Simulation of semiconductor superlattices

We are simulating pseudomorphic superlattices using modern electronic structure methods. We are interested in the design of Si-Ge-C superlattices epitaxially grown on Si, whose composition can be controlled during growth for each lattice plane, that have reduced overall strain in order to be compatible with Si based cmos technology, and which have interesting optical properties.

The simulations are performed within first-principles density functional theory using codes mostly developed within the simulation group at INESC-MN. First we construct a structural model of a tetrahedrally coordinated superlattice with controlled composition in the growth direction. The enthalpy of that structure is minimized by allowing the relaxation of atomic positions and cell parameters with the constraint of epitaxial growth. For this epitaxial relaxed structure the band structure and optical properties are calculated, with particular emphasis on the optical matrix elements near the gap.

An example of what we are simulating is shown in the figure. In the center we have a representation of the atomic structure of a superlattice of 10 Ge atomic layers and 10 Si atomic layers grown in the (001) orientation. 

On the left pannel we have the band-structure for that structure calculated in the Brillouin zone of the supercell. As the supercell is very large, with 4 electrons per atom, the Brillouin zone  is very small and it has many bands. The zero of energy is chosen at the top of the valence band, and we have apparently a direct band gap material. Due to the large number of bands, it is a very dense figure and it is a difficult to interpret. However unfolding the bands into the parent fcc Brilloin zone of the diamond structure,  using a methos we developed, we recover  a figure that is similar to the familiar "band structure" of diamond and zincblende crystals, and we can see that the top of the valence band has a distinct character from the bottom of the conduction band and that the gap is pseudo-direct, which is confirmed by an independent calculation of the optical matrix elements.