Note on Semiconductrs

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Semiconductors

  1. Intrinsic semiconductor

These are pure semiconductor (absence of doping or impurities).

  1. Extrinsic semiconductor (doped semiconductor)

Two types of impurities are generally added too increase electrical conductivity of semiconductor. Pentavalent atoms to form n-type semiconductor and trivalent atoms to form p-type semiconductor.

Intrinsic semiconductor:

How the conductivity of intrinsic semiconductor can be increased? Show the relationship between electrical conductivity and intrinsic semiconductors.

Ans: The numbers of electrons in conduction bands in intrinsic semiconductors is a function of temperature and energy gap or band gap. Number of electrons in conduction band increases exponentially with temperature as,

$$n=CT^\frac{3}{2} exp^\bigg(\frac{-E_g}{3K_BT}\biggr)\dotsm(1)$$where

C=constant

\(E_g\)=band gap

\(K_B\)=Boltzmann constant

T=temperature in Kelvin scale

When electron density in conduction band increase number of holes form due to movement of electron in valence band also increases. When electric field is set up in the material the applied electric field provides drift velocity for both electron and holes due to which conductivity increases. The total conductivity of intrinsic semiconductor is given by

\(\sigma\)=[conductivity due to motion of electron in conduction band] + [conductivity due to motion of holes in valence band]

$$\sigma=n|e|\mu_e+p|e|\mu_n\dotsm(2)$$where

n=electron concentration in conduction band

p=hole concentration in valence band

|e|=magnitude of charge of electron=magnitude of charge of hole

\(\mu_e\)=electron mobility

\(\mu_p\)=hole mobility

fig: Mobility for electron and holes
fig: Mobility for electron and holes(ecee.colorado.edu)

Electrons in conduction band are more mobile than holes in valence band i.e.

\(\mu_e>\mu_h\)

\(\therefore \sigma=ne[\mu_e+\mu_h]=p|e|[\mu_e+\mu_h]\dotsm(3)\)here n=p, for intrinsic semiconductor.

In semiconductor, the conductivity increases with increase in temperature where as in metal conductivity decreases with increases in temperature. It is pure semiconductor without lattice distortion.

Inintrinsic semiconductor, with increase carrier concentration with temperature increase the electrical conductivity.

fig: conductivity vs temperature of semiconductor
fig: conductivity vs temperature of semiconductor(www.springer.com)

What is doping? What is the effect of doping on extrinsic semiconductor? Explain the variation of conductivity due to temperature and doping.

Ans: in n-type semiconductor the concentration of electron is higher than that of holes. The increase in concentration of electron is due to doping. The electrical conductivity in extrinsic semiconductor is dominated by impurity atoms. The doping is done by two methods

  1. Diffusion
  2. Ion implantation

In p-type semiconductor the concentration of hole is greater than that of electrons. The majority charge carriers are holes and electrons are minority charge carrier. The hole created in valence band is due to presence of impurity atoms is more mobile than the hole presence initially.

When phosphorous atom is mixed in silicon then the concentration electron due to phosphorous i.e. donar is represented by \(N_D\) i.e. the concentration of phosphorous \(\simeq\)n=concentration of electrons.

The hole created in state is n type semiconductor for from valence band and its immobile conduction occur mainly by donated electrons. Therefore for n-type semiconductor.

\(\sigma \simeq n|e|\mu_e\simeq N|e|\mu_e\dotsm(1)\)

Similarly for p-type semiconductor conduction is due to holes and concentration of holes is almost equal to concentration of holes is almost equal of concentration of acceptor.

p\(\simeq N_A\simeq\)N_{Boron}\)(Boron is trivalent)

$$\therefore \sigma\simeq|e|\mu_h\simeq N_A|e|\mu_h\dotsm(2)$$

The presence of doping in semiconductor increases the concentration of donar and accepter which increases electrical conductivity. In all donar state electrons are thermally excite and concentration of electron increases in n-type of semiconductor with increase in semiconductor, whereas concentration of hole increases in p-type semiconductor. The graph of electron concentration and temperature for n-type extrinsic semiconductor has three different regions:-

  • Freeze out region
  • Extrinsic region
  • Intrinsic region

In freeze out region, the temperature of specimen is too low. So the large number of electrons in n-type of semiconductor remains in valence band.

In extrinsic region, all donar state is thermally excited. So the concentration of carrier is almost constant whereas for intrinsic region excitation across band gap dominates and concentration of intrinsic carrier sharply increases with increase in temperature as shown in figure

fig: Impurities
fig: Impurities(ecee.colorado.edu)

From above figure we can say that presence of donar impurity increases with concentration of carrier low temperature.

References:

Callister, W.D and D.G Rethwisch. Material Science and Engineering. 2nd. New Delhi: Wiley India, 2014.

Lindsay, S.M. Introduction of Nanoscience . New York : Oxford University Press, 2010.

Patton, W.J. Materials in industry . New Delhi : Prentice hall of India, 1975.

Poole, C.P. and F.J. Owens. Introduction To Nanotechnology. New Delhi: Wiley India , 2006.

Raghavan, V. Material Science and Engineering. 4th . New Delhi: Pretence-Hall of India, 2003.

Tiley, R.J.D. Understanding solids: The science of Materials. Engalnd : John wiley & Sons , 2004.

1. Types of semiconductor :

intrinsic semiconductor ,

extrensic semiconductor

2.$$n=CT^\frac{3}{2} exp^\bigg(\frac{-E_g}{3K_BT}\biggr)$$

$$\sigma=n|e|\mu_e+p|e|\mu_n$$

\(\therefore \sigma=ne[\mu_e+\mu_h]=p|e|[\mu_e+\mu_h]\)

3. Types of doping

diffusion 

ion implantation

4. different regions

  • Freeze out region
  • Extrinsic region
  • Intrinsic region

 

 

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