Theory of the Cyclotron Resonance in Si and Ge

A quantum theory is developed for the cyclotron resonance (CR) in silicon(Si) and germanium(Ge). The angular dependent CR peaks for heavy ``holes'' are analyzed, using the Dresselhaus-Kip- Kittel (DKK) formula: $\omega=(\omega_{t}^{2}cos^2\theta + \omega_{t}\omega_{l}sin^2 \theta)$, $\omega_{t}\equiv\frac{eB}{\m_{t}}$ ,$\omega_{l} \equiv\frac{eB}{\m_{l}}$.Their Fermi surfaces for Si(Ge) are spheroids oriented along $\left\langle 100\right\rangle$ axes with the transverse mass $m_{t}=0.46(0.29)m$ and the longitudinal mass $m_{l}=1.03(0.78)m$.The fluted energy surfaces represented by the quartic dispersion relations used by DKK were avoided.The CR should be observed only, when a substantial number of conduction electrons with a quadratic dispersion relation resonate at a single frequency.