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Abstract
The non-steady-state photoelectromotive force is excited in a monoclinic gallium oxide crystal at wavelength λ = 457 nm. The crystal grown in an oxygen atmosphere is insulating and highly transparent for a visible light, nevertheless, the formation of dynamic space-charge gratings and observation of the photo-EMF signal is achieved without application of any electric field to the sample. The dependencies of the signal amplitude on the frequency of phase modulation, light intensity, spatial frequency and light polarization are measured. The material demonstrates the anisotropy along the [100] and [010] directions, namely, there is a small difference in the transport parameters and a pronounced polarization dependence of the signal. The crystal’s photoconductivity, responsivity and diffusion length of electrons are estimated for the chosen light wavelength and compared with the ones for other wide-bandgap crystals.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Gallium oxide seems to be one of the wide-bandgap materials that will meet the challenges of future electronics and optics [1,2]. The large band gap of $\sim 4.8$ eV makes it highly transparent for the visible light and partially for UV. This advances the development of solar-blind detectors of deep ultraviolet radiation based on nanowires [3], nanobelts [4], thin films [5–10], and bulk crystals [11]. Due to the high breakdown field (6-8 MV/cm), reasonable mobility of carriers and high thermal stability this material is very attractive for development of radio frequency and power field-effect transistors, as well as Schottky rectifiers [12–14]. The crystal possesses the photocatalytic properties and can be used as an photoelectrode for the water splitting under UV radiation [15]. The gas sensors based on Ga$_2$O$_3$ were also proposed [16].
The operation and characteristics of Ga$_2$O$_3$ photodetectors are usually studied for continuous wave or amplitude modulated light only [3–11], whereas the modern communication systems, including optical ones, use the frequency- and phase-modulated signals as well. The interferometric systems using principles of dynamic holography allow detection of such signals [17,18]. One of the possible implementations is based on adaptive sensors using the effect of the non-steady-state photo-EMF [19–24].
The effect of the non-steady-state photo-EMF reveals itself as an alternating electric current arising in a semiconductor illuminated by an oscillating interference pattern [19,25,26]. The electric current appears due to time-varying relative spatial shifts of the space-charge and photoconductivity distributions. These distributions are recorded in the crystal volume as a product of joint action of carrier generation, diffusion, drift in an electric field and recombination to local centers. The characteristics and features of these elementary processes are translated to the resulting electric current making the non-steady-state photo-EMF a powerful tool for investigation of the photoelectric phenomena and material characterization [27–35].
In this paper we apply the non-steady-state photo-EMF technique for characterization of $\beta$-Ga$_2$O$_3$ crystal at $\lambda =457$ nm assuming its possible utilization as adaptive sensor of frequency- and phase-modulated optical signals. In spite of the great interest to $\beta$-Ga$_2$O$_3$ for ultraviolet applications, the investigations of optically induced processes for the sub-bandgap wavelengths are necessary for a better understanding of the crystal’s optical and electronic properties [35,36].
2. Experimental setup
The excitation and detection of the non-steady-state photo-EMF are carried out in $\beta$-Ga$_2$O$_3$ with the arrangement shown in Fig. 1. The radiation of the solid state diode pumped laser with the wavelength of $\lambda =457$ nm is expanded and split into two beams, which then create the interference pattern with spatial frequency $K$, contrast $m=0.38$ and average intensity $I_0$ on the crystal surface. The electro-optic modulator introduces phase modulation with amplitude $\Delta =0.51$ and frequency $\omega$ into the signal beam. The photocurrent arising in the sample produces a voltage across the load resistor $R_L=100$ k$\Omega$, which is amplified and then measured by the lock-in voltmeter. The polarization plane is perpendicular to the incidence plane in the most of the experiments. The placement of the half-wave plate in front of the sample allows the rotation of the polarization plane, when it is necessary.
Fig. 1. Experimental setup for the investigation of the non-steady-state photo-EMF. $EOM$ is the electrooptic modulator, $BS$ is the beam splitter, $BE$ is the beam expander, $M$ is the mirror, $A$ is the amplifier.
$\beta$-Ga$_2$O$_3$ is a monoclinic crystal with the cell dimensions $a=12.23$ Å, $b=3.04$ Å, $c=5.80$ Å and $\beta =103.7^\circ$ [37]. The band gap is indirect with $E_g=4.6-4.9$ eV [1,2]. The static dielectric constant of the material is a tensor with eigenvalues $\epsilon _{11}=10.84$, $\epsilon _{22}=11.49$ and $\epsilon _{33}=13.89$ [38,39].
We study the same sample of $\beta$-Ga$_2$O$_3$ as in our previous work [35]. It has the dimensions of $2.00\times 2.15\times 1.35$ mm along the crystallographic directions [100], [010] and direction perpendicular to the plane (001), respectively. The front and back surfaces ($2.00\times 2.15$ mm) are the (001) crystal’s cleaved facets, no additional treatment was applied to them. The silver paste electrodes are deposited on the opposite pairs of lateral surfaces in the experiments with the light pattern grating vector $\mathbf {K}||[100]$ and $\mathbf {K}||[010]$.
3. Experimental results
The non-steady-state photo-EMF effect exists in the studied crystal at chosen wavelength, and this is the first result to be reported. The signal amplitude is rather small but ensures the reliable detection with the signal-to-noise ratio of $0-60$ dB. The phase of the signal corresponds to the electron type of photoconductivity.
The frequency dependencies of the non-steady-state photo-EMF amplitude are presented in Fig. 2. The dependencies look rather standard for this effect, namely there are a growing part and plateau. Such a behavior is well described by the following expression for the current amplitude known from the theory of the effect [25,27]:
Here $\sigma _0$ is the average photoconductivity, $E_D=(k_BT/e)K$ is the diffusion field [18], $\tau _M=\epsilon _0\epsilon /\sigma _0$ is the Maxwell relaxation time, $L_D$ is the diffusion length of electrons, $S$ is the electrode’s area, $\mathrm {J}_n(\Delta )$ is the Bessel function of the first kind of the $n$-th order. The growing and frequency-independent regions are separated by the cut-off frequency $\omega _1$
The signal at low $\omega$ is small since both the space charge field grating and the grating of free electrons (photoconductivity grating) follow the movement of the interference pattern. The spatial shift between them keeps nearly equal to $\pi /2$, which results in small value of the average drift component of the current. The space-charge grating has the larger relaxation time in high-resistive materials. It becomes “frozen-in” at higher frequencies, the spatial shifts between gratings increase, and the holographic current reaches its maximum at the frequency-independent region.
Fig. 2. Frequency dependencies of the non-steady-state photo-EMF measured for two orientations of the Ga$_2$O$_3$ crystal.
The grating amplitude of photoelectrons density (photoconductivity grating) is a function of illumination level, that is why the dependencies of the signal characteristics versus light intensity are usually measured (Fig. 3). Both the signal amplitude at the plateau and the cut-off frequency are proportional to the average light intensity: $J^\omega ,\omega _1\propto I_0$. The dark conductivity can contribute in the initial stage of dependence $\omega _1(I_0)$ resulting in the deviation of experimental points from the linear law. As seen from Eq. (2) the measurements of the cut-off frequency $\omega _1$ at low $K$ provide the estimate of the Maxwell relaxation time and corresponding photoconductivity of the sample. For the chosen intensities $I_0=0.28\div 3.8$ W/cm$^2$ of TE-polarized light the photoconductivity ranges $\sigma _0=(0.22\div 2.3)\times 10^{-9}$ $\Omega ^{-1}$cm$^{-1}$ along the [100] axis and $\sigma _0=(0.15\div 1.6)\times 10^{-9}$ $\Omega ^{-1}$cm$^{-1}$ along the [010] axis. The specific photoconductivity can also be estimated from the amplitude of the non-steady-state photo-EMF $J^\omega$ measured for certain $m$, $\Delta$, $K$, $\omega$. This provides the following estimates: $\sigma _0=(0.12\div 1.5)\times 10^{-9}$ $\Omega ^{-1}$cm$^{-1}$ along the [100] axis and $\sigma _0=(0.041\div 0.58)\times 10^{-9}$ $\Omega ^{-1}$cm$^{-1}$ along the [010] axis. We attribute the discrepancy between the corresponding estimates to the nonuniformity of the average light intensity $I_0$ as well as the mentioned dark conductivity.
Fig. 3. Dependencies of the non-steady-state photo-EMF amplitude and cut-off frequency on the light intensity.
Both the photoconductivity and space-charge grating amplitudes are functions of the spatial frequency, so the dependence of the signal on this parameter is measured as well (Fig. 4). The growth of the signal at low $K$ is due to the increase of the space charge field amplitude [18]. The decay at high $K$ is resulted from the diffusion “blurring” of the photoconductivity grating. The maximum of the signal is achieved at $K=L_D^{-1}$, so the electron diffusion length can be estimated from the experimental curves: $L_D=200$ nm for $\mathbf {K}||[100]$ and $L_D=230$ nm for $\mathbf {K}||[010]$. These estimates are almost the same within the experimental errors, which indicates the slight anisotropy of transport parameters containing $\mu \tau$-product.
Fig. 4. Dependencies of the non-steady-state photo-EMF amplitude and cut-off frequency on the spatial frequency.
Figure 4 also presents the dependencies of the cut-off frequency versus spatial frequency. These experimental dependencies are approximated by Eq. (2) with $L_D=110$ nm for both $\mathbf {K}||[100]$ and $\mathbf {K}||[010]$. The dependence $\omega _1(K)$ suggests a smaller value for the diffusion length than that for the dependence $J^\omega (K)$. This may be explained by the following factors. First, the increased light reflection at large incident angles leads to the decrease of the light intensity in the crystal volume, and this additionally reduces both the signal level and cut-off frequency for $K>10$ $\mu$m$^{-1}$. Second, we use the relatively large amplitude of phase modulation $\Delta$, this can modify the standard frequency dependence and affect the cut-off frequency determination. Additional errors can be originated from the nonuniformity of the average light intensity $I_0$ due to both the light absorption along the sample thickness and residual Gauss profile of the light beams.
The monoclinic $\beta$-Ga$_2$O$_3$ expectedly reveals its anisotropy in Figs. 2–4 demonstrating the larger non-steady-state photo-EMF signal and cut-off frequency for the $K||[100]$ geometry. In order to find out the origin of such an anisotropy of the studied effect we have measured the dependence of the signal amplitude on the angle of the polarization plane (Fig. 5). The experimental dependencies are well approximated by the phenomenological truncated Fourier series:
As seen from the experimental dependencies we can confine ourselves with the zeroth component and first harmonic for the case $\mathbf {K}||[010]$, while the all three components $a_0,a_1,a_2\ne 0$ should be taken into account for the case $\mathbf {K}||[100]$. The amplitude of the signal in the absolute maxima in these dependencies differs only by 5%. This means that the studied geometries are almost equivalent in their efficiency: the signal amplitude would maintain its maximum value, if we rotated the polarization plane synchronously with the crystal. In our previous work [35] we observed the similar dependencies at $\lambda =532$ nm, and then we attributed such polarization dependencies to the angular dependence of quantum efficiency: $\beta =\beta _0+c_\beta \cos 2\Theta$. We think this assumption is valid at $\lambda =457$ nm as well, at least for the first angular harmonic in Fig. 5 and Eq. (3).
Fig. 5. Dependencies of the non-steady-state photo-EMF on the angle between polarization and incidence planes. The approximation by Eq. (3) is shown for $a_2=0$ (dashed lines) and $a_2\ne 0$ (solid line).
4. Discussion
First, let us compare the characteristics of the $\beta$-Ga$_2$O$_3$ crystal with other materials studied in the same spectral range (Table 1). Since the measurements were carried out at different experimental conditions, we estimate the normalized maximal photo-EMF amplitude:
where $J^\omega _m$ is the amplitude of the non-steady-state photo-EMF measured at $\omega >\omega _1$ and $KL_D=1$, $P_0$ is the total light power, which is the sum of powers of the signal $P_s$ and reference $P_r$ beams illuminating the sample. The value given by Eq. (4) can be particularly useful for the interferometric applications, where the contrast and amplitude of phase modulation are small ($m,\Delta \ll 1$), and where it reduces to $R^\omega _m\simeq J^\omega _m/(P_s\Delta )$ being an analog of the photodiode responsivity (sensitivity) [19].
Table 1. Parameters of the wide-bandgap materials and non-steady-state photo-EMF amplitude in the blue-green region of light spectrum.
According to Table 1 the Ga$_2$O$_3$ crystal has much lower responsivity than other crystals studied before. In order to find out the origin of this, we can rewrite Eq. (4) using Eq. (1):
where $L_x$ is tne interelectrode spacing, $L_z$ is the effective thickness of the sample, $\alpha$ is the absorption coefficient and $\beta$ is the quantum efficiency, $h\nu$ is the photon energy. The Ga$_2$O$_3$ crystal is transparent for visible light ($\alpha L_z\sim 0.1$ [35]), while Bi$_{12}$SiO$_{20}$ and SnS$_2$ absorbs blue light almost completely ($\alpha L_z\simeq 1$). The relatively low diffusion length $L_D$ (or $\mu \tau$-product) is another evident reason of low sensitivity.Nevertheless, the studied Ga$_2$O$_3$ crystal has some advantages over other crystals. The frequency transfer function of the former is rather flat in the range of $0.1-500$ kHz, while the signal in Bi$_{12}$SiO$_{20}$ decays over 3 kHz. No influence of shallow traps has been revealed (compare Fig. 2 with those in Refs. [33,34]). The material has a moderate static dielectric constant $\epsilon \simeq 10$ [38,39], which is about 5 times lower than that in sillenite crystals, and this allows to achieve the appropriate cut-off frequency at low illumination levels.
On comparing the Ga$_2$O$_3$ parameters obtained for $\lambda =457$ nm and $\lambda =532$ nm we can state that there is no dramatic change in their values, which can be considered as another advantage: the sensor based on this material would have rather flat spectral characteristics. Some differences in behavior should be pointed out, however. First, the cut-off frequency is the linear function of the intensity of blue light, while it demonstrated the nonlinearity for the green one [35]. Furthermore, the second harmonic appears in the polarization dependence measured at $\lambda =457$ nm, but not at $\lambda =532$ nm. If we address to Eq. (5), we can suppose that second harmonic arises as product of two angular-dependent functions: $\alpha =\alpha _0+c_\alpha \cos 2\Theta$ and $\beta =\beta _0+c_\beta \cos 2\Theta$. Since this peculiarity appears only for $\lambda =457$ nm and certain sample orientation, coefficient $c_\alpha$ should be a function of the wavelength and some vector, e.g. [100] component of the space charge field: $c_\alpha (\lambda ,\mathbf {E_{sc}}\cdot \mathbf {a})$. In other words, there can be some effect of electric field induced absorption analogous to Franz-Keldysch effect [40]. This hypothesis surely requires more confirmations with other wavelengths, samples and approaches.
The experiments presented in this paper are performed in the absence of an external electric field. The space charge formation and photo-EMF excitation can acquire the resonant behavior in a high dc field [27], while the application of an ac voltage can increase the photo-EMF amplitude both resonantly and nonresonantly [26]. Since the mentioned processes in external fields significantly differ from the ones presented above, they will be considered for Ga$_2$O$_3$ at $\lambda =457$ nm separately in our next paper.
5. Conclusion
In conclusion, we have demonstrated the capabilities of the non-steady-state photo-EMF technique in characterization of the wide-bandgap monoclinic Ga$_2$O$_3$ crystal. The diffusion mechanism of the signal excitation is used. The photoelectric parameters such as photoconductivity and diffusion length of electrons are estimated. There is a weak anisotropy of the photo-EMF and electric parameters along the [100] and [010] axes and a pronounced polarization dependence of the quantum efficiency and resulting signal. The rather high amplitude of the signal and flatness of the frequency response in Ga$_2$O$_3$ makes this crystal a potential candidate for the fabrication of adaptive sensors of phase- and frequency-modulated optical signals.
Funding
Russian Science Foundation (19-12-00323).
Acknowledgments
I.S. and Yu.K. acknowledge a support grant from the Russian Science Foundation.
Disclosures
The authors declare no conflicts of interest.
References
1. S. J. Pearton, J. Yang, P. H. Cary IV, F. Ren, J. Kim, M. J. Tadjer, and M. A. Mastro, “A review of Ga2O3 materials, processing, and devices,” Appl. Phys. Rev. 5(1), 011301 (2018). [CrossRef]
2. S. I. Stepanov, V. I. Nikolaev, V. E. Bougrov, and A. E. Romanov, “Gallium oxide: properties and application – a review,” Rev. Adv. Mater. Sci. 44, 63–86 (2016).
3. P. Feng, J. Y. Zhang, Q. H. Li, and T. H. Wang, “Individual β-Ga2O3 nanowires as solar-blind photodetectors,” Appl. Phys. Lett. 88(15), 153107 (2006). [CrossRef]
4. L. Li, E. Auer, M. Liao, X. Fang, T. Zhai, U. K. Gautam, A. Lugstein, Y. Koide, Y. Bandoa, and D. Golberga, “Deep-ultraviolet solar-blind photoconductivity of individual gallium oxide nanobelts,” Nanoscale 3(3), 1120 (2011). [CrossRef]
5. Y. Kokubun, K. Miura, F. Endo, and S. Nakagomi, “Sol-gel prepared β-Ga2O3 thin films for ultraviolet photodetectors,” Appl. Phys. Lett. 90(3), 031912 (2007). [CrossRef]
6. D. Guo, Z. Wu, P. Li, Y. An, H. Liu, X. Guo, H. Yan, G. Wang, C. Sun, L. Li, and W. Tang, “Fabrication of β-Ga2O3 thin films and solar-blind photodetectors by laser MBE technology,” Opt. Mater. Express 4(5), 1067–1076 (2014). [CrossRef]
7. S. Oh, Y. Jung, M. A. Mastro, J. K. Hite, C. R. Eddy Jr., and J. Kim, “Development of solar-blind photodetectors based on Si-implanted β-Ga2O3,” Opt. Express 23(22), 28300–28305 (2015). [CrossRef]
8. G. C. Hu, C. X. Shan, N. Zhang, M. M. Jiang, S. P. Wang, and D. Z. Shen, “High gain Ga2O3 solar-blind photodetectors realized via a carrier multiplication process,” Opt. Express 23(10), 13554–13561 (2015). [CrossRef]
9. W. Li, X. Zhao, Y. Zhi, X. Zhang, Z. Chen, X. Chu, H. Yang, Z. Wu, and W. Tang, “Fabrication of cerium-doped β-Ga2O3 epitaxial thin films and deep ultraviolet photodetectors,” Appl. Opt. 57(3), 538–543 (2018). [CrossRef]
10. X. Zhang, L. Wang, X. Wang, Y. Chen, Q. Shao, G. Wu, X. Wang, T. Lin, H. Shen, J. Wang, X. Meng, and J. Chu, “High-performance β-Ga2O3 thickness dependent solar blind photodetector,” Opt. Express 28(3), 4169–4177 (2020). [CrossRef]
11. T. Oshima, T. Okuno, N. Arai, N. Suzuki, S. Ohira, and S. Fujita, “Vertical solar-blind deep-ultraviolet Schottky photodetectors based on β-Ga2O3 substrates,” Appl. Phys. Express 1(1), 011202 (2008). [CrossRef]
12. P.-C. Chang, Z. Fan, W.-Y. Tseng, A. Rajagopal, and J. G. Lu, “β-Ga2O3 nanowires: synthesis, characterization, and p-channel field-effect transistor,” Appl. Phys. Lett. 87(22), 222102 (2005). [CrossRef]
13. M. Higashiwaki, K. Sasaki, A. Kuramata, T. Masui, and S. Yamakoshi, “Gallium oxide (Ga2O3) metal-semiconductor field-effect transistors on single-crystal β-Ga2O3 (010) substrates,” Appl. Phys. Lett. 100(1), 013504 (2012). [CrossRef]
14. S. J. Pearton, F. Ren, M. Tadjer, and J. Kim, “Perspective: Ga2O3 for ultra-high power rectifiers and MOSFETS,” J. Appl. Phys. 124(22), 220901 (2018). [CrossRef]
15. T. Oshima, K. Kaminaga, H. Mashiko, A. Mukai, K. Sasaki, T. Masui, A. Kuramata, S. Yamakoshi, and A. Ohtomo, “β-Ga2O3 single crystal as a photoelectrode for water splitting,” Jpn. J. Appl. Phys. 52(11R), 111102 (2013). [CrossRef]
16. M. Fleischer and H. Meixner, “Oxygen sensing with long-term stable Ga2O3 thin films,” Sens. Actuators, B 5(1-4), 115–119 (1991). [CrossRef]
17. L.-A. de Montmorillon, P. Delaye, and G. Roosen, “Photorefractive interferometer for ultrasound detection,” Progress in Photorefractive Nonlinear Optics, K. Kuroda, ed. (Taylor & Francis, London, 2002), pp. 213–282.
18. M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive crystals in coherent optical systems, vol. 59 of Springer Series in Optical Sciences (Springer-Verlag, 1991).
19. S. Stepanov, “Photo-electromotive-force effect in semiconductors,” Handbook of Advanced Electronic and Photonic Materials and Devices, vol. 2H. S. Nalwa, ed. (Academic Press, 2001), pp. 205–272.
20. S. I. Stepanov, I. A. Sokolov, G. S. Trofimov, V. I. Vlad, D. Popa, and I. Apostol, “Measuring vibration amplitudes in the picometer range using moving light gratings in photoconductive GaAs:Cr,” Opt. Lett. 15(21), 1239–1241 (1990). [CrossRef]
21. M. A. Bryushinin, K. T. V. Grattan, V. V. Kulikov, and I. A. Sokolov, “Adaptive interferometers using photorefractive crystals and the non-steady-state photoelectromotive force effect,” J. Mod. Opt. 53(5-6), 857–864 (2006). [CrossRef]
22. M. Bryushinin, V. Kulikov, I. Sokolov, P. Delaye, and G. Pauliat, “Non-steady-state photo-EMF in semi-insulating GaAs under frequency-modulated illumination,” EPL 105(6), 64003 (2014). [CrossRef]
23. M. A. Bryushinin, I. A. Sokolov, and A. M. Balbashov, “Visualization of oscillatory stresses in transparent media using a β-Ga2O3 adaptive detector,” Appl. Opt. 56(2), 170–178 (2017). [CrossRef]
24. M. A. Bryushinin, V. V. Kulikov, A. A. Petrov, I. A. Sokolov, R. V. Romashko, and Y. N. Kulchin, “Non-steady-state photo-EMF interferometer for detection of mechanical oscillations in transparent scattering objects,” Appl. Opt. 59(8), 2370–2374 (2020). [CrossRef]
25. M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electro-motive force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68(5), 2216–2225 (1990). [CrossRef]
26. I. A. Sokolov and M. A. Bryushinin, Optically induced space-charge gratings in wide-bandgap semiconductors: techniques and applications (Nova Science Publishers, Inc., 2017).
27. I. A. Sokolov and S. I. Stepanov, “Non-steady-state photoelectromotive force in crystals with long photocarrier lifetimes,” J. Opt. Soc. Am. B 10(8), 1483–1488 (1993). [CrossRef]
28. U. Haken, M. Hundhausen, and L. Ley, “Analysis of the moving-photocarrier-grating technique for the determination of mobility and lifetime of photocarriers in semiconductors,” Phys. Rev. B 51(16), 10579–10590 (1995). [CrossRef]
29. H. Veenhuis, K. Buse, E. Krätzig, N. Korneev, and D. Mayorga, “Non-steady-state photoelectromotive force in reduced lithium niobate crystals,” J. Appl. Phys. 86(5), 2389–2392 (1999). [CrossRef]
30. M. C. Gather, S. Mansurova, and K. Meerholz, “Determining the photoelectric parameters of an organic photoconductor by the photoelectromotive-force technique,” Phys. Rev. B 75(16), 165203 (2007). [CrossRef]
31. T. O. dos Santos, J. Frejlich, and K. Shcherbin, “Photo electromotive force in CdTe:Ge: manifestation of two photorefractive centers,” Appl. Phys. B 99(4), 701–707 (2010). [CrossRef]
32. M. Bryushinin, V. Kulikov, E. Mokhov, S. Nagalyuk, and I. Sokolov, “Non-steady-state photoelectromotive force in an AlN crystal,” Phys. Rev. B 86(8), 085209 (2012). [CrossRef]
33. M. A. Bryushinin, V. V. Kulikov, E. V. Mokrushina, E. N. Mokhov, A. A. Petrov, and I. A. Sokolov, “Nonstationary holographic currents in neutron-irradiated SiC crystal,” J. Phys. D: Appl. Phys. 47(41), 415102 (2014). [CrossRef]
34. M. A. Bryushinin, A. A. Petrov, R. V. Pisarev, and I. A. Sokolov, “Non-steady-state photoelectromotive force in the wide-band-gap dielectric MnO,” Phys. Solid State 57(5), 907–913 (2015). [CrossRef]
35. M. A. Bryushinin, I. A. Sokolov, R. V. Pisarev, and A. M. Balbashov, “Space-and-time current spectroscopy of a β-Ga2O3 crystal,” Opt. Express 23(25), 32736–32746 (2015). [CrossRef]
36. A. Singh, O. Koksal, N. Tanen, J. McCandless, D. Jena, H. G. Xing, H. Peelaers, and F. Rana, “Intra- and inter-conduction band optical absorption processes in β-Ga2O3,” Appl. Phys. Lett. 117(7), 072103 (2020). [CrossRef]
37. S. Geller, “Crystal structure of β-Ga2O3,” J. Chem. Phys. 33(3), 676–684 (1960). [CrossRef]
38. B. Liu, M. Gu, and X. Liu, “Lattice dynamical, dielectric, and thermodynamic properties of β-Ga2O3 from first principles,” Appl. Phys. Lett. 91(17), 172102 (2007). [CrossRef]
39. A. Fiedler, R. Schewski, Z. Galazka, and K. Irmscher, “Static dielectric constant of β-Ga2O3 perpendicular to the principal planes (100), (010), and (001),” ECS J. Solid State Sci. Technol. 8(7), Q3083–Q3085 (2019). [CrossRef]
40. J. I. Pankove, Optical processes in semiconductors (Prentice-Hall, Inc., 1971).
