In this work, we demonstrate a high mobility two-dimensional electron gas (2DEG) formed at the β-(AlxGa1-x)2O3/Ga2O3 interface through modulation doping. Shubnikov-de Haas (SdH) oscillations were observed in the modulation-doped β-(AlxGa1-x)2O3/Ga2O3 structure, indicating a high-quality electron channel formed at the heterojunction interface. The formation of the 2DEG channel was further confirmed by the weak temperature dependence of the carrier density, and the peak low temperature mobility was found to be 2790 cm2/Vs, which is significantly higher than that achieved in bulk-doped Beta-phase Gallium Oxide (β-Ga2O3). The observed SdH oscillations allowed for the extraction of the electron effective mass in the (010) plane to be 0.313 ± 0.015 m0 and the quantum scattering time to be 0.33 ps at 3.5 K. The demonstrated modulation-doped β-(AlxGa1-x)2O3/Ga2O3 structure lays the foundation for future exploration of quantum physical phenomena and semiconductor device technologies based on the β-Ga2O3 material system.
Beta-phase gallium oxide (β-Ga2O3) is a promising candidate for electronic device applications because of the large bandgap energy (4.7 eV) and the expected high breakdown field of 8 MV/cm.1 Significantly, β-Ga2O3 is the first wide bandgap material that can be grown from the melt, which makes it feasible to achieve large area bulk substrates on a manufacturable scale.2–6 The expected good transport properties (a mobility of >200 cm2/Vs, and a saturation velocity of ∼2 × 107 cm/s)1,7–9 make β-Ga2O3 very promising for a range of technological applications including high power electronics, detectors, and high frequency transistors. Further bandgap tunability can be realized through the introduction of In and Al into β-Ga2O3, leading to β-(In,Ga)2O3 and β-(Al,Ga)2O3 alloys. β-(Al,Ga)2O3 is expected to be stable in the monoclinic phase over a broad range of compositions, and the bandgap can be tuned from the bandgap of β-Ga2O3 (4.7 eV) to above 6 eV.10,11 This enables the realization of several semiconductor heterostructure designs such as modulation-doped electron channels, quantum wells, and superlattices in this semiconductor system.
Recent efforts have led to the demonstration of various device structures with excellent performance, including Schottky diodes,12,13 metal-oxide-semiconductor field effect transistors (MOSFETs),1,14–21 and metal-semiconductor field effect transistors (MESFETs).1 Experimental observations of high breakdown fields above 5 MV/cm for vertical Schottky diodes12 and 3.8 MV/cm for lateral MOSFET transistors have been reported,16 which have already surpassed the material limit for GaN and SiC. While excellent device performance has been demonstrated using homoepitaxial β-Ga2O3 device structures, the β-(AlxGa1-x)2O3/Ga2O3 heterojunctions have remained under-explored.
Preliminary demonstration of modulation-doped field effect transistors (MODFETs) using β-(AlxGa1-x)2O3/Ga2O3 heterostructures has been reported.22–24 Sheet charge densities above 5 × 1012 cm−2 were measured based on either Si-delta doping22 or Ge doping23 in the β-(AlxGa1-x)2O3 layer, but the presence of parallel conduction through the low mobility channel in the (AlxGa1-x)2O3 layer compromised the transport properties of the two-dimensional electron gas (2DEG). In this study, we show a direct evidence of a quantum confinement of electrons at the β-(AlxGa1-x)2O3/Ga2O3 interface based on temperature-dependent Hall measurements and Shubnikov-de Haas (SdH) oscillations. We demonstrate the room temperature mobility of 180 cm2/Vs and the low temperature mobility of 2790 cm2/Vs achieved using the modulation-doped structure.
Figure 1(a) shows the β-(AlxGa1-x)2O3/Ga2O3 MODFET structure studied in this work. The samples were grown on a (010)-oriented Fe-doped semi-insulating β-Ga2O3 substrate using oxygen plasma-assisted molecular beam epitaxy (PA-MBE).25,26 It consists of an unintentionally doped (UID) β-Ga2O3 buffer layer, a 4.5 nm β-(AlxGa1-x)2O3 spacer, a Si delta-doped layer, and a 22.5 nm β-(AlxGa1-x)2O3 cap layer. The growth details could be found in the supplementary material. Two samples were compared in this study, with the only difference being the UID β-Ga2O3 buffer layer thickness, which is 130 nm and 360 nm for samples A and B, respectively. The (AlxGa1-x)2O3 layer thickness and the Al composition were estimated to be 27 nm and 18%, respectively, for both samples, based on high resolution XRD measurements of the (020) diffraction [Fig. 1(b)].27 The observed diffraction fringes indicate sharp heterointerfaces. Both samples showed smooth surfaces with a RMS roughness of ∼0.45 nm obtained from AFM measurements as shown in Fig. S1.
The energy band diagram of the MODFET structure was obtained based on a self-consistent solution of the Schrodinger-Poisson equation assuming a conduction band offset (ΔEC) of 0.4 eV, a surface depletion barrier of 1.4 eV, and a back-depletion due to the Fe-doped semi-insulating substrate (assuming the Fermi level pinned at the midgap), as shown in Fig. 1(c). A 2DEG is expected to form at the (AlxGa1-x)2O3/Ga2O3 interface. When a donor concentration of 4.7 × 1012 cm−2 was adopted in the delta-doped layer, the simulated 2DEG density increased from 1.12 × 1012 cm−2 to 1.50 × 1012 cm−2 as the buffer layer was increased from 130 nm to 360 nm because of a corresponding reduction of backside depletion. It should be noted that the parameters adopted for the band simulations are based on the best estimates we have currently and do provide a self-consistent description of the system. Detailed studies using independent sample series may be necessary to extract these parameters accurately.
To achieve ohmic contact to the channel, the contact regrowth of n++ Ga2O3 with a high Si doping concentration above 1020 cm−3 was carried out using SiO2 as a regrowth mask. The contact regrowth and device fabrication processes are described in the supplementary material. The highly degenerate doping prevented carrier freeze-out at cryogenic temperatures and ensured the reliability of the low temperature electrical measurements. Ohmic contacts were verified by transfer length measurements, with extracted contact resistances of 9.3 Ω mm for sample A and 4.1 Ω mm for sample B, which were limited by the sidewall contacts between the regrown contacts and the low charge density 2DEG channel.
Temperature-dependent Hall measurements were carried out using a van der Pauw structure with regrown n++ Ga2O3 contacts, as shown in Fig. 2. Both samples showed a weak temperature dependence in the measured carrier density, which dropped from 1.12 × 1012 cm−2 to 1.07 × 1012 cm−2 in sample A and from 2.25 × 1012 cm−2 to 2.05 × 1012 cm−2 in sample B upon lowering the temperature. This is in contrast to carrier freeze-out in bulk-doped β-Ga2O3 at low temperatures28 and serves as a direct proof of a degenerate electron gas with no parallel conduction in the (AlxGa1-x)2O3 barrier layer. Using a higher Si sheet density in the delta-doped layer led to partial freeze-out of charge at low temperatures, which could be attributed to a parallel conduction channel in the barrier layer. The maximum charge density that can be confined in the adopted (Al0.18Ga0.82)2O3/Ga2O3 MODFET structure with a 4.5 nm spacer without introducing a parasitic channel is estimated to be approximately 2 × 1012 cm−2. A further increase in the 2DEG charge density requires higher conduction band offset or using a relatively thinner spacer layer.
The room temperature mobility was measured to be 162 cm2/Vs and 180 cm2/Vs for samples A and B, respectively. Both samples showed a sharp increase in the Hall mobility with decreasing temperature, with a peak mobility of 990 cm2/Vs at 60 K for sample A and 2790 cm2/Vs at 50 K for sample B. These are significantly higher than the highest reported mobility values28,29 obtained in bulk-doped β-Ga2O3, an expected benefit of the spatial separation between the impurities and the modulation-doped 2DEG channel. Their mobility values dropped off slightly upon further lowering of the measurement temperature. A similar phenomenon has been observed in early works on modulation-doped AlGaAs/GaAs transistors30 and was attributed to impurity scattering. To understand the scattering mechanisms that cause differences between the samples, the temperature dependence of electron mobility was analyzed by considering various scattering mechanisms (discussed in the supplementary material).
The measured and calculated mobility results are shown in Fig. 2. At low temperature, the remote impurity scattering limited mobility is estimated to be significantly above the measured values, indicating that remote impurity scattering is not a limiting mechanism for the studied MODFET structure. To fit the measured data, the interface roughness and the background impurity density were adjusted in the calculations. The vertical/lateral displacement of the interface was assumed to be 0.45 nm/4.7 nm for both samples for the best fittings of the measured data. The extracted effective charged impurity density was estimated to be 1.2 × 1018 cm−3 in sample A, while it is 1.5 × 1017 cm−3 in sample B. The reduction of the background impurity density in sample B contributed to the notable mobility increase at low temperatures, and it is attributed to less impurity (such as Fe) diffusion from the substrate surface due to a thicker buffer layer growth. The residual background charge could also have contributions from native defects formed during the MBE growth,8 such as Ga vacancies (VGa), which are expected to be deep acceptors.31 We note here that these estimates are based on monovalent charged impurities. Since Ga vacancies can be charged up to the 3+ state, the true background defect density (as opposed to effective defect density) could be lower than 1.5 × 1017 cm−3.
Even though an apparent increase in the low temperature mobility was achieved by increasing the buffer layer thickness, the electron scattering is dominated by polar optical phonon scattering in the high temperature range,8,9,32 leading to similar mobility values at room temperature for both samples. While longitudinal optical-plasmon coupling could lead to better screening of the optical phonon scattering and therefore higher electron mobilities at room temperature,8,9 this effect is not significant in the low carrier density range below 2 × 1012 cm−2 and was therefore not considered in the mobility calculations. Increasing the 2DEG density is necessary to take advance of the screening effects.
The high channel mobility at low temperature allowed for the measurement of Shubnikov-de Haas oscillations of the transverse magnetoresistance (Rxx) with varied magnetic fields perpendicular to the sample surface. Both samples showed negative magnetoresistance at low magnetic fields (Fig. S2), attributed to weak localization,33–35 with SdH oscillations developing above four Tesla. Only one period of oscillation was observed for sample A in the magnetic field range below 14 T (Fig. S2), while multiple oscillations developed below 7 T for sample B at varied measurement temperatures benefitting from the higher channel mobility. The oscillation components of Rxx of sample B, with the background subtracted, are shown in Fig. 3(a) as a function of the reciprocal magnetic field (1/B). The 2DEG concentration can be estimated based on the period of Δ(1/B) through the expression Δ(1/B) = e/πℏn2D.33 The determined 2DEG densities from SdH oscillation are 1.15 × 1012 cm−2 and 1.96 × 1012 cm−2 for samples A and B, respectively, which are consistent with low-field Hall measurements.
The angular dependence of the SdH oscillations for sample B was also measured at 3.5 K by tilting the sample surface normal away from the magnetic field direction as shown in Figs. 3(b) and 3(c). Oscillations were observed at tilt angles lower than 60°, and the extracted oscillation periods of Δ(1/B) fell in a linear dependence of cos(θ), indicating that the oscillations only depend on the perpendicular component of the applied magnetic field. This unique feature reinforces the 2DEG nature of the channel formed at the hetero-interface. Notably, spin splitting was observed at low tilt angles (θ) when the magnetic field was above 10 T. The Hall resistivity (Rxy) also exhibited the onset of plateaus (Fig. S3), which corresponds to the quantization of Landau levels. These features enable the further analysis of the quantum phenomena in Ga2O3.
The obtained SdH oscillations in sample B make it possible to analyze both the effective mass of the 2DEG and the quantum scattering time (τq) in β-Ga2O3. The temperature dependence of the SdH oscillation amplitude (A) at a fixed magnetic field (B) can be used to determine the effective mass of the 2DEG. The oscillation amplitude is related to the measurement temperature (T) by36
where kB is the Boltzmann constant and C1 is a temperature-independent constant at a fixed magnetic field. The dependence of ln(A/T) on temperature and the fittings for the effective mass are plotted in Fig. 4(a) at three magnetic fields. The electron effective mass is extracted to be m* = 0.313 ± 0.015 m0. While the electron transport is confined in the (010) plane, near isotropic effective mass was predicted37 for β-Ga2O3, and the extracted effective mass is in close agreement with the theoretical calculations,37 band structure measurements,38,39 and optical Hall measurements.40
Following the estimation of the effective mass, the quantum scattering time (τq) can be evaluated using a Dingle plot.41,42 At a fixed temperature, the oscillation amplitude is related to the inverse of the magnetic field by41,42
where , R0 is the zero field resistance, and C2 is a constant that is independent of the magnetic field at a given temperature. Figure 4(b) shows the dependence of ln[(A/4R0)(sinh(χ)/χ)] on 1/B extracted from the SdH oscillation at 3.5 K. Linear fitting of the experimental data gives a quantum scattering time of 0.33 ps. In comparison, the transport lifetime (τt) was estimated to be 0.44 ps from the low field Hall mobility (τt = m*μ/e) using the extracted effective mass of 0.313m0. The ratio between the transport lifetime and quantum scattering time is therefore τt/τq ∼ 1.3. This is close to unity and indicates that the electron scattering events are dominated by large angle scatterings, such as interface roughness scattering or background impurity scattering,43 in agreement with the mobility calculations shown in Fig. 2(c).
To demonstrate the feasibility of device applications, modulation-doped field effect transistors were fabricated using a Pt/Au (=30/130 nm) metal stack to define the Schottky gate contact for sample B. The output and transfer characteristics of three-terminal transistors are shown in Fig. 5. A maximum drain current of IDS = 46 mA/mm was obtained at a VDS of 10 V and a VGS of 2 V. The transconductance (gm) showed a peak of 39 mS/mm and dropped off at higher gate bias, which we attribute to the decrease in modulation efficiency due to charge transfer into the barrier layer.44 IDS showed above 9 orders of magnitude rectification, and the subthreshold slope is estimated to be 91 mV/decade. The extracted threshold voltage is 0.5 V, corresponding to normally-off operation under the Pt-gate. High frequency small-signal measurements on this device showed a cutoff frequency of 3.1 GHz and the maximum oscillation frequency of 13.1 GHz at a VDS of 10 V and a VGS of +1.5 V.
In summary, the formation of a high mobility 2DEG channel was achieved using modulation doping in a (010)-oriented β-(AlxGa1-x)2O3/Ga2O3 heterostructure with Si delta-doping in the barrier layer. The temperature dependent Hall measurement showed nearly constant charge density in the temperature range of 5 K–300 K. Both the room temperature mobility of 180 cm2/Vs and the low temperature peak mobility of 2790 cm2/Vs exceeded the highest experimental mobility values for bulk β-Ga2O3. This is attributed to the spatial separation between ionized impurities and the 2DEG. The high mobility values allowed for the observations of the SdH oscillations at cryogenic temperatures. The effective mass in the (010) plane is estimated to be m* = 0.313 ± 0.015 m0 based on the SdH oscillations. The demonstration of a high-quality heterojunction and quantum transport in the β-(AlxGa1-x)2O3/Ga2O3 wide bandgap semiconductor system reported here lays the foundation for future investigation of the materials science, physics, and device applications of the monoclinic β-(AlxGa1-x)2O3 semiconductor system.
See supplementary material for more information about the material growth, device fabrication, mobility calculations, and the original data on SdH oscillations.
We acknowledge funding from the Office of Naval Research under Grant No. N00014-12-1-0976 (EXEDE MURI). The project or effort depicted was or is sponsored by the Department of the Defense, Defense Threat Reduction Agency (Grant No. HDTRA11710034). This material is partially based upon the work supported by the Air Force Office of Scientific Research under Award No. FA9550-18RYCOR098. The content of the information does not necessarily reflect the position or the policy of the federal government, and no official endorsement should be inferred. We acknowledge funding from The Ohio State University, Institute of Materials Research (IMR), Multidisciplinary Team Building Grant. We thank Dr. Susanne Stemmer for helpful discussions.