Cyclotron Resonance Experiments in Uniaxially Stressed Silicon: Valence Band Inverse Mass Parameters and Deformation Potentials

Abstract

Cyclotron resonance of holes in unstressed or "cubic" silicon fails to specify uniquely the valence band parameters because of the complex shape of the warped energy surfaces. The application of uniaxial stresses to the crystal lifts the cubic symmetry and removes the degeneracy at k=0 of the valence band which is responsible for the warping of the surfaces. The ellipsoidal energy surfaces of the decoupled bands give cyclotron resonance masses amenable to simple interpretation. From the measured masses (at 1.26\ifmmode^\circ\else\textdegree\fi{}K and \ensuremath{\sim}9000 Mc/sec) the following quantities have been determined: the inverse mass band parameters (in units of $\frac{{\ensuremath{\hbar}}^{2}}{2{m}_{0}}$) $A=\ensuremath{-}4.28\ifmmode\pm\else\textpm\fi{}0.02$, $|B|=0.75\ifmmode\pm\else\textpm\fi{}0.04$, and $|N|=9.36\ifmmode\pm\else\textpm\fi{}0.10$; the absolute value of the ratio of the band splitting deformation potentials $|\frac{D_{u}^{}{}_{}{}^{\ensuremath{'}}}{{D}_{u}}|=1.31\ifmmode\pm\else\textpm\fi{}0.03$; and the signs of the quantities $B{D}_{u}<0$ and $ND_{u}^{}{}_{}{}^{\ensuremath{'}}<0$. The interaction of the spin-orbit split-off band with the valence band edge under strain allows the signs and magnitudes of the deformation potentials to be obtained. They are ${D}_{u}=+(2.04\ifmmode\pm\else\textpm\fi{}0.20)$ eV and $D_{u}^{}{}_{}{}^{\ensuremath{'}}=+(2.68\ifmmode\pm\else\textpm\fi{}0.25)$ eV. The results indicate that the ${M}_{J}=\ifmmode\pm\else\textpm\fi{}\frac{1}{2}$ band moves "up" and the ${M}_{J}=\ifmmode\pm\else\textpm\fi{}\frac{3}{2}$ band "descends" under compressive stresses along the [001] and [111] crystallographic axes. This fact in conjunction with the ratio of deformation potentials shows that the quantization and band energy splitting are approximately isotropic with respect to the direction of stress. Finally, the signs of $B$ and $N$ were determined to be negative, the negative sign of $B$ being contrary to that predicted by band theory. An investigation of the shape of the split-band hole resonance confirms the line-broadening mechanism proposed by Hasegawa.