Quantum cascade laser design based on impurity–band transitions of donors in Si/GeSi(111) heterostructures

Abstract

The concept of quantum cascade laser based on impurity-band transitions in n-type Si/GeSi heterostructures has been analyzed. Silicon-germanium heterostructures are attractive for development of devices emitting in the terahertz spectral range, where the use of III–V compounds is limited by their reststrahlen band. The mechanism of population inversion is based on fast ionization of donor centers into continuum of the lower neighboring subband by phonon-assisted tunneling [1]. The fast tunneling is caused by hybridization between the impurity ground state and the 2D continuum in the neighboring quantum well. It is essential that the mentioned subband is closely matched with the ground state level of donor. Apopulation of the ground state therefore is smaller than that of2Dcontinuum of the higher subband. Peculiar features of silicongermanium heterostructures are related to multivalley character of the conduction band. It involves a lot of intra- and intervalley acoustical and optical phonons in tunneling and relaxation processes. The laser scheme is analyzed for n-type selectively doped Si/GeSi(111) heterostructures. The choice of the growth plane arises from two circumstances. First, the quantization effective mass, m = 0.26m0, is fairly small. This enables one to use thicker layers in heterostructures that reduces the sensitivity of the laser scheme to a dispersion of dopants through the period and to a fluctuation of heterostructure parameters. Second, build-in strain in the Si/GeSi(111) heterostructures leaves the valleys degenerate that eliminates additional relaxation channels. An undesirable impact of the remaining degeneracy is the decrease of filling factors of continuum states in the upper (working) subband. Four- and six-layer-period-superlattice cascade laser are treated. Taking into account electron heating up to 100 K amplification coefficient is of the order of 10 cm−1 for doping concentration of 5 × 1011 cm−2 per period at 24–29 μm wave lengths. Selective doping is assumed to be in the centre of a quantum well of the period. For comparison, uniform dopant distribution reduces the amplification coefficient by more than five times.