Electron injection-induced effects in Si-doped $β$-Ga₂O₃ Open Access

Wide bandgap semiconductors such as GaN and ZnO are important for a number of applications ranging from flame detection and high temperature electronics to solar-blind ultraviolet detectors and sensors for use in extreme environmental conditions.^1–3 An emerging semiconductor with a direct bandgap of 4.69 eV (ultra-wide bandgap), Ga₂O₃ has become an attractive candidate for radiation applications in terms of its superior stability over GaN and ZnO.^1,4–9

So far, the main limiting factor in Ga₂O₃ technology is related to difficulties of p-type conductivity realization.^7,9–11 Previous studies indicate that holes in β-Ga₂O₃ have characteristics of low dispersion, high effective mass and high density of states. This results in formation of weak polarons (or localized holes), trapped by lattice distortions in the vicinity.^12–16 Contradicting these claims, Refs. 6 and 10 has recently experimentally shown a possibility of p-type conductivity in Ga₂O₃. It is additionally reported that the self-trapping nature of holes is destroyed at temperatures above 90-120 K.¹¹ Given the current state-of-the-art and ever mounting interest in p-type Ga₂O₃, one can reasonably claim that a robust p-type Ga₂O₃ electrical conductivity, if not yet fully feasible, will be possible in the foreseeable future.

In Ga₂O₃, if bipolar devices become available, minority carrier transport (diffusion length) will be of primary importance. Minority carrier diffusion length defines the performance of bipolar devices such as p-n junction diodes, bipolar transistors and p-i-n detectors.^6,9,17 One of the major issues in the current ZnO and GaN device technology, is the low diffusion length of minority carriers, partially due to dislocation scattering.^18,19 It has been previous shown that in p-type GaN and ZnO, electron injection either with an electron beam or forward bias, results in significant increase in minority carrier diffusion length.^18,20–23 Such an increase in the diffusion length translates into changes in the material’s optical properties and improved photovoltaic detector performance.

Recent studies on diffusion length of minority holes in n-type β-Ga₂O₃ report the value ∼ 400 nm at room temperature.^24,25 Hence, like in the case of ZnO and GaN, the issue of short diffusion length for minority carriers also exists in β-Ga₂O₃ and limits its possible applications in bipolar devices. This paper demonstrates the impact of electron injection on minority carrier transport in Si-doped β-Ga₂O₃. This study testifies that: 1) one can engineer minority carrier diffusion length with electron injection (increase it several times); 2) the non-equilibrium holes, generated due to electron beam, are not self-trapped and contribute profoundly to the Electron Beam-Induced Current.

Electron Beam-Induced Current (EBIC) and Cathodoluminescence (CL) techniques^3,18,20–23 were employed in-situ in Philips XL30 Scanning Electron Microscope (SEM) to study the effect of electron injection on minority carrier transport, namely, diffusion length (L) and lifetime (τ) in β-Ga₂O₃. The samples involved in the study consisted of epitaxial Si-doped β-Ga₂O₃ grown on Sn-doped β-Ga₂O₃ substrate. The epitaxial layer growth was carried out by Halide Vapor-Phase Epitaxy (HVPE), courtesy Novel Crystal Technology, and the Sn-doped β-Ga₂O₃ substrate with [001] orientation was grown by edge-defined film-fed method (Tamura Corporation, Japan). Hall measurements on the n⁺- doped substrate showed a carrier concentration of ∼ 2.2×10¹⁸ cm^-3. The initial thickness of epitaxially grown Si-doped (with electron concentration ∼ 3.6×10¹⁶ cm^-324) β-Ga₂O₃ layer was 20 μm, which was subsequently reduced to 10 μm after chemical-mechanical polishing. Schottky rectifiers were obtained by making Schottky contacts (Ni – 20 nm/Au – 80 nm) on the epitaxial Si-doped β-Ga₂O₃ layer with photolithography/liftoff technique, and Ohmic contact on the Sn-doped β-Ga₂O₃ substrate (Ti – 20 nm/Au – 80nm) by blanket evaporation over the entire back side of the substrate. The diameter of the top contacts, used for measurements, was 210 μm.

The diffusion length of minority carriers was determined using line-scan EBIC technique in the planar configuration^24,26–30 with electron beam energy of 10 keV (corresponding to the electron range of ∼ 0.4 μm and the absorbed current of ∼ 0.4 nA in the material) in the temperature range of 23-120 °C (hot-stage of Gatan MonoCL2 system, integrated with Philips SEM, was used for varying temperature). A single line-scan, carried out from the edge of the Schottky barrier outwards (cf. Fig. 1, top-right inset), takes about 6 seconds. While L values can be extracted from this single line-scan, in this work, a scanning of the region of interest was not interrupted and was continued for a total duration of electron injection up to 720 seconds with periodic L measurements. Since this material was very sensitive to electron injection, the measurements for various temperatures were done at different locations, to exclude any possibility of uncalibrated electron injection. Line-scans were recorded using a home-made software interfaced with Stanford Research Systems Low-Noise Current Amplifier (SR570) and Keithley DMM 2000 digital multimeter.

Variable-temperature CL measurements were carried out using Gatan MonoCL2 attachment to the SEM and an integrated temperature controller with an accuracy of 0.5 °C. The CL spectra were recorded with a single grating (1200 lines/mm blazed at 500 nm) monochromator and a Hamamatsu photomultiplier tube, sensitive in the 150-850 nm range. SEM electron beam with energy of 10 keV was used for excitation of 1 μm x 1 μm area, located at 10 μm distance from the Schottky contact, for a total electron injection duration of 3000 seconds.

The material was first analyzed at “zero” electron injection dose before studying the impact of electron injection. A single line-scan of 6 seconds was used, which had virtually no impact on L. A typical EBIC line-scan taken at room temperature is shown in Fig. 1, where the current is shown as a function of beam position measured from the edge of the Schottky contact.

L was extracted from the experimental data in Fig. 1 using the following equation:^{27,29,31–33}

where, x is the beam-to-junction distance, I₀ is a scaling constant, L is the diffusion length of minority carriers (holes, in this case), and α represents a surface recombination velocity and takes values between -1/2 and -3/2. Equation (1) is true for x>>d, where d is the depletion region width. Width of the depletion region is calculated as d = [2εε_r(V_bi-V)/(qN_B) ]^0.5, where ε_r is the relative permittivity, V is the applied voltage, V_bi is the Schottky barrier built-in potential, q is the electron charge, and N_B is the bulk doping level in β-Ga₂O₃. In this case, ε_r=10.5,¹ V_bi=1.025 V,³⁴ V=0 V, and N_B=3.6×10¹⁶ cm^-3, resulting in d ≈ 179 nm, which is at least 8 times less than x.

In equation (1), I₀, α, and L are fit parameters, and the fit was performed at the knee region of the curve in Fig. 1, which ensures the accuracy of the extracted parameters according to the constraint x > 2L.^31,35 Moreover, a modified form of equation (1), given below, reduces the three-parameter nonlinear fit to a linear one, as shown in the bottom-left inset of Fig. 1:

L was calculated as the inverse slope of the linear fit according to equation (2). The best linear fit was obtained for α = -3/2, which is, therefore, used throughout the article.

Temperature dependence of the L is given by:³² 

where k is the Boltzmann constant, L₀ is the asymptotic diffusion length, and T is the temperature in Kelvin. ΔE_A,T is the activation energy associated with a charge trap in the forbidden gap.³² Temperature dependence of L is shown in Fig. 2. Similar to the previously reported results,²⁵ L exhibits a decrease from ∼ 430 nm at room temperature to ∼ 320 nm at 120 °C.

The decrease in L with temperature is not commonly observed in other semiconductors. In GaAs, ZnO and GaN, for example, L increases with temperature.^3,18,31 The activation energy, estimated from the Arrhenius plot (Fig. 2, inset) using equation (2), is ∼ 53 meV. This energy is most likely associated with Si-donors, which form fairly shallow 50 meV levels.^36,37 A likely cause for L reduction with growing temperature could be related to thermalization of carriers.³⁸ Carrier-carrier interaction significantly contributes to thermalization only for high carrier concentrations (> 1x10¹⁸ cm^-3). For elevated temperatures and relatively low doping levels, such as in this case, carrier-phonon interaction becomes a dominating factor,^39,40 which leads to L decrease.

Continuous exposure of the sample to electron beam resulted in a significant x4.5 increase in L as shown in Fig. 3. A similar effect was also observed in p-type ZnO and GaN as reported previously.^18,21 Fig. 3 (top inset) shows the EBIC line-scans for repeated exposures up to 720 seconds. A clear elongation (tail) is observed in the EBIC signal decay (compare a line-scan after 120 and 720 seconds of continuous electron beam excitation). As can be seen from equation (1), a longer tail in the EBIC signal dependence on distance, manifests in longer minority carrier diffusion length. A marked increase in the amplitude of the EBIC signal is also observed at the same time (cf. top and bottom insets of Fig. 3). The increase in the EBIC signal amplitude is attributed to the rise of the collection efficiency of minority carriers: longer L results in larger number of non-equilibrium minority electrons swept by built-in field of the Schottky barrier used in the measurements. The EBIC collection efficiency increases up to a certain value of L, after which any increase in L (which slows down with electron injection duration; cf. Fig.3, top inset) has no effect on the EBIC signal amplitude.^41–43 The diffusion length in Fig. 3 exhibits a saturation (not shown on the plot), following a saturation of I_max (cf. Fig. 3, bottom inset). It should be noted that the increased values of L, achieved due to electron beam injection, persist for at least one day at room temperature following injection.

Fig. 4 shows the effect of moderate electron injection duration on minority carrier diffusion length. This study was carried out at variable temperature to understand its impact on the rate of L increase (μm/sec) due to electron injection. The plot for room temperature in Fig. 4 can be correlated with the 0-100 second segment of L versus electron injection duration in Fig. 3, with a slight mismatch in slope attributed to different locations for two experiments.

The effect of temperature on the rate, R, of L increase with electron injection duration can be described as:¹⁸ 

where R₀ is a constant, ΔE_A,T is thermal activation energy for diffusion length (from equation (3)), and ΔE_A,I is the activation energy due to electron injection effect.

As R implicitly contains the injection information in the form of L versus electron injection duration, t (R=dL/dt), use of equation (4) to calculate ΔE_A,I is justified. In equation (4), the first exponent represents L dependence on temperature (cf. equation (3), in which a ½ factor in the exponent is due to equation (5) (see below)); the second exponent is a Boltzmann factor, which is used to model the temperature dependence of electron injection effect. One can see from Fig. 4 that R decreases with increasing temperature. Fig. 4 (inset) shows the Arrhenius plot with a linear fit of R vs. 1/kT, according to equation (4), yielding ΔE_A,I to be ∼ 74 meV. Similar activation energy, attributed to yet unknown recombination center, was recently observed in an independent study.⁴⁴ 

The diffusion length of minority carriers is an integral quantity, which is related to the lifetime of non-equilibrium carriers in the band by the relation:¹⁹ 

where D is the diffusion coefficient and τ is the minority carrier lifetime. A larger lifetime of non-equilibrium carriers in the band indicates lower number of radiative recombination events.⁴⁵ If L increase is due to an increase in τ, the CL intensity from the radiative recombination process should decrease with duration of electron injection. Indeed, from the CL experiment performed at room temperature (Fig. 5), a decrease in the CL intensity I, was observed with the duration of electron injection.

Earlier studies have shown that $I−1∝τ$⁠.⁴⁵ Moreover, L depends linearly on electron injection duration (Figs. 3, 4) and on $τ$ (equation (5)). Hence, it is concluded that the dependence of CL intensity on electron injection duration, t, should be given by $I−1/2∝t$⁠.⁴⁵ This relation was verified by the linear fit in Fig. 5, inset, which is also in agreement with the assumption that the linear increase of L with injection duration is due to an increased lifetime for minority carriers.

The proposed model for the observed electron injection-induced effects in β-Ga₂O₃ is as follows:

• Non-equilibrium electron-hole pairs are generated in β-Ga₂O₃ due to electron beam irradiation. The total charge, injected into the region under investigation due to this irradiation, is up to 1.2 μC.

• We expect that the unknown traps with activation energy of 74 meV (see above) can capture some non-equilibrium electrons. A similar situation was observed in Mg-doped GaN and Sb-doped ZnO.^3,18,21–23

• As a portion of non-equilibrium electrons is captured, these traps stop playing a role in the recombination process (mostly radiative, cf. Fig. 5) and the non-equilibrium electrons and holes live longer life (τ) in the conduction and valence bands, respectively. Increased τ leads to longer minority carrier diffusion length L (as measured by EBIC) and suppressed CL intensity from the region subjected to electron irradiation (cf. Fig. 5). As the electron injection continues, the number of traps, available to capture non-equilibrium electrons, saturates. As a result, the EBIC signal amplitude (cf. insets of Fig. 3) and the CL intensity (cf. Fig. 5) reach their saturation levels.

• As the temperature increases, trapped electrons have a higher chance to escape and recombine with holes in the valence band. At the same time, the traps again become available for recombination. This leads to a reduced rate R (for L increase with electron irradiation duration) at elevated temperatures (cf. Fig. 4).

In conclusion, this study demonstrates a significant increase of minority hole diffusion length in n-type β-Ga₂O₃. Enhancement of minority carrier transport is accompanied by the consistent changes in the material’s optical properties. Both effects are related to an increased lifetime for non-equilibrium carriers in the conduction and valence bands (non-equilibrium electrons and holes are generated in pairs). Additionally, the experiments show that minority holes may substantially contribute to current in β-Ga₂O₃ semiconductor, which is an argument against self-trapping at room and elevated temperatures.

Research at UCF and the Weizmann institute was supported in part by NATO (award # G5453) and NSF (UCF award # ECCS1802208). The work at UF was sponsored by the Department of Defense, Defense Threat Reduction Agency, HDTRA1-17-1-011, monitored by Jacob Calkins.