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) by introducing the concept of the cyclotronic planes (CP) in which the conduction electrons ("electrons", "holes") complete circulations. The angular dependent CR peaks for heavy "holes" are analyzed, using the Dresselhaus-KipKittel (DKK) formula omega=(omega(2)(t) cos(2)theta+omega(t)omega(1)sin(2)theta)(1/2), omega(t) eB/m(t), omega(1) eB/m(1). The Fermi surfaces for Si (Ge) are spheroids oriented along < 100 > axes, with transverse mass m(t) = 0.46 (0.29) m, and longitudinal mass m(1) = 1.03 (0.78) m. The fluted energy surfaces used by DKK are avoided. The angular-independent CR peaks for light "holes" in Ge (Si) arise from the spherical Fermi surface, with effective mass m* = 0.16 (0.042) m with the CP in {100}. The reason why there are light and heavy "holes" with the same CP in {100} is shown by decomposing the fcc lattice in two sets of sublattices.