Question

calculate built-in potential, maximum electric field and width of the depletion layer in Si p-n diode doped with donors and acceptors to concentration of 2x10^17cm^-3 and 5x10^16 cm^-3 respectively

estimate the maximum voltage which can be safely applied to the diode descibed above

estimate density of reverse current in the diode desribed in top if the diffusion constants and the diffusion lengths of holes and electrons are about 30cm^2/s and 100mm respectively

Answer 1

built in potential for diode is given as

   where KB = Boltzman's Constant

T = Absolute Tempreture

e = Electron Charge

Vbi = 0.08170 Volt

Breakdown Voltage VB electric field strength free electrons gain sufficient kinetic energy to break other electrons free from the valance bonds. This impact ionization field strength (E_B) depends on the magnitude of the energy band gap (between conduction and valance bands) of the semiconductor material and has a typical value of 2 x 10⁵ V/cm for silicon. If the reverse bias voltage exceeds V_B impact ionization will release a large number of free carriers by avalanche multiplication process and the p-n junction will undergo “reverse break down” characterized by a large reverse current (from n to p side) flowing across the junction. Such large current quickly destroys the junction by overheating. Therefore, a p-n junction should never be operated at reverse break down voltage. The reverse break down voltage can be calculated as follows.

for silicon

Band Gap Energy Eb = 1.12 eV

Vb = 1.032*10^-8 volt

Reverse saturation current is given by

= 1.2*10^-35 Amp