By combining temperature-dependent resistivity and Hall effect measurements, we investigate donor state energy in Si-doped β-Ga2O3 films grown using metal-organic vapor phase epitaxy. High-magnetic field (H) Hall effect measurements (–90 kOe ≤ H ≤ +90 kOe) showed non-linear Hall resistance for T < 150 K, revealing two-band conduction. Further analyses revealed carrier freeze out characteristics in both bands yielding donor state energies of ∼33.7 and ∼45.6 meV. The former is consistent with the donor energy of Si in β-Ga2O3, whereas the latter suggests a residual donor state. This study provides critical insight into the impurity band conduction and the defect energy states in β-Ga2O3 using high-field magnetotransport measurements.

β-Ga2O3 possesses wide bandgap (4.6–4.9 eV),1 high theoretical electrical breakdown (∼8 MV/cm),2 and high conductivity with reasonably high room-temperature mobility,3 ∼184 cm2 V−1 s−1, making it an attractive candidate for high-power device applications including ultra-violet (UV) photodetectors.4–8 Furthermore, access to low-cost, large-scale (up to 6 in.) native substrates with low threading dislocation density (103–104 cm−2) offers significant advantages for β-Ga2O3 epitaxy.5β-Ga2O3 has monoclinic symmetry (space group C2/m), with lattice parameters of a = 12.214 Å, b = 3.037 1 Å, c = 5.798 1 Å, and β = 103.83°, and is the only stable polymorph of Ga2O3 up to the melting point.9 Within the structure, Ga3+ ions are both tetrahedrally and octahedrally coordinated, while O2– ions are either trigonally or tetrahedrally coordinated.10 This structural complexity complicates the doping study. For instance, it is conceivable that the local electronic structure can vary significantly depending on the dopant size and the sites that it occupies. Despite this obvious challenge, the thermal, optical, and electrical transport properties of β-Ga2O3 have been studied extensively, both experimentally and using first-principles calculations2–5,9,11–24

Silicon (Si) is shown to be a shallow n-type donor in β-Ga2O3.5,9 Yet, there remains a large inconsistency in the reported ionization energy of Si. For instance, activation energy of donors in Si-doped β-Ga2O3 ranges from 16 to 50 meV.13,25 The variation in donor activation energies has been attributed to the donor density25 and to the presence of defects and impurities arising from various growth techniques.26,27 Relatively deeper donors with activation energies of 80–120 meV have also been reported, the origin of which is attributed to the presence of antisites, interstitials, and/or extrinsic impurities.3,20,28 Deep level states such as DX centers, which are defect complexes formed between the isolated substitutional donor atom (D) and an unknown lattice defect (X), are also studied in β-Ga2O3. Using the electron paramagnetic resonance (EPR) study, Son et al. reported the DX center in unintentionally doped β-Ga2O3 with activation energies of 44–49 meV for partially activated centers, reducing to 17 meV for fully activated DX centers.29 However, recent transport measurements refuted the presence of DX centers in doped β-Ga2O3 based on the low-field magnetotransport analysis.25 As the presence of DX centers is determinantal for Ga2O3-based heterojunction devices, this certainly raises important questions: why there is such discrepancy in the reports of DX centers in β-Ga2O3? Can this be due to the variation in the materials depending on the synthesis conditions? Clearly, further investigations of the growth condition-structure-defect-property relationships would help address these questions.

In an attempt to investigate donor state energies in Si-doped β-Ga2O3, we performed detailed temperature-dependent magnetotransport studies of homoepitaxial Si-doped β-Ga2O3 films grown via metal-organic vapor phase epitaxy (MOVPE). Low-magnetic field (H) Hall effect measurements (–20 kOe ≤ H ≤ +20 kOe) showed single band conduction with an activation energy of ∼17 meV. In sharp contrast, high-magnetic field (–90 kOe ≤ H ≤ +90 kOe) Hall effect measurements revealed two-band conduction with activation energies of ∼34 and ∼46 meV. We discuss the origin of these energy states in the context of Si donor state energy and a residual donor state, respectively.

Si-doped β-Ga2O3 films were grown on (010) Fe-doped semi-insulating β-Ga2O3 substrates using an MOVPE reactor (Agnitron Agilis). Triethylgallium (TEGa) and molecular O2 were used as a source of Ga and oxygen in the presence of Ar as a carrier gas. The substrate temperature was fixed at 810 °C. Si was used as an n-type dopant and was controlled by varying the molar ratio of diluted silane (SiH4) to TEGa.16 Ohmic contacts were achieved by sputtering Ti/Au (50 nm/50 nm) stacks using shadow mask followed by a rapid thermal annealing at 470 °C in nitrogen for 90 s. Temperature-dependent electrical measurements were performed in Van der Pauw geometry using a physical property measurement system (PPMS® DynaCoolTM). Excitation currents of 1–10 μA were used.

Figures 1(a) and 1(b) show temperature-dependent resistivity (ρ) and carrier density, respectively, for a 655 nm Si-doped β-Ga2O3/Fe-doped β-Ga2O3 (010). The schematic of the sample structure is shown in the inset. It is noted that the Hall measurement in the low-field between ±20 kOe yielded linear behavior. The Hall coefficient (RH) in Fig. 1(b) is, therefore, extracted from the linear slope of Hall resistance (Rxy) vs H, where H was varied between ±20 kOe. Temperature dependence carrier density showed a decrease in carrier density from 7.8 × 1017 cm−3 at 300 K to 6.74 × 1016 cm−3 at 65 K followed by an unexpected upturn at low temperatures, 40 ≤ T ≤ 65 K, which saturates to a value of 2.15 × 1017 cm−3 for T < 40 K. The inset shows electron mobility as a function of temperature, revealing drift-diffusive transport as evident from the relatively high low-temperature mobility of ∼10 cm2 V−1 s−1 for T < 40 K. To further elucidate this observation, we show in Figs. 1(c) and 1(d) Arrhenius plots of ρ and RH, revealing nominally three distinct regimes: (i) 225 ≤ T ≤ 300 K where ρ decreases and RH increases with decreasing temperature, (ii) 65 K ≤ T ≤ 225 K where there is a rapid increase in ρ with decreasing temperature accompanied by an increase in RH, and (iii) 40 ≤ T ≤ 65 K where ρ continues to increase with decreasing temperature but now RH begins to decrease. Below 40 K there is nearly no variation in RH. This behavior is remarkably similar to the previously observed temperature dependence of ρ and RH in doped germanium (Ge) and other heavily doped semiconductors.30,31 These characteristics have further been attributed to impurity band conduction where carrier conduction occurs in both conduction and impurity bands. Most recently, Kabilova et al. also observed an identical behavior in Sn-doped β-Ga2O3 and attributed it to the two-band conduction.32 At higher T, conduction is dominated by electrons in the conduction band, whereas at low temperatures, donor-derived impurity band conduction dominates.31 Given two-band conduction and drift-diffusive transport, one can, therefore, write the overall resistivity and Hall coefficient (RH) as

ρ(T)=tfilm(n1eμ1+n2eμ2)1,
(1)
RH=n1μ12+n2μ22e(n1μ1+n2μ2)21,
(2)

where (n1, μ1) and (n2, μ2) represent the temperature-dependent sheet carrier density and mobility in the conduction band and the impurity band, respectively. tfilm represents the film thickness.

FIG. 1.

(a) Temperature-dependent ρ and RH from a 655 nm Si-doped β-Ga2O3/Fe-doped β-Ga2O3 (010). The inset shows the schematic of the sample structure. (b) 3D carrier density (eRHtfilm)−1 as a function of temperature, where RH is the Hall coefficient, tfilm is the film thickness, and e is an electronic charge. (c) and (d) Arrhenius plots of ρ and RH. The red symbols in parts (c) and (d) are calculated ρ and RH using the two-band conduction model.

FIG. 1.

(a) Temperature-dependent ρ and RH from a 655 nm Si-doped β-Ga2O3/Fe-doped β-Ga2O3 (010). The inset shows the schematic of the sample structure. (b) 3D carrier density (eRHtfilm)−1 as a function of temperature, where RH is the Hall coefficient, tfilm is the film thickness, and e is an electronic charge. (c) and (d) Arrhenius plots of ρ and RH. The red symbols in parts (c) and (d) are calculated ρ and RH using the two-band conduction model.

Close modal

To further investigate two-band conduction in our films, we performed high-field Hall measurements. Figure 2(a) shows Rxy as a function of H at 40 K ≤ T < 150 K. H was swept between ± 90 kOe. Longitudinal resistance (Rxx) as a function of H is shown in supplementary material Fig. S1, revealing a positive magnetoresistance behavior at all temperatures, whereas Rxy (H) showed non-linearity as illustrated in Fig. 2(a). The latter is consistent with two-band conduction. It is also noted that the non-linearity arising from the magnetic field dependence of the Hall scattering factor is ruled out (see the supplementary material). We analyzed our experimental results using the two-band conduction model. In this model, Rxy (H) can be written as

RxyH=H/en1μ12+n2μ22+H2μ12μ22n1+n2n1μ1+n2μ22+H2μ12μ22n1+n22.
(3)
FIG. 2.

(a) Rxy vs H at T < 150 K showing non-linear behavior. (b) Hall conductance, Gxy=Rxy/Rxy2+Rxx2, along with fits (black solid lines) using the two-band conduction model.

FIG. 2.

(a) Rxy vs H at T < 150 K showing non-linear behavior. (b) Hall conductance, Gxy=Rxy/Rxy2+Rxx2, along with fits (black solid lines) using the two-band conduction model.

Close modal

In this equation, there are four unknowns (n1, μ1 n2, and μ2) that can be further reduced to two unknowns by calculating Hall conductance, GxyH using experimentally measured Rxy(H) and Rxx(H),

GxyH=RxyRxy2+Rxx2=eH(C1μ1C2μ1μ211+μ22H2+C1μ2C2μ2μ111+μ12H2),
(4)

where C1=n1μ1+n2μ2 and C2=n1μ12+n2μ22. It should be noted that C1 and C2 are known experimentally from the conductance and the linear slope of the Hall conductance at zero magnetic field, respectively. Details of this analysis can be found elsewhere.33,Figure 2(b) shows calculated GxyH along with fits (solid lines) using Eq. (4) at different temperatures, revealing an excellent match between experiments and the two-band conduction model. This analysis yielded μ1 and μ2 (from the fits), which, in turn, allowed us to calculate n1 and n2.33 

Figure 3 shows T-dependent n1, μ1, n2, and μ2 at 40 K ≤ T ≤ 150 K. Using n1, μ1 n2, and μ2 as a function of T, we calculated ρ and RH using Eqs. (1) and (2). The calculated ρ (T) and RH (T) are shown in Figs. 1(c) and 1(d) using open red symbols, revealing an excellent match with experimental data. Our analysis, therefore, shows self-consistent results providing further confidence in the two-band conduction model. We, however, note that our analysis yielded reasonably good fits with similar values of μ1 and for a μ2 value between 0.1 and 10 cm2 V−1 s−1. In Fig. 3(a), we show μ2 = 10 cm2 V−1 s−1, which is closer to the mobility values at low temperature using our low-field Hall measurements and is also reported for impurity band conduction in β-Ga2O3.13,15,34 It is also noted that this value of μ2 = 10 cm2 V−1 s−1 remains independent of T for T < 40 K as shown in the inset of Fig. 1(b). On the other hand, μ1 first increases with decreasing temperature, reaching a peak value of 796 cm2 V−1 s−1 at 65 K, and then begins to decrease. The increase in μ1 follows T−0.5 behavior [Fig. 3(c)], which is consistent with phonon-related scattering in β-Ga2O3 in agreement with the previous reports,14,25 whereas the drop in mobility for T < 65 K is consistent with the ionized impurity scattering. Significantly, this temperature is the same at which RH was found to decrease in Fig. 1(d), suggesting that the scattering centers are likely the donor-derived ionized impurities. Unlike μ1, μ2 was found to be low and T-independent, which is again consistent with the presence of the impurity band.13,15

FIG. 3.

(a) 3D carrier densities, n13D and n23D, and their corresponding mobilities μ1 and μ2 extracted from the two-band conduction model as a function of temperature. (b) Arrhenius plots with linear fits for n13D and n23D with corresponding activation energies En1a and En2a. The inset shows defect state energies illustrating En1a and En2a. Here, Ed and Edef refer to the Si donor state and residual state energies, respectively, within the bandgap. (c) μ1 vs T−1/2 along with a linear fit. The dashed lines are given as guides to the eye.

FIG. 3.

(a) 3D carrier densities, n13D and n23D, and their corresponding mobilities μ1 and μ2 extracted from the two-band conduction model as a function of temperature. (b) Arrhenius plots with linear fits for n13D and n23D with corresponding activation energies En1a and En2a. The inset shows defect state energies illustrating En1a and En2a. Here, Ed and Edef refer to the Si donor state and residual state energies, respectively, within the bandgap. (c) μ1 vs T−1/2 along with a linear fit. The dashed lines are given as guides to the eye.

Close modal

We now turn to the discussion of donor state energy. First, we present results from the analyses of low-field Hall effect measurements, yielding single band conduction with an activation energy of ∼17 meV (supplementary material Fig. S2). This energy state is in good agreement with the published results of Si activation energy in Si-doped β-Ga2O3 near the Mott insulator-to-metal transition.25 However, our analyses using high-field Hall effect measurements resulted in a deeper understanding of transport activation behavior. Figure 3(b) shows Arrhenius plots for n13D (n1/tfilm) and n23D (n2/tfilm) extracted from the two-band conduction model. This plot yielded linear slopes with activation energies of Ean1 = 33.7 meV and Ean2 = 11.9 meV, respectively. The donor ionization energy of Si in β-Ga2O3 is reported to be ∼36 meV, which is close to Ean1, suggesting that Si shallow donors are the source of high-mobility carriers and that they are responsible for conduction at higher temperatures.13,25 The corresponding high mobilities, 285 cm2 V−1 s−1 (T = 150 K) < μ1 < 678 cm2 V−1 s−1 (40 K), further corroborate with the transport occurring in the conduction band. In addition, we found a residual donor state ∼12 meV lying below the primary Si donor state, as shown schematically in the inset of Fig. 3(b), with a donor state energy of 45.6 meV (= 33.7 + 11.9 meV). We note that our analyses have assumed the temperature-independent μ2 as discussed above. Previously, a defect state with an activation energy of 46 meV below conduction band minima has been attributed to the DX center.29 We, however, note that while this study provides evidence of a residual donor state at ∼46 meV, it is non-trivial to assign it to a specific defect type. It should also be noted that our analysis does not account for the Hall scattering factor, which can depend on both the temperature and the magnetic field and can, therefore, also influence the carrier density.14 Future study should be directed to investigate the relationship between synthesis conditions and defect formation in β-Ga2O3.

In summary, we have investigated donor state energy in doped β-Ga2O3 films via temperature-dependent resistivity and Hall effect measurements. The two-band conduction model described experimental data in addition to yielding donor state energies, ∼34 meV and ∼46 meV, which we attribute to the Si donor and a potential DX center, respectively. In contrast, low-field transport yielded only one carrier type with an activation energy of ∼17 meV in agreement with the published results. Our work provides critical insight into the nature of the donor types in Si-doped β-Ga2O3 with implications in the development of high-power electronic devices.

See the supplementary material for magnetoresistance data, the temperature dependence of the low-field measured Hall carrier density, and our discussion on the role of the Hall scattering factor in β-Ga2O3.

This work was supported primarily by the National Science Foundation through the University of Minnesota MRSEC under Award No. DMR-2011401. Part of this work was supported through the Air Force Office of Scientific Research (AFOSR) through Grant No. FA9550-19-1-0245 and through No. DMR-1741801. Portions of this work were conducted in the Minnesota Nano Center, which was supported by the National Science Foundation (NSF) through the National Nano Coordinated Infrastructure Network (NNCI) under Award No. ECCS-1542202. Part of this work was also carried out in the College of Science and Engineering Characterization Facility, University of Minnesota, which received capital equipment funding from the NSF through the UMN MRSEC program. Thin film synthesis work at the University of Utah was supported primarily by the Air Force Office of Scientific Research under Award No. FA9550-18-1-0507 monitored by Dr. Ali Sayir. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the United States Air Force. Material synthesis effort at the University of Utah also acknowledges support from the National Science Foundation (NSF) under Award No. DMR-1931652. Part of this work was performed at the Utah Nanofab sponsored by the College of Engineering and the Office of the Vice President for Research.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Supplementary Material