Effects of strain and quantum confinement in optically pumped nuclear magnetic resonance in GaAs: Interpretation guided by spin-dependent band structure calculations

A combined experimental-theoretical study of optically pumped nuclear magnetic resonance (OPNMR) has been performed in a $\mathrm{GaAs}\text{/}\mathrm{A}{\mathrm{l}}_{0.1}\mathrm{G}{\mathrm{a}}_{0.9}\mathrm{As}$ quantum well film epoxy bonded to a Si substrate with thermally induced biaxial strain. The photon energy dependence of the Ga OPNMR signal was recorded at magnetic fields of 4.9 and 9.4 T at a temperature of 4.8–5.4 K. The data were compared to the nuclear spin polarization calculated from the electronic structure and differential absorption to spin-up and spin-down states of the electron conduction band using a modified $\mathbf{k}·\mathbf{p}$ model based on the Pidgeon-Brown model. Comparison of theory with experiment facilitated the assignment of features in the OPNMR energy dependence to specific interband Landau level transitions. The results provide insight into how effects of strain and quantum confinement are manifested in optical nuclear polarization in semiconductors.

Figure 1

Schematic structure of EA-124, which is composed of layers of GaAs (orange), $\mathrm{A}{\mathrm{l}}_x\mathrm{G}{\mathrm{a}}_{1-x}\mathrm{As}$ (blue), and Si-δ-doping (red dashed lines). The Si-δ-doping level is $4\times {10}^{11}\mathrm{c}{\mathrm{m}}^{-2}$ for the bottom dashed line and $2\times {10}^{11}\mathrm{c}{\mathrm{m}}^{-2}$ for middle and top dashed lines. The Al composition is $x$ = 0.1 in the MQW layers, $x$ = 0.1 → 0.55 in the superlattice layers, and $x$ = 0.55 in the stop etch layers. Thicknesses of each layer are specified to the right of the structure along with the repeat multiple. The entire structure is epoxy-bonded (black) to a Si support (gray).

Figure 2

(a) Thermally polarized ${}^{71}\mathrm{Ga}$ NMR spectrum of EA-124 at 4.2 K and 9.4 T acquired immediately after cooling the sample. (b) ${}^{71}\mathrm{Ga}$ OPNMR spectrum of EA-124 at 4.2 K, acquired using ${\tau }_{\mathrm{ONP}}=50\mathrm{s}$.

Figure 3

Calculated magnetic field dependence of conduction band (top) energies for $C{B}_1$ $\left(•\right)$ and $C{B}_2$ (○) and the valence band (bottom) energies for ${\mathit{LH}}_1$ $\left(\blacksquare \right)$, ${\mathit{HH}}_1$ $\left(▴\right)$, and ${\mathit{HH}}_2$ $\left(▵\right)$ in EA-124. The dashed vertical lines are 4.9 T and 9.4 T. Colors correspond to PB indices of −1 (red), 0 (black), 1 (orange), 2 (blue), 3 (green), and 4 (purple).

Figure 4

Upper panels: Photon energy dependence of the experimental OPNMR data $\mathrm{T}=5.1\pm 0.3\mathrm{K}$ (black points, arbitrary units), $I_z\left(h{\nu }_l\right)$ calculated using Eq. (4) (red curve, arbitrary units), and $S_z^0$ (dashed blue curve) at 4.9 T for ${\sigma }^{-}$ and ${\sigma }^{+}$ light. Lower panels: Decomposition of the total optical absorption coefficients according to PB manifold, as indicated. Gray dotted vertical lines mark prominent features in the data, which are labeled according to transition, ${\mathrm{T}}_{\mathrm{i}}$.

Figure 5

Upper panels: Photon energy dependence of experimental OPNMR data at $\mathrm{T}=5.1\pm 0.3\mathrm{K}$ (black points, arbitrary units), $I_z\left(h{\nu }_l\right)$ calculated using Eq. (4) (red curve, arbitrary units), and $S_z^0$ (blue dashed curve) at 9.4 T for ${\sigma }^{-}$ and ${\sigma }^{+}$ light. Lower panels: Decomposition of the total optical absorption coefficients according to PB manifold, as indicated. Gray dotted vertical lines mark prominent features in the data, which are labeled according to transition, ${\mathrm{T}}_{\mathrm{i}}$.

Figure 6

Calculated photon energy dependence of $S_z^0\left(h{\nu }_l\right)$ at 4.9 T for ${\sigma }^{+}$ light for the values of ${\varepsilon }_{zz}$ given to the right of the plot.

Figure 7

OPNMR photon energy dependence of EA-124 (blue circles) and bulk GaAs (red circles) at 3.0 T using unpolarized light. Data have been normalized to the largest OPNMR signal for each data set.

Figure 8

OPNMR photon energy dependence of EA-124 at 3.0 T using unpolarized light oriented at angles of 0° (blue circles) and 6° (green squares) with respect to the magnetic field. Angles refer to the orientation of the growth direction with respect to the magnetic field.