Question

Calculate the built-in potential barrier of a pn junction. Consider a silicon pn junction at T = 300 K, doped N_A = 13.1 x10¹⁶ cm^-3 in the p-region, N_D = 121.6 x10¹⁷ cm^-3 in the n-region and n_i = 8.8 x10¹⁴ cm^-3. Take fundamental charge q=1.602 x 10^-19 C; Boltzmann's contact K_B = 1.38x10^-21 J/K.

Answer 1

$$V_b=\frac{kT}{q}\ln{\frac{N_AN_D}{n_i^2}}\\ V_b=\frac{(1.38\cdot10^{-21})(300)}{(1.602\cdot10^{-19})}\ln{\frac{13.1\cdot10^{16}\cdot121.6\cdot10^{17}}{(8.8\cdot10^{14})^2}}\\V=37.6\ V$$