In this letter, carrier transport in graded AlxGa1-xN with a polarization-induced n-type doping as low as ∼1017 cm−3 is reported. The graded AlxGa1-xN is grown by metal organic chemical vapor deposition on a sapphire substrate, and a uniform n-type doping without any intentional doping is realized by linearly varying the Al composition from 0% to 20% over a thickness of 600 nm. A compensating center concentration of ∼1017 cm−3 was also estimated. A peak mobility of 900 cm2/V·s at room temperature is extracted at an Al composition of ∼7%, which represents the highest mobility achieved in n-Al0.07GaN with a carrier concentration of ∼1017 cm−3. A comparison between experimental data and theoretical models shows that, at this low doping concentration, both dislocation scattering and alloy scattering are significant in limiting electron mobility and that a dislocation density of <107 cm−2 is necessary to optimize mobility near 1016 cm−3. The findings in this study provide insights into key elements for achieving high mobility at low doping levels in GaN, a critical parameter in the design of novel power electronics taking advantage of polarization doping.

GaN has sparked intense research interest and found its way to a wide variety of electronic1–3 and photonic4 applications thanks to its unique properties, including the wide bandgap, polarization effects,5 and a high electron mobility. Although n-type doping in GaN is most commonly achieved by incorporating Si substitutional donors, it is also possible to introduce n-type doping in graded AlxGa1-xN through the polarization-induced internal electric field without the involvement of intentional impurities (Pi-doping).6 The mobility of electrons generated by polarization-induced doping in AlGaN has been previously studied7 at an electron concentration near 1.5 × 1018 cm−3, a carrier concentration relevant to RF devices,8 showing that alloy scattering and phonon scattering are the main scattering mechanisms while neglecting dislocation scattering.

In this letter, the electron mobility in the Pi-doped AlGaN with a much lower electron concentration of ∼1017 cm−3 is studied, with an aim to implement polarization-induced doping in power electronic devices, where a low carrier concentration is desired: about 1015–1016 cm−3 for unipolar drift regions as in metal-oxide-semiconductor field effect transistors (MOSFETs)9 or about 1017 cm−3 for bipolar drift regions such as super-junctions.10 The electron mobility is extracted experimentally using the split C-V method by combining current-voltage (IV) and capacitance-voltage (CV) characterizations of a field effect transistor (FET). Theoretical calculations of the electron mobility, taking into account the ionized/neutral impurity, phonon, charged dislocation, and alloy scattering, are carried out and compared with the experimental data. The comparison reveals that for an electron concentration of <1017 cm−3 in both Pi-doped AlGaN and Si-doped GaN, the key to achieving a high electron mobility is to reduce dislocation density to <107 cm−2. Pi-doped AlGaN is shown to have an advantage in electron mobility over Si-doped GaN at high electron concentrations due to the absence of impurity scattering.

The wafer in this study was grown by metalorganic chemical vapor deposition (MOCVD). The epitaxial growth started on a sapphire substrate with buffer layers, followed by an unintentionally doped (UID) semi-insulating Ga-face GaN with a thickness of 5 μm and a Pi-doped AlGaN with a thickness of t ≅ 600 nm. Over this thickness, the Al composition was linearly increased from 0% to 20% toward the wafer surface. During the entire MOCVD growth, the Si precursor was not flown. The one-dimensional (1D) Poisson calculation incorporating polarization effects shows that a uniform electron concentration of ρπρsurfρbulkt 2 × 1017 cm−3 is expected due to the spontaneous and piezoelectric polarization in AlxGa1-xN.

The secondary ion mass spectrometry (SIMS) scan of the sample shown in Fig. 1(a) confirms that the Al composition varies linearly from 20% at the surface to 0% at a depth of 600 nm. Both Si and H levels are at their detection limits of the SIMS measurement, and an increase in C and O (unintentional impurities) with increasing Al composition is observed. The morphology observed using an atomic force microscope (AFM), shown in Fig. 1(b), shows a very smooth surface after growth with a roughness root mean square (RMS) value smaller than 1 nm for the 5 × 5 μm2 scan. Clear atomic steps are also observed in the AFM image, indicating a good crystal quality of the Pi-doped AlGaN, although pit-like features are also visible, which are often observed on AlGaN surfaces.11 

Electron transport in Pi-doped AlGaN is characterized with Hall effect measurements at both room temperature (RT) and 77 K. The measured electron sheet concentration drops from 1 × 1013 cm−2 at RT to 5.9 × 1012 cm−2 at 77 K, while the electron mobility increases from 590 cm2/Vs to 1540 cm2/Vs at 77 K. Taking into account the surface depletion depth induced by an assumed surface barrier height of 1 eV, the electron bulk concentration is calculated to be 1.91 × 1017 cm−3 at RT and 1.17 × 1017 cm−3 at 77 K. Since carriers due to polarization-induced doping are activated by the electric field, they are expected to exhibit a temperature-independent behavior, as opposed to electrons thermally ionized from shallow donors like O that can be largely frozen out at 77 K, thus allowing an accurate measurement of the net polarization-induced doping concentration. The lower than expected carrier concentration of 1.17 × 1017 cm−3 at 77 K is attributed to the presence of compensating centers (e.g., C and Ga-vacancies).12,13 In Fig. 1(c), the temperature-dependent electron concentration of the Pi-doped AlGaN is shown, assuming an unintentional donor concentration of ND=6 × 1016 cm−3 with an activation energy of 34 meV14 along with an unintentional deep acceptor concentration of NA=1 × 1017 cm−3. For comparison, the electron concentration of GaN with a Si doping (GaN:Si) concentration of 2 × 1017 cm−3 and the same unintentional impurities is also modeled and shown. The plot shows a close match between the model and experimental data. It again confirms that Pi-doping is much more resistant to freeze-out despite the presence of unintentional impurity dopants and compensating centers.

Metal-semiconductor FETs (MESFETs) were fabricated on the Pi-doped AlGaN sample to further characterize electron transport properties. The process flow includes source/drain ohmic contacts by regrowth using molecular beam epitaxy (MBE)15 and Ti/Au metallization by e-beam evaporation, mesa device isolation with Cl2-based inductive-coupled-plasma dry etching, followed by gate metal deposition of Ni/Au. The measured DC characteristics of the MESFETs are plotted in Fig. 2, while the device schematic is shown in the inset. The transfer curve of the MESFET (Fig. 2(a)) shows an on/off ratio larger than 105 at VDS=0.5 V and the gate leakage current being low < 10 nA/mm throughout the measurement, benefitting from regrown ohmics.16 The measured family curves are plotted in Fig. 2(b), showing an on-current larger than 0.2 A/mm.

Capacitance-Voltage (C-V) measurements were carried out at RT on the MESFETs with source/drain electrically grounded. The effective carrier concentration profile was then extracted by calculating the derivative of 1/C2, which is plotted in Fig. 3 along with the electron energy band diagram and the electron concentration from the 1D Poisson simulation, the CV result, and the depletion depth as a function of VGS. The experimentally extracted doping profile shows a concentration of around 1017 cm−3 up to 450 nm deep in the sample followed by a decrease. At 600 nm below the surface, the effective doping concentration drops to ∼1016 cm−3, indicating that the depletion region in the CV measurement has reached the UID GaN layer underneath the Pi-doped AlGaN. No freeze-out effect is observed when the CV measurement is conducted at -60 °C compared to RT. The effective doping concentration of ∼1017 cm−3 is about 2 times smaller than the expected 2 × 1017 cm−3 from 1D Poisson calculations, which, as pointed out in the Hall effect measurement analysis, is most likely due to compensation effects from C incorporated in the epitaxy. A more detailed study of the compensation centers in the Pi-doped AlGaN will be carried out in future studies.

With the C-V measurement results and DC characteristics of the MESFET, electron low-field mobility could be extracted under the gradual channel approximation,7,17 i.e., the split C-V method. The circuit model used for mobility extraction is shown in Fig. 2. The contact resistance and the resistance from the access regions are accounted for using the results from transfer length method (TLM) measurements. The DC characteristics were carried out with a 20 μm long gate under a low drain at a source voltage of VDS=0.1 V, corresponding to an effective electric field of ∼50 V/cm, to minimize the impact of the non-uniform electric field along the FET channel, which is particularly important near the FET pinchoff. The drain current can be written as

ID(VGS)=dep(VGS)600nmn(x)×q×μ(x)×Echanneldx,
(1)

where VGS is the applied voltage between the gate and the source, dep is the depletion depth which is extracted from CV results, Echannel=Vy is the lateral electric field in the channel calculated from the voltage drop across the channel region, and n(x) and μ(x) are the effective doping concentration and the electron mobility at the depth x. n(x) can be extracted from CV results as shown in Fig. 3(c). Taking the derivative with respect to VGS on both sides of Eq. (1):

dID(VGS)dVGS=n(dep(VGS))×q×μ(dep(VGS))×Echannel×d[dep(VGS)]dVGS,
(2)

where all quantities except the electron mobility are either directly measured or calculated from the IV or CV measurement data. With the temperature-dependent DC characteristics and CV results, the electron field effect mobility profile can be extracted, which is shown in Fig. 4(a). The electron mobility increases with increasing depth, which is expected since alloy scattering reduces in the lower Al composition layers.7 Beyond the 450 nm depth, the electron mobility starts to decrease due to the decreasing electron concentration and thus reduced screening of dislocation scattering, as will be explained next. Another trend shown in Fig. 4(a) is the increase in mobility as the temperature decreases, which is a result of the decrease in phonon scattering.18 The weighted average mobility is calculated by

μaverage=dep(0)600nmn(x)×μ(x)dxdep(0)600nmn(x)dx.
(3)

The maximum and average electron mobility values are shown in Fig. 4(b). At RT, the extracted electron field mobility ranges from 500 cm2/Vs to 901 cm2/Vs, with an average mobility of 724 cm2/Vs. In comparison, the best electron Hall mobility reported in Si doped GaN grown on sapphire substrates with a similar electron concentration is 830 cm2/Vs at RT.19 This suggests that the average electron field mobility in Pi-doped AlGaN is comparable to that in Si doped GaN with comparable defect densities near a doping concentration of 1017 cm−3. The monotonic increase in both average and maximum electron mobility as temperature decreases is observed in Fig. 4(b), with the maximum mobility at 213 K exceeding 2000 cm2/V. The extracted mobility of 900 cm2/Vs at n∼1017 cm−3 in Pi-doped Al0.07GaN is among the highest mobility obtained in n-Al0.07GaN at a similar doping level.

To understand the limiting factors of electron mobility in Pi-doped AlGaN, a RT electron mobility model is constructed,20 taking into consideration acoustic and optical phonon scattering, alloy scattering, ionized/neutral impurity scattering, and dislocation scattering.21,22 For improved accuracy, the Al composition and impurity densities of carbon and oxygen from the SIMS measurements and the electron concentration from the C-V measurements are employed in the mobility modeling, as shown in Fig. 5(a). A dislocation density of 109 cm−2 is used, which is typical in GaN on the sapphire substrate; since not all dislocations are charged and charged dislocations induce a higher scattering rate, a charge occupation probability also needs to be determined. A good fit using a charge occupation probability of 55% was found between the measured and calculated mobility, as shown in Fig. 5(a); therefore, this value is used throughout all the modeling in this work, and the unoccupied dislocations are treated as neutral impurities. The electron component-mobilities limited by various scattering mechanisms for Al0.07GaN (peak mobility observed in this work) with a dislocation density of 109 cm−2 are modeled and plotted in Fig. 5(b) along with the total electron mobility calculated using the Matthiessen's rule;20 impurity scattering of carbon and oxygen is neglected in Fig. 5(b) in order to delineate the effect of dislocation scattering. Experimental data from this work and Ref. 7 are also plotted for comparison. It is seen that dislocation scattering is the only scattering mechanism that has a significant electron concentration dependence; dislocation-scattering-limited electron mobility decreases with decreasing electron concentration due to weakening of the screening effect at lower electron concentrations. The effect of dislocation scattering can be understood as follows: charged dislocations scatter carriers largely like ionized impurities; a scatter-center volume concentration induced by charged dislocations can be estimated by Ndis/c ∼109 cm−2/0.5 nm = 2 × 1016 cm−3, where Ndis is the dislocation density and c is the unit cell height of GaN along the [0001] direction. For n ≫ Ndis/c, the effect of dislocations is sufficiently screened, as in the Al0.15->0.07GaN layer in this work (∼1017 cm−3) and in Ref. 7 (∼1018 cm−3); for n  ND/c, dislocation scattering is not negligible, thus leading to lower mobility in the Al0.07->0GaN layer. If dislocation scattering were neglected, on the other hand, the calculated mobility at low carrier concentrations would be much higher, as is the case presented in Ref. 7. It is also believed that in Ref. 7, a large error is associated with the experimental extraction of the mobility in the Al0.07->0GaN layer since it was extracted near the FET pinchoff but at a constant current, and thus, a high applied field was used in calculating the carrier mobility.

To further illustrate the impact of dislocations on Pi-doped and Si-doped n-GaN, the theoretical electron mobility of Pi-doped AlGaN is plotted in Fig. 6(a) as a function of electron concentration with two dislocation densities and at two Al compositions. The modeled electron mobility in Pi-doped Al0.05GaN is then compared with Si-doped GaN, shown in Fig. 6(b). In these models, all the aforementioned scattering mechanisms are considered; however, impurity scattering is excluded in Pi-doped AlGaN, assuming an ideal epitaxy, while in Si doped GaN, alloy scattering is excluded, and impurity scattering is included using an activation energy of Si: ΔED∼20 meV. It can be found in Fig. 6(a) that at a low dislocation density of 107 cm−2, the electron mobility in Pi-doped GaN is largely independent of electron concentration. This is because of the dominance of alloy scattering, which is independent of electron concentration in the nondegenerate regime.20 An increase in dislocation density from 107 cm−2 to 109 cm−2 results in an increasingly high dependence of electron mobility on the electron concentration. The effect of dislocation scattering is more pronounced in Al0.07GaN compared to Al0.15GaN because of a lower alloy scattering in Al0.07GaN. The significant effect of dislocation scattering is also observed in Si-doped GaN with low electron concentrations, also compared to Pi-doped GaN in Fig. 6(b). At low carrier concentrations (<2 × 1017 cm−3), the presence of dislocations severely degrades mobility in layers doped in both schemes. The experimentally reported mobility values (symbols) for Ndis ∼ 109 cm−2 are also included. The difference between the experimental values and the modeled values can be attributed to experimental errors and scattering due to compensating point defects, which is not included in the models.

For n > 2 × 1017 cm−3, the electron mobility is severely degraded by impurity scattering in GaN:Si;23,24 on the contrary, the electron mobility in Pi-doped AlGaN remains high for high electron concentrations since there is no impurity scattering. At low electron concentrations, dislocation scattering has a significant impact on electron mobility in both Pi-doped AlGaN and Si-doped GaN. Thus, the key to improving electron mobility for electron concentration < 1017 cm−3 is to reduce Ndis. As a much lower Ndis (< 107 cm−2) is achievable in today's bulk GaN substrates and the subsequent epitaxial layers25,26 than GaN on SiC/sapphire substrates, it is feasible to achieve improved electron mobility in Pi-doped AlGaN.

In summary, linearly graded AlxGa1-xN is grown by MOCVD on sapphire substrates with a polarization induced doping at a low and uniform electron concentration near 1017 cm−3. A peak electron mobility of ∼900 cm2/Vs at RT is extracted in Al0.07GaN. By comparing the experimental data to carrier transport models, dislocation scattering is found to be the significant factor limiting electron mobility when the electron concentration is below 1017 cm−3. At low electron concentrations <1017 cm−3, much improved electron mobility can be expected in epitaxial layers grown on bulk GaN substrates with a dislocation density lower than 107 cm−2.

This work was partly supported by the ARPAe SWITCHES project monitored by Dr. Tim Heidel and Dr. Isik C. Kizilyalli.

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