Mobility and quantum mobility of modern GaAs/AlGaAs heterostructures

In modern GaAs/${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterostructures with record high mobilities, a two-dimensional electron gas (2DEG) in a quantum well is provided by two remote donor $\delta$ layers placed on both sides of the well. Each $\delta$ layer is located within a narrow GaAs well, flanked by narrow AlAs layers which capture excess electrons from donors. We show that each excess electron is localized in a compact dipole atom with the nearest donor. Nevertheless, excess electrons screen both the remote donors and background impurities. When the fraction of remote donors filled by excess electrons $f$ is small, the remote donor limited quantum mobility grows as $f^3$ and becomes larger than the background impurity limited one at a characteristic value $f_c$. We also calculate both the mobility and the quantum mobility limited by the screened background impurities with concentrations $N_1$ in ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ and $N_2$ in GaAs, which allows one to estimate $N_1$ and $N_2$ from the measured mobilities. Taken together, our findings should help to identify avenues for further improvement of modern heterostructures.

Figure 1

(a) A schematic view of a modern GaAs/${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterostructure. The 2DEG (shown in blue) resides in a GaAs well of thickness $w$ and is provided by two doping layers (shown in red) separated by ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ barriers of thickness $d$ (shown in gray). Here, $-$ and $+$ represent negative and positive charges in the 2DEG and the doping layers, respectively. (b) An enlarged view of a small section of the doping layer at a filling fraction $f\simeq 0.6$. Excess electrons ($-$) in AlAs form compact dipoles (ellipses) with the nearest donors ($+$) in GaAs. Empty donors (also shown by $+$) alternate with compact dipoles due to Coulomb repulsion between the excess electrons. Only empty donors are shown in (a). An example of a pair of anomalously close donors separated by distance $\rho$ is shown in the middle (see Sec. 3).

Figure 2

Schematic image of the electron wave function cloud (blue) in the AlAs layer of thickness $t$. This cloud is bound to a Si donor ($+$) in the GaAs layer a distance $s$ away from the midpoint of the AlAs layer. $\xi$ is the electron localization length in the $x-y$ plane.

Figure 3

The binding energy $E_b$ in $Ry$ (thick line) and the variational parameter $b$ in units of the in-plane effective Bohr radius $a_{xy}$ (thin line) as a function of the distance $s$ to the binding donor in units of $a_{xy}$ as obtained from the variational calculation for $t=2$ nm.

Figure 4

The upper half of the structure shown in Fig. 1 with an impurity (plus) at a distance $z$ from the midplane of the 2DEG. Due to EES, an image charge (red minus) is produced at a distance $2d_w-z$ from the midplane that reduces the potential of the impurity.