# PHY301 Circuit Theory GDB Solution Fall 2013

The topic is:

“Tell the type of materials in which we can make control over charge carriers. Describe the current types in such materials and their respective directions”.

Solution:

Charge Carriers in Semiconductors

Current is the rate at which charge ows.
In a semiconductor, two types of charge carrier, the electron and the hole, can contribute to a current. Since the current in a semiconductor is determined largely by the number of electrons in the conduction band and the number of holes in the valence band, an important characteristic of the semiconductor is the density of these charge carriers.
1.1 Equilibrium Distribution of Electrons and Holes
Equilibrium Distribution of Electrons and Holes
The distribution (with respect to energy) of electrons in the conduction band is given by the density of allowed quantum states times the probability that a state is occupied by an electron. This statement is written in equation form as
n(E) =gc(E)fF(E) ……………………..(1) where gc(E)
is the density of quantum states in the conduction band and fF(E) is the Fermi-Dirac probability
function. The total electron concentration per unit volume in the conduction band is found by integrating Equation (1) over the entire conduction-band energy. The distribution (with respect to energy) of holes in the valence band is the density of allowed quantum states in the valence band multiplied by the probability that a state is not occupied by an electron:
p(E) =gv(E) [1fF(E)]……………(2)
The total hole concentration per unit volume is found by integrating this function over the entire valence-band
energy. To nd the thermal-equilibrium electron and hole concentrations, we need to determine the position
of the Fermi energy EF , with respect to the bottom of the conduction-band energy Ec and the top of the valence-band energy Ev