtained using this method. For the "waveguide–grating" GMR sensors, a linear relationship between the grating period and groove depth was obtained, which leads to excellent FOM values for both the angular and wavelength resonance. Such higher performance GMR sensors will pave the way to lower detection limits in biosensing.

**Keywords:** guided mode resonance; figure of merit; biosensor; detection limits

#### **1. Introduction**

Guided mode resonance (GMR) is a physical effect that occurs in thin-film structures that contain diffractive elements and a waveguide layer ("grating–waveguide" GMR structure) [1] or a planar dielectric-layer diffraction grating ("waveguide–grating" GMR structure) [2]. Light can be coupled into the waveguide modes by different grating diffraction orders. Due to periodic modulation in the waveguide, part of the guided light will leak, and thus, guided modes cannot be sustained on the waveguide grating and will interfere with the noncoupled reflected or transmitted waves [3]. The GMR effect occurs within a narrow spectral band at a particular wavelength, angle, and polarization [4].

Since Magnusson and Wang suggested the application of the GMR effect for sensing purposes due to its narrow, controllable linewidth and high efficiency [5], many researchers have shown great interest in GMR sensors, especially in biosensing [6–13]. To date, there are four main detection schemes for GMR sensors, including wavelength detection [14–17], angular shift detection [18–20], intensity shift detection [21–25], and phase shift detection [26–29]. The wavelength and angular shift detection schemes are used most often as the incident light is totally reflected with highly angular and spectral selectivity at resonance [30]. To reduce the cost of detection systems, for example, by eliminating the need for an expensive spectrometer and laser source, several intensity detection schemes have been proposed [21–24]. In addition, the sensing performance can also be enhanced by implementing phase detection schemes [26–29].

Although different detection methods result in different detection effects, the structural parameters and optical properties of GMR sensors are also important because these factors directly determine the sensors' performance [31–36]. In a label-free biosensing system, a figure of merit (FOM), which combines the sensitivity (S) and the full width at half maximum (FWHM) of the resonance, is the accepted marker to compare the performance of biosensors, which can be defined as FOM = S/FWHM [37]. This value can simultaneously reflect the effects of the magnitude of a measured quantity change and the ability to measure small wavelength shifts [38]. In addition, a FOM can be considered as a good indicator for the expected performance of a sensor [39]. However, a narrow resonant linewidth will result in a sacrifice in the sensitivity, as resonant modes are mostly confined within the solid dielectric medium, rather than the sensing medium [40]. In contrast, highly resonant sensitivity may result in a broadened resonant linewidth, which limits the capability to measure small resonant wavelength shifts with higher accuracy [37]. To solve this problem, Ge et al. proposed an external cavity laser (ECL) GMR sensor using an active resonator laser that maintains the high resolution of laser biosensors without sacrificing sensitivity [41–43]. However, although the properties of sensitivity and linewidth have been investigated widely by varying structural parameters [31–36], the optimization of a FOM has not been considered for most GMR sensors. Most recently, Lan et al. investigated the FOM of a "waveguide-grating" GMR sensor by varying the geometric parameters and incident angle [44]. However, their work only investigated one GMR sensor for wavelength resonance rather than providing a design guideline that is suitable for all GMR sensors. Therefore, a convenient and effective design method to achieve an optimized FOM of GMR sensors for both angular and wavelength resonance is necessary.

In this work, by combining an analytical model and numerical simulation, we provide a convenient and efficient method as a guideline for parametric design to achieve the optimized FOM of "grating–waveguide" GMR sensors for both angular and wavelength resonance. Focusing on "waveguide–grating" GMR sensors, a linear relationship between the grating period and grating groove depth was found as a guideline to achieve optimized FOM.

#### **2. Analytical Model for GMR Sensors**

Lin et al. proposed a model for calculating the wavelength sensitivity of GMR sensors [35]. Briefly, as the incident light λ passes through the grating with an incident angle θ*i*, the diffraction grating equation can be expressed as follows [17]:

$$
\Lambda \left[ n\_{w\mathcal{g}} \sin(\theta\_d) - n\_c \sin(\theta\_i) \right] = m\_{\mathcal{g}} \lambda\_\prime m\_{\mathcal{g}} = 0, \pm 1, \pm 2, \dots, \tag{1}
$$

where Λ is the grating period, *nwg* is the refractive index of the waveguide layer, *nc* is the refractive index of the surrounding medium, θ*d* is the diffraction angle and *mg* is the order of the diffracted wave. The grating diffracted wave will couple into the waveguide layer, once the diffracted wave is phase-matched to the waveguide mode, and the diffraction angle θ*d* is the propagation angle in the waveguide layer because the grating groove depth (*dg*) is assumed to be extremely thin, and thus, other influences are ignored. The guided wave condition of the planar waveguide can be defined as follows:

*k*0*nwgdwg* cos(θ*d*) − *m*π = φ*t* + φ*d*, *m* = 0, 1, 2, ... , (2)

where *k*0 = 2π/λ is the wavenumber in a vacuum, *dwg* is the thickness of the waveguide layer, *m* is a positive integer number that stands for the mode number of a waveguide, ϕ*t* and ϕ*d* represent phase shifts that occur due to the total internal Fresnel reflection at the waveguide grating interface and the waveguide substrate interface, respectively. For a given waveguide structure, we can use Equation (2) to calculate the θ*d*, and thus the incident angle θ*i* in Equation (1) will be obtained. When the surrounding refractive index *nc* is changed, the different incident angles can be solved using Equations (1) and (2), and thus the angular sensitivity *Sa* = Δθ*i*/Δ*nc* can be solved, where Δθ*i* is the shift in the resonant angle induced by a change in the refractive index of the surrounding medium Δ*nc*.

As Equation (2) only stands for a single wavelength, it needs to be modified as follows to be suitable for multiple wavelengths (suitable for normal incidence only) [35]:

$$\frac{2\pi}{\Lambda}m\_{\&}d\_{\&\|}\cot(\theta\_d) - m\pi = \phi\_l + \phi\_{d\!\!/}m = 0, 1, 2, \dots, \tag{3}$$

Using Equations (1) and (3), the wavelength sensitivity *Sw* = Δλ/Δ*nc* can be solved, where Δλ is the shift in the resonant wavelength induced by a change in the refractive index of the surrounding medium Δ*nc*.

#### **3. Simulation Results and Analysis**

The RSoft 7.1 (RSoft Design Group, Inc., Ossining, NY, USA) based on rigorous coupled-wave analysis (RCWA) was used to simulate the GMR effect [36]. To calculate the field distributions, we used COMSOL Multiphysics 5.2a (COMSOL Inc., Stockholm, Sweden), which is based on the finite element (FEA) analysis method [45]. In our case, we simulated the GMR sensors made of a high-index material, such as silicon nitride (Si3N4, *ng* = *nwg* = 2.00) immersed in water (*nc* = 1.333) and with silicon dioxide (SiO2, *ns* = 1.45) as a substrate. The filling factor (FF) of the grating is fixed at 0.5 and the total thickness of the grating and waveguide layer *d* was also kept constant.

#### *3.1. Angular Shift Detection Scheme for "Grating–Waveguide" GMR Sensors*

For an angular interrogation technique, a monochromatic light source, such as a He–Ne laser, is typically used to measure the GMR effect in this case. The incident wavelength λ is set at 633 nm, and Λ is set at 280 nm. The total thickness of the grating and waveguide layer *d* is fixed at 100 nm. *dg* and *dwg* are the thicknesses of the grating and waveguide layer, respectively.

The schematic geometries of the angular GMR sensors are depicted in Figure 1a. The incident light can excite transverse electric (TE) or transverse magnetic (TM) modes, depending on the electric field *Ez* or magnetic field *Hz* perpendicular to the plane of incidence (*x*–*y* plane). When *nc* varies, the resonant angle θ*i* will change according to Equation (1). The angular position of the resonant peak will shift as illustrated in Figure 1b. Figure 1c shows the sensitivity and FWHM versus *dg* for TE polarization. *Sa* increases and the resonant linewidth broadens as *dg* increases for TE polarization. Consequently, the angular FOM cannot achieve a higher value with higher sensitivity, as shown in Figure 1d. However, *Sa* increases and the resonant linewidth decreases as *dg* decreases for TM polarization when *dg* is below 60 nm, as shown in Figure 1e. Figure 1f shows that, for TM polarization, the angular FOM increases as the *dg* decreases. A maximum FOM of 5709 was achieved when *dg* was 10 nm and *dwg* was 90 nm, which is higher than previously reported values [18]. The higher FOM not only arises from a lower *dg* resulting in a lower resonance linewidth, but also generates a higher sensitivity. The maximum FOM is 16.3 times higher than the minimum FOM of 350, as shown in Figure 1f.

**Figure 1.** (**a**) Schematic structure of the "grating–waveguide" guided mode resonance (GMR) structure for angular resonance. (**b**) An example of reflection spectra for oblique incidence at the resonance of a monochromatic light (*dg* = *dwg* = 50 nm for transverse magnetic (TM) polarization). Calculated sensitivity, resonant linewidth and FOM versus *dg* for transverse electric (TE) polarization (**c**,**d**) and TM polarization (**e**,**f**). Electric field distribution of the angular resonance of the GMR structure with different *dg* values of 50 nm (*dwg* of 50 nm), 10 nm (*dwg* of 90 nm) and for TE (**g**,**h**) and TM (**i**,**j**). (*d* is 100 nm, Λ is 280 nm, and the filling factor (FF) is 0.5).

TE and TM polarization have different performances when *d* is fixed at 100 nm. To investigate the different performances between TE and TM polarization, the COMSOL Multiphysics 5.2a (COMSOL Inc., Stockholm, Sweden) software was used to calculate the field distributions of resonant positions. Figure 1g,h, respectively, show the electric field distributions of TE polarization when *dg* is 50 nm and 10 nm. The electric fields are mainly stored in the waveguide layer. Therefore, a thick waveguide layer confines more electric energy, which results in a narrower resonant linewidth but reduces the sensitivity. Therefore, the value is mainly attributed to a narrow linewidth of 0.016 degrees at the cost of sensitivity, although a higher FOM of 881 was obtained for TE polarization. For the TM case, most electric energy is not confined in the waveguide layer and is distributed in the cover medium and substrate, as shown in Figure 1i,j. In the case where *dg* = 50 nm, up to 70.65% of the total resonance energy is distributed in the substrate, which is 82.56% of the total evanescent energy, and only 19.55% of the total resonance energy is distributed in the cover medium, which is 17.44% of the total evanescent energy. In the *dg* = 10 nm case, 62% and 25% of the total resonance energy is distributed in the substrate and cover medium, respectively, which respectively contain 69.72% and 30.38% of the total evanescent energy. Therefore, the evanescent energy increases by almost 13%, which leads to a higher angular sensitivity. Meanwhile, an obvious increase in the maximum electric intensity from 9.27 × 105 V/m (*dg* = 50 nm) to 4.44 × 106 V/m (*dg* = 10 nm) is observed for TM polarization, as shown in Figure 1i,j. This indicates that more energy was confined in the structure, thus decreasing the resonant linewidth. This result can also be proven by referencing [46], because the grating groove depth controls the coupling-loss coefficient in an exponential manner, thus the coupling-loss coefficient tends to be smaller as *dg* decreases. Therefore, when *d* is fixed at 100 nm for TM polarization, a shallow *dg* facilitates a narrow linewidth, and a relatively thick *dwg* (near 90 nm) also results in a higher sensitivity. A much higher FOM will be obtained thanks to the higher sensitivity and narrower linewidth.

To explain this phenomenon, we used the previous angular model to calculate *Sa*. The red curve in Figure 2a depicts the *Sa* of TE polarization, and a higher sensitivity region is located near *dwg* = 50 nm. The curved sensitivity line of TM polarization has the largest sensitivity region near *dwg* = 100 nm, as shown in Figure 2b. The highest sensitivity is 25.9 degrees/RIU (refractive index unit), which is very close to the highest sensitivity value in Figure 1f for TM polarization. Moreover, this largest sensitivity region *dwg* = 100 nm is the same as the value of the total depth of the grating and waveguide layer *d* that we set in Section 3.1. Combined with these results, the extremely high FOM accompanied by a high sensitivity and narrow linewidth shown in Figure 1f can be explained as follows: a shallower *dg* facilitates a narrower linewidth and a thicker *dwg*, approaching the highest sensitivity region (100 nm) and resulting in higher sensitivity.

**Figure 2.** The red curved line represents the analytical model of the *Sa* calculation for the transverse electric (TE) (**a**) and transverse magnetic (TM) (**b**) modes. Blue, green, and magenta marked symbols respectively represent calculation results of 10 nm, 25 nm and 50 nm *dg* of the rigorous coupled-wave analysis (RCWA) simulation method.

To further verify the analytical result, an RCWA method was used to compare the results. In Figure 2, blue, green, and magenta marked symbols represent the numerical results for cases with a *dg* of 10 nm, 25 nm, and 50 nm, respectively. The results display evident differences when *dg* is relatively high because the influence of the grating on both the phase shift and total internal reflection cannot be ignored. However, this model is still useful for calculating the angular sensitivity when the grating depth is small.

For optimizing the FOM of "grating–waveguide" GMR sensors, a high value region of sensitivity should be evaluated first and then *d* should be maintained near this value. Finally, by fabricating a shallower grating depth, higher sensitivity and narrower linewidth will be achieved, resulting in a higher FOM. This is a design guideline for "grating–waveguide" GMR sensors to achieve optimized FOM.

However, the TE polarization has its highest sensitivity region near *dwg* = 50 nm, as shown in Figure 2a. Based on the previous deduction, we set *d* = 50 nm and simultaneously varied *dg* and *dwg* (more details are shown in Table 1). A maximum FOM (with a narrower linewidth and higher sensitivity) of 1158 was achieved when *dg* = 10 nm and *dwg* = 40 nm. The missing values in Table 1 indicate the instances when the phase-matched condition was not satisfied [17,35].

**Table 1.** Linewidth (FWHM), sensitivity (S) and figure of merit (FOM) of angular resonance for *d* = 50 nm in transverse electric (TE) mode.

#### *3.2. Wavelength Shift Detection Scheme for "Grating–Waveguide" GMR Sensors*

The most common detection technique for GMR sensors is the wavelength shift-tracking method. A broadband light source is used, such as an LED light and white light source. To investigate the wavelength detection scheme, a normal incidence light was used and Λ was set at 410 nm. Similarly, we set *d* at 100 nm and *dg* and *dwg* were simultaneously varied. The schematic geometry of the GMR sensors is depicted in Figure 3a. When *nc* is varied, the resonant wavelength λ changes according to Equation (1). Thus, the resonant peak position of the wavelength will shift, as illustrated in Figure 3b.

Figure 3c,d demonstrates the relationship among resonant linewidth, sensitivity, and FOM for TE polarization. As *dg* decreases, a narrow linewidth and low *Sw* is obtained, and thus the FOM cannot achieve a relatively high value combined with high sensitivity. On the other hand, for TM polarization, *Sw* increases and the resonant linewidth decreases when *dg* decreases (*dwg* increases), as shown in Figure 3e. A maximum FOM of 2154 was achieved when the *dg* was 10 nm (*dwg* was 90 nm), as shown in Figure 3f, which is higher than those of common "grating–waveguide" GMR sensors [39].

**Figure 3.** (**a**) Schematic representation of the "grating–waveguide" structure for wavelength resonance. (**b**) An example of reflection spectra for normal incidence at the resonance of a broadband light (*dg* = *dwg* = 50 nm for transverse magnetic (TM) polarization). Calculated sensitivity, resonant linewidth and figure of merit (FOM) versus dg for transverse electric (TE) polarization (**c**,**d**) and TM polarization (**e**,**f**). Electric field distribution of the wavelength resonance of the guided mode resonance (GMR) structure with different *dg* of 50 nm (*dwg* of 50 nm), 10 nm (*dwg* of 90 nm) and for TE (**g**,**h**) and TM (**i**,**j**), for which the resonance wavelengths are 628.91, 651.51, 601.76 and 611.26 nm, respectively. *d* is set at 100 nm, Λ is 410 nm, and filling factor (FF) is 0.5.

The electric field distributions for both TE and TM polarization were simulated to further explain the previous results and are shown in Figure 3g–j. Compared to Figure 1g–j, similar results can be achieved here. For the TE mode, most of the evanescent field energy exists in the waveguide layer, and thus the sensing performances were affected. TM cases have a larger light-matter interaction region in the cover medium, and more light is strongly confined (the maximum electric intensity up to 3.61 × 106 V/m), making it more suitable to achieve better performances in biosensing. The sensitivity curve of the TM polarization has the largest sensitivity region near *dwg* = 100 nm, which is the same as the value of *d* that we set here. On the other side, the TE polarization has the largest sensitivity region near the 50 nm of *dwg*, and *d* = 50 nm is maintained. Table 2 shows the difference in performance caused by varying *dg* and *dwg*. As shown in Table 2, a higher FOM is obtained with a narrower linewidth and higher sensitivity.

**Table 2.** Linewidth (FWHM), sensitivity (S) and figure of merit (FOM) of wavelength resonance for *d* = 50 nm in transverse electric (TE) mode.

Combining these results with those of Section 3.1, TM polarization has better results for both angular and wavelength resonance, although different detection methods were used. This phenomenon can be explained in two respects: first, TM polarized modes have a larger phase shift length at the resonance point compared to TE modes, resulting in higher sensitivity, as shown in Figure 4. The red and blue curves represent the TM polarization phase shift in the waveguide layer at different surrounding *nc*. Yellow and green curves represent the TE polarization phase shift at different surrounding *nc*. The label *dwg* = 60 nm (purple curve) and *dwg* = 90 nm (gray curve) represent the calculated results coming from the left side of Equations (2) and (3) (called structure relation [35]). The intersection points of the structure relation curve and phase shift curve represent the points of resonant condition, where the GMR effect occurs. The length between two intersection points is proportional to resonant angle or wavelength shift. Therefore, a larger phase change length at different *nc*, results in greater sensitivity. In Figure 4, the TM polarization has a larger phase change length compared to the TE mode, when the *dwg* was 90 nm. Second, the coupling-loss coefficient for a TM polarization was smaller than that for the TE polarization, resulting in a narrow linewidth [46]. Furthermore, the phase shift length of *dwg* = 90 nm (purple curve) exceeds that of the *dwg* = 60 nm (gray curve) condition for TM polarization. This also explains why a higher sensitivity was obtained for the case where *dwg* = 90 nm, as shown in Figures 1f and 3f.

**Figure 4.** Phase shift curve in waveguide layer at different propagation angle, (**a**) angular resonance, (**b**) wavelength resonance.

#### *3.3. Optimized FOM for "Waveguide–Grating" GMR Sensors*

The schematic geometries of angular and wavelength resonance of the "waveguide–grating" GMR sensors are depicted in Figure 5a,b, respectively. Aimed at "waveguide–grating" GMR sensors, different *dg* values were swept by a "MOST Optimize/Scanner" (DiffractMod, RSoft 7.1, RSoft Design Group, Inc., Ossining, NY, USA) under certain Λ values to investigate whether a minimum resonant linewidth and a higher sensitivity exist for both the TE and TM modes. The chosen parameters are similar to those presented in Section 3.1 for the angular shift and Section 3.2 for the wavelength shift detection schemes, except *d* (*dg* and *dwg*).

For angular resonance, a better result was obtained under TM polarization; the series of results for different *dg* (from 150 nm to 400 nm) are shown in Figure 5c,d. Figure 5c shows the resonant linewidth and *Sa* versus *dg* for TM polarization. A minimum resonant linewidth and a higher sensitivity occur for a value of *dg* of 300 nm. A higher FOM, almost up to 106, was achieved, as shown in Figure 5d, which is 168 times greater than the highest FOM value presented in Figure 1f. For wavelength resonance, a superior result was obtained under TE polarization, and the series of results for different *dg* values (from 100 nm to 500 nm) are shown in Figure 5e,f. Figure 5c shows the resonant linewidth and *Sw* versus *dg* for TE polarization. A minimum resonant linewidth and a higher sensitivity will occur under 380 nm of *dg*. Thus, a high FOM of 1618 will be achieved as shown in Figure 5d. The electric energy distribution helps us to further understand the mechanism, as shown in Figure 5a,b. For both angular and wavelength resonance, the electric field will ascend from the substrate to the grating and the surrounding medium as *dg* increases. Therefore, the total evanescent energy will increase in the surrounding medium, thus increasing the sensitivity. Meanwhile, an obvious increase in the maximum electric intensity from 7.44 × 105 V/m (*dg* = 200 nm) to 3.89 × 107 V/m (*dg* = 300 nm) was observed for angular resonance under TM polarization, as shown in Figure 4g,h. For wavelength resonance, the maximum electric intensity increased from 1.84 × 105 V/m (*dg* = 200 nm) to 2.31 × 106 V/m (*dg* = 380 nm) for TE polarization, as shown in Figure 5i,j. These results indicate that more energy was confined in the GMR structure, and thus, the linewidth was decreased. Combining these two points, a higher FOM value was achieved, accompanied by high sensitivity and a narrow linewidth.

**Figure 5.** Schematic structure of the "waveguide–grating" structure for angular (**a**) and wavelength (**b**) resonance. Calculated sensitivity, resonant linewidth and figure of merit (FOM) versus *dg* for angular resonance under transverse magnetic (TM) polarization (**c**,**d**), and for wavelength resonance under transverse electric (TE) polarization (**e**,**f**). Electric field distribution of the "waveguide–grating" guided mode resonance (GMR) structure of the wavelength resonance with *dg* values of 200 nm and 300 nm for TM (**g**,**h**) and angular resonance with *dg* values of 200 nm, 380 nm for TE (**i**,**j**). Λ is 280 and 410 nm for the angular and wavelength resonance respectively and filling factor (FF) is 0.5.

Different Λ were chosen to determine the *dg* value that lead to a superior FOM. For wavelength resonance, different Λ varying from 330 nm to 550 nm, were chosen to calculate the position at which there is a minimum resonant linewidth and higher sensitivity for TE polarization, as shown in Table 3. The relationship among Λ, *dg*, and the corresponding FOM is depicted in Figure 6a.

**Table 3.** Linewidth (FWHM), sensitivity (S) and figure of merit (FOM) of the wavelength resonance

under different Λ and corresponding *dg* for transverse electric (TE) modes. **Λ (nm)** *dg* **(nm) FWHM (nm)** *S* **(nm**/**RIU) FOM** 330 306.44 0.12 195 1625 410 380.00 0.15 242.75 1618.333 450 417.50 0.16 266.00 1662.500 550 509.74 0.20 325.25 1626.250

**Figure 6.** The best figure of merit (FOM) value for wavelength (**a**) and angular resonance (**b**) under different Λ and corresponding *dg* values. Λ as a function of *dg* for wavelength (**c**) and angular (**d**) resonance.

For angular resonance, different Λ, varying from 260 nm to 320 nm, were chosen to determine the best FOM under TM polarization, as shown in Table 4. The angular sensitivity is inversely proportional to Λ. The relationship between Λ, *dg*, and the corresponding FOM is depicted in a three-dimensional schematic diagram in Figure 6b. All FOM values are higher than those of already reported values [18,39]. Λ as a function of *dg* for the wavelength and angular resonance are respectively shown in Figure 6c,d. The ratio of Λ to *dg* for the wavelength resonance was 0.925. A linear relationship was obtained between Λ and *dg* for the angular resonance, as shown in Figure 6d, and the formula of the best-fit line is *y* = 1097.411 − 2.808*x*. We can apply the linear relationship to design "waveguide–grating" GMR sensors with optimized FOM.

**Table 4.** Linewidth (FWHM), sensitivity (S) and figure of merit (FOM) of the angular resonance under different Λ and corresponding *dg* for transverse magnetic (TM) modes.

The point of these optimized FOM results is that a narrow resonant linewidth occurred abruptly, as shown in Figure 5c,e. Norton et al. investigated linewidth of "waveguide–grating" GMR structure through coupled-mode theory [47]. Briefly, the angular and wavelength linewidth is proportional to the coupling loss coefficient, and this coefficient is determined by the overlap of the bound mode and the radiation mode. At higher grating depths, the orthogonality of the two modes decrease the overall magnitude of the coupling loss, resulting in a narrow resonant linewidth. In our work, similar resonant linewidth phenomenon can be found in Figure 5c,e. Although Norton et al. just investigated one grating period, it can be predicted that different grating periods have their own grating depths, where the narrow resonant linewidth occurs abruptly.

#### **4. Conclusions**

In summary, with the aim of achieving a higher angular and wavelength FOM for GMR sensors, we systematically presented a parametric analysis elucidating the influence of structural design factors on the performance of GMR sensors. Combining an analytical model and numerical algorithm, we determine an effective and convenient method to achieve higher angular and wavelength FOM of "grating–waveguide" GMR sensors. A suitable fixed depth of the grating and waveguide will facilitate a higher FOM. This method is suitable for both angular and wavelength resonance. A linear relationship to design "waveguide–grating" GMR sensors with optimized FOMs was determined using numerical stimulations. These high FOM values can facilitate the performance of GMR sensors to achieve lower detection limits.

**Author Contributions:** Conceptualization, Y.Z. and X.W.; methodology, Y.Z. and X.W.; software, Y.Z., Z.G. and B.W.; validation, X.W., Z.G. and B.W.; writing—original draft preparation, Y.Z.; writing—review and editing, X.W.; funding acquisition, X.W.; All authors discussed the results and commented on the manuscript.

**Funding:** This work was supported by the Special Project of National Key Technology R&D Program of the Ministry of Science and Technology of China (2016YFC0201401), the National Key Basic Research Program of China (973 program-No. 2015CB352006) and the National Natural Science Foundation of China (NSFC) (61378080, 61327008, 61505032, and 61705039).

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

#### **References**

© 2019 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 (http://creativecommons.org/licenses/by/4.0/).

## *Article* **High-Performance Ultraviolet Light Detection Using Nano-Scale-Fin Isolation AlGaN/GaN Heterostructures with ZnO Nanorods**

#### **Fasihullah Khan, Waqar Khan and Sam-Dong Kim \***

Division of Electronics and Electrical Engineering, Dongguk University, Seoul 100-715, Korea<EMAIL_ADDRESS>(F.K<EMAIL_ADDRESS>(W.K.) **\*** Correspondence<EMAIL_ADDRESS>Tel.: +822-2260-3800

Received: 24 February 2019; Accepted: 8 March 2019; Published: 15 March 2019

**Abstract:** Owing to their intrinsic wide bandgap properties ZnO and GaN materials are widely used for fabricating passive-type visible-blind ultraviolet (UV) photodetectors (PDs). However, most of these PDs have a very low spectral responsivity *R*, which is not sufficient for detecting very low-level UV signals. We demonstrate an active type UV PD with a ZnO nanorod (NR) structure for the floating gate of AlGaN/GaN high electron mobility transistor (HEMT), where the AlGaN/GaN epitaxial layers are isolated by the nano-scale fins (NFIs) of two different fin widths (70 and 80 nm). In the dark condition, oxygen adsorbed at the surface of the ZnO NRs generates negative gate potential. Upon UV light illumination, the negative charge on the ZnO NRs is reduced due to desorption of oxygen, and this reversible process controls the source-drain carrier transport property of HEMT based PDs. The NFI PDs of a 70 nm fin width show the highest *R* of a ~3.2 × 107 A/W at 340 nm wavelength among the solid-state UV PDs reported to date. We also compare the performances of NFI PDs with those of conventional mesa isolation (MI, 40 × 100 μm2). NFI devices show ~100 times enhanced *R* and on-off current ratio than those of MI devices. Due to the volume effect of the small active region, a much faster response speed (rise-up and fall-off times of 0.21 and 1.05 s) is also obtained from the NFI PDs with a 70 nm fin width upon the UV on-off transient.

**Keywords:** high-responsivity; ultraviolet photodetectors; nano-scale fin isolation; wide-band gap semiconductors; ZnO nanorods; two-dimensional electron gas; visible-blind

#### **1. Introduction**

Ultraviolet (UV) light detection with high responsivity is of great interest, due to its promising applications in pathology [1], water treatment, safety, and defense-technologies [2]. In most commercialized systems, UV detection has been realized by photomultiplier tubes (PMTs), thermal detectors, Si or Ge based photodetectors (PDs), and charge-coupled devices (CCDs). However, these detection methods pose various problems for practical applications. For example, PMTs exhibit fragile vacuum-tube construction and require a high-voltage bias. Moreover, PMTs are sensitive to the magnetic-field; therefore, they need to be shielded from ambient light. Si based PDs or CCDs are one of the most commonly used solutions, due to their highly matured process technology [3]. Recently, n-Si/p+-B photodiodes of a very high sensitivity and stability have been demonstrated, but they still exhibit responsivity in the order of ~10−1 A/W [4]. Many attempts have been made to improve the limited responsivity of Si PDs working in linear mode. Among them, avalanche-mode PDs are now very popular, and single-photon avalanche diodes are also used to obtain high-gain responsivity [5]. However, the use of stop-band filters for visible light reduces the quantum efficiency of these devices in the UV range.

In recent years, the nanostructures of wide bandgap (WBG) materials, such as diamond, ZnO, III-nitride, and SiC based UV PDs have attracted tremendous research interest for their many advantages [6]. For instance, they are capable of room temperature (RT) operation and have intrinsic optical transparency (visibly-blindness) in the visible spectral range. Furthermore, they have a low thermal conductivity, high breakdown field, and stability at elevated temperatures. In spite of these promising advantages, the WBG semiconductors have very low electron mobility. Even though noble heterostructures with a very high electron mobility of ~106 cm2/V·s using a material system such as MgZnO/ZnO [7] have been reported, most of the passive PDs fabricated using conventional WBG semiconductors have very low spectral responsivity [8]. Moreover, the response speeds of PDs based on ZnO or GaN are very slow in general because the photoresponse characteristics depend on the well-known bottle-neck chemisorption process of oxygen at the surface of such materials [9].

Zinc oxide (ZnO) nanorod (NR) based UV PDs [10–15] have shown promising results in terms of response speed and spectral responsivity [16]. Significant research effort has been made to improve the performance of the PDs, either by improving the crystalline quality of NRs or by utilizing the composite coaxial structure of ZnO with other materials, such as copper oxide [17] and graphene [18]. However, most of the passive type PDs reported to date exhibit very slow response speed (tens of seconds) and low responsivity (~hundreds of A/W). Recently, an active-type UV PD using the ZnO NR-gated AlGaN/GaN high electron mobility transistor (HEMT) structure has been attempted as a part of an effort to attain a breakthrough in responsivity (~105 A/W) and to obtain a relatively fast response speed [19]. However, due to the very high dark current of the device, the HEMT based PD showed a relatively low on-off current ratio of ~3.

In this study, we demonstrate high-responsivity UV PDs based on the ZnO NR-gated AlGaN/GaN HEMT structure with nano-scale fin isolation (NFI). ZnO NRs act as the floating gate while the UV driven chemisorption process of oxygen at the surface of ZnO NRs [20] controls the conduction of the underlying two-dimensional electron gas (2-DEG) channel. The 2-DEG present at the interface of the AlGaN (barrier) and GaN (channel) layers is due to polarization induced electric potential in the heterostructure [21]. In the NFI PD structure, ZnO NRs surround the channel in the gate area. Consequently, the carriers in the 2-DEG channel are confined along the channel and in perpendicular direction to the interface. Therefore, under dark conditions, the 2-DEG channel is fully depleted due to negative surface potential generated via oxygen adsorption at the surface of ZnO NRs [9]. This structure resembles enhancement-mode (normally-off) AlGaN/GaN fin-shaped field-effect transistors (FINFETs) [22], demonstrating extremely broad transconductance and excellent off-state characteristics. In this study, the performance of the NFI PDs is compared to conventional mesa isolation (MI) AlGaN/GaN HEMT based PD of ~100 × 40 μm2 active area. We examine various photoresponse characteristics of NFI and MI devices and investigate how structural differences influence their performance.

#### **2. Device Fabrication and Characterization**

Figure 1 shows schematic illustrations of two different HEMT based PD structures examined in this study. The interface of the GaN (channel) and AlGaN (barrier) layers have a confinement of 2-DEG, which acts as channel of very high electron concentration and mobility.

Figure 2 illustrates the essential process steps for our gateless NFI and MI HEMT photodetectors (PDs). The epitaxial layers of AlGaN/GaN were deposited on a 6 inch Si (111) by a metal-organic chemical vapor deposition system at NTT-AT (NTT-Advanced Technology Corporation, Kanagawa, Japan). As shown in the schematics, the undoped GaN buffers and channel layers of 3000–4000 nm thickness were grown first, followed by subsequent growths of the barrier layer of ~20 nm Al0.25GaN0.75 and the GaN cap layer of ~1.2 nm. The measured electron sheet carrier concentration and Hall mobility of the epitaxial layer were ~5 × 1012/cm2 and ~1750 cm2/V·s, respectively. The active area (100 × 40 μm2) for the gateless HEMT was defined by a mesa etching of 100 nm depth in the case of conventional MI structures, as shown in Figure 1. The NFI structure, on the other hand, was fabricated

with 10 nano-fin-shaped isolations (10 gate fingers) with the same mesa depth of 100 nm and two different fin widths (*Wfin*) of 70 and 80 nm. By opening the 100 nm Si3N4 passivation layers deposited on the active region by plasma-enhanced chemical vapor deposition (PECVD), the gate area of a 2 μm gate length was defined. The ZnO NRs were then selectively grown as an active element for the UV light detection.

**Figure 1.** Schematics of the NFI (nanoscale fin isolation) and MI (mesa isolation) structures for the AlGaN/GaN HEMT (high electron mobility transistor)-based UV photodetectors.

**Figure 2.** Schematic illustration of the major process steps used for the fabrication of the NFI and MI devices.

The epitaxial layers were cleaned and agitated with acetone and ethanol in bath sonication to remove dust and surface contamination, followed by rinsing in deionized (DI) water, then drying with nitrogen (N2) gas. Optical lithography (Karl Suss, Garching, Germany, MA6 mask aligner, 365 nm) was used to define the active MI regions, including all the device patterns used in this experiment. However, patterning for the NFIs was performed by an electron beam lithography tool (Jeol, Tokyo,

Japan, JBX-9300FS, 100 keV) with a 70 nm PECVD SiO2 hard mask to avoid the mask pattern erosion during the mesa etching. After the pattern development of the active regions, mesa etching was performed by removing 100 nm of thickness from the peripheral areas in a reactive ion etching system (RIE, STS Multiplex ICP) using BCl3 and Cl2 gases. Ohmic contacts were achieved by depositing the metal stack of Ti/Ni/Au (20/30/80 nm), by using an electron beam evaporation system, and a pattern lift-off method, using image reversal photoresist. Ohmic metals were then subjected to a subsequent rapid thermal alloy process at 900 ◦C for 35 s in N2. The samples were then passivated by a 100 nm silicon nitride (Si3N4) layer deposited in a PECVD system at 200 ◦C and RF power of 1 kW using a NH3/SiH4 gas flow rate ratio of 1.5. The gate areas (2 × 100 μm) of two different structures were opened by etching the Si3N4 passivation using RIE in CF4 plasma at a gas flow rate of 110 sccm and a chamber pressure of 40 mTorr (at an etching rate of ~9.4 nm/min) under the RF power of 100 W.

ZnO NRs were then grown in the gate area by using the hydrothermal synthesis method. Prior to the growth of NRs, a 20 nm thick seed layer (SL) (as shown in the top-right inset of Figure 3c) was deposited by spin coating the seed solution (3000 rpm and prebaking at 120 ◦C for 60 s) repeatedly 15 times. After that, the crystalline quality of the SL was improved by annealing the samples at ~350 ◦C on a hotplate for 1 h. The seed solution used in this study was prepared by dispersing 0.66 g of zinc acetate-dehydrate (C4H6O4Zn·2H2O) salt in 30 mL of 1-propanol (CH3CH2CH2OH). In this work, a 20 mM zinc-acetate-dehydrate concentration for seed solution was selected for the desired SL film quality, assuring the ZnO NR crystalline characteristics to be used for this PD application [23]. Various attempts, such as vacuum annealing and O2 plasma post-treatment methods [10,24] to improve the SL film quality, which is the key to the high-quality NR crystallites, are also underway in our laboratory. The growth of ZnO NRs was limited to the gate area, which was done by etching the SL from all other areas except the gate region. The samples were then placed in a growth solution for 6 h on a hotplate at ~90 ◦C to grow ZnO NRs. The growth solution was prepared by mixing 0.25 mole equimolar concentration of zinc-nitrate-hexahydrate (Zn(NO3)2·6H2O, 99%) and hexamethylenetetramine (HMTA) (C6H12N4, 99.5%) in deionized (DI) water. After growth of the the NRs, the samples were carefully cleaned with acetone, ethanol, and DI water, sequentially.

Sloped etching profiles for the NFI structure, the growth morphology of NRs, and the processed device structures were examined by plane-view scanning electron microscopy (SEM, 10 kV S-4800S-Hitachi, Tokyo, Japan). As shown in the top-right inset of Figure 3a, the measured bottom dimensions of the trapezoidal fins were 170 nm after RIE for the *Wfin* of 70 nm. The transmission electron microscope (TEM, 9500-Hitachi) was used to characterize the cross-sectional view and crystalline quality of the as-grown NRs. The RT photo-luminescence (PL) emission spectra from the as grown NRs was obtained by using a He-Cd laser illumination source with a 325 nm wavelength. Gate areas opened with a trench-shaped pattern inside the dark-shaded Si3N4 passivation and the NRs grown on them are shown in the plane-view SEM micrographs in Figure 3a,b. An inset (bottom-right) of Figure 3a shows the morphology of the ZnO NRs grown around the underlying nano-fins in the gate area of the NFI structures at a magnification of ×3000. Across the gate region, 10 fingers of NFIs are running in parallel, whereas the NRs are grown all the way vertically along the gate area in the MI structure, as shown in Figure 3b. The SEM image in Figure 3c shows that the NRs exhibit an average diameter of ~85 nm and a length of ~1.4 μm. Figure 3d shows a PL spectrum measured at RT from the as-grown ZnO NRs employed as a light absorbing structure in this work. PL characterization at RT is one of the most efficient tools to evaluate the crystalline quality for the WBG ZnO NRs of a direct band gap property. The spectrum exhibits a strong near band edge emission peak at a wavelength of ~380 nm, which is mainly associated with the band-to-band excitonic recombination of ZnO [25]. The near band edge emission intensity was increased about two times with the increase of the NR aspect ratio (AR, length/diameter) from ~8 to ~16. For this reason, NRs with an AR of ~16 were used in this experiment. Emissions in a visible range (420–650 nm) are due to various form of intrinsic defects, such as oxygen vacancy, zinc vacancy, and hydrogen and oxygen interstitials [10]. Despite the inevitable intrinsic defects and consequent visible emissions, as observed from most of

the nano-crystallites grown through the aqueous solution based growth methods, our PL spectrum reveals fairly good optical properties in our ZnO crystallites compared to those of the NRs grown using similar methods [2,26,27].

**Figure 3.** Plane-view SEM images of (**a**) 70 nm NFI PDs (photodetectors) (×1000) with an enlarged top-view of the NFI (*Wfin* = 70 nm) (top-right inset, ×5000) and ZnO NR (nanorod) profiles (bottom-right inset, ×3000) and (**b**) MI PDs (×500) with enlarged ZnO NRs profile (bottom-right inset, ×3000). (**c**) Cross-sectional SEM image of the as-grown NRs. Cross-sectional TEM image of the NRs and SL (seed layer) (top-right inset). Top-view of the NRs (bottom-right inset). (**d**) RT (room temperature) PL (photo-luminescence) spectrum of the as-grown ZnO NRs.

A wide band (300–700 nm) Xenon (Xe) lamp was employed as a light source to measure the photoresponse characteristics of the fabricated devices under optical intensities ranging from 0.5 to 16.5 μW/cm2 (100–300 W lamp power). The transient characteristic measurements, according to the UV light (370 nm) on-and-off transient, were carried out by a programmable light shutter controlled in our measurement set-up. The transients of the drain current (*Ids*) for the HEMT PDs as a function of time were recorded in a Keithley source measurement unit with a floating gate configuration at a drain voltage (*Vds*) of 4 V. The spectral response of the PDs was measured by a focused illumination of a monochromatic light from a wide band (300–1100 nm) Xe-lamp (Ushio UXL-75XE, Ushio Inc., Tokyo, Japan) light source of a 16.5 μW incident optical power. In this measurement set-up, the responsivity was measured at a light chopping frequency of 30 Hz using a lock-in amplifier in a series configuration with drain-source probes for the detection of an amplified change in current. The change of *Ids* as a function of incident light wavelength varying from 300 to 800 nm was recorded under a floating gate configuration at a *Vds* of 4 V. To obtain a monochromatic light from the Xe-lamp, a spectral optics monochromator (CM110 1/8 m) with 2400 lines/mm grating was used.

#### **3. Sensing Mechanism**

As illustrated in the schematics of Figure 4, the UV sensing mechanism of the HEMT based PDs depends on the chemisorption of oxygen at the surface of NRs and the consequent change in carrier concentration in underlying 2-DEG. The as-grown crystalline ZnO-NRs are n-type in nature due to a large number of donor defects, such as hydrogen interstitial and Zn interstitial [28]. Under dark conditions (no UV light illumination), oxygen molecules (O2) transported from the ambient air to the ZnO NR surface tend to trap electrons from the conduction band of ZnO and leave behind positively charged ionized donors in the surface space charge region, while the negatively charged O2 molecules are fixed to the surface of NRs as adsorbed oxygen ions (O− 2ads ):

$$\text{O}\_2 + \text{e}^- \rightarrow \text{O}\_{2\_{\text{ads}}}^-. \tag{1}$$

This reaction leads to the expansion of the space charge region near the surface of the NRs due to the depletion of the surface electron states by O− 2ads , as depicted in the left of Figure 4a. As a consequence, the adsorption process gives rise to a negative potential at the gate of our HEMT based PDs (as shown in the left of Figure 4b,c), thereby dropping the carrier concentration in the 2-DEG channel at the interface of AlGaN/GaN. This process will eventually reduce the conductance of channel and drain-to-source current (*Ids*) in dark conditions. The Schottky gate (Ni/Au) HEMTs (2 μm gate length, 100 μm gate width) fabricated in our group using the same epitaxial structure and Si3N4 passivation showed a threshold voltage (*VTH*) of ~−3V[29]. This result demonstrates that our HEMT devices with an Au/Ni gate electrode are normally on at zero gate voltage *Vgs* (depletion-mode). We suppose that the *VTH* of the HEMTs is given by [30]

$$
\left(\oslash\!\_{\text{b}} - \Delta E\_{\text{c}} - \left(\ulcorner \text{en}\_{\text{s}} \text{d}^{2}\right) / \text{2}\varepsilon\right) / \text{2}\varepsilon \tag{2}
$$

where ∅*b* is the Schottky barrier height, Δ*Ec* is the conduction band offset, *e* is the electron charge, *ns* is the 2-DEG sheet carrier density, *d* is the barrier layer thickness, and *ε* is the dielectric constant. Because the difference between the estimated ∅*b* of Ni at the interface with GaN (~1.1 eV) [31] and the GaN surface band bending (~1.0 eV) [32] in ambient air (fully saturated by O− 2ads in the dark state) is quite small, it can be reasonably assumed that a significant amount of dark current (*Idark*) through the 2-DEG channel is unavoidable from our gateless MI HEMT devices under a floating gate condition due to their normally-on characteristics as shown in Figure 4c.

On the other hand, a different mode of operation is expected for the NFI structure because the 2-DEG channel region inside the nano-fins is three-dimensionally surrounded by a free surface, whereon the ZnO NRs are grown with many O− 2ads around the surface in dark conditions, as shown in Figure 4b. This makes the NFI PDs operate more closely to a normally-off mode (enhancement mode), thereby exhibiting a much lower *Idark*, because the carriers in the 2-DEG region can be highly depleted, even under the floating gate conditions, due to the surface depletion of the NRs by the O− 2ads surrounding the extremely small volume of the active region. The same phenomenon was also observed in the AlGaN/GaN heterojunction FinFETs [33]. With the decrease of *Wfin* from 200 to 60 nm, it was observed from the HEMT devices that electron density in the 2-DEG channel at zero *Vgs* rapidly drops with a positive shift in *VTH* because of the fringing-field from the side gates depleting the 2-DEG channel. As a result, the fin-HEMT showed a change in the conduction mechanism from normally-on to normally-off modes.

Due to light absorption, UV light illumination generates electron-hole pairs near the surface of the ZnO NRs [34]. The generated holes recombine with the electrons trapped by O− 2ads at the surface. In this way, the O2 molecules start to desorb from the surface, as shown in the right of Figure 4a. This phenomenon gives rise to a reduction of negative charge in the gate region, thereby increasing the carrier concentration in the 2-DEG channel and the drain to the source current (*Iphoto*) under UV illumination, as shown in the right parts of Figure 4b,c.

**Figure 4.** Schematic illustrations of (**a**) oxygen adsorption (left: in the dark) and desorption (right: under UV illumination) at the surface of ZnO-NRs. Oxygen adsorption (left: in the dark) and desorption (right: under UV illumination) processes are taking place at the surface of ZnO NRs grown on the gate areas of (**b**) NFI and (**c**) MI PDs. Cross-sectional schematics of each PD structure viewed in y-axis direction are illustrated; 2-Deg (two-dimensional electron gas).

As long as the response speed of PDs is accounted for, it can be assumed that the response kinetics upon the UV light on-and-off transient are not controlled by the drift motion of electrons in the 2-DEG channel but by the adsorption and desorption reaction of O2 on the ZnO NR surface. This result occurs because the mobility of the electrons confined two-dimensionally in the channel region (~1750 cm2 V−1s−1) [33,35] is so fast that the carrier channel transit time cannot be a bottleneck parameter controlling the whole sensor response speed. As proposed in our previous study, the rate of charge change *dQ*/*dt* can be given by [35]:

$$d\mathbf{Q}/dt = -\mathfrak{a}e^{\mathfrak{f}\mathbf{Q}}\tag{3}$$

where *α* and *β* are the constants. By numerically solving Equation (3), it can be determined that one critical parameter affecting the response time is the gate area. From the calculations based on this model, the response (or recovery) time increases with the increase of gate area caused by the consequent increase of the total gate charge. We have much smaller gate capacitance in the NFI PD structure than in the MI structure; therefore, a faster response speed upon UV transient illumination can be expected from the NFI structure.

Spectral responsivity *R*, which can be defined as a ratio of *Iphoto* − *Idark* to the incident optical power *Pi*, is one of the key measures to evaluate the performance of PDs. As reported in our previous studies [19,35], a significant enhancement in *R* was shown from the NR-gated PDs due to a vast surface area of the ZnO nanostructure and a much higher surface-to-volume ratio than that of the planar ZnO thin film gate structure. In our HEMT-based PDs, the *R* can be also significantly influenced by the gain characteristic for the HEMT, which can be expressed by the change of *Iphoto* according to the change of light power irradiating on the gate area.

#### **4. Results and Discussion**

Figure 5a shows the equivalent electrical circuit diagram of both MI and NFI devices, where MI PD is illustrated as a normally-on transistor while the NFI PD is a normally-off transistor. To examine the characteristic difference of UV responses from the two different PD structures, we first measured *Ids* in dark conditions (*Idark*) and under UV illumination (*Iphoto*) at drain voltage (*Vds*), ranging from 0–5 V. UV light exposure was provided from an Xe lamp, operating at 300 W power, with a monochromatic light filter at 370 nm. This UV source produced an incident light intensity of 16 μW/cm2, as measured by a power meter. Figure 5b demonstrates that our MI PD exhibits a high *Idark* of ~10 mA/mm at a *Vds* of 4 V due to the enhancement-mode operation, as discussed in the previous section. In the case of NFI PDs, significantly reduced values of *Idark* (~0.19 and ~0.27 mA/mm for *Wfin* of 70 and 80 nm, respectively) were measured at a *Vds* of 4 V.

**Figure 5.** Photoresponse of MI and NFI PDs. (**a**) Equivalent electrical circuits of MI (left) and NFI devices (right). (**b**) Measured *Ids* versus *Vds* and (**c**) on-off current ratio (*Iphoto/Idark*) of MI and NFI PDs. Time resolved photoresponse characteristics of (**d**) NFI and (**e**) MI PDs (*Vds* = 4 V). (**f**) Magnified views of transient characteristics of NFI (left) and MI (right) PDs.

The performance of PDs can be evaluated by few important parameters, such as spectral responsivity *R*, photoconductive gain *G*, specific detectivity *D*\*, and sensitivity *S* [36]. Despite the high *R* nature of our MI HEMT-based PDs, this high *Idark* of the MI structure can critically deteriorate the photo-sensitivity performance associated with *S,* which is given by (*Iphoto* − *Idark*)/*Idark*), or the on-off current ratio (*Iphoto*/*Idark*), as well as *D*\*. As shown in Figure 5c, much improved on-off current ratios (290~340) were recorded from the NFI PDs compared to those of the MI devices (~4). This result is mainly due to the suppression of *Idark* caused by the fully depleted 2-DEG channel of the NFI devices in dark conditions.

The high-speed transient characteristic of the UV PD is one of the key factors for real-time application. Specific cases, such as the non-invasive assessment of cancer cells by optical biopsy [37], require ultra-fast PDs with response and recovery time in the order of a few milliseconds. To assess the photocurrent transient of the fabricated devices, the change in *Ids* as a function of the on-and-off of the UV light exposure time was measured using a programmable shutter. Figure 5d,e shows that both the NFI and MI PDs produce sharp increases in *Ids* upon UV illumination and a slower fall-off upon termination of UV exposure. The NFI device with a 70 nm *Wfin* showed the fastest rise-up time (or UV response time) and fall-off time (or recovery time) of 0.21 and 1.05 s, respectively. We hereafter define the rise-up and fall-off time as the time intervals for *Ids* to ramp up to 90% of the maximum saturation value after UV turn-on and to ramp down by 90% from the maximum value after UV-off. On the other hand, the MI device showed much slower response and recovery times of ~0.71 s and ~1.84 s, respectively. This significant improvement in response speed of the NFI device is due to the minimized dimension of gate area where the light absorption takes place; therefore, less time is required to complete the O2 adsorption-desorption process in the smaller area of the NFI PDs than in the larger area of the MI device, as discussed in the previous section. The ZnO NR based photoconductive PDs [26,38] still show a long recovery time on a seconds scale, even though a great amount of research effort has been made on enhancing the response speed of these passive PDs. UV PDs based on ZnO nanowire networks with Pt contacts have been fabricated on glass substrates by exhibiting a fast recovery time of 0.2 s with a high photosensitivity (~5 × 103) at 365 nm [39]. The fastest UV PDs of GaN-based metal-semiconductor-metal, p-i-n, or metal Schottky barrier devices [6] have shown extremely high speed (from microseconds to picoseconds) and low-noise capabilities. However, PDs of these GaN-based structures, developed specially to improve the UV response characteristics, exhibit a very low spectral responsivity of less than 1 A/W [8].

Figure 6a shows the schematic illustration of PD before and after the growth of the ZnO NRs. Shown in Figure 6b,c are the measured *Idark* values of the two different device structures before and after NR growths on the gate region. For the MI PDs, the dark currents were significantly reduced by the attachment of NRs on the gate region. However, the *Idark* values measured over the entire drain voltage range were still very high (~10 mA/mm) due to the incomplete depletion of the 2-DEG channel in a large volume of the active region. The measured *Idark* of the NFI PDs before the NR growth were very high, reaching up to ~560 mA/mm, but they rapidly dropped to a very low level of ~hundreds of μA/mm by the attachment of NRs. This result reveals that both the surface depletion effect in the small volume of an active region and the attachment of the NRs with many O− 2ads on their surfaces lead to the formation of a fully-depleted 2-DEG channel in the NFI structure.

**Figure 6.** (**a**) Schematic illustration of NR-gated PD and Gateless PD. Measured *Idark* of MI (**b**) and NFI (**c**) device structure before (gateless) and after NR growths (NR-gated).

The performance of the PDs can be also assessed by spectral responsivity *R* and specific detectivity *D*\*, which are expressed in the following equations [36]:

$$R = \frac{I\_{photo} - I\_{dark}}{P\_l} \tag{4}$$

$$D\* = \sqrt{A} \text{R} / \sqrt{2qI\_{dark}}\tag{5}$$

where *A* is the active area of device, *q* is the electron charge, and *Pi* is the radiant light power incident on the active area of the device. The responsivities of our PDs were measured using an incident light intensity of 16 μW/cm2 with an effective area of 2.4 × 2.4 mm2. NFI PDs showed an extremely high responsivity of ~3.2 × 107 A/W at 340 nm, which is the best performance among any solid-state PDs reported to date [40–44], and even ~100 times higher than that (~2 × 105 A/W at 340 nm) of the MI device, as shown in the right of Figure 7a. This improvement in responsivity of the NFI PD is attributed to a higher photonic transconductance (hereafter, we call it *gm,photo*) characteristic of our HEMT-based PDs, which represents the ratio of the photocurrent change at the drain terminal to the change in incident optical power at the gate terminal. We define the *gm,photo* as following.

$$\mathcal{g}\_{m,photon} = \frac{\Delta I\_{photo}}{\Delta P\_l} (A/W). \tag{6}$$

**Figure 7.** (**a**) Specific detectivity (left) and spectral responsivity (right) as functions of radiant light wavelength measured from NFI and MI UV detectors. (**b**) *Iphoto* versus *Pi* of the NFI (left) and MI (right) PDs measured at *Vds* of 5 V.

To calculate the *gm,photo* values of the two different device structures, the *Iphoto* values were measured at various optical intensities, varying from 0.5 to 16 μW/cm2 at a *Vds* of 5 V. Shown in Figure 7b is the measured *Iphoto* versus *Pi* from the MI and NFI PDs. The estimated *gm,photo* values for the NFI and MI PDs were 3.63 × 108 and 2.58 × 106 A/W, respectively. Even though this *gm,photo* parameter does not directly represent the gain (*gm* = Δ*Ids*/Δ*Vgs*) characteristics of the field-effect transistors, it can be used as a performance measure to estimate the gain characteristic of our gateless HEMT PDs, because the change of incident optical power is directly associated with the virtual Δ*Vgs* induced by the change in numbers of O− 2 ads on the ZnO NR surface under the illumination of UV light.

FinFET technology has recently shown a major increase in adoption of use within Si integrated circuits. The advantages of a FINFET structure, even though there are a number of subtly different forms, can be numerous, but they are basically based on "channel controllability" in a nano-scale channel-length regime of FETs [45]. Furthermore, Si-based FINFETs have shown a significant enhancement in the dependence of *Ids* on *Vgs* at any applied bias in the sub- and near-threshold regimes by the superior electrostatics of the device architecture [46]. Normally-off Al2O3/GaN metal-insulator FINFETs (*Wfin* = 50 nm, 1 μm gate length) also showed very high maximum *Ids*, *gm*, and maximum field-effect mobility of 1.51 A/mm, 580 mS/mm, and 293 cm2V−1s−1, respectively, due to the more effective increase of 2-DEG electron concentration and higher electron mobility by enhanced gate controllability than the planar devices [47,48]. The superior performance of *R* in our NFI PDs is most likely attributed to this enhancement of "gate controllability" screening the field lines effectively from the interface traps or the defects near the 2-DEG channel, thereby reducing the electron scattering in the GaN channel.

The *D*\* of a PD, as defined in Equation (5), is also an important figure of merits used to describe performance. The NFI PDs of 70 nm *Wfin* exhibited a maximum *D*\* of ~3.2 × 1012 Jones (cm·Hz−1/2/W) at 340 nm, which is four orders of magnitude higher than that of MI PDs (~4 × 108 Jones), as shown in the left of Figure 7a, which is mainly due to the very low *Idark* of the NFI structure. A very high *D*\* up to a value of 1.4 × 1015 Jones [14] was reported from the ZnO NRs based UV PDs. However, the *R* achieved by this device was much lower (~103 A/W) than that of PDs.

#### **5. Conclusions**

Most of the performance parameters, such as *R*, *D*\*, on-off current ratio, and response speed, were all significantly improved by employing the NFI structure for the AlGaN/GaN HEMT based UV PDs with a ZnO NR UV-absorbing structure. The NFI PD, especially, exhibited an extremely high *R* of ~3.2 × 107 A/W. This performance enhancement was due to the subsequent characteristic change of the gateless HEMTs, induced by the reduction of *Wfin* to 70–80 nm. The NFI structure significantly improved the gain characteristics caused by enhanced gate controllability in nano-fin channels beyond the inherent high performance in conversion efficiency of the photon to electron-hole pair generation due to the large surface-to-volume ratio of the ZnO NRs grown in the active region. As the width of the 2-DEG channel is reduced by the NFI profile, the side-wall surface depletion in nano-fins and the attachment of NRs with numerous O− 2ads on the surface of the NRs lead to the formation of a fully-depleted 2-DEG channel and pushed the *VTH* to a positive value. The measured high on-off current ratio and *D*\* are mainly due to this normally-off operation of the NFI PD structure. An improvement in response speed of the PDs is associated with the minimized dimension of the gate area and the resulting gate capacitance of the NFI structure, where much less time for charging or discharging is required for the O2 adsorption-desorption process. The fabricated PDs also showed a linear dependence of photocurrent on the input light intensity in a range of 0.5–16.5 μW/cm2, regardless of device structure. The measured *gm,photo* value for the NFI PDs of 70 nm *Wfin* was 3.63 × 108 A/W, which was ~100 times greater than that of the MI PDs.

**Author Contributions:** Conceptualization, F.K.; methodology, F.K.; validation, F.K.; formal analysis, F.K.; investigation, F.K.; resources, S.-D.K.; data curation, F.K.; writing—original draft preparation, F.K.; writing—review and editing, F.K. and S.-D.K.; visualization, S.-D.K.; supervision, S.-D.K. and W.K.; project administration, S.-D.K.; funding acquisition, S.-D.K.

**Funding:** All the experiments performed in this work are financially sponsored by National Research Foundation (NRF) grant<PHONE_NUMBER>) under the program: "Mid-career Researchers" by the Ministry of Science and Technology, Republic of Korea. Similarly, the materials characterization was achieved with the financial support from NRF, Republic of Korea under the program: "Nano-materials Technology Development" (2009-0082580) managed by Ministry of Science, ICT and Future Planning.

**Acknowledgments:** The authors would like to thank Jihyun Kim, Hafiz Muhammad Salman Ajmal, Kiyun Nam and Noor ul Huda from Dongguk University for the continued encouragement, help, and support in carrying out the experiments and preparation of results.

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

#### **References**

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## *Article* **Porous Si-SiO2 UV Microcavities to Modulate the Responsivity of a Broadband Photodetector**

#### **María R. Jimenéz-Vivanco 1, Godofredo García 1, Jesús Carrillo 1, Francisco Morales-Morales 2, Antonio Coyopol 1, Miguel Gracia 3, Rafael Doti 4, Jocelyn Faubert 4 and J. Eduardo Lugo 4,\***

Received: 28 November 2019; Accepted: 9 January 2020; Published: 28 January 2020

**Abstract:** Porous Si-SiO2 UV microcavities are used to modulate a broad responsivity photodetector (GVGR-T10GD) with a detection range from 300 to 510 nm. The UV microcavity filters modified the responsivity at short wavelengths, while in the visible range the filters only attenuated the responsivity. All microcavities had a localized mode close to 360 nm in the UV-A range, and this meant that porous Si-SiO2 filters cut off the photodetection range of the photodetector from 300 to 350 nm, where microcavities showed low transmission. In the short-wavelength range, the photons were absorbed and did not contribute to the photocurrent. Therefore, the density of recombination centers was very high, and the photodetector sensitivity with a filter was lower than the photodetector without a filter. The maximum transmission measured at the localized mode (between 356 and 364 nm) was dominant in the UV-A range and enabled the flow of high energy photons. Moreover, the filters favored light transmission with a wavelength from 390 nm to 510 nm, where photons contributed to the photocurrent. Our filters made the photodetector more selective inside the specific UV range of wavelengths. This was a novel result to the best of our knowledge.

**Keywords:** photonic nanoscience; nanotechnology; porous Si-SiO2; UV filters; responsivity

#### **1. Introduction**

Porous silicon (PS) is a promising material for many different applications, such as solar cells, specifically as anti-reflection coating [1], chemical sensing [2,3], biomedical applications [4], biosensing [5,6], as a photodetector [7], or light-emitting diode [8]. The anti-reflection coating (ARC) reduces reflection losses thereby increasing the photocurrent and efficiency in solar cells [9–12]. A microcavity filter (MF) obtained in the IR range has been used as the ARC, where the maximum transmission at the localized mode wavelength was 95.2%, with a minimum reflectance of 4.8% at the same wavelength. The PS ARC was deposited onto a solar cell, where the entire surface of the solar cell was covered, and its external quantum efficiency (EQE) was measured, with and without the MF. The EQE at different wavelengths matched the shape of the MF transmission spectra [9]. ARCs are used to convert down the higher energy solar radiation into a wide range of light spectra, which is absorbed more efficiently into bulk Si [10]. In another interesting application, silver nanoparticles were infiltrated within a porous silicon photonic crystal to detect the trace of explosives (Rhodamine 6G dye

and Picric acid explosives) using surface-enhanced Raman scattering [13]. Recently, porous silicon nanoparticles (PSN) have been used for the tunable delivery of camptothecin, a small therapeutic molecule, where PSN acted as a therapeutics nanocarrier into the electrospun composite of poly fibers [14]. Additionally, mesoporous Si has been investigated for applications in biology and medicine, and an example is a porous silicon container employed to enclose the drug and release it in a controlled manner [15]. Previously, PS MFs have been fabricated to work as red-infrared filters coupled with a silicon photodetector, where the localized mode can be tuned by changing the optical path of the defect layer [16]. The reflectivity at the localized mode wavelength also increases. This effect occurs because PS has less absorption at long wavelengths [16,17]. This kind of filter can be lifted off from the Si substrate creating a free-standing PS MF. This MF can be transferred to another substrate such as quartz and glass [18,19]. Infrared long-wave pass and short-wave pass filters based in macroporous Si have been investigated [20]; they can be used together to suppress the radiation from shorter wavelengths. Consequently, the signal-to-noise performance of detectors may improve [18]. Moreover, luminescent silicon quantum dots embedded in free-standing PS and PS MFs infiltered with CdSe/ZnS and AgInS2/ZnS quantum dots have been reported [21–23]. The localized mode of the PS MF was tuned experimentally to match the emission spectra of CdSe/Zn and AgInS2/ZnS quantum dots to achieve enhanced photoluminescence. The authors mentioned that the localized mode of the MF modulated the photoluminescence of the quantum dots [22,23]; where electrical and thermal tuning of localized modes could also be achieved by infiltrating liquid crystals in PS MFs [24]. PS was also utilized as an anode for fast charge-discharge in lithium-ion batteries [25,26], and it was found that laser carbonization and wet oxidation PS structures had memristive properties. The first memristor showed properties of plasticity and short/long term memory, whereas the second exhibited strong filamentary-type resistance switching; and they have been used as two terminal resistive memory cells [27].

As the reader already noticed, PS is a versatile material, and herein, we will focus on the optical properties of PS, which allow the design of various kinds of interference filters in a broad range of wavelengths. Among these designs, we found rugate filters [28,29], Fibonacci filters [30], Bragg reflectors filters (BRF) [31,32], and MFs [33]. However, many drawbacks have been found in these filters, such as high chemical instability, high photon losses due to light absorption, and scattering in the visible and UV ranges. Some solutions to these problems have been identified by carrying out dry oxidation in PS structures [32,34], and recently it has been possible to manufacture porous Si-SiO2 filters (BRF and MF) in the UV range [34–36]. Our specific goal is integrating a PS MF in a photodetector to enlarge the responsivity spectrum bandwidth. In the past, the integration of different PS bandpass filters in Si photodetectors was attainable to achieve different filtering effects. It was possible to tune the responsivity spectrum from green to the near-infrared range obtaining all-Si color-sensitive photodetectors in that wavelength interval but with no below the green range [16,31,37]. It has been reported that UV filters based in multilayer stacks show substantial drawbacks in the deep UV spectral range due to the limited number of transparent materials within that range. They have been proposed as an alternative to extending optoelectronic technology towards the UV spectral range; for instance, PS filters based on macroporous silicon and low-pressure chemical vapor deposition were tested for many solar-blind applications such as electrical spark imaging and non-line of sight (NLOS) UV optical communications [18,38]. Following the same line of thought of extending silicon-based selective filters towards the UV spectral range; in this work, porous Si-SiO2 microcavities were used to modulate the responsivity of a broad photodetector with a detection range from 300 to 510 nm. The porous Si-SiO2 microcavities made the photodetector more selective in the UV range; and all microcavities had a localized mode close to 360 nm in the UV-A range. The maximum transmission at the localized mode wavelength (360 nm) was dominant in the UV-A range, allowing high energy photons to pass and produce a maximum peak in the photodetector.

This work is divided as follows: In Section 2, we give some technical details for materials and methods. Section 3 describes the results and their discussion. Finally, in Section 4, we present some conclusions.

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

#### *2.1. Porous Silicon Microcavities Filters*

PS microcavities filters were fabricated using p-type Si wafers, with (100) orientation and electrical resistivity between the range 0.01–0.02 Ω cm. The microcavities were etched anodically in an aqueous electrolyte based in HF and ethanol with a volume ratio of 1:1. Before etching, the Si wafers were cleaned with HF and ethanol for 5 min to remove the native oxide. A Keithley 2460 current source controlled by a laptop was employed to deliver a current profile for the microcavities formation, where the current profile consisted of switching two different current pulses, with each current pulse producing low/high porosity layers that respectively corresponded to the low/high refractive index layers. This process produced a stack of layers with specific refractive indexes, while anodization time determined the thickness of the layers. A pause of 3 s was introduced between each current pulse to prevent any porosity gradient.

Anodization etching included low/high current pulses of 5 mA/cm2 and 80 mA/cm2 to obtain layers with porosities of 39% and 64%, respectively. Meanwhile, the anodization times of 4.1 and 1.1 s were applied to form the first and second porous layers, and finally a third porous layer (defect) was built-in using a current pulse of 80 mA/cm2 for 2.2 s. The PS microcavities filters were detached from the Si substrates using the same aqueous electrolyte before mentioned, but a high current density (450 mA/cm2) was applied for 2 s. This process created a free-standing PS microcavity filter, which was transferred to a quartz substrate. All samples were rinsed with ethanol and dried at room temperature after the anodization process.

#### *2.2. Dry Oxidation in PS Microcavities Filters*

Microcavities filters were systematically oxidized using two stages of dry oxidation. In the first stage, a temperature of 350 ◦C for 30 min was used. In the second stage the oxidation temperature was increased to 900 ◦C for 1 h. During the oxidation process, the oxygen flow was changed from 1.15 to 4.52 SLPM (standard liter per minute) to observe any change in the microcavity optical response. The reasons behind the two dry oxidation steps were: the first step was a low-temperature pre-oxidation needed to equilibrate the silicon structure. That is, this step prevented the aggregation of the pores during further treatments at higher temperatures. The second step was applied to grow an oxide layer of greater thickness than that obtained in the last oxidation step. The layer thickness is higher than the natural native oxide grown in the environment resulting in the consolidation of SiO2.

Transmittance and reflectance spectra measurements were carried out before and after dry oxidation with a Varian (Agilent Technologies, CA, USA) UV-Vis-NIR spectrophotometer at normal incidence, and 20◦ from 200 to 800 nm. The cross-section SEM images of an oxidized microcavity was obtained using a JEOL-JSM7600F (Jeol, MA, USA).

#### *2.3. Photocurrent Modulation by Porous Si-SiO2 Microcavities Filters*

The photodetector employed to modulate its responsivity was a GVGR-T10GD (Electro Optical Components Inc., CA, USA) based in indium gallium nitride with a spectral detection range from 300 to 510 nm. In the experimental process, an optical chopper SR540 (Stanford Research Systems Inc., CA, USA) with a frequency of 287 Hz was used to cut off the light coming from the Xenon lamp 6254 (Oriel Corporation, CT, USA), concentrated at the input of a monochromator. A lens was used to focus the output light from the chopper, on the photodetector. The PS microcavity filter was placed before the photodetector, which was polarized with 5 volts using a Keithley 2460 source (Keithley, OHIO, USA), and then the photodetector photocurrent inputted a Look-in amplifier SR-530 (Stanford

Research Systems, CA, USA)). The filtered and amplified photocurrent versus light wavelength (from 276 to 536 nm) was displayed in a PC. The experimental set-up is shown in Figure 1.

**Figure 1.** Experimental set-up used to obtain the responsivity of a commercial photodetector with different porous silicon (PS) microcavity filters (up panel). The bottom panel shows the scheme and cross-section SEM images of an oxidized microcavity filter with a total thickness of 1.92 μm.

#### *2.4. Theoretical Mechanism to Modulate the Responsivity of a Broadband Photodetector in the UV Optical Range with Porous Si-SiO2 Microcavities*

In an ideal photodetector, its responsivity is proportional to the input light power being the proportional factor, the so-called quantum efficiency η, which is a function of the light reflection *R* at the surface, the fraction of electron-hole pairs that contribute effectively to the photocurrent ζ, the light absorption in the bulk of the material α, the photodetector depth *d*, and the light wavelength.

Herein, we proposed to modulate the responsivity of a commercial photodetector by changing *R*. This was done by adding a microcavity filter, where the spectral reflection response of the microcavity filter modifies the original reflection spectral response at the surface of the commercial photodetector completely. The microcavity filter reflection depends on the high and low refractive indexes and thickness values, as well as the refractive index and thickness of the defect layer values. Initially, the microcavities are made of PS to filter out blue light. This means that the layers' refractive index values, controlled by the porosities and in which the crystalline silicon nanostructures remains, were chosen to respond in that particular region of the light spectrum. However, our primary goal was to achieve responsivity modulation within the UV region using a silicon-based filter. We cannot use the sensitive blue light microcavities for that purpose because the crystalline silicon nanostructures strongly absorb light within the UV and blue regions. This absorption process is equivalent to having a 100% reflection at the photodetector surface. Thus, the quantum efficiency, and consequently, the responsivity, tends to zero. The oxidation process helps to avoid this problem in two ways: first, since there is a phase change, from crystalline silicon to silicon dioxide, the layers' refractive index values decrease, pushing the filter response towards the UV region. Second, there is much less light absorption in the UV band. The oxygen flow value determines the concentration of silicon dioxide, followed by the layer's refractive index values, and consequently, the spectral response of the filter. More specifically, the filters spectral response contains a unique photonic state known as a localized state represented as a

resonant peak in the reflection spectrum. It is a state that drastically modifies the responsivity, and therefore, it is the flow of oxygen that determines the final position of the localized state along with its reflection amplitude.

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

#### *3.1. Porous Silicon Microcavities Filters in the Blue Range*

The averaged theoretical (red line) and experimental (black line) reflection (broken line) and transmission (solid) spectra from the PS microcavities filters are depicted in Figure 2a. This corresponded to the average measurements of transmittance and reflectance spectrum from four microcavities. All four MCs were designed to show a localized mode in the same wavelength (590 nm). Experimental transmission and reflection measurements of the microcavities were taken using a UV-VIS-NIR spectrophotometer in the wavelength range from 200 to 800 nm. The transmission spectrum was measured at normal incidence and reflectance spectrum of the same microcavities was obtained at 20◦. Meanwhile, theoretical transmission and reflection spectrum were obtained using the matrix method. This method is well known (Supplementary Materials) for obtaining the theoretical spectrums that we considered the angle measurements taken with the UV-VIS-NIR spectrophotometer.

**Figure 2.** Experimental averaged transmission and reflection spectra of four microcavities compared to its theoretical spectra. (**a**) The theoretical (red line) and experimental (black line) averaged reflection and transmission spectra for four unoxidized microcavities obtained in the blue optical range; (**b**) the averaged band structure of the same microcavities. (**c**,**d**) are the comparison of the averaged theoretical and experimental defect mode locations. In (**d**), two angles of incidence (zero and 20 degrees) were considered.

The theoretical reflection spectrum of the microcavity predicts more reflection in the UV range than its experimental counterpart, while the theoretical and experimental transmission spectra matched very well. Moreover, the light transmission was low in the UV-VIS range due to strong absorption of Si. The localized mode of the microcavity was located at 490 nm and exhibited a maximum transmission peak of 4%, while that in the visible range from 555 to 800 nm showed high light transmission. This result was because PS had small absorption losses in this range of the electromagnetic spectrum, where the primary photon loss was light scattering. When the reflection spectrum of the microcavity was taken at 20◦, the position of the localized mode changed, and it shifted towards high energies (483 nm). It could also be observed in the theoretical reflection spectrum. Figure 2b shows the averaged photonic bandgap (PBG) of an unoxidized microcavity. It was obtained using the dispersion relation

inside the first Broullin zone. We calculated it only in one dimension and both measurement angles were considered, which were mentioned before.

We obtained the defect frequency can be obtained using a combination of the transfer matrix technique and variational methods. The defect modes are represented by the maximum peak of transmission in the microcavities [39,40]. When the symmetry of the photonic structure is broken up by a defect layer, it is possible to have a confined state, where photons are trapped and cannot escape, being confined inside the bandgap. We calculated the defect mode frequency for an antisymmetric state because our photonic structures were built as follows:

$$(HL)\_8L(HL)\_7$$

Our antisymmetric photonic structures based on PS and porous Si-SiO2 consisted of 31 layers, alternating between high refractive and low refractive indexes, with a low refractive index defect layer, and where the structure was surrounded by air.

The averaged theoretical defect mode frequency location is shown in Figure 2d, where it is compared with the averaged transmission and reflection spectra (Figure 2c). The defect mode is shown as a transmission maximum or as a reflection minimum at a specific wavelength between the photonic bandgap (PBG) edges. The variational method defect mode location was 18 nm off, concerning the experimental result from the reflection measurements, which was taken at 20 degrees. In this case, the defect mode location is depicted in Figure 2d (red broken line). Using the same variational method, the defect mode location was 16 nm off for the experimental transmission spectrum, which was taken at normal incidence. The localized mode is shown in Figure 2d (black broken line). The transfer matrix method predicted the same position as the experimental result. Both theoretical methods showed good agreement with the experiments.

#### *3.2. Porous Si-SO2 Microcavities Filters in the UV*

Averaged transmission (solid line) and reflection (broken line) spectra from porous Si-SiO2 microcavities filters are depicted in Figure 3a. The theoretical (red line) and experimental (black line) spectrum showed a good fit. The theoretical spectra were obtained by the transfer matrix (Supplementary Materials) considering both measurement angles, where one was 0◦, which corresponded to the transmission measurements, and the other was 20◦, considered for the reflection measurements. The microcavity to the left was first oxidized at 350 ◦C for 30 min and then at 900 ◦C for 1 hr, and the oxygen flow was 1.15 SLPM (standard liter per minute). The microcavity shown to the right was oxidized using the same temperature and oxidation time mentioned above. In this case, an oxidation flow of 2.21 SLPM was applied. The microcavity MF2 exhibited a maximum transmission amplitude of 70%, and the microcavity MF3 showed a maximum transmission amplitude of 57% in the localized mode wavelength, which indicated that the microcavity MF3 had more absorption losses than the microcavity MF3. Porous Si-SiO2 microcavities filters in Figure 3a show a transmission maximum peak (356 and 364 nm) and a reflection minimum peak (349 nm) in the UV range. We observed a mismatch between both peaks because the measurements were taken at different incidence angles.

Figure 3c shows the averaged transmission and reflection spectrum from UV filters compared to the defect mode location obtained with the variational method (Figure 3d). The defect mode location corresponding to the reflection spectrum was 4 nm off using the variational method, which is shown in Figure 3d (red broken line). The position of the defect mode obtained from the variational method (black broken line, Figure 3d) was 9 nm off for the transmission spectrum, as compared to what was predicted using the transfer matrix method.

**Figure 3.** The averaged theoretical and experimental transmission and reflection spectra of two UV microcavities filters, with the averaged photonic bandgap and defect mode locations. (**a**) The averaged theoretical (red line) and experimental (black line) reflection (broken line) and transmission (solid line) spectra of oxidized microcavities obtained in the UV range; (**b**) the averaged photonic bandgap structure (empty box) of the microcavities. (**c**,**d**) show the comparison of the averaged theoretical and experimental defect mode locations. In (**d**), two angles of incidence (zero and 20 degrees) were considered.

Figure 4a depicts the averaged theoretical (red line) and experimental (black line) transmission (solid line) and reflection (broken line) spectra of two oxidized MF. In this case, the porous Si-SiO2 microcavity filter MF4 showed a maximum transmission peak (368 nm) in the UV range, with an amplitude of 42%. Meanwhile, the microcavity MF5 displayed a maximum transmission peak at 369 nm, with an amplitude of 21% (red and black solid lines). A reflection minimum peak (349 nm) is also shown in both microcavities (red and black broken lines). The maximum transmission peaks were less intense than the microcavities shown in Figure 3. Here, the same temperature and oxidation time were employed to obtain the UV filters, but the oxygen flow applied for sample MF4 was 3.39 SLPM, while for sample MF5, it was 4.52 SLPM. The oxygen flow was increased gradually.

**Figure 4.** The averaged theoretical and experimental reflection and transmission spectrum of another two UV microcavities filters. Additionally, its averaged photonic bandgap and the defect mode locations are depicted. (**a**) The averaged theoretical (red line) and experimental (black line) reflection (broken line) and transmission (solid line) spectra of oxidized microcavities obtained in the UV range; (**b**) the averaged photonic bandgap structure (empty box) of the microcavities. (**c**,**d**) are the comparison between the averaged theoretical and experimental defect mode locations. In (**d**), two angles of incidence (zero and 20 degrees) were considered.

Figure 4c,d shows the averaged theoretical (red line) and experimental (black line) reflection (broken line) and transmission (solid line) spectra near to the defect mode location. The variational method was employed to obtain the defect mode location between the PBG edges. The broken red plots (Figure 4d) corresponded to the defect mode position of the microcavities measured at 20◦. The defect mode locations of microcavities measured at normal incidence are depicted as broken black lines in Figure 4d. There was a mismatch between the defect mode position calculated using the transfer matrix and the variational method.

#### *3.3. Refractive Index of Porous Silicon and Porous Si-SiO2*

The complex refractive index (refractive index and extinction coefficient) of the PS was obtained using the effective medium approximation Maxwell–Garnett. For porous Si-SiO2, we used a three-component model developed from the J.E. Lugo model. Figure 5a,b shows the refractive index values, and Figure 5c,d depicts the extinction coefficient values of PS and Porous SiO2, respectively, obtained from both models. The continuous lines in Figure 5a correspond to a high refractive index (red line) and a low refractive index (blue line) for PS. Their extinction coefficients are displayed with dotted lines (red and blue) in Figure 5c, where these values were used to fabricate PS microcavities filters in the blue range. The continuous lines of different colors in Figure 5b between 1.45 and 1.6, and the green line with values between 1.35 and 1.5, represent high and low refractive indexes for the porous Si-SiO2 layers (see Figure 5b). Their corresponding extinction coefficients are shown below the value of 0.1 (dotted lines) in Figure 5d. The vertical black dotted lines that intersect the complex refractive index components (Figure 5) indicate the exact values utilized to design MF in the blue and UV range.

**Figure 5.** Theoretical values of the complex refractive index for PS layers and porous Si-SiO2 layers. (**a**,**b**) shows the refractive index values for PS and porous Si-SiO2, and (**c**,**d**) depicts the extinction coefficient values of PS and Porous Si-SiO2, respectively, obtained from both models.

Figure 5 shows the refractive index and extinction coefficient are high when the PS is not oxidized. Meanwhile, the complex refractive index component values for porous Si-SiO2 are lower than the PS values. The growth of SiO2 inside PS layers decreased the refractive index and extinction coefficient. Moreover, during the PS layers' oxidation process, some air and Si fractions were replaced by SiO2, causing a lattice expansion and a decrement on the layer's porosity, as shown in Table 1.

**Table 1.** Theoretical values of porosity before and after dry oxidation, thickness, Si fraction, and oxide fraction of five microcavities.

Knowing the refractive index of each layer that made up the microcavity allowed estimation of the theoretical thickness of each layer by fitting the theoretical transmission and the reflection spectrum (applying the matrix method) with its experimental result. The thickness values displayed in Table 1 correspond to theoretical thickness for different microcavities. On the other hand, an increase in the thickness for the oxidized microcavities (MF2, MF3, MF4, and MF5) was shown after dry oxidation compared to the thickness of the unoxidized microcavity (MF2).

Additionally, the thickness of an oxidized microcavity was obtained using SEM measurements. Figure 1 (down panel) shows where the porous Si-SiO2 UV filter has a total thickness of 1.92 μm and it can observe a defect between two BRF. The light gray thickness (*dH* = 48 nm) corresponds to layers with high refractive index (low porosity) and the dark gray thickness (*dH* = 75 nm) depicts the layers with low refractive index (high porosity). Meanwhile, the defect in the microcavity had twice the thickness of the high porosity layer. The thickness found using both methods showed a difference of a few nanometers, and both results give an approximate thickness value for each layer of an oxidized microcavity filter.

Furthermore, the optical path was modified by decreasing the refractive index and increasing the physical thickness. Finally, the vertical black dotted lines that intersected with the complex refractive index components (Figure 5) indicated the exact values utilized to design MF in the blue and UV range.

#### *3.4. Optical Losses Due to Light Absorption*