Question

Concentration of electrons in conduction band formula on n side

Answer 1

Answer:

Your answer is here.

Explanation:

Melissinos, eq.(1.4), gives the formula, valid at thermal equilibrium,

ni = Ns exp

µ

¡

Eg

2kBT

¶

(1)

where,

- ni

is the intrinsic carrier concentration, i.e., the number of electrons in the conduction band

(and also the number of holes in the valence band) per unit volume in a semiconductor

that is completely free of impurities and defects

- Ns is the number per unit volume of effectively available states; its precise value depends

on the material, but it is of order 10

19

cm¡3

at room temperature and increases with

temperature

- Eg is the energy gap (between the bottom of the conduction band and the top of the valence

band)

- kB is Boltzmann's constant, kB = 1:381 ¢ 10

¡23 Joules/Kelvin

- T is the absolute temperature in Kelvin; it is assumed that kBT . Eg=5:

The physical basis of eq. (1) can be understood as follows:

conduction band

The probability of exciting an electron from the top of the

" valence band to the bottom of the conduction band is

Eg proportional to the Boltzmann factor exp

µ

¡

Eg

kBT

¶

:

# This process leaves behind a hole in the valence band and

is called electron-hole pair creation. The total pair creation

valence band rate (see below) is also proportional to this factor.

At thermal equilibrium, the creation of electron-hole pairs is balanced by their recombina-

tion. If n is the concentration of conduction-band electrons and p the concentration of valence-

band holes, the electron-hole recombination rate is proportional to the product np, according

to the general law of mass action of chemical physics. Equating creation to recombination, we

conclude that

np = K exp

µ

¡

Eg

kBT

¶

(2)

where K is a proportionality factor. In an intrinsic semiconductor, by definition, n = p = ni

:

Then eq. (2) is equivalent to eq. (1) with K = N2

s

.

To compute Ns; we must compute the total pair creation rate. We recognize that an electron

can make a transition from any state in the valence band to any state in the conduction band

and we integrate over all these possible transitions, with a weighting factor to account for the