Wat fraction of the surface centers at e fn e ei and e

Question

Question 1: The energy band diagram for a reverse-biased Si pa-junction diode under steady-state conditions is pictured in Fig

(a) With the aid of the diagram and assuming single-level R-G center statistics, T_n = T_p = T, and E_T' = E_i, simplify the general steady-state net recombination rate expression to obtain the simplest possible relationship for R at (i) x = 0, (ii) x = - x_pp, (iii) x = x_nn (iv) x = -x_p and (v) x = x_n.

(b) Sketch It versus x for x-values lying within the electrostatic depletion region (-x_p ≤ x ≤x_n).

(c) What was the purpose or point of this problem?

Question 2: The energy band diagram for a forward-biased Si pn-junction diode maintained under steady-state conditions at room temperature (T = 300 K) is pictured in Fig. Note that E_Fn - E_j = E_i, E_Fp = E_G/4.

(a) For the particular situation pictured in Fig. and assuming single-level R-G center statistics, τ_n = τ_p = τ, and E_T' = E_j, show that the steady-state net recombination rate inside the electrostatic depletion region (-x_p ≤ x ≤ x_n) can be simplified to

R ≅ n_i/T [e^E_G/4kT/c^{(F_N - E_i)kT} + e^{(Ei - Fp)/kT}]

(b) Plot R/(n_i/τ) versus x for -x_p ≤ x ≤ x_n' Assume the E_i variation between x = -x_p and x = x_n is approximately linear in constructing the plot.

(c) What is the purpose or point of this problem?

Question 3: The surface of an n-bulk solar cell is subjected to intense illumination giving rise to high level injection (Δn_s = Δp_s >> nso). The surface region of the device is characterized by the energy band diagram shown in fig.

(a) What fraction of the surface centers at E = F_N, E = E_i, and E = F_P will be filled for the specified steady-state situation? (Let D_Filled be the number of filled surface centers per eV-cm² at E. the fraction of filled surface centers is then D_Filled/D_IT.) Sketch D_Filled/D_IT versus E for E_V ≤ E ≤ E_c. Assume c_ns = cps for all E in this part of the problem.

(b) Defining R_s = s*Δp_s, obtain an approximate closed-form expression for s* involving only ΔE = F_N - F_p and the parameters c_ns' cps, and D_IT evaluated at mid-gap. Invoke and record all reasonable assumptions and simplifications needed to complete this problem.