By Galperin Yu.M.
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Extra resources for Doped semiconductors: Role of disorder
At low temperatures it becomes less than the concentration contributed by impurities. In this region the conduction is called extrinsic since it depends on the impurities. A schematic plot of temperature dependence of the conductance is shown in Fig. 1 The region A corresponds to intrinsic conduction, while the regions B − D correspond to extrinsic conductance. If the impurities are shallow, then there exists the region B which is called the the saturation range. In this range, all the impurities are ionized and hence the carrier concentration is temperature independent.
Let us count the energy i of i-th donor from the energy of an isolated donor, −E0 . We have don 1 − n e2 acc 1 k − . i = κ l |ri − rl | k=i |ri − rk | The occupation numbers have to be determined to minimize the free energy (at T = 0 – electrostatic energy). A typical dependence of the Fermi level µ on the degree of compensation, K = NA /ND , is shown in Fig. 3 Below we discuss limiting cases of small and large K. 29 30 CHAPTER 3. IMPURITY BAND FOR LIGHTLY DOPED SEMICONDUCTORS. 1: Position of the Fermi level µ as a function of the degree of compensation, K.
It is valid only at rµ . a. 3. SPECIFIC FEATURES OF THE TWO-DIMENSIONAL CASE 35 Long-range fluctuations At 1 − K 1 it is a large and important effect because screening is weak. To obtain an estimates we can repeat the discussion for K 1 and replace the donor concentration by the total concentration, Nt , of donors and acceptors. In this way we get for a typical potential energy of an electron, γ(R) = e2 (Nt R3 )1/2 . κR It also diverges at large R. How the screening takes place. The excess fluctuating density is ∆N = (Nt R3 )1/2 /R3 .