SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

82 CHAPTER 2. ELECTRONIC LEVELS IN SEMICONDUCTORS

system the separation between the HH and LH state is given byδ=− 5. 966 eV. The effect
of strain on bandstructure for both conduction band and valence band states is illustrated by
examining the direct bandgap material InxGa 1 −xAs grown on GaAs and the indirect bandgap
material GexSi 1 −xalloy grown on Si. For direct bandgap materials conduction bands, the strain
tensor only moves the position of the bandedge and has a rather small effect on the carrier mass.

TENSILE STRAIN IN

GROWTH PLANE

UNSTRAINED COMPRESSIVE STRAIN IN

GROWTH PLANE

Light hole

Heavy hole

LH

HH

LH

HH

Figure 2.35: Effect of strain on bandedges of a direct bandgap material. Due to the epitaxial
strain, the valence band degeneracy is lifted.

In figure 2.35 we show a schematic of how strain in a layer grown along the (001) direction
influences the bandedges in a direct gap semiconductor. The conduction bandedge moves up or
down with respect to its unstrained position as discussed earlier, but since it is a non-degenerate
state there is no splitting. The valence bandedge is degenerate in the unstrained system. This de-
generacy is lifted by quantum confinement even in an unstrained quantum well, but the splitting
produced by quantum confinement is usually small (∼10–15 meV). Under biaxial compressive
strain the bandgap of the material increases and the HH and LH degeneracy is lifted. The split-
ting can easily approach 100 meV making strain an important resource to alter valence band
density of states. Under biaxial compressive strain the HH state is above the LH state, while
under biaxial tensile strain the LH state is above the HH state, as shown in figure 2.35.
In the case of the indirect bandgap Si 1 −xGexalloy grown on Si, the conduction band also is
significantly affected according to equation 2.11.4 through equation 2.11.6. For (001) growth
there is splitting in the 6 equivalent valleys.The results on the bandedge states are shown in
figure 2.36. Note that the biaxial compressive strain causes a lowering of the four-fold in-plane
valleys below the 2 two-fold out of plane valleys. We see that the bandgap of SiGe falls rapidly
as Ge is added to Si. This makes the SiGe very useful for Si/SiGe heterostructure devices such
as heterojunction bipolar transistors. the splitting of the HH, LH and SO bands also cause a
sharp reduction in the density of states mass near the bandedge. The splitting of the conduction
bandedge valleys also reduces the conduction band density of states in SiGe.