Modeling hole effective mass of Si modulated by external field

Abstract

Figure 1 shows the confinement effective mass (m* zz,2D-hole,n-par(001) ) dependence on t S for F ext =104 V/cm; the transport effective mass (m* xx,2D-hole,n-par(001) ) and bulk mass values are also shown for comparison. It is seen that in such a low field the 2-D heavy hole mass value (m* zz,2D-hole,n-par(001) ) decreases as t S increases for the parameters appearing in [5], although the 2-D heavy hole mass (m* zz,2D-hole,n-par(001) ) slightly increases as t S increases for the parameters appearing in [6], almost holding its bulk value. On the other hand, the light hole mass value increases as t S increases regardless of parameters. Subsequently, the impact of band nonparabolicity on the 2-D hole effective mass of valence band holes appears for a large range of t S . This is directly related the magnitude of band bending in the Si layer; the perturbation energy is roughly expressed by (1/2)et S F ext and this reduces the hole energy. In contrast to the behavior of the confinement effective mass, the estimated transport effective mass along the k x axis (m* xx,2D-hole,n-par(001) ) is almost free from confinement. This behavior is specified only for the (001) surface, but the transport effective mass for the (011) surface is sensitive to confinement (not shown here). If the physical confinement is normal to the (011) surface, we can see that this is due to the weak sensitivity of hole band dispersion to the external field because the ground-state level energy of 2-D holes is determined by the heavy hole mass.