Anisotropy of the electrongfactor in lattice-matched and strained-layer III-V quantum wells

The influence of quantum confinement and built-in strain on conduction-electron g factors in lattice-matched ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{0.35}{\mathrm{Ga}}_{0.65}\mathrm{As}$ and strained-layer ${\mathrm{In}}_{0.11}{\mathrm{Ga}}_{0.89}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ quantum wells is investigated for well widths between 3 and 20 nm. The magnitude, sign, and anisotropy of the g factors were obtained from quantum beats due to Larmor precession of electron spins in time-resolved, polarization-sensitive, pump-probe reflection at 10 K in magnetic fields applied along and at 45° to the growth axis. Slowly varying shifts of precession frequency, due to buildup of nuclear polarization in the samples over ∼1 h and equivalent to up to 0.5 T, occurred for fixed circular pump polarization and oblique applied fields. These Overhauser shifts confirmed the sign of the g factors and were eliminated by modulation of pump polarization to give precise g factors. For both material systems, variation of the g factor with well width follows qualitatively the dependence on energy, determined by quantum confinement, calculated from three-band $\mathbf{k}\cdot \mathbf{p}$ theory in the bulk well material. For the lattice-matched system there is excellent quantitative agreement with a full three-band $\mathbf{k}\cdot \mathbf{p}$ calculation including anisotropy effects of the quantum-well potential. For the strained-layer system, detailed quantum-well calculations do not exist but $\mathbf{k}\cdot \mathbf{p}$ theory for epitaxial layers predicts 10 times greater anisotropy for wide wells than we observe. This discrepancy is also apparent in previous, less complete, investigations of strained-layer systems and highlights the need for further theoretical effort.