Reducing disorder in Ge quantum wells by using thick SiGe barriers

Abstract

We investigate the disorder properties of two-dimensional hole gases in Ge/SiGe heterostructures grown on Ge wafers, using thick SiGe barriers to mitigate the influence of the semiconductor-dielectric interface. Across several heterostructure field effect transistors we measure an average maximum mobility of $(4.4 \pm 0.2) \times 10^{6}~\mathrm{cm^2/Vs}$ at a saturation density of $(1.72 \pm 0.03) \times 10^{11}~\mathrm{cm^{-2}}$, corresponding to a long mean free path of $(30 \pm 1)~\mathrm{μm}$. The highest measured mobility is $4.68 \times 10^{6}~\mathrm{cm^2/Vs}$. We identify uniform background impurities and interface roughness as the dominant scattering mechanisms limiting mobility in a representative device, and we evaluate a percolation-induced critical density of $(4.5 \pm 0.1)\times 10^{9} ~\mathrm{cm^{-2}}$. This low-disorder heterostructure, according to simulations, may support the electrostatic confinement of holes in gate-defined quantum dots.

Figures (4)

• Figure 1: (a) HAADF-STEM image of the active layers of the Ge/SiGe heterostructure field effect transistor. The 16 nm strained Ge quantum well is grown coherently on a Si$_{0.17}$Ge$_{0.83}$ strain-relaxed buffer. A 135 nm Si$_{0.17}$Ge$_{0.83}$ barrier separates the quantum well from the dielectric stack. The dielectric stack comprises a thin native silicon oxide layer followed by a 30 nm Al$_{2}$O$_{3}$ film obtained by atomic layer deposition at $300 ~^\circ\mathrm{C}$. (b) Close-up image of the Ge quantum well with a superimposed average of the intensity profile (red curve). (c) Hall density $p$ as a function of gate voltage $V_{\mathrm{g}}$ for 9 heterostructure field effect transistors from the same wafer (colored lines) and corresponding linear fits (black lines). (d) Hole mobility $\mu$ as a function of Hall density $p$ for the same heterostructure field effect transistors (colored lines) and distribution of maximum mobility $\mu_{\mathrm{max}}$ (inset). Maximum mobility from all the devices (diamonds), average value, and standard deviation (black) are shown.
• Figure 2: Mobility $\mu$ as a function of density $p$ from a representative heterostructure field effect transistor with a 135 nm thick SiGe barrier. The dashed-dotted black curve is a theoretical fit to the data considering scattering from a uniform background of charged impurities (BI) and interface roughness (IR). The individual contributions from BI and IR are shown as dashed black curve and dotted black curve, respectively. The dashed orange curve is from a similar heterostructure with a thinner SiGe barrier of 55 nm stehouwer2023germanium.
• Figure 3: (a) Map of $\log(1 - R^2)$ as a function of variables $\alpha$ and $\Delta p$, where $R^2$ is the coefficient of determination obtained by fitting the density-dependent conductivity $\sigma_{\mathrm{xx}}(p)$ from the device in Fig. \ref{['fig:two']} to the theoretical model $A(p - p_{\mathrm{p}})^{\alpha}$. Both $A$ and the percolation density $p_{\mathrm{p}}$ are free fitting parameters, while $\Delta p$ is the density range over which the data is fitted, starting from the minimum measured density. The dashed white curve $\overrightarrow{s}(\alpha,\Delta p)$ follows the local minima of $\log(1 - R^2)$. For $\alpha=1.31$, which is the critical exponent expected from percolation theory in 2D, the local minimum is found at $\Delta p = 2\times10^{10} ~\mathrm{cm^{-2}}$ (red dot). (b) Corresponding map of the fitted $p_{\mathrm{p}}$ as a function of $\alpha$ and $\Delta p$, with superimposed dashed white curve $\overrightarrow{s}(\alpha,\Delta p)$ and red dot as in (a). (c) Values of $p_{\mathrm{p}}$ as a function of the displacement $\Delta \overrightarrow{s}$ along the curve $\overrightarrow{s}(\alpha,\Delta p)$, relative to the position of the red dot. (d) Experimental $\sigma_{\mathrm{xx}}(p)$ curve (orange) and best fit to percolation theory in 2D (dashed black line). $\alpha$ and $\Delta p$ are fixed to the values identifying the red dot in (a).
• Figure 4: (a) Simulated ground state heavy hole (HH) band edge ($HH_{\mathrm{0}}$) as a function of the $x$ and $z$ coordinates. The strained Ge quantum well is positioned 135 $~\mathrm{nm}$ below the gate stack ($z < 0$). The plunger gate and the barrier gates are $160$ nm and $30$ nm wide, respectively. All gates are $30$ nm thick. (b) Hole population of the HH ground state, showing a quantum dot-like confinement.