Electronic Devices and Circuits Engineering Sciences 154

Some preliminaries

"The Law of the Junction"

p_n(x_n)  = p_n0 exp(V_A/V_T) and n_p(x_p)  = n_p0 exp(V_A/V_T)

Diffusion currents components

J_n = D_n dn/dx  and J_p = -D_p dp/dx

Drift currents components

J_n = q n m_n E   and  J_p = q p m_p E

Einstein relation

D_n/m_n = D_p/m_p =  V_T

"Mass Action Law"

p_n0 n_n0 = p_p0 n_p0 = p_i n_i = n_i²= B T³ exp(-E_G/V_T)

Shockley equation for the diode i-v characteristic

I(V_A) = A q n_i² {D_p/L_p N_d + D_n/L_n N_a}[ exp(V_A/V_T) - 1]

I(V_A) = I_sat [ exp(V_A/V_T) - 1]

(source) Working model of real silicon diode

Semilog version of the "Shockley" ("ideal") current-voltage characteristic

See supplimentary discussion of reverse bias diode breakdown

Current-voltage characteristic of a "real" silicon diode.  (a) Generation-recombination region.  (b) "Ideal" or Shockley diffusion current region. (c) High-injection current region. (d) Series resistance effect.  (f) Reverse leakage current due to generation-recombination and surface effects. (After S. M. Sze, Physics of Semiconductor Devices) See supplimentary discussion of reverse bias diode breakdown