“Diffusion Size Effect” in Bismuth at Liquid Helium Temperatures

Observations of the “diffusion size effect” in bismuth at liquid helium temperatures were used to study recombination of electrons and holes in the bulk and at the surface. Recombination at the surface dominates at high magnetic fields. The transverse magnetoresistance extrapolated to infinite thickness clearly follows an H 2 dependence in the classical high magnetic field region. The partial mobilities µ 2 and ν 3 were calculated to have the values µ 2 =1.8×10 6 cm 2 /V-sec and ν 8 =2.3×10 6 cm 2 /V-sec, when reduced for a resistivity ratio of about 160. Surface recombination velocities due to interband transitions are calculated to be greater than the velocities of sound, and they exhibit a magnetic field dependence, approaching 4×10 5 cm/sec at infinite magnetic field. Values for the surface recombination velocity and the electron hole recombination time due to interband transitions are presented for the different configurations. For the magnetic field parallel to the trigonal axis, the bulk recombination time is ∼6.5×10 -9 sec.