Spin and cyclotron energies of electrons in GaAs/Ga1-xAlxAs quantum wells

A five-level P center dot p model of the band structure for GaAs-type semiconductors is used to describe the spin g(*) factor and the cyclotron mass m(c)(*) of conduction electrons in GaAs/Ga1-xAlxAs quantum wells in an external magnetic field parallel to the growth direction [001]. It is demonstrated that the previous theory of the g(*) factor in heterostructures is inadequate. Our approach is based on an iteration procedure of solving 14 coupled differential P center dot p equations. The applicability of the iteration procedure is verified. The final eigenenergy problem for the conduction subbands is reduced to two differential equations for the spin-up and spin-down states of consecutive Landau levels. It is shown that the bulk inversion asymmetry of III-V compounds is of importance for the spin g(*) factor. Our theory with no adjustable parameters gives an excellent description of experimental data on the electron spin g(*) factor in GaAs/Ga0.67Al0.33As rectangular quantum wells for different well widths between 3 and 21 nm. The same theory describes very well experimental cyclotron masses in GaAs/Ga0.74Al0.26As quantum wells for the well widths between 6 and 37 nm.