Motion of free carriers in a semiconductor

• Drift
  Caused by an electric field due to an externally applied voltage
  
• Diffusion
  Due to the thermal energy - movement from regions where the carrier density is high to regions where the carrier density is low

Thermal equilibrium

Reached by the diffusion of electrons/holes close to the metallurgical junction across the junction into the p-type/n-type regions

Depletion region is created - region depleted of mobile carriers

        Extends from x = -x_p to x = x_n

Ionized donors and acceptors behind the depletion layer cause the electric field

       Causes the drift of carriers in the opposite direction

Diffusion current balanced by the drift current - thermal equilibrium is reached

Thermal equilibrium indicated by a constant Fermi energy

Built-in potential

Internal potential, f_i, equals the potential across the depletion region in thermal equilibrium

Equals the difference in the Fermi energies, E_Fn and E_Fp, divided by the electronic charge

Equals also the sum of the bulk potentials of each region,

Thermal voltage

           (V_t = 25.86 mV for T = 300K)

Electron charge q = 1.6 10-19 C

Boltzman's constant k = 1.38 10-23 JK-1

Intrinsic carrier density:

function of the effective density of states in the conduction and valence band, and the bandgap energy E_g = E_c - E_v:

Bias voltage

• Forward bias

Application of a positive voltage to the anode (p-type region)

Potential across the semiconductor decreases

Depletion layer width decreases

• Reverse bias

Application of a negative voltage to the cathode (n-type region)

Potential across the semiconductor increases

Depletion layer width increases

Current versus voltage characteristics of a p-n junction diode

Mathematical approximation:

I_S ... saturation current

V_t ... thermal voltage