Density of states effective

E is tire density of states between E and E + AE. A simpler way of calculating n is to represent all tire electron states in tire CB by an effective density of states at tire energy E (band edge). The electron density is tlien simply n = NJ (Ef. 

The distributions of states in conduction and valence bands are commonly described by the effective density of states. The concentration of electrons, n, in the conduction band can be calculated as... 

Population inversion is easier to achieve when the effective density of states in the conduction band is low. 

In an intrinsic semiconductor, charge conservation gives n = p = where is the intrinsic carrier concentration as shown in Table 1. Ai, and are the effective densities of states per unit volume for the conduction and valence bands. In terms of these densities of states, n andp are given in equations 4 and... 

It can be shown from quantum mechanics that the effective density of states for the conduction and valence bands, (Vc and (Vt, respectively, are... 

Here and N are the effective densities of states in the conduction and valence bands respectively, and ws are the mobilities. The final expression for the electrical conductivity of an intrinsic semiconductor is given by... 

In this equation, Ey is the energy level of the valence band edge, Ny the effective density of states of the valence band, p the concentration of photo-generated positive holes, and pp that of Positive holes in thermal equilibrium in the dark which can be eventually ignored in a semiconductor of large band gap such as Zn°. ... 

Fig. 15. Calculated effective densities of states for 40-nm bismuth nanowires (solid curve) and bulk bismuth (dashed curve). The zero energy refers to the band edge of bulk bismuth. The nonparabolic effects of the electron carriers are considered in these calculations.

Here is the hole trap density, g is the degeneracy factor (taken as unity in the calculations), Etp is the ionization energy of the hole traps, Ev is the valence band edge (i.e. HOMO), Ny is the effective density of states for holes, at is the standard deviation of the Gaussian distribution of traps, and the factor expOS /F/fcr) arises due to the Poole-Frenkel effect. Analytical solution of (3.58) and (3.60) can not be obtained. Numerically computed results are shown in Fig. 3.29. 

The bulk electronic properties of extrinsic semiconductors are largely determined by the level of doping that is used to make the materials n-type or p-type. For non-degenerate semiconductors, the electron concentration in the conduction band and the hole concentration in the valence band are related to the Fermi energy EF and to the effective densities of states in the conduction and valence bands (Nc and Ny respectively) by... 

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