The change in sound velocity due to donor pairs in Ge

The authors calculate the effects of the temperature, the magnetic field and the uniaxial stress of the sound velocity change Delta upsilon due to donor pairs in moderately Sb-doped Ge in the low-frequency limit. The nearly degenerate ground-state structure of an Sb donor is explicitly taken into account in calculating the eigenstate of a donor pair. The following results are found. The temperature and the stress dependences of Delta upsilon are qualitatively similar to those in the isolated donor system, although their magnitudes are smaller. The magnetic field (B) dependences for B//(111) and the (110) longitudinal mode are different; that is, Delta upsilon (B)= Delta upsilon (B)- Delta upsilon (B=0) becomes negative in the low-field region, while Delta upsilon (B) in the isolated donor system is always positive provided that existing theories of the magnetic field dependence of the donor ground state are correct. The scattering of high-frequency phonons by donor pairs is briefly discussed.