Xt–Xlvalley crossover and deformation potential in AlP/GaP quantum wells

Abstract

We investigate the properties of quasi-two-dimensional electrons in a wide range of modulation-doped AlP quantum wells (between 3 and 15 nm) with GaP barriers by measuring cyclotron resonance, quantum Hall effect, and Shubnikov--de Haas oscillations. The degeneracy of the three $X$ valleys is lifted due to both strain and confinement: In wider wells the strain contribution dominates, and the lowest energy states are the transverse $X$ valleys ${X}_{t}$. On the other hand, in narrower wells, the quantum confinement energy dominates, and the lowest energy states are the single longitudinal valleys ${X}_{l}$. The transition between these two configurations occurs for wells between 5 nm and 4. The effective mass components for the AlP $X$ valleys are determined from the cyclotron resonance data to be ${m}_{t}=(0.30\ifmmode\pm\else\textpm\fi{}0.01){m}_{0}$ and ${m}_{l}=0.90{m}_{0}$. From these effective mass values and the degeneracy data, we calculate the deformation potential for AlP to be ${\ensuremath{\Xi}}_{u}^{\text{AlP}}=3.3\ifmmode\pm\else\textpm\fi{}0.5\text{ }\text{eV}$.