Microscopic origin of the anomalous low-temperature dephasing in a disordered AlGaN/GaN two-dimensional electron gas grown on Si(111)

Weak-localization analysis of the low-field magnetoconductance of an Al$_{0.15}$Ga$_{0.85}$N/GaN high-electron-mobility-transistor (HEMT) structure grown on p-type Si(111) — a high-density two-dimensional electron gas (2DEG) with $n\approx9.2\times10^{12}$ cm$^{-2}$ and mobility $\approx700$ cm$^2$/Vs at 0.3 K (values as reported in the source paper), weakly disordered in the $k_Fl\gg1$ sense but far dirtier than a typical GaAs 2DEG — yielded a dephasing rate $1/\tau_\varphi$ approximately linear in $T$ that extrapolates to a finite value as $T\to0$ (Zhang et al., J. Korean Phys. Soc. 61, 1471 (2012)). The microscopic origin of this anomalous dephasing behavior — additional or unaccounted dephasing channels, an experimental or analysis artifact, or a breakdown of the theoretical limits used for comparison — has not been identified. The problem is to determine and quantify the mechanism(s) governing $\tau_\varphi(T)$ in this system so that the magnitude of $1/\tau_\varphi$, its approximately linear-in-$T$ dependence over the measured range, and the finite $T\to0$ intercept are all quantitatively accounted for.

Background

The AlGaN/GaN high-electron-mobility transistor (HEMT) is the workhorse of radio-frequency and power electronics. Its conducting channel is a two-dimensional electron gas (2DEG): a sheet of electrons confined at the AlGaN/GaN interface by spontaneous and piezoelectric polarization charges rather than by dopants. Growing this structure on silicon is attractive for cheap, large-area integration with CMOS technology, but the large lattice and thermal mismatch with Si produces dislocation densities high enough to make the 2DEG much dirtier than a typical GaAs 2DEG while remaining weakly disordered in the $k_Fl\gg1$ sense. The sample studied in the source paper (Al$_{0.15}$Ga$_{0.85}$N/GaN on p-type Si(111), grown by the same group that developed the SiN-treatment growth technique) had a carrier density $n\approx9.2\times10^{12}$ cm$^{-2}$ but a Hall mobility of only $\approx700$ cm$^2$/Vs at 0.3 K; from these values one estimates $k_F l\approx25$–$30$, where $k_F$ is the Fermi wave vector and $l$ the mean free path, i.e. weakly disordered but far dirtier than a typical GaAs 2DEG. It showed no Shubnikov–de Haas oscillations (the oscillatory magnetoresistance produced by Landau quantization) up to 15 T.

In such a dirty 2D conductor, the low-field magnetoconductance is dominated by weak localization (WL): quantum interference between diffusive electron paths that retrace one another enhances backscattering at zero field, and a small perpendicular magnetic field destroys this interference, producing a characteristic magnetoconductance curve. Fitting that curve with the standard Hikami–Larkin–Nagaoka (HLN) expression yields the phase-coherence time $\tau_\varphi$, the timescale over which an electron's quantum phase survives decoherence. For a nonmagnetic diffusive 2DEG, theory predicts: (i) the Nyquist mechanism — dephasing by the low-frequency Johnson–Nyquist electromagnetic fluctuations of the electron gas itself, equivalent to electron–electron interactions with small energy transfer — gives $1/\tau_\varphi\propto T\ln(T^*/T)$, approximately linear in $T$; (ii) the Fermi-liquid channel (collisions between quasiparticles with large energy transfer) gives a faster, roughly $T^2$-in-2D growth. Both vanish as $T\to0$, a consequence of time-reversal symmetry (unitarity). A finite $1/\tau_\varphi$ extrapolated to $T=0$ ('zero-temperature dephasing') is therefore anomalous, and ever since Mohanty, Jariwala and Webb reported low-temperature saturation of $\tau_\varphi$ in metal films it has been debated whether such saturation is intrinsic decoherence or an extrinsic artifact (residual electron heating, dilute magnetic impurities, or parallel conducting channels). Moreover, the comparison between measured and predicted $\tau_\varphi$ in 2DEGs is itself on uncertain footing: Burke, Pfeiffer and West found that applying external Johnson–Nyquist noise to a 2DEG does not change the dephasing rate measured through weak localization, contradicting the standard Nyquist-dephasing picture; anomalous dephasing rates have been reported in double quantum wells and in a parabolic quantum well; states at the Fermi energy in doped layers were shown to shorten and saturate $\tau_\varphi$ in quantum-well 2DEGs; and saturation of the coherence length at the lowest temperatures was still being reported in high-mobility two-dimensional hole gases in 2018.

The source experiment measured magnetotransport on this AlGaN/GaN-on-Si HEMT between 0.28 and 20 K. Three findings frame the open question. First, the longitudinal resistivity $\rho_{xx}(B)$ shows an approximately temperature-independent crossing at a field $B_c$ with $\rho_{xx}(B_c)\approx1$ k$\Omega$. Second, the Hall slope decreases approximately logarithmically with $T$, as expected from the Altshuler–Aronov electron–electron-interaction (EEI) correction to the conductivity tensor of a weakly disordered 2D conductor; this correction can be subtracted using the standard interaction formula with a prefactor $K_{ee}$, a procedure developed in the 2D interaction literature. Third — the central subject of this problem — HLN fits to the low-field magnetoconductance give $1/\tau_\varphi$ approximately linear in $T$ over the measured range, extrapolating to a finite value as $T\to0$; the source paper further reports fitted $\tau_\varphi$ values about five times longer than both the Nyquist and the Fermi-liquid predictions evaluated for the sample's density and mobility, i.e. dephasing simultaneously too weak in its linear-$T$ magnitude and too strong at $T\to0$ relative to standard theory. No dephasing mechanism has been identified that reproduces this behavior in nitride 2DEGs on Si.

Problem Statement

For the disordered Al$_{0.15}$Ga$_{0.85}$N/GaN two-dimensional electron gas grown on p-type Si(111) of Zhang et al. (J. Korean Phys. Soc. 61, 1471 (2012)) — with the sample parameters as reported in the source paper, $n\approx9.2\times10^{12}$ cm$^{-2}$, Hall mobility $\approx700$ cm$^2$/Vs at 0.3 K, no Shubnikov–de Haas oscillations up to 15 T — determine the microscopic origin of the measured phase-coherence behavior, specifically (a) why the dephasing rate $1/\tau_\varphi(T)$ extracted from Hikami–Larkin–Nagaoka fits to the low-field magnetoconductance is approximately linear in $T$ over the measured range; and (b) why $1/\tau_\varphi$ extrapolates to a finite value as $T\to0$. A complete answer must either identify and quantify the dephasing channel(s) — or the experimental or analysis artifact — that reproduces the measured $\tau_\varphi(T)$ quantitatively — an approximately linear temperature dependence over the measured range $\approx0.3$–$20$ K with $\tau_\varphi$ about five times longer than the standard Nyquist and Fermi-liquid predictions at the sample's density and mobility, together with a finite $T\to0$ intercept; or demonstrate that the standard Nyquist/Fermi-liquid comparison does not apply to this regime (for example because of multi-subband occupation, disorder beyond the weak-localization regime, or the validity limits of the single-subband diffusive formulas) and supply the corrected quantitative description. If the finite intercept is attributed to an extrinsic cause (e.g., residual electron heating, parallel conduction through the Si substrate or buffer layers, or dilute magnetic impurities), the answer must show quantitatively that the proposed cause produces the intercept without spoiling the observed linear-in-$T$ behavior.

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