Suppose a pure Si crystal has \\(5\times 10^{28}\\) atoms \\(m^{-3}\\). it is doped by 1 ppm concentration of pentavalent As. Calculate the number of electrons and holes. Given that \\(n_{1}=1.5\times 10^{16}m^{-3}\\).

1 atom of Si doped out of \\(10^{6}\\) atoms (1 ppm of As)\\( \Rightarrow \\) In \\( 5 \times 10^{28}\\) atoms net doped =\\(\frac{5\times10^{28}}{10^{6}} = 5\times 10^{22} \\) atoms1 As atom creates \\(1 e^{\circleddash }\\) excenso, no. of excen electron \\( = 5 \times 10^{22} = n_{e}\\)also, \\( n_{e}n_{n}=n_{1}^{2}\\)\\( \Rightarrow n_{n}=\frac{n_{1}^{2}}{n_{e}} = \frac{(1.5\times10^{16})^{2}}{5\times 10^{22}} = 4.5\times 10^{9}\\)\\( \therefore \\) No. of holes formed \\( = 4.5 \times 10^{9}.\\)as \\( n_{e} > n_{n} \rightarrow \\) It is a N - type semiconductor formed.

Write down 5 difference between N-type and P-type semiconductors.

Difference between the P and N type semiconductors Sl No P-type Semi conductor N-type semi conductor 1P-type semiconductor is formed due to the dopping of III group elements i.e. Boron, Aluminium, Thallium.N-type semi conductor is formed due to dopping of Nitrogen, Phosporus, Arsenic, Antimony, Bismoth. 2These are also known as Trivalent semi conductors.These are also known pentavalent semiconductor. 3P-type semiconductors is positive type semiconductor it means it deficiency of 1 electron is required.N-type semiconductor is negative type semi-conductor it means excess of 1 electron is required. 4In P-type semiconductor majority charge carries are holes and minority charge carries are electrons.In N-type semiconductor majority charge carries are electrons and minority charge carries are hole. 5A hole indicates a missing electron. In this no. of holes is more than the no. of electrons.In N-type semiconductor the no. of holes is less than the no. of free electron.

The number of silicon atoms per \\(m^3\\) is \\(5\, \times\, 10^{28}\\). This is doped simultaneously with \\(5\, \times\, 10^{22}\\) atoms per \\(m^3\\) of arsenic and \\(5 \times\, 10^{20}\\) per \\(m^3\\) atoms of indium. Calculate the number of electrons and holes. Given that \\(n_i\, =\, 1.5\, \times\, 10^{16}\ /m^{3}\\). Is the material n-type or p-type?

Number of silicon atoms, \\(N=5\times10^{28}\ atom/m^3\\)Number of arsenic atoms, \\(n_{AS}=5\times10^{22}\ atom/m^3\\)Number of indium atoms, \\(n_{IN}=5\times10^{22}\ atom/m^3\\)\\(n_i=1.5\times10^{16}\ electron/m^3\\)\\(n_e=5\times10^{22}-1.5\times10^6=4.99\times10^{22}\\)Let number of holes be \\(n_h\\)In thermal equilibrium, \\(n_en_h=n_i^2\\)so, \\(n_h=4.51\times10^9\\)\\(n_e>n_H\\), material is an n-type semiconductor.

Pure \\(Si\\) at \\(500\ K\\) has equal number of electron \\(\left({n}_{e}\right)\\) and hole \\(\left({n}_{h}\right)\\) concentration of \\(1.5 \times {10}^{16} \ {m}^{-3}\\). Doping by indium increases \\({n}_{h}\\) to \\(4.5 \times {10}^{22}\ {m}^{-3}\\). The doped semiconductor is of

\\({n}_{i}^{2} = {n}_{e}{n}_{h}\\)\\({\left(1.5 \times {10}^{16}\right)}^{2} = {n}_{e}\left(4.5 \times {10}^{22}\right)\\)\\({n}_{e} = 0.5 \times {10}^{10}\\)\\({n}_{e} = 5 \times {10}^{9}\\)\\({n}_{h} = 4.5 \times {10}^{22}\\)\\({n}_{h} \gg {n}_{e}\\)Semiconductor is \\(p\\)-type and \\({n}_{e} = 5 \times {10}^{9} {m}^{-3}\\).

A semiconductor has equal electron and hole concentration of \\( 6 \times 10^8 / m^3 \\). On doping with certain impurity , electron concentration increases to \\( 9 \times 10^{12} / m^3 \\). Calculate the new hole concentration.

\\( n_e n_h = n^{2}_{i} \\) \\( \Rightarrow \\) \\( n_h = \dfrac{n^{2}_{i}}{n_e} = \dfrac{(6 \times 10^8)^2}{9 \times 10^{12}} = 4 \times 10^4 \, per \, m^3 \\).

A silicon specimen is made into a p-type semiconductor by doping on the average one indium atom per \\(5\times 10^7\\) silicon atoms. If the number density of atoms in the silicon specimen is \\(5\times 10^{28}\\) atoms\\(/m^3\\). Then the number of acceptor atoms in silicon will be.

Number density of atoms in Si\\(=\displaystyle 5\times 10^{28}\frac{atoms}{m^3}=5\times 10^{22}\frac{atoms}{cm^3}\\)Since \\(1\\) atom of indium is doped in \\(5\times 10^7\\) silicon atoms,\\(\therefore\\) Total number of doped indium atoms\\(\displaystyle =\frac{5\times 10^{22}}{5\times 10^7}=1\times 10^{15}\frac{atoms}{cm^3}\\)\\(\therefore\\) Number of acceptor atoms in silicon\\(=\displaystyle 1\times 10^{15}\frac{atoms}{cm^3}\\).

If the ratio of the concentration of electrons to that of holes in a semiconductors is \\(\dfrac{7}{5}\\) and the ratio of currents is\\(\dfrac{7}{4}\\), then the ratio of drift velocities is

The drift velocity of charge carriers in the material of constant cross-sectional area A is given as:\\(v=\dfrac{I}{nAq}\\)(here I is the current flowing through the material, n is the charge-carrier density, and q is the charge on the charge-carrier.)We have the ratio of I as \\(\dfrac{7}{4}\\) and ratio of n as \\(\dfrac{7}{5}\\).Thus we get the ratio of v as \\(\dfrac{5}{4}\\)

Explain the term 'doping'

Doping is the process of adding some impurity atoms in a pure or (intrinsic) semiconductor so as to increase the conductivity of a semiconductor. Doping can be done in two ways:n-type dopant is added, or a pentavalent dopant is added to an intrinsic semiconductor, to form an n-type semiconductor.When p-type dopant or a trivalent dopant atom is added to an intrinsic semiconductor, a p-type semiconductor is formed.

In an intrinsic semiconductor, the number of electrons in the conduction band is ________ the number of holes in the valence band.

In an intrinsic semiconductor, the number density of electrons is equal to the number density of holes i.e \\(ne=nh\\).Since there is no doping, no extra hole or electron is produced.

Let \\(n_p\\) and \\(n_e\\) the number of holes and conduction electrons in an intrinsic semiconductor. Then:

In an intrinsic semicondutor, number of holes carriers are equal to number of electrons as no doping is there in intrinsic material.In extrinsic materials, due to doping, numbers of holes are different to those of electrons.So, \\(n_p=n_e\\)

Intrinsic Semiconductor | Definition, Examples, Diagrams

definition

Intrinsic semiconductors

An intrinsic semiconductor is a semiconductor in which no other material is intentionally doped (similar to mixing). Example: Si, Ge.
Notes:
1. It behaves as an insulator at absolute zero.
2. Electrons are excited by thermal energy.
3. They are different from pure semiconductors and may consist of some level of impurities. The conductivity of intrinsic semiconductor is more than that of a pure semiconductor as the impurities provide a few energy levels in the bandgap.
Note:
Pure semiconductors are semiconductors that have no impurities. Ideally, no semiconductor is pure in nature.

definition

Holes

In its crystalline structure, Si and Ge tends to share one of its valence electrons and also take share of one electron from its neighbour atoms. As temperature is increased, some of the electrons break free and behave as conduction electrons. This creates a vacancy in the bond and creates a positive charge also known as a hole. It behaves as an apparent free charge similar to an electron and contributes to conduction.
Notes:
1. Holes do not actually move in the semiconductor. The movement of electrons from the valence band to the conduction band and neighbouring atom can be viewed as movement of hole.
2. Mobility of holes is less than electrons.

result

Importance of holes

When an electron jumps from one atom to another atom with an available hole via the conduction band, it appears as if a hole has moved from the second atom to the first. Hence, holes also contribute to conduction in a semiconductor.

definition

Total current in a semiconductor

Total current in the semiconductor is given by the sum of electron current and hole current in a semiconductor.

I = I_{e} + I_{h}

Note:
Since the electrons and holes move in opposite direction and their charges are opposite, the net effect is the adding up of the two currents.

definition

Generation or recombination of holes and electrons

Generation:
When energy is supplied from external sources, electron jumps into the conduction band. This process is hence associated with the generation of an electron and a hole.
Recombination:
During the process of conduction of semiconductor, some electrons in the conduction band fall back to the valence band. This process is called recombination of an electron and a hole.
Note:
At equilibrium, rate of generation equals the rate of recombination of electron-hole pairs and net current is zero.

law

Law of Mass Action (Intrinsic Semiconductors)

According to the mass-action law:

n_{e} n_{h} = n_{i}^{2}

where

n_{e} :

Electron concentration

n_{h} :

Hole concentration

n_{i} :

Intrinsic concentration
For intrinsic semiconductors,

n_{e} = n_{h} = n_{i}

Intrinsic Semiconductor

definition

Intrinsic semiconductors

definition

Holes

result

Importance of holes

definition

Total current in a semiconductor

definition

Generation or recombination of holes and electrons

law

Law of Mass Action (Intrinsic Semiconductors)

REVISE WITH CONCEPTS

Extrinsic Semiconductor

Electron Hole Concentration Calculation

Quick Summary With Stories

Introduction to Intrinsic Semiconductors