Current Transport in Metal-semiconductor Diodes

The Metal-Semiconductor diodes is a majority current device. The mechanisms of current transport in M-S diodes are

.  Transport of electrons from semiconductor over the potential barrier into the metal (dominating factor for moderately doped semiconductor with operated at room temperature).

.  Quantum mechanical tunnelling of electrons through the barrier (important for heavily semiconductor and responsible for most of ohmic contacts.

.  Electron hole recombination in their depletion region.

.  Electron hole recombination in the neutral semiconductor region.

Transport over potential barrier

For high mobility materials thermionic emission theory

For low mobility materials diffusion theory Actually a combination of two processes. thermionic emission theory

.  Barrier ht.

.  Thermal equilibrium

.  Net current flow does not effect this equilibrium 2 currents flux one from Metal to Semiconductor, other from semiconductor to metal, shape of the barrier profile is not important current flow depends only on .

current density

concentration of electrons with energies

min energy needed to thermionically emit into metal.

Carrier velocity in x direction

electron density in energy range E and E+dE

density of states occupancy function

We assume that all energy in conduction band=Kinetic energy

is the number of electrons /unit volume that have speed between v and v + dv over all direction as shown in Fig 12.9

Rectangular coordinates from radial v

is the minimum velocity required in x direction to go over the potential barrier

Again,

Effective Richardson Const.

Free electrons Richardson const.

For GaAs, isotropic in the lowest minimum of conductive band.

rest mass.

Multi vally semiconductors 

are direction cosines of the normal to the emitting plane relative to the principal axes ellipsoid are the components of the effective mass tensor.

For

transverse mass

longitudinal mass

Barrier height for electrons moving from metal to semiconductor remains the same, unaffected by a voltage. It must be therefore equal and opposite to the current with V=0 at room temperature

Thus

Thus Total current density for a = majority carriers.

Diffusion theory (Schottky) for current

It is for the current from semiconductor to the metal again

.  Barrier

.  Effect of electron collision within depletion region is included

.  Carrier conductance at x=0 and x=w are unaffected by current flow

.  Impurity concentration of semiconductor is non nondegenerate

Current in depletion region depends on local field and concentration gradient

Steady state, current density is independent of x

Thus Integrating both sides with an integrating factor

Boundary condition are

Putting these Boundary conditions

Similar to thermoinic expression- drift depends on Temperature T

Diffusion explanation is dominant if n semiconductor is heavily doped.

Tunneling current

When semiconductor is highly doped then depletion region is very narrow and electrons can tunnel through it.