4. Consider an intrinsic semiconductor. Let & be the energy of an electron. Let Dc (ε) be the density of states in the conduction band and D, (e) be the density of states in the valence band (see figure below). Assume ->>kT,ε - ε >> kT and Dc (8)=C₁ (ε-εc) as D₁ (8)=C₁₂ (ε-8) as where & represents the energy of the bottom of the conduction band and Є, represents the top of the valence band. The Fermi energy is ε. a. Dc(8) EC εν Dy (E) D(E) Find an expression for n-the concentration of conduction electrons in terms of k,T,C₁,&c. & and a dimensionless definite integral of the form jexp(-x)√xdx (hint: make a substitution of the form x= k₂I b. Find an expression for p-the concentration of valence holes in terms of *,,T,C,,&,,&, and a dimensionless definite integral of the form [exp(-x)√xdx (hint: make a substitution of the form x=- (8) (8) k₂T c. Find an explicit expression for &, in terms of kg, T. C₂, C₁, &,&c (8)