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Physics Topics such as mechanics, thermodynamics, and electromagnetism are fundamental to many other scientific fields.
What is Meant by Doping in Semiconductors? What are p -type Semiconductors?
Definition: lf some special kind of Impurities be mixed with an intrinsic semiconductor in a controlled manner, the conductivity of the semiconductor increases drastically. The semiconductor thus developed is known as extrinsic semiconductor. The method of mixing of impurities is called doping and the mixed impurities are called dopants.
A few milliampere (10-3 A) current can be passed through silicon or germanium crystals by doping with impurities. The current increases to a high value because the energy gap between the valence band and the conduction band decreases considerably due to doping. As a result, the concentration of charge carriers in the crystal increases many fold.
Extrinsic semiconductors are of two types-
- n -type and
- p-type.
n-type Semiconductors
Structure: A little amount of pentavalent impurity [of group V (nitrogen group) elements,] like arsenic (As) or phosphorus (P), is doped in a controlled way in pure silicon (Si) or germanium (Ge) crystals to produce these kind of semiconductors. Each dopant atom contains 5 electrons in its outermost orbit.
Working principle: In Fig.(a), a silicon crystal doped with arsenic is shown, Inside the crystal, an arsenic atom finds itself surrounded by silicon atoms. It forms four covalent bonds with 4 neighbouring silicon atoms. The extra electron in its outermost orbit finds no place to occupy in any bond and hence acts as a free electron or conduction electron. These electrons are known as donor impurity. If only 1 phosphorus or arsenic atom is doped per 106 germanium or silicon atoms, sufficient number of conduction electrons are released, thereby raising the electrical conductivity of the crystal by a factor of 106.
In Fig.(b), the energy band of n -type semiconductor has been shown. The dotted line indicates the energy level of the excess electrons generated by the doping of the pentavalent element. These electrons can easily be excited to the conduction band. This line is known as donor level.
Definition : If pentavalent elements (like arsenic or phos-phorus) be doped as impurities in the crystal of an intrinsic semiconductor in a controlled manner, the crystal thus formed is called an n-type semiconductor.
Discussions:
- The n -type crystal, as a whole, is chargeless. It is not negatively charged because although some electrons remain free, the arsenic or phosphorus atoms present inside the crystal are electrically neutral.
- The energy gap between fermi level and conduction band is approximately 0.05 eV
- In n -type semiconductor, majority carriers are electrons and minority carriers are holes.
- Only a single impurity atom on an average is to he doped in approximately 106 atoms of the original crystal. Hence the host silicon or germanium crystal should be absolutely pure. The cost of a semiconducting crystal is almost entirely due to its purification. But still the crystal is very cheap.
- Phosphorus or arsenic atoms donate free electrons to the pure semiconducting crystal and hence they are called donor elements.
Since the negatively charged electrons act as majority charge carriers, this type of crystal is called n-type.
p-type Semiconductors
Structure : A little amount of trivalent impurity (of group III elements) like boron (B), aluminium (Al), is doped in a controlled manner in pure silicon (Si) or germanium (Gi) crystals to produce these kind of semiconductors. Each dopant atom contains 3 electrons in its outermost orbit.
Working Principle : A silicon crystal doped with boron is shown in Fig.(a). Inside the crystal, a boron atom finds itself surrounded by four silicon atoms of which the boron atom can complete 3 covalent bonds with 3 neighbouring silicon atoms.
Due to the deficit of one electron in the outermost orbit of boron, the fourth bonding cannot be completed and hence a hole appears there. If suitable potential difference is applied, the holes having effective positive charges can drift inside the crystal. These holes act as charge carriers. As a result, it is possible to bring the electrical conductivity of the crystal up to its desired value.
In Fig.(b), the energy band of p-type semiconductor is shown. The dotted line denotes an electron accepting level. The electrons of the valence band can easily be excited to the acceptor level. Thus, charge carrier holes are created in the valence band.
Definition : If trivalent elements (like boron or aluminium) be doped as impurities in the crystal of an intrinsic semiconductor in a controlled manner, the crystal thus obtained is called a p -type semiconductor.
Its majority carriers are holes and its electrical conductivity is many times greater than that of an intrinsic semiconductor.
Discussions
- The p -type crystal as a whole, is electrically neutral.
- The energy gap between valence band and fermi level is approximately 0.05 eV.
- In p -type semiconductor, majority carriers are holes and minority carriers are electron.
- Only a single atom on an average is to be doped in approximately 106 atoms of the original crystal.
- When boron or aluminium atoms are doped in the semi-conducting crystal, holes are generated which can accept electrons. Thus, boron or aluminium are called acceptor elements.
Since positively charged holes act as majority charge carriers in this type of crystal. It is called p-type.
Difference between n-type and p-type Semiconductors
n-type semiconductor | p-type semiconductors |
1. This kind of semiconductor is produced by doping pentavalent element in intrinsic semiconductor. | 1. This kind of semiconductor is produced by doping trivalent element in intrinsic semiconductor. |
2. Negatively charged electrons act as majority charge carriers. | 2. Positively charged holes act as majority charge carriers |
Drift of Charge Carriers in Semiconductors
In case of current conduction through a metal wire, the current through the wire is
I = nevA
where, e = charge of an electron,
v = drift velocity of free electrons through the metallic wire and
n = number density or concentration of free electrons = number of free electrons in unit volume of metal and A = area of cross section.
Intrinsic semiconductors: Consider a cylindrical block of intrinsic semiconductor of length l and area of cross section A. Here, electron-hole pairs act as charge carriers. Let potential difference V be applied across two ends of the semiconductor block. As a result, both electrons and holes start drifting in opposite directions [Fig.]. As electrons are negatively charged and holes are positively charged, so current will flow in same direction for both the charges. Conventionally, this direction is along the drifting of holes, i.e., opposite to the drifting of electrons.
So, the current passing through the semiconductor,
I = neveA + pevhA = Ae(nve + pvh) ….. (1)
Here, n = number density of electrons
p = number density of holes
ve = drift velocity of electrons
vh = drift velocity of holes
For intrinsic semiconductor, the number of thermal electrons and thermal holes as charge carriers are the same.
Therefore, n = p = ni, where ni is number density of electron hole pairs in intrinsic semiconductor.
So, from the equaflon (1), we get,
I = Aeni(Ve + vh) ….. (2)
The current through unit area i.e., current density for equation
J = \(\frac{I}{A}\) = e(nve + pvh) ……… (3)
For intrinsic semiconductor,
J = eni(ve + vh)
The effective electric field in the semiconductor is E = \(\frac{V}{l}\).
So, J = \(\frac{I}{A}\) = \(\frac{1}{A} \frac{V}{R}\) [∵ I = \(\frac{V}{R}\)]
or, J = \(\frac{1}{A} \cdot \frac{V}{\rho \frac{l}{A}}\) = \(\frac{1}{\rho} \frac{V}{l}\) = \(\frac{1}{\rho} E\) = σE
Here, R = \(\frac{\rho l}{A}\) = resistance of the block of a semiconductor,
ρ = resistivity
and σ = e(n\(\frac{v_e}{E}\) + p\(\frac{v_h}{E}\)) = e(nμe + pμn) ….. (4)
Here, μe = \(\frac{v_e}{E}\) = mobility of electrons
and μh = \(\frac{v_h}{E}\) = mobility of holes
This is the equation of conductivity of the semiconductor crystal.
In case of intrinsic semiconductor,
σ = eni(μe + μn) …. (5)
It should be borne in mind that in an intrinsic semiconductor, charge carrier electrons reside outside atomic bonds, whereas charge carrier holes remain inside atomic bonds. Therefore the holes cannot move as easily as electrons. So, it can be said that the effective mass of each hole is larger than that of each electron. Hence, at the time of current flow through the semiconductor, drift velocity and mobility of electrons are larger than those of holes i.e., ve > vh and μe > μh.
It is important to note that each equation depends on the temperature T of the semiconductor. So, the number densities, drift velocities and mobilities of electrons and holes are changed with change in temperature.
Extrinsic semiconductor: We have seen how in an n-type semiconductor, electrons act as majority carriers and in a p -type semiconductor, holes in the host crystal act as the majority carriers. Hence, In an extrinsic semiconductor, the number densities of electrons and holes are not the same i.e., n ≠ p
In an n -type semiconductor, as the number of majority charge carriers goes on increasing by doping, the holes get annihilated due to recombination with newly generated electrons. Hence, with increase of electron concentration (n), the hole concentration (p) gradually decreases. On the other hand, for p -type semiconductor, n decreases with increase of p.
In either case, the condition of equilibrium is
np = \(n_i^2\) ….. (6)
The equation (6) is known as the law of mass action.
Law of mass action: Under thermal equilibrium, the product of free electron concentration (n) and free hole concentration (p) is constant. This constant is equal to the square of carrier concentration (ni) in intrinsic semiconductor.
Incidentally, in SI the charge of an electron or hole is 1.6 × 10-19C.
Unit of number density is m-3, unit of drift velocity is m ᐧ s-1, unit of mobility is m2 ᐧ V-1 ᐧ s-1 and unit of conductivity is mho ᐧ m-1 i.e., ℧ ᐧ m-1 or, S ᐧ m-1.
Numerical Examples
Example 1.
An intrinsic semiconductor has 5 × 1028 atoms and the carrier concentration 1.5 × 1016 m-3. If it is doped by a pentavalent impurity in the ratio 1 : 106, then calculate number density of holes as charge carriers.
Solution:
On doping by pentavalent impurity, n -type semiconductor is formed. Here, we neglect the number density of the thermal electrons in respect to the number density of electrons as majority carriers. Hence the number density of electrons in
n -type semiconductor,
n = \(\frac{5 \times 10^{28}}{10^6}\) = 5 × 1022 m-3
Given, ni = 1.5 × 1016 m-3
So, the number density of holes,
p = \(\frac{n_i^2}{n}\) = \(\frac{\left(1.5 \times 10^{16}\right)^2}{5 \times 10^{22}}\) = 4.5 × 109 m-3
Example 2.
A semiconductor has equal electron and hole concentration of 6 × 108 m-3. On doping with a certain impurity, the electron concentration of the semiconductor increases to 8 × 1012 m-3.
(i) What type of semiconductor is obtained on doping?
(ii) Calculate the new hole concentration of the semiconductor.
Solution:
Here, n = p = ni = 6 × 108 m-3 i.e., in initial state, it is an intrinsic semiconductor.
i) As the concentration of electrons as majority carriers increase on doping, so n – type semiconductor is formed.
ii) In n-type semiconductor, the electron concentration,
n = 8 × 1012 m-3
Here, np = \(n_i^2\)
Therefore, the new hole concentration,
p = \(\frac{n_i^2}{n}\) = \(\frac{\left(6 \times 10^8\right)^2}{8 \times 10^{12}}\) = 4.5 × 104 m-3
Example 3.
A semiconductor has the electron concentration 0.45 × 1012 m-3 and the hole concentration 5 × 1020 m-3. Calculate the conductivity of the material of this semiconductor.
Given, Electron mobility = 0.135 m2 ᐧ V-1 ᐧ s-1 and hole mobility = 0.048 m2 ᐧ V-1 ᐧ s-1.
Solution:
Here, n = 0.45 × 1012 m-3,
p = 5 × 1020 m-3,
μe = 0.135 m2 ᐧ V-1 ᐧ s-1,
μh = 0.048 m2 ᐧ V-1 ᐧ s-1
So, the conductivity of the material of this semiconductor,
σ = e(nμe + pμh)
= 1.6 × 10-19[(0.45 × 1012) × 0.135 + (5 × 1020) × 0.048]
= 3.84 mho ᐧ m-1