Forward and reverse biased pn junction

A pn junction in equilibrium has a depletion region of width $W_0$ and a built-in barrier $V_0$ that stops majority carriers from diffusing across. Applying an external voltage changes this barrier: lowering it is forward bias, raising it is reverse bias.

Forward bias (p to +, n to −)

   + |  p  |-|+|  n  | -
     | --> holes      |
     |      electrons<--
          W small, barrier V0 - V

• The applied voltage $V$ opposes the built-in field. Barrier becomes $V_0 - V$; depletion width shrinks:

$$W = \sqrt{\frac{2\varepsilon(N_a+N_d)(V_0-V)}{eN_aN_d}}$$

• Many more majority carriers can now cross. Holes are injected into the n side and electrons into the p side, where they become excess minority carriers:

$$p_n(0) = p_{n0}e^{eV/kT},\qquad n_p(0) = n_{p0}e^{eV/kT}$$

• These carriers diffuse away from the junction and recombine, giving a diffusion current that rises exponentially with V.
• Large current (mA) flows once V exceeds the cut-in voltage (~0.6–0.7 V Si, ~0.2–0.3 V Ge).

Reverse bias (p to −, n to +)

   - |  p  |--|++|  n  | +
     |  majority pulled away  |
     | minority swept across  |
          W large, barrier V0 + Vr

• The applied voltage adds to the built-in field; barrier becomes $V_0 + V_r$ and the depletion region widens.
• Majority carriers cannot cross. Only minority carriers generated thermally near the junction are swept across by the field.
• A tiny, almost constant reverse saturation current $I_0$ (nA in Si, µA in Ge) flows. It increases with temperature.
• At a large reverse voltage, breakdown (Zener or avalanche) occurs and the current rises sharply.

Diode equation and characteristic

$$I = I_0\left(e^{eV/\eta kT} - 1\right)$$

        I (mA)
         |      /
         |     /  forward
         |    /
 Vbr ____|___/______ V
     |   |-I0 (uA/nA)
     |  reverse