1. Introduction

$\beta$-Ga₂O₃ crystals belong to the group of transparent conductive oxides (TCO), for example, indium tin oxide (ITO), with a wide band gap and high electrical conductivity. ITO has been extensively investigated due to important applications such as in flat panel displays, thermal windows, and solar cells [1]. As $\beta$-Ga₂O₃ crystals exhibit a large band gap of E_g = 4.8 eV, the transparency extends from the visible into UV regions [2]. The electrical conductivity exhibits a semiconductor behavior even at low temperatures [3]. The band-to-band excitation (E>4.8 eV) produces UV/blue and blue/green luminescence [2,4]. The decay curves of the blue luminescence in $\beta$-Ga₂O₃ single crystals were observed in time ranges from 0.5 $\mu$s to 10 ms [4]. The fastest decay component gives a lifetime of 1.5 $\mu$s, which is assigned to self-trapped excitons composed of self-trapped holes and electrons [4]. The other decay components in the range from 10 $\mu$s to 10 ms may be due to distant electron-hole pairs, which are created by the band-to-band excitation. Recombination of distant electron-hole pairs with lifetimes longer than 1 s, called persistent phosphorescence, was observed at low temperatures below 150 K [5].

The basic mechanism responsible for the persistent phosphorescence is very similar to the donor-acceptor recombination process in semiconductors [6]. If donors and acceptors, being uniformly distributed in semiconductors, recombine radiatively through tunnelling, the decay curve of the recombination luminescence can be described by a t^-1 power function [6, 7]. The decay times for the donor-acceptor recombination and the persistent phosphorescence have distributions in the ranges of 10⁻⁴ to 1 s and 1 to 10⁴ s, respectively. The difference in time scales is mainly due to separation distance and energy depth of the trapped charges [7].

In this paper, we discuss the relationship between the persistent phosphorescence and the electrical conductivity observed in $\beta$-Ga₂O₃ single crystals, that is, how shallowly trapped electrons contribute to both the persistent phosphorescence as insulators and the electrical conductivity as semiconductors.

2. Experimental procedure

$\beta$-Ga₂O₃ has a monoclinic structure with the space group C2/m [3]. The lattice parameters at room temperature are a = 1.223 nm, b = 0.304 nm, and c = 0.5807 nm and the unique axis $\beta$ = 103.7° [3]. Ga ions are surrounded by O ions in either a tetrahedral or an octahedral coordination. A separated chain structure of the two Ga sites is formed along the b-axis [8].

Single crystals of $\beta$-Ga₂O₃ were grown from starting powders of 4N and 6N Ga₂O₃ by the floating zone technique. $\beta$-Ga₂O₃ single crystals doped with Si were also grown. Si doping concentrations were ~10¹⁹ cm⁻³ and carrier densities as donors was estimated to be (1-2)$\times$ 10¹⁸ cm⁻³ from the Hall measurement with the Van der Pauw configuration [9–11]. The details of the growth procedure were described in previous papers [2, 3, 9–11]. Samples were prepared by cleaving along the (100) and (001) planes, with approximate dimensions of 10$\times$10$\times$0.5 mm³ for optical and electrical measurement, and 2$\times$0.4$\times$0.2 mm³ for electron spin resonance (ESR) measurement.

Optical absorption, luminescence and excitation spectra were measured in the temperature range between 10 and 300 K using the tunable source (100-700 nm) in the UVSOR facility at Institute for Molecular Science at Okazaki. Optical absorption and luminescence spectra were also measured using a Perkin Elmer Lambda950 spectrophotometer and an Ocean Optics HR4000 spectrophotometer, respectively. Decay curves of luminescence intensities were measured using a Hamamatsu Photonics Quantaurus-Tau C11367 spectrometer.

Persistent phosphorescence was measured as follows. A sample was excited for five minutes with 266-nm laser light with a width of ~10 ns from a Spectra-Physics GCR100 pulsed Nd:YAG laser. Measurement of whole phosphorescence intensities started at 1 s after removal of the excitation light. Optical signals were detected using a photomultiplier and a Keithley 428 current amplifier. Signals were sampled, integrated in a period of 1 s, changed to digital signals, and stored in a personal computer. Sample temperatures between 15 and 300 K were achieved using an Iwatani CA201 cryo-refrigerator.

ESR measurement was carried out using a Bruker EMX10/12 X-band spectrometer with ~9.45 GHz and 100 kHz field modulation in the temperature range of 110-500 K.

Photocurrent measurement was carried out using 266-nm pulsed laser light at 300 K. Photocurrent was amplified using a Keithley 428 current amplifier with a filter rise time of 10 $\mu$s and a filter frequency response of 35 kHz.

3. Experimental results

3.1 Optical spectra

Figure 1 shows the optical absorption spectra at 300 K in the wavelength range between 200 and 2500 nm for the $\beta$-Ga₂O₃ (4N), (6N) and $\beta$-Ga₂O₃:Si single crystals. The band edges are observed approximately at 275 nm for these samples [11]. The absorption coefficients for the 4N pure and Si-doped samples gradually increase in the infrared (IR) region from 1000 to 2500 nm. The IR absorption is associated with the plasma oscillation, which is determined by free carrier densities [12]. Concerning the Si-doped sample, the carrier density of ~10¹⁸ (cm⁻³) estimated from the Hall measurement gives rise to a wavelength (33 µm) corresponding to the plasma frequency [9,12]. On the other hand, the optical absorption spectrum for the 6N pure sample is flat and negligibly small in the range between 300 and 2500 nm. The lack of the plasma absorption/reflection in this range is due to a further shift of the plasma frequency to the far-infrared, which is linked to the decrease in the carrier densities.

 

Fig. 1 Absorption spectra for various$\beta$-Ga₂O₃ single crystals at 300 K.

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Figure 2(a) shows the luminescence spectra in $\beta$-Ga₂O₃:Si excited in the range from 210 to 270 nm at 20 K. Excitation below 260 nm produces UV/blue broad bands with double peaks at 350 and 390 nm, whereas the UV/blue bands excited above 260 nm are weakened and a blue/green band appears around 520 nm [2,12]. The blue/green band, denoted by a dot-dashed line in Fig. 2(a), is decomposed through subtracting the UV/blue bands with the 210 nm excitation from the luminescence spectrum with 270 nm excitation. The luminescence spectra observed at 300 K in Fig. 2(b) are independent of the excitation wavelengths and coincident with those observed at 20 K with excitation wavelengths of below 260 nm in Fig. 2(a). Such observation is related to red-shift of the absorption edge due to the lattice expansion [13].

 

Fig. 2 Luminescence spectra observed for $\beta$- Ga₂O₃:Si with various excitation wavelengths at (a) 20 K and (b) 300 K.

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Figures 3(a) and (b) show temperature dependence of the luminescence spectra excited at 210 and 270 nm for $\beta$-Ga₂O₃:Si, respectively. Although the luminescence intensity excited at 210 nm decreases drastically above 160 K, the line shape does not change as shown in Fig. 3(a). The 20 K luminescence spectrum excited at 270 nm is decomposed into the weak UV/ blue and relatively strong blue/green bands, denoted by two dot-dashed lines Fig. 3(b). In increasing temperatures, the blue/green band gradually decreases, and disappears above 220 K. On the other hand, the intensities of the UV/blue bands are nearly constant below 180 K, and increase above 180 K. The intensity at 300 K is three times larger than that at 20 K. These results suggest that the emission centers associated with the blue/green band are unstable above 180 K and energy transfer occurs from the blue/green-band to the UV/blue-bands centers.

 

Fig. 3 Temperature dependence of the luminescence spectra for $\beta$-Ga₂O₃:Si excited with (a) 210 nm and (b) 270 nm.

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Figure 4 shows the persistent phosphorescence (PP) spectra for $\beta$-Ga₂O₃ (4N) and $\beta$-Ga₂O₃:Si excited at 266 nm at 15 K when the spectra were observed at 2 s after removal of 266 nm UV light. The UV/blue bands for both samples as shown in Fig. 2(a) completely disappear. The spectrum for $\beta$-Ga₂O₃:Si is slightly red-shifted. The intensity for $\beta$-Ga₂O₃:Si is one order of magnitude weaker than that for $\beta$-Ga₂O₃ (4N). The reason will be discussed later. In addition, the PP intensities for $\beta$-Ga₂O₃ (4N) decrease gradually in increasing the temperature above 15 K and completely disappear above 150 K [5].

 

Fig. 4 Persistent phosphorescence spectra for $\beta$-Ga₂O₃ (4N) and $\beta$-Ga₂O₃:Si at 15 K when measured at 2 seconds after removal of 266 nm UV light.

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Figure 5(a) shows the decay curves of the UV/blue band fixed at 390 nm in the $\beta$-Ga₂O₃:Si observed in the time range between 0 and 400 $\mu$s. The decay curves cannot fit a single exponential function, but are composed of, at least, two exponential components. The fastest decay component with a decay time of 1.5 $\mu$s, denoted by a dotted line in Fig. 5(a), is assigned to a self-trapped exciton composed of electron and self-trapped hole [4]. The other decay time is ten times longer than the fastest one and may be due to excitons bound to Si impurities. The decay curves are independent of temperature from 20 to 300 K. Figure 5(b) shows the decay curves of the blue/green band fixed at 520 nm when measured at 50 and 300 K. The non-exponential curves indicate a distribution of the decay times in the range from ~10 to 400 $\mu$s. The fastest component below 5 $\mu$s is associated with the tail of the UV/blue bands extended to longer wavelengths.

 

Fig. 5 Decay curves of the luminescence intensities at (a) 390 nm and (b) 520 nm for$\beta$-Ga₂O₃:Si when measured at 50 and 300 K with 270 nm excitation in the time range of 0-400 $\mu$s.

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In order to confirm the distribution model of the decay time, the decay curves $\beta$-Ga₂O₃:Si are redrawn in log-log scales as shown in Fig. 6(a). The decay curves at 50 and 300 K fit a function of t^-n with n = 1.14 and 1.32, respectively, except for the fastest decay components below 5 $\mu$s. When temperature increases, the enhancement of the slope of the decay curve at 300 K indicates that a nonradiative decay process is added in the deexcitation process. In comparison, the decay curves of the whole persistent phosphorescence intensities in $\beta$-Ga₂O₃ (4N) in the time range between 1 and 10³ s are shown in Fig. 6(b). The decay curves in the temperature range from 15 to 110 K fit a function of t^-n (n~0.8-0.9). The initial intensities at t = 1 s drastically decrease in increasing temperature. Above 150 K, the intensities disappear.

 

Fig. 6 (a) Decay curves of the luminescence intensities at 520 nm excited at 270 nm in the time range of 3-400 $\mu$s for$\beta$-Ga₂O₃:Si with log-log scales. (b) Decay curves of the phosphorescence intensities excited at 266 nm and at 15 and 110 K in the time range of 1-10³ s for $\beta$-Ga₂O₃ (4N) with log-log scales.

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3.2 ESR spectra

The ESR measurement gives information on carriers of electrical conductivity. The anisotropic g values of less than 2 estimated from the sharp ESR line in $\beta$-Ga₂O₃ (4N) deduce that electrons move in the chain structure along the b-axis direction [3]. On the other hand, the ESR signals for $\beta$-Ga₂O₃ (6N) are two orders of magnitude weaker than those for $\beta$-Ga₂O₃ (4N). The decrease of the ESR signals corresponds to the decrease of free electron densities, that is, the disappearance of the absorption/reflection in the near-IR region as shown in Fig. 1.

The ESR spectra for $\beta$-Ga₂O₃:Si are coincident with those for $\beta$-Ga₂O₃ (4N) except the intensity [2,3]. Inset in Fig. 7 shows the typical ESR line due to conduction electrons. The line widths in Fig. 7 drastically increase above 200 K. Such line-broadening can be explained by the spin-lattice relaxation process [14]. There are three processes; (1) direct process, (2) Raman process, and (3) Orbach process [14]. The Orbach process is dominant at high temperatures. The line width is proportional to the inverse of the longitudinal spin-lattice relaxation time (T₁). The width ($\gamma$), defined as the peak-to-peak width, is given in the form of [14]

 

Fig. 7 Temperature dependence of the ESR line width of conduction electrons in $\beta$-Ga₂O₃:Si. Solid curve is calculated using Eq. (1) and parameters of a = 0.053, b = 0.5 and $\Delta$ = 1430 K ( = 120 meV).

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3.3 Photoconductivity

Electrical conductivity of $\beta$-Ga₂O₃ single crystals is in the range from 0.02 to 50 ($\Omega$⁻¹cm⁻¹), which is determined by concentrations of oxygen vacancies as donors [2, 3, 9, 10]. On the other hand, the conductivity of $\beta$-Ga₂O₃:Si can be intentionally controlled over three orders of magnitude by Si doping [9, 10]. The related free-carrier concentrations, varying between 10¹⁶ and 10¹⁸ cm⁻³, correspond to a 25%–50% effective Si donors and the remains are trapped electrons.

Figure 8 shows photocurrent responses produced in $\beta$-Ga₂O₃ (4N) by 266 nm pulsed laser light with ~10 ns. The pulse width was determined by a current amplifier with a filter frequency response (<35kHz) of a low pass filter. The photocurrent is independent of applied voltage, and proportional to light power. The photocurrent for $\beta$-Ga₂O₃ (6N) could not be observed even at high power of 8 mJ because lifetimes of electron and hole, close to the decay time (1.5 $\mu$s) of the self-trapped excitons, are too short to be detected as photocurrent. In consequence, the observed photocurrent is strongly associated with distant electron and hole pairs.

 

Fig. 8 Pulse response of photocurrent produced by 266 nm light with a width of ~10 ns for $\beta$-Ga₂O₃ (4N) as a function of (a) applied voltage and (b) light power.

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4. Mechanism of persistent phosphorescence

The intrinsic luminescence spectrum for $\beta$-Ga₂O₃ consists of the UV/blue and blue/green bands. The broadband feature is ascribed to strong electron-phonon interaction, that is, localized states of electron and hole. The UV/blue bands are due to self-trapped excitons which are composed of self-trapped hole bound to electron [4, 15]. The decay curves of the bands at 390 nm with the 210 nm excitation do not change in the temperature range between 50 and 300 K as shown in Fig. 5(a). This result suggests the self-trapped excitons are stable up to 300 K. The blue/green band excited around the band tail in the range from 260 to 290 nm is responsible for the persistent phosphorescence as shown in Fig. 4. In a previous paper [16], the ESR results for persistent phosphor Ca₂SiAl₂O₇ doped with Ce³⁺ were reported that electron and hole created by the UV excitation are trapped at oxygen vacancies and Al lattice sites in tetrahedra, respectively. Taking account of these results, holes in $\beta$-Ga₂O₃ are expected to be self-trapped at Ga sites in tetrahedra and electrons are trapped at oxygen vacancies of sites sharing two octahedra and one tetrahedron [3]. In consequence, the persistent phosphorescence occurs through tunneling recombination of self-trapped holes and nearby trapped electrons. With an assumption that trapped electrons and self-trapped holes are distributed uniformly in the crystal, the decay curve is approximately represented by the t⁻¹ power function [7], and is consistent with the decay curves of the persistent phosphorescence for $\beta$-Ga₂O₃ (4N) and $\beta$-Ga₂O₃:Si with different time scales of 1-10³ s and 1-10² $\mu$s in Fig. 6 (b) and (a), respectively.

Next, we consider the difference in the decay times of the persistent phosphorescence in $\beta$-Ga₂O₃ (4N) and $\beta$-Ga₂O₃:Si. The theoretical calculation of the decay curve using the recombination model of a nearest neighbor pair consisting of self-trapped electron and self-trapped hole in PbBr₂ crystals, proposed by Iwanaga et al. [17], and given in the form of,

The difference in the persistent phosphorescence intensities in $\beta$-Ga₂O₃ (4N) and $\beta$-Ga₂O₃:Si is explained by a distribution model of electrons trapped at oxygen ion vacancies, or Si-impurities [4]. The concentration of trapped electrons for $\beta$-Ga₂O₃:Si can be controlled by Si-doping level and is larger than that for $\beta$-Ga₂O₃ (4N) [9]. In increasing the concentration of trapped electrons, the average distance between self-trapped hole and trapped electron decreases. In consequence, the recombination time of self-trapped hole and trapped electron is shortened, that is, the value of $\tau$₂ is decreased and approaches the lifetime of self-trapped excitons [17]. The concentration is low enough to increase the recombination times in the range from $\mu$s to ms or s. This expectation is in agreement with the fact that recombination lifetimes of donors and acceptors in semiconductors, for example, GaP:S:C, are distributed in the range between 1 $\mu$s and 1 ms [6].

5. Conclusions

The observation of persistent phosphorescence spectra below 150 K for $\beta$-Ga₂O₃ (4N) and $\beta$-Ga₂O₃:Si indicates that there are stably trapped electrons and self-trapped holes at low temperatures. The concentration of trapped electrons in the $\beta$-Ga₂O₃ determines the recombination times of electron and hole from sub-millisecond to second. The persistent phosphorescence observed in the time range between 1 and 10³ s is due to electron-hole pairs with the long average distances.

The temperature dependence of the ESR line widths of the conduction electrons, the electrical resistivity, and the persistent phosphorescence intensities is observed in the $\beta$-Ga₂O₃ (4N). These results suggest the existence of electrons trapped at ~120 meV below the bottom of the conduction band. In increasing temperatures, electrons trapped at low temperatures are excited thermally into the conduction band, and move in the crystal. The electron migration reduces the persistent phosphorescence intensity and enhances the electric conductivity and the photocurrent. In consequence, the transparent conductive oxide$\beta$-Ga₂O₃ single crystal behaves not only like a wide-gap semiconductor, but also like an insulator with persistent phosphorescence properties.

The present results have shown the important role of the intrinsic deficits associated with oxygen vacancies and Si-doping in the host crystal. The oxygen vacancies are formed through evaporation in GaO and O₂ from the molten zone. It is very difficult to control the concentration of the oxygen vacancies through the growth conditions. On the other hand, the electrical conductivity can be intentionally controlled through the Si-doping level. The shallowly trapped electrons in $\beta$-Ga₂O₃ contribute to both the persistent phosphorescence below 150 K and the high conductivity above 200 K. In order to observe the persistent phosphorescence at room temperature, deep electron-trapped centers are required. However, they do not contribute to the conductivity below room temperature.

At last, a good understanding of the formation of these defects centers leads to high electrical conductivity and/or intense persistent phosphorescence in wide-gap semiconductors for the desired optical and electrical response to special applications.