Shallow Donor Levels of Germanium in an Intermediate Magnetic Field

Abstract

The magnetic field dependence of the shallow donor levels 1 s , 2 p 0 , 2 p -1 and 3 p -1 in germanium was calculated by using two types of variational wave functions each of which is appropriate either for weak magnetic fields or strong magnetic fields. In the range up to γ=0.7 ( H =43 kOe), it became evident that for the 1 s and 2 p 0 states the hydrogen-like wave functions give lower eigenvalues, whereas for the 2 p -1 and 3 p -1 states the harmonic oscillator-type wave functions become more appropriate above about 10 kOe. The effect of the magnetic field on the triplet and singlet ground states was evaluated with inclusion of the central-cell correction for both arsenic and antimony impurities. The optical transitions in the case of H //[111] and E ⊥[111] were considered.