Direct measurement of the camel-back energy surface in AlAs and its evolution in an electric field

We report the direct measurement of the AlAs conduction band dispersion near the band edge. The six lobes of its constant energy surface are much more spherical than previously supposed, with a ratio of major to minor axes of less than 2. The existence of a “camel back” is confirmed. The $\mathbf{k}\bullet \mathbf{p}$ interaction responsible for the camel back is found to be about three times the presently accepted value. A consequence is that above some critical electric field applied perpendicular to an AlAs quantum well, the sub-band constant energy surface is rotated by 45°. We confirm this behavior experimentally in the same sample.

Figure 1

The ${\Gamma }_1$ and $X_1$ conduction band profiles at $P>10\mathrm{kbar}$ and zero bias. Inset: Schematic diagram showing $\mathbf{k}\bullet \mathbf{p}$ induced repulsion between $X_1$ and $X_3$ states leading to the camel-back dispersion.

Figure 2

The $X_{XY}\left(1\right)\to X_{XY}\left(1\right)$ resonance in a 70–40–70 sample at $4.2\mathrm{K}$ and $9\mathrm{kbar}$, measured at zero magnetic field (dash) and at an in-plane magnetic field of $15\mathrm{T}$ (solid) parallel to [100] and [110]. Inset: The bias separation between forward and reverse bias peaks plotted as a function of the field angle.

Figure 3

Dependence of the peak bias position on the magnetic field direction in the plane of the quantum well for the $X_{XY}\left(1\right)\to X_{XY}\left(1\right)$ resonance of a 60–40–60 sample at $12\mathrm{kbar}$ demonstrating clear “cloverleaf” symmetry. In this case the outside interface between the collector AlAs well and the GaAs contact layer was doped with $\sim 0.9\mathrm{ml}$ of InAs, but this does not appear to have a noticeable effect on the symmetry of the results. Note that the bias scale goes to roughly half the range of that for the inset of Fig. 2 (which plots the separation between peaks in both bias directions) and it is also expanded to enhance the appearance of the cloverleaf.

Figure 4

Fits at $10\mathrm{kbar}$ of $R\left(m_z^{\prime }\right)$ to the data in Fig. 2 (inset) for offset voltages of $V=0$, 100, and $130\mathrm{mV}$ $\left(R_{\mathrm{V}}\right)$, to measurements of Landau level splittings at $10\mathrm{kbar}$ ($R_{\mathrm{A}}$ and $R_{\mathrm{B}}$), and to $1\mathrm{bar}$ high field cyclotron resonance data $\left(R_{\mathrm{CR}}\right)$. For $R_{\mathrm{CR}}$, the pressure difference was taken into account by shifting $m_z^{\prime }$ as described in the text. The dashed line is a fit to the data in Fig. 2 (inset) under the assumption of no camel back. The dashed ellipse shows the unique intersection point for all three sets of data. Inset: The dispersion at ambient pressure, deduced from the values at the intersection point, which clearly exhibits a camel back.

Figure 5

Fan of $X_{X,Y}$ Landau levels in a $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{As}$ double-barrier structure at a pressure of $10\mathrm{kbar}$: experimental data from Ref. 22 (symbols) and best fit using method in Ref. 23 (solid lines).

Figure 6

Cyclotron resonance measurement at ambient pressure on AlAs at $145\mathrm{K}$ from Ref. 26 (inset) and best fit for $m_z^{\prime }=0.16m_0$ which occurs at $R=3.4\mathrm{eV}\mathrm{\AA }$. All transitions between different Landau levels, $L\left(i\right)$, with $i=1,2,3,\dots$, are shown that contribute to the final peak. An empirical broadening parameter has been used.

Figure 7

Angle dependence of the field induced shift in a 60–40–60 sample at $4.2\mathrm{K}$ and $15\mathrm{T}$ for the $X_{XY}\left(1\right)\to X_{XY}\left(3\right)$ resonance peak in forward bias at $1\mathrm{bar}$ (solid triangle), in reverse bias at $1\mathrm{bar}$ (open triangle), and in forward bias at $10\mathrm{kbar}$ (solid circle).