High mobility InAs 2DEGs on GaSb substrates: a platform for mesoscopic quantum transport
C. Thomas A. T. Hatke A. Tuaz R. Kallaher T. Wu T. Wang R. E. Diaz G. C. Gardner M. A. Capano M. J. Manfra




These two authors contributed equally.
Station Q Purdue and Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907 USA



These two authors contributed equally.
Station Q Purdue and Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA



Station Q Purdue and Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907 USA


Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907 USA
Microsoft Quantum at Station Q Purdue, Purdue University, West Lafayette, Indiana 47907, USA


Station Q Purdue and Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA


Station Q Purdue and Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907 USA


Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907 USA


Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907 USA
Microsoft Quantum at Station Q Purdue, Purdue University, West Lafayette, Indiana 47907, USA


Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907 USA
School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA


Station Q Purdue and Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907 USA
School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
School of Materials Engineering, Purdue University, West Lafayette, IN, 47907 USA

 
December 30, 2023


High mobility, strong spin-orbit coupling, and large Landé g-factor make the two-dimensional electron gas (2DEG) in InAs quantum wells grown on nearly-lattice-matched GaSb substrates an attractive platform for mesoscopic quantum transport experiments. 
Successful operation of mesoscopic devices relies on three key properties: electrical isolation from the substrate; ability to fully deplete the 2DEG and control residual sidewall conduction with lithographic gates; and high mobility to ensure ballistic transport over mesoscopic length scales.  
Simultaneous demonstration of these properties has remained elusive for InAs 2DEGs on GaSb substrates.  
Here we report on heterostructure design, molecular beam epitaxy growth, and device fabrication that result in high carrier mobility and full 2DEG depletion with minimal residual edge conduction.  
Our results provide a pathway to fully-controlled 2DEG-based InAs mesoscopic devices.
 


High mobility InAs 2DEGs on GaSb substrates: a platform for mesoscopic quantum transport
    M. J. Manfra
    December 30, 2023
========================================================================================






§ INTRODUCTION


With low effective mass, strong spin-orbit coupling and high Landé g-factor <cit.>, the two-dimensional electron gas (2DEG) in InAs quantum wells is an interesting platform for mesoscopic physics experiments, but only a few realizations of mesoscopic devices have been reported with trench-etched quantum point contacts, e.g. <cit.>.
More recently, lithographically-defined nanowires comprised of the s-wave superconductor aluminum proximity-coupled to InAs 2DEG grown on semi-insulating InP have experimentally revealed evidence of Majorana zero modes <cit.>.
Motivated by the possibility to explore mesoscopic phenomena and novel topological states in a lower disorder environment, significant effort is now dedicated to improvement of InAs 2DEG electronic properties.
For example, the growth of composite quantum wells of InGaAs/InAs <cit.> enabled improvement of the carrier mobility to μ = 1.0 × 10^6cm^2/Vs for InAs quantum wells buried 120nm below the top surface and grown on semi-insulating (100) InP substrates <cit.>. 
However, growth of InAs on InP substrates must accommodate the nearly 3.5% lattice mismatch to InAs through the use of thick graded buffer layers that introduce dislocations and modify surface morphology.

By growing InAs quantum wells on quasi-lattice-matched (100) GaSb substrates, 2DEG mobility has reached μ∼ 2.4 × 10^6cm^2/Vs at density n ∼1×10^12cm^-2 <cit.>, for a quantum well buried 25nm from the top surface, through reduced defect generation and use of AlGaSb barriers that increase electron wavefunction confinement.  
Many body effects associated with the fractional quantum Hall effect <cit.> have been recently reported on such structures, indicative of improved quality.

 
However, mesoscopic experiments using high quality InAs 2DEGs on GaSb substrates still present challenges. 
Specific limitations include: 1) parasitic conduction through the substrate; due to the small bandgap of GaSb, substrates are not perfectly insulating which may limit operation of high impedance quantum devices in the tunnelling regime; 2) the inability to fully deplete the 2DEG and residual sidewall conduction with surface gates. 
High mobility 2DEGs utilizing a GaSb buffer layer have been successfully grown <cit.>. 
However simple GaSb buffers are not expected to result in sufficient isolation from the GaSb substrate. 
Growth of lattice matched buffers composed of higher bandgap materials such as AlSb_yAs_1-y <cit.> or Al_xGa_1-xSb_yAs_1-y <cit.> appears promising to address these issues but no data have been published detailing device isolation or full 2DEG depletion.
Additionally, it has been reported that high mobility InAs 2DEGs suffer from excess conductance attributed to side wall conduction, most probably associated with charge accumulation at the exposed InAs edge. 
Mueller et al. <cit.> reported edge resistivity of 1.3-2.5 kΩ/μm. 
Edge resistivity was subsequently increased to 72.8 kΩ/μm  by Mittag and coworkers by incorporating an Al_2O_3 gate dielectric deposited by atomic layer deposition (ALD) on an heterostructure designed to host a low density (n ∼ 5 × 10^11cm^-2) InAs 2DEG <cit.>.



Here we report on the design, fabrication, and operation of devices based on InAs 2DEGs on (100) GaSb substrates that address the aforementioned limitations. 
To better understand the impact of epilayer design on device performance, a series of heterostructures was grown by molecular beam epitaxy with various buffer and cap layer materials. Buffer layers must electrically isolate the 2DEG from the substrate and cap layers that terminate the semiconductor stack must promote strong electrostatic gate control.  
Our principal results can be summarized as follows. With its large bandgap, a buffer layer of the quaternary compound Al_0.8Ga_0.2Sb_0.93As_0.07 is found to effectively isolate the 2DEG from the GaSb substrate and yields mesa device isolation larger than 1GΩ.  
Moreover, the precise lattice-match of Al_0.8Ga_0.2Sb_0.93As_0.07 with GaSb enables the growth of InAs quantum wells on a dislocation free buffer resulting in electron mobility      
 μ=2.1×10^6 cm^2/Vs at density n=6.7×10^11 cm^-2.
A thin InAs cap layer has enabled complete depletion of the 2DEG with minimal residual sidewall conduction and has proved to be favorable in this context over the commonly used GaSb <cit.>. 
Interestingly, the choice of an InAs or GaSb capping layer dramatically impacts scattering in the 2DEG. The GaSb cap layer appears to screen the 2DEG from surface defect scattering, enhancing mobility, but simultaneously prevents full 2DEG depletion.  The InAs cap layer does not screen surface charge as efficiently, but does facilitate full 2DEG depletion.



 





§ MOLECULAR BEAM EPITAXY GROWTH AND DEVICE FABRICATION




InAs-based 2DEGs (see Fig. <ref>(a) for a typical layer stack) were grown on undoped GaSb (100) substrates by molecular beam epitaxy in a Veeco Gen 930 using ultra-high purity techniques and methods as described in Ref. gardner:2016. 
Substrate temperature was measured by blackbody radiation emission. 
To improve epilayer morphology, the native oxide of the substrate was removed at  400C using atomic hydrogen without Sb flux. 
This process is found to improve surface morphology significantly by limiting the formation of surface defects generated during thermal oxide desorption <cit.>. 
The substrate temperature was then increased to 500C, under Sb flux and growth was initiated with a 25nm smoothing layer of GaSb followed by a thick buffer layer of 800nm.  
Five samples (A - E) were grown to investigate buffer layers of varying complexity ranging from a pure GaSb to Al_0.8Ga_0.2Sb_0.93As_0.07 lattice matched to GaSb, as summarized in Table <ref>. 
Precise control of substrate temperature is of principal importance for the ternary AlSb_yAs_1-y (Sample D) and the quaternary Al_xGa_1-xSb_yAs_1-y (Sample E) layers since it directly controls the incorporation ratio of Sb and As and thus the lattice parameter. Growth of Al(Ga)SbAs compounds (Samples D and E) following the hydrogen-assisted oxide removal process enables smooth buffer layers to be grown free of pyramidal defects typically observed on the surface of GaSb grown on GaSb <cit.>. 


The active region of the heterostructure is composed of 24nm of InAs flanked by Al_xGa_1-xSb barriers with x= 0.8. 
The top barrier thickness is 20nm unless otherwise specified. 
Finally, the growth was terminated by deposition of a cap layer, whose primary role is to avoid oxidation of the underlying Sb-containing layers and prevent formation of parasitic conduction channels. 
As we shall demonstrate, the cap layer plays a crucial role for electrostatic control of the 2DEG. 
GaSb, AlGaSbAs, and InAs cap layers were explored in three different samples (E - G).
For all samples in this study, transitions between InAs and Sb-containing compounds made use of a shutter sequence pioneered in Ref. tuttle:1990. 
The growth of InAs was performed with an effective As-to-In ratio slightly larger than 1 to prevent the formation of void defects associated with As etching of the Sb-based layer underneath. 
Under these conditions, flat surface morphology was obtained with a roughness on the order of a monolayer.
Throughout the entire growth the Sb flux was kept constant with a beam equivalent pressure of 4.0 × 10^-7torr.



Devices were processed with standard wet etching techniques to define straight and L-shaped Hall bars of width w=50 and 150 μm to measure transport along different crystallographic directions.
To avoid complications arising from oxidation of etched surfaces, we first deposit Ohmic Ti/Ni/Au (20/200/100nm) contacts.
Our samples are then etched with a H_2O : citric monohydrate : H_3PO_4 : H_2O_2 (220 mL: 55 g: 3 mL: 5 mL) solution to define the Hall bar mesas, where the etch is terminated in the buffer layer. 
After deposition of a dielectric of or using thermal ALD at 150C and 90C, respectively, or sinusing plasma enhanced chemical vapor deposition at 250C, a Ti/Au (20/150nm) gate is deposited.
Processing is completed with deposition of a Ti/Ni/Au (20/200/100nm) bond pad after a BOE etch to open a window in the dielectric over the Ohmic contacts.






§ RESULTS



 §.§ Device isolation

Samples were measured in a ^3He system at a base temperature of T=300mK using standard low frequency lock-in and dc techniques.  
We first discuss the impact of heterostructure design on device electrical isolation.  
Mesoscopic devices must be well isolated from the substrate in order to operate in a high impedance configuration.  
We test the degree of isolation by applying dc voltage bias between Ohmic contacts on neighboring mesas and monitoring the current that flows between them.


The resistance between different etched Hall bars was measured by floating all contacts on two adjacent Hall bars except one test contact on each mesa and applying a voltage between the two mesas.
This configuration forces any current flow between the mesas to, presumably, occur either at the interface of the etched semiconductor layer and the dielectric or down through the buffer layers into the weakly conducting substrate and back up through the buffer again to the other mesa.
We investigated I-V curves in the range -0.5V<V<0.5V, where V is an applied voltage between Ohmic contacts.
The mesa-to-mesa resistances for different buffer layer and dielectric combinations are summarized in Table <ref> for Samples A - G,. 
In each case, the mesa etch is terminated in the buffer layer.
For resistances labelled as >GΩ no current is observed above the noise floor of our measurement circuit.  As the current noise floor is approximately 0.5pA, 1GΩ is a lower bound on the actual resistance.





We first consider Sample A, where GaSb has been used as the buffer layer, similarly to Ref. tschirky:2017. 
A low resistance between mesas on the order of 10-100kΩ is measured with sinas a dielectric. 
For Sample B, the GaSb buffer is terminated with a superlattice (SL) made of 1nm-thick GaSb and 1nm-thick AlSb layers, repeated 100 times.  
With the same sindielectric, the incorporation of the SL results in an increase of the mesa-to-mesa resistance to the order of a few MΩs. 
While this constitutes a significant improvement over the bare GaSb buffer, the resistance is still not sufficient to isolate nanostructures as efficiently as a semi-insulating substrate. 
Sample C is comprised of an Al_0.35Ga_0.65Sb buffer that has a larger bandgap (1.2eV <cit.>) but is not well lattice-matched (mismatch of 0.23%) in comparison with the GaSb buffer of Sample A.  
Sample D has a buffer made of the ternary alloy AlSb_0.91As_0.09 that is characterized by a bandgap twice as large (2.4eV <cit.>) and better lattice matching to GaSb (mismatch ≲ -0.1%) than Sample C. 
For these samples, is used as dielectric to reduce the thermal budget during processing.
Despite the nominally better intrinsic properties of these two buffer materials, we still measured a resistance of a few MΩs.
Sufficient isolation, >GΩ, was only obtained by increasing the complexity of the buffer layer to the quaternary Al_0.8Ga_0.2Sb_0.93As_0.07 alloy, which is used for Samples E - G. 
Note that Al_0.8Ga_0.2Sb_0.93As_0.07 is fully lattice-matched to the underlying GaSb substrate. 
We additionally infer that the addition of gallium and arsenic to the buffer limits the oxidation of the exposed buffer layer surface after the mesa etch.  
For Sample E, three chips were prepared with the three different dielectric materials: sin, and and all gave device isolation  >GΩ. 
In the remainder of this manuscript, the measurements presented for Sample E are on devices having as dielectric. 
These results highlight the primary importance of the epitaxial buffer layer material over the particular dielectric used for improvement of device isolation. 



 §.§ Structural characterization

With the validation of the electronic properties of the Al_0.8Ga_0.2Sb_0.93As_0.07 buffer, we comment on its structural properties. 
To determine the strain state and test for possible relaxation in these heterostructures, high resolution x-ray reciprocal space mapping (RSM) has been performed using a X'pert PANalytical diffractometer. 
Performing RSM along an asymmetric reflection provides insight into the in- and out-of-plane lattice parameters and thus enables extraction of the strain profile of the different layers of our heterostructures. 
Figure <ref> (b) displays an RSM centered on the GaSb asymmetric (224) diffraction peak using a glancing exit configuration. 
The mapping has been collected over a 2θ-ω range of 4 with 0.02 steps and an ω range of 1.6 with steps of 0.02. 
Note that with the use of a copper X-ray tube, an X-ray mirror and a channel-cut Ge (2 2 0) crystal, photons were provided at an energy of 8.048keV and a divergence of 0.008. 
The  acceptance angle of the detector was 0.2.   
The Al_0.8Ga_0.2Sb_0.93As_0.07 and GaSb peaks cannot be resolved which indicates good lattice matching of the buffer to the substrate. 
All peaks share a common in-plane scattering vector (q_x= -0.4640 Å^-1) that confirms the constituent layers possess the same in-plane lattice parameter. The vertical alignment of peaks in the RSM demonstrates all layers are coherently strained and there is no evidence of relaxation.
The crystalline quality of this heterostructure is confirmed by scanning transmission electron microscopy (STEM). STEM was performed using a Thermo Scientific Talos 200X TEM and images were acquired with a high angle annular dark field along the [110] zone axis. The STEM image of Fig. <ref>(c) highlights a uniform AlGaSbAs buffer layer with no evidence of threading dislocations. 
















 §.§ Carrier depletion

The second identified challenge for InAs/GaSb heterostructures is the inability to fully deplete the carriers in fabricated devices. 
Given that we employ high bandgap materials for both the barriers surrounding the quantum well and the buffer (see the bandstructure of Fig. <ref>(a)), we focus our attention on the capping layer as the possible location of bands crossing the Fermi level that may limit full depletion of the 2DEG.
Selection of GaSb as the cap layer (Sample F) is natural because it is lattice matched to the structure and Ga compounds are known to inhibit oxide formation better than Al-rich compounds, such as those used as our top barrier. This choice is widely reported with various GaSb capping layer thicknesses <cit.>. Full carrier depletion, however, was not observed in our experiments. This observation is corroborated by Nextnano simulations <cit.> that suggest an absence of a clear depletion region without hole accumulation.


In Fig. <ref> (a) we present magnetotransport data for Sample E that employs a higher bandgap 3nm-thick Al_0.8Ga_0.2Sb_0.93As_0.07 cap layer.
Note that, at most, a 5% anisotropy between the [011] and [011̅] crystallographic directions has been detected for all samples so only the [011̅] direction will be considered for the remainder of the manuscript.
Here we observe well defined quantum plateaus of the Hall resistance ρ_xy with corresponding vanishing minima of the longitudinal resistance ρ_xx indicative of high quality transport without significant parallel conduction. 


Despite the excellent transport and very high 2DEG mobility, this device does not fully deplete as demonstrated in Fig. <ref> (b).
Starting from zero gate voltage, a linear relation between the carrier density n and the gate voltage  is observed for -0.5 <≤ 0V and would extrapolate to full depletion of the device at ∼-0.7V. 
However, for ≤ -0.5V, the density is no longer linearly varying with . 
A saturation of n is instead observed for ≤ -0.7V with n ∼ 2.0 × 10^11cm^-2. 
The  sweep is truncated at =-1V. 






Within the saturation regime, n is not stable and increases with time t, as indicated in the inset of Fig. <ref> (b). 
After t∼ 15min, the density equilibrates at n ∼ 3.2 × 10^11cm^-2, which represents an increase of  ∼ 1.2 × 10^11cm^-2 at fixed gate voltage.
Once n is stabilized, magnetotransport measurements in this low density regime demonstrate high quality transport with well defined integer quantum Hall effects through both vanishing minima of the longitudinal resistance and quantized Hall plateaus, as shown in Fig. <ref> (c). 
High carrier mobility of μ∼ 1.0 × 10^6cm^2/Vs is demonstrated. 

These results clearly indicate that the gate does not fully deplete the 2DEG in the quantum well. 
Furthermore, the magnetotransport data of Fig. <ref>(c) does not appear to be consistent with trivial InAs edge conduction, as reported in Ref. mueller:2017.  
The high mobility maintained at low density suggests the 2DEG is well screened from charged scattering sites that invariably must exist at the dielectric/semiconductor interface.  
Taken as a whole, these data suggest the formation of a mobile screening layer present between the electrostatic gate and the 2DEG.
It is worth noting that similar results were obtained for Sample F where the 2DEG density in the saturation regime was n∼ 1.3 × 10^11cm^-2 and equilibrium density of n∼ 2.5 × 10^11cm^-2 was observed.
 






 
The gate response of Sample G, grown with a 2nm InAs cap layer, is investigated next. 
Figure  <ref> (a) displays the resistance per square, r (left axis), and conductance, σ (right axis), versus  obtained by biasing the source and drain contacts of a straight Hall bar of width 150  μm and length 1200  μm.
From the n versus  dependence, we estimate that complete depletion of the 2DEG should occur at ∼ -0.525V, or, possibly, at slightly larger negative voltage if the system were to undergo a metal-insulator-transition <cit.>.
In the  regime beyond pinch off we observe r>50MΩ/sqr., corresponding to a variation of nearly five orders of magnitude within the measurement range; concurrently σ→ 0. 
Deep in the depletion regime accurate determination of resistance is limited by the measurement circuit. 
While we have not explicitly performed an analysis to determine residual edge resistivity, our measurements demonstrate electrostatic control of conductivity in the depleted regime at least comparable to that reported in Ref. mittag:2017 for low density InAs 2DEGs.
For the samples investigated here, and dielectrics resulted in similar performance. Our results suggest that the use of a thin InAs cap layer coupled with the quaternary Al_0.8Ga_0.2Sb_0.93As_0.07 buffer facilitate strong electrostatic control of the conductivity.







 §.§ Mobility versus density




We continue our investigations by analyzing the impact of the cap layer material on the scattering mechanisms of the 2DEG. 
In particular, we investigate μ versus n at T=300mK for Samples E - G (see Table <ref>), plotted in Fig. <ref>.
For all three samples μ versus n is non-monotonic. 
At low n, μ first increases until n ∼ 6 -7× 10^11 cm^-2 and then a sharp decrease is observed for n≳ 7.5 × 10^11cm^-2, corresponding to the density at which the second subband of the quantum well starts to be populated.
Samples E and F present nearly identical μ variation with n with a  maximum mobility of μ = 2.1 × 10^6cm^2/Vs at n = 6.7 × 10^11cm^-2 (magnetotransport at this peak mobility was plotted in Fig. <ref> (a) for Sample E), indicating again that the GaSb and AlGaSbAs cap layers are playing a similar role.
Note that these results appear to compare favorably with Ref. tschirky:2017 in which a peak mobility of μ∼ 2.4 × 10^6 cm^2/Vs was measured but at nearly twice the density of n ∼ 12 × 10^11 cm^-2 in a 400 μm Hall bar.
The μ vs n dependence of Sample G is visibly different in both its dependence and lower peak mobility of μ∼ 8.2 × 10^5cm^2/Vs, for which the magnetotransport data are presented in Fig. <ref>(b). 

 
At low temperature and high carrier density where semiclassical Boltzmann transport theory is valid, the relation μ∝ n^α is often used to characterize the dominate scattering mechanisms <cit.>. 
The value of α reflects the distribution of charged point impurities, which can be localized in a plane parallel to the 2DEG (e.g. delta doping or a nearby surface) or distributed uniformly in bulk of the structure. 
More specifically, α→ 0.5 in the case where the mobility is limited by uniformly distributed 3D ionized background impurities and α→ 1.5 when remote ionized impurity scattering is the limiting factor <cit.>.
Assuming μ∝ n^α, for both Samples E and F we estimate α∼ 0.7-0.75, similar to Ref. tschirky:2017; the grey dotted line in Fig. <ref> overlaid on the data for α=0.725 is a guide to the eye of the estimated relationship.  
At first blush this relationship is surprising considering that the 2DEG resides just ∼ 20 nm below the dielectric/semiconductor interface where a high density of charged defects may be expected.
Repeating the same exercise for Sample G, an exponent α∼ 1.2-1.4 is extracted.
In our study the α values have been determined using a log-log scale (not shown here) and μ(n) has been fitted on a limited n range for n ≤ 6 × 10^11cm^-2, below the onset of 2^nd subband occupation. 
While our values of α are only estimations, it is nevertheless clear that differences in behavior are observed.
Differences in peak mobility value and in α between Samples E and F and Sample G strongly indicate different limiting scattering mechanisms for the structures terminated with Sb-containing layers compared to InAs cap layers. 
These observations suggest that with Sb-based cap layers the 2DEG is well-screened from ionized impurity scattering sites residing at the sample surface that is located only ∼ 20nm away. 
The formation of a weakly conducting layer under negative gate bias between the gate and the 2DEG could explain such behavior. 
A screening layer may also explain the lack of full 2DEG depletion; once enough charge is induced to fully screen the electric field of the gate, the 2DEG density saturates.  
This mechanism is consistent with our observations of a high mobility 2DEG persisting beyond the range of linear gate voltage control.





 §.§ Low density devices


Sample H incorporates a 60nm top barrier and an Al_0.8Ga_0.2Sb_0.93As_0.07 cap layer. 
The as-cooled density drops to n= 3.9 × 10^11 cm^-2, more than two times lower than for Sample E where the only difference between the two is an additional 40nm of the same top barrier material. 
As we observed a negligible amount of structural disorder in the buffer layer (see STEM image of Fig. <ref> (c)) and our samples lack an intentional doping layer it is reasonable to assume that the charge in the well is primarily supplied by the surface such that an increase in the top barrier thickness results in a decrease in the density transferred to the quantum well, in agreement with our density measurements on Samples E and H.





Even at this low starting density, Sample H exhibits a high mobility of μ = 4.1 × 10^5cm^2/Vs at n=3.7 × 10^11 cm^-2.
In Fig. <ref> (a) we plot the low field magnetoresistance after removal of a slowly varying background, Δρ, where the high quality of the 2DEG is apparent in the onset of the Shubnikov-de Haas oscillations (SdHOs), occurring at 90 mT.
As a lower bound we estimate the quantum scattering time, ∼ 2ps, from the condition ∼ 1, where =/eB is evaluated at the onset of the SdHOs and =0.03  m_e <cit.>.
Additionally, Δρ contains a well defined node. 
Fast Fourier Transform of the magnetoresistance of Fig. <ref> (a) is plotted in Fig. <ref> (b) as a function of frequency f. 
We observe a single split peak indicative of two nearly identical oscillation periods due to zero field spin splitting. The spin up and spin down densities are labeled n_+ and n_-, respectively <cit.>, and can be determined from n_±=ef/h.
From these two densities we estimate the Rashba parameter, =Δ nħ^2/√(π/2(-Δ n))=3.39 × 10^-12eV m, where Δ n = - and =+.
Concurrently the spin-orbit length is also estimated through =1/Δ n√(-Δ n/2π)= 379nm.

Interestingly, despite the use of a AlGaSbAs cap layer in Sample H, the n vs  variation was completely linear and  we were able to fully deplete the carriers at =-0.5V (data not shown here). The as cooled =0V density of sample H was only 3.9×10^11cm^-2.
Evidently, the reduced negative gate voltage required for depletion of the low density 2DEG in Sample H limits interfacial charge accumulation under the gate.
This behavior contrasts with our previous observations for sample E with higher as-cooled density in which 2DEG density saturated for ≤ -0.7V without full depletion. Possible explanations for this behavior are discussed below.





§ DISCUSSION

For InAs 2DEGs on GaSb substrates, careful consideration of both the buffer layer and cap layer is needed to produce electrical isolation of devices from the substrate and full electrostatic control with lithographic gates while maintaining high 2DEG mobility. 
Only in the case of an InAs cap layer, have we experimentally demonstrated full carrier depletion for near-surface InAs 2DEGs of arbitrary density. 



Bandstructure simulations with Nextnano suggest that the conduction band of InAs cap layers may cross the Fermi level.
Keeping the InAs thickness below 2nm is thus important to avoid unintentional population of states at the surface. 
A depletion range on the order of a few hundred mV can be estimated before the Fermi level crosses the valence band of the Al_0.8Ga_0.2Sb barriers. 
In simulations, the gate voltage response in structures employing an Al_0.8Ga_0.2Sb_0.93As_0.07 cap layer appears to be very similar to what is observed with an InAs cap layer and a depletion range of the same order of magnitude is expected. 
The simulated gate voltage response with a GaSb cap behaves differently; the  conduction band minimum of the InAs quantum well and the valence band maximum of the GaSb can coincide with the Fermi level under reverse bias. 
In this case, a hole gas may occur near the semiconductor surface.
Such a hole gas is likely to act as a screening layer between the metallic gate and the 2DEG, limiting gate response for further increase of reverse bias.


While the gate voltage dependence of the bandstructure might explain the incomplete depletion with GaSb cap layer, the situation is less clear for the AlGaSbAs cap layer. 
A major difference between Sb-containing and As-based cap layers is the potential of oxidation and formation of charged states at the surface.  
AlSb-containing alloys are particularly prone to oxidation.
It has been reported that deposition of InAs on GaSb limits the number of defects that were mostly attributed to Sb-oxide at the dielectric/semiconductor interface <cit.>.  
Charges accumulated at the dielectric/semiconductor interface during application of negative gate bias may be expected to impact gate control of 2DEG density.  
Simulations also indicated that the gate voltage value required to reach complete depletion depends on the thickness of the barrier and thus of the as-cooled density. 
The depletion voltage is estimated to be approximately a factor of two smaller for a 60nm barrier (∼ -0.6V) compared to the 20nm case (∼ -1.4V). 
It is likely that structures with thicker barriers and lower density 2DEGs naturally avoid formation of unintentional charge accumulation layers under reverse bias and are thus easier to control with top gates.


Given the bandstructure evolution with gate voltage and the assumption of charge at the dielectric/semiconductor interface, we have identified two scenarios that could explain the difficulty of depleting high density, near surface 2DEGs having GaSb and AlGaSbAs cap layers. 
GaSb and AlGaSbAs cap layers do appear to limit surface scattering better than InAs capping layers and result in higher mobility.  
Further studies are needed to draw stronger conclusions on the mechanisms responsible.




§ CONCLUSION

In conclusion, we have shown that near-surface InAs 2DEGs grown on GaSb substrates utilizing an Al_0.8Ga_0.2Sb_0.93As_0.07 buffer and an InAs cap layer exhibit all the properties required to operate quantum devices: proper isolation from the substrate, strong electrostatic control of 2DEG density, and high mobility.  Low density structures, with thicker top barriers, are promising for experiments involving the coupling of superconductivity and integer quantum Hall effect at very low magnetic fields <cit.> or investigations of the fractional quantum Hall effect using readily available superconducting magnets <cit.>.





§ ACKNOWLEDGMENTS

This work was supported by Microsoft Quantum. 
We thank Jan Gukelberger for useful discussions. 

apsrev


25
natexlab#1#1bibnamefont#1#1bibfnamefont#1#1citenamefont#1#1url<#>1urlprefixURL 


[Lutchyn et al.(2018)Lutchyn, Bakkers,
  Kouwenhoven, Krogstrup, Marcus, and Oreg]Lutchyn:2018
authorR. Lutchyn,
  authorE. Bakkers,
  authorL. Kouwenhoven,
  authorP. Krogstrup,
  authorC. Marcus, and
  authorY. Oreg,
  journalNature Review Materials volume3,
  pages52 (year2018).

[Debray et al.(2009)Debray, Rahman, Wan,
  Newrock, Cahay, Ngo, Ulloa, Herbert, Muhammad, and Johnson]Debray:2009
authorP. Debray,
  authorS. Rahman,
  authorJ. Wan,
  authorR. Newrock,
  authorM. Cahay,
  authorA. Ngo,
  authorS. Ulloa,
  authorS. Herbert,
  authorM. Muhammad, and
  authorM. Johnson,
  journalNature Nanotechnology volume4,
  pages759 (year2009).

[Shabani
  et al.(2014a)Shabani, McFadden, Shojaei, and
  Palmstrom]shabani:2014
authorJ. Shabani,
  authorA. P. McFadden,
  authorB. Shojaei, and
  authorC. J. Palmstrom,
  journalApplied Physics Letters volume105,
  pages262105 (year2014a).

[Nichele et al.(2017)Nichele, Drachmann,
  Whiticar, O'Farrell, Suominen, Fornieri, Wang, Gardner, Thomas, Hatke
  et al.]nichele:2017
authorF. Nichele,
  authorA. C. C. Drachmann,
  authorA. M. Whiticar,
  authorE. C. T. O'Farrell,
  authorH. J. Suominen,
  authorA. Fornieri,
  authorT. Wang,
  authorG. C. Gardner,
  authorC. Thomas,
  authorA. T. Hatke,
  et al., journalPhys. Rev. Lett.
  volume119, pages136803
  (year2017).

[Suominen et al.(2017)Suominen,
  Kjaergaard, Hamilton, Shabani, Palmstrom, Marcus, and
  Nichele]suominen:2017
authorH. J. Suominen,
  authorM. Kjaergaard,
  authorA. R. Hamilton,
  authorJ. Shabani,
  authorC. J. Palmstrom,
  authorC. M. Marcus,
  and authorF. Nichele,
  journalPhys. Rev. Lett. volume119,
  pages176805 (year2017).

[Wallart et al.(2005)Wallart, Lastennet,
  Vignaud, and Mollot]wallart:2005
authorX. Wallart,
  authorJ. Lastennet,
  authorD. Vignaud, and
  authorF. Mollot,
  journalApplied Physics Letters volume87,
  pages043504 (year2005).

[Hatke et al.(2017)Hatke, Wang, Thomas,
  Gardner, and Manfra]hatke:2017
authorA. T. Hatke,
  authorT. Wang,
  authorC. Thomas,
  authorG. C. Gardner,
  and authorM. J.
  Manfra, journalApplied Physics Letters
  volume111, pages142106
  (year2017).

[Tschirky et al.(2017)Tschirky, Mueller,
  Lehner, Falt, Ihn, Ensslin, and Wegscheider]tschirky:2017
authorT. Tschirky,
  authorS. Mueller,
  authorC. A. Lehner,
  authorS. Falt,
  authorT. Ihn,
  authorK. Ensslin, and
  authorW. Wegscheider,
  journalPhys. Rev. B
  volume95, pages115304
  (year2017).

[Ma et al.(2017)Ma, Hossain, Rosales,
  Deng, Tschirky, Wegscheider, and Shayegan]ma:2017
authorM. K. Ma,
  authorM. S. Hossain,
  authorK. A. V. Rosales,
  authorH. Deng,
  authorT. Tschirky,
  authorW. Wegscheider,
  and authorM. Shayegan,
  journalPhys. Rev. B volume96,
  pages241301 (year2017).

[Shojaei
  et al.(2016a)Shojaei, O'Malley, Shabani, Roushan,
  Schultz, Lutchyn, Nayak, Martinis, and Palmstrom]sho:2016
authorB. Shojaei,
  authorP. O'Malley,
  authorJ. Shabani,
  authorP. Roushan,
  authorB. Schultz,
  authorR. Lutchyn,
  authorC. Nayak,
  authorJ. Martinis, and
  authorC. J. Palmstrom,
  journalPhys. Rev. B volume93,
  pages075302 (year2016a).

[Shojaei et al.(2018)Shojaei, McFadden,
  Pendharkar, Lee, Flatte, and Palmstrom]shojaei:2018
authorB. Shojaei,
  authorA. McFadden,
  authorM. Pendharkar,
  authorJ. Lee,
  authorM. Flatte, and
  authorC. J. Palmstrom,
  journalarxiV  (year2018).

[Shojaei
  et al.(2016b)Shojaei, Drachmann, Pendharkar,
  Pennachio, Echlin, Callahan, Kraemer, Pollock, Marcus, and
  Palmstrom]shojaei:2016
authorB. Shojaei,
  authorA. C. C. Drachmann,
  authorM. Pendharkar,
  authorD. J. Pennachio,
  authorM. P. Echlin,
  authorP. G. Callahan,
  authorS. Kraemer,
  authorT. M. Pollock,
  authorC. M. Marcus,
  and authorC. J.
  Palmstrom, journalPhys. Rev. B
  volume94, pages245306
  (year2016b).

[Mueller et al.(2017)Mueller, Mittag,
  Tschirky, Charpentier, Wegscheider, Ensslin, and Ihn]mueller:2017
authorS. Mueller,
  authorC. Mittag,
  authorT. Tschirky,
  authorC. Charpentier,
  authorW. Wegscheider,
  authorK. Ensslin, and
  authorT. Ihn,
  journalPhys. Rev. B volume96,
  pages075406 (year2017).

[Mittag et al.(2017)Mittag, Karalic,
  Mueller, Tschirky, Wegscheider, Nazarenko, Kovalenko, Ihn, and
  Ensslin]mittag:2017
authorC. Mittag,
  authorM. Karalic,
  authorS. Mueller,
  authorT. Tschirky,
  authorW. Wegscheider,
  authorO. Nazarenko,
  authorM. V. Kovalenko,
  authorT. Ihn, and
  authorK. Ensslin,
  journalApplied Physics Letters volume111,
  pages082101 (year2017).

[Gardner et al.(2016)Gardner, Fallahi,
  Watson, and Manfra]gardner:2016
authorG. C. Gardner,
  authorS. Fallahi,
  authorJ. D. Watson,
  and authorM. J.
  Manfra, journalJournal of Crystal Growth
  volume441, pages71  (year2016).

[Weiss et al.(2007)Weiss, Klin, Grossman,
  Greenberg, Klipstein, Akhvlediani, Tessler, Edrei, and Hoffman]Weiss:2007
authorE. Weiss,
  authorO. Klin,
  authorS. Grossman,
  authorS. Greenberg,
  authorP. Klipstein,
  authorR. Akhvlediani,
  authorR. Tessler,
  authorR. Edrei, and
  authorA. Hoffman,
  journalJ. Vac. Sci. Technol. A volume25,
  pages736 (year2007).

[Murray et al.(2013)Murray, Yildirim,
  Provence, Norton, Boggess, and Prineas]murray:2013
authorL. Murray,
  authorA. Yildirim,
  authorS. Provence,
  authorD. Norton,
  authorT. Boggess, and
  authorJ. Prineas,
  journalJ. Vac. Sci. Technol. B volume31,
  pages03C108 (year2013).

[Tuttle et al.(1990)Tuttle, Kroemer, and
  English]tuttle:1990
authorG. Tuttle,
  authorH. Kroemer, and
  authorJ. English,
  journalJourn. of Appl. Phys. volume67,
  pages3032 (year1990).

[nex()]nextnano
noteThe Nextnano software can be obtained from
  http://www.wsi.tum.de/nextnano3 and http://www.nextnano.de.

[Shim(2005)]Shim:2015
authorK. Shim, journalSolid
  State Communications volume134, pages437
  (year2005).

[Shabani
  et al.(2014b)Shabani, Sarma, and
  Palmstrom]shabani:2014_MIT
authorJ. Shabani,
  authorS. D. Sarma, and
  authorC. J. Palmstrom,
  journalPhys. Rev. B volume90,
  pages161303 (year2014b).

[Sarma and Hwang(2013)]sarma:2013
authorS. D. Sarma and
  authorE. H. Hwang,
  journalPhys. Rev. B volume88,
  pages035439 (year2013).

[Datta and Das(1990)]datta:1990
authorS. Datta and
  authorB. Das,
  journalAppl. Phys. Lett. volume56,
  pages665 (year1990).

[Yokoyama et al.(2015)Yokoyama, Yokoyama,
  Takenaka, and Takagi]Yokoyama:2015
authorM. Yokoyama,
  authorH. Yokoyama,
  authorM. Takenaka, and
  authorS. Takagi,
  journalApplied Physics Letters volume106,
  pages122902 (year2015).

[Lee et al.(2017)Lee, Huang, Efetov, Wei,
  Hart, Taniguchi, Watanabe, Yacoby, and Kim]Lee:2017
authorG.-H. Lee,
  authorK.-F. Huang,
  authorD. Efetov,
  authorD. Wei,
  authorS. Hart,
  authorT. Taniguchi,
  authorK. Watanabe,
  authorA. Yacoby, and
  authorP. Kim,
  journalNature Physics volume13,
  pages693 (year2017).




