** Introduction**

**Electronic Devices:**It is the branch of physics that deals with the emission and effects of electrons emission and effects of electrons and the use of electronic devices.**Electronic Circuits:**Components are connected together to create an electronic circuit with a particular function. Active components are sometimes called devices.

** Semiconductor Materials**

- The term conductor is applied to any material that will support a generous flow of charge when a voltage source of limited magnitude is applied across its terminals.
- An insulator is a material that offers a very low level of conductivity under pressure from an applied voltage source.
- A semiconductor, therefore, is a material that has a conductivity level somewhere between the extremes of an insulator and conductor.
**Band Theory:**A bonding of atoms, strengthened by the sharing of electrons, is called**covalent bonding**. In the crystal, closely spaced energy levels form a band called as**energy band**. Each orbit has a separate energy band. A band of energy levels associated with valence shells is called as valence band. Electrons from other bands cannot be removed but electrons from valence band can be removed by supplying a little energy. The conduction band is generally empty. The valence band and**conduction band**are separated by a gap called forbidden energy gap.**Compound Semiconductors:**Such as Gallium Arsenide (GaAs), Cadmium Sulphide (CdS), Gallium Arsenide Phosphide (GaAsP), Gallium Nitride (GaN) are constructed by two or more semiconductor materials of different atomic structures are called compound semiconductors.

** Intrinsic Semiconductors**

- At 0
^{o}K, no free carriers are available, Si behaves as an insulator. - At room temperature, a few covalent bonds will be broken by the thermal energy, electron‐hole pair generation as free carriers.
- Both electrons and holes are free to move, can contribute to current conduction

** Extrinsic semiconductor**

- Extrinsic (doped) semiconductor = intrinsic semiconductor + impurities
- According to the species of impurities, the extrinsic semiconductor can be either n‐type or p‐type.

**n‐type semiconductor**

- The donor impurities have 5 valence electrons are added into silicon.
- P, As Sb, are commonly used as a donor.
- The Si atom is replaced by a donor atom.
- Donor ions are bounded in the lattice structure and thus donate free electrons without contributing holes.
- By adding donor atoms into an intrinsic semiconductor, the number of electrons increases (n > p) → n‐type semiconductor.
- Majority carrier: electron.
- Minority carrier: hole

**p‐type semiconductor**

- The acceptor impurity has 3 valence electron (Boron).
- Th Si atom is replaced by an acceptor atom.
- The boron lacks one valence electron. It leaves a vacancy in the bond structure.
- This vacancy can accept electron at the expense of creating a new vacancy.
- Acceptor creates a hole without contributing free electron.
- By adding acceptor into an intrinsic semiconductor, the number of holes increase (p > n) → p‐type semiconductor.
- Majority carrier: hole.
- Minority carrier: electron

** Properties of Semiconductor Materials**

Various materials are classified based on the width of forbidden energy gap. In metal, there is no forbidden gap and valence and conduction band are overlapped. In an insulator, the forbidden gap is very large up to 7eV while in semiconductors it is up to 1eV. The silicon and germanium are widely used semiconductors. Intrinsic materials are those semiconductor that has been carefully refined to reduce the impurities to a very level-essentially' as pure as can be made available through modern technology.

- The conductivity of an intrinsic semiconductor is very less. The properties like conductivity can be changed by adding an impurity to the intrinsic semiconductor. The process of adding impurity is called
**doping**. - A semiconductor doped with trivalent impurity atoms forms p-type material. It is called
**acceptor impurity**with concentration N_{A}atoms per unit volume. - A semiconductor doped with pentavalent impurity atoms forms n-type material. It is called
**donor impurity**with concentration N_{D}atoms per unit volume. - In p-type, holes are majority carriers and in n-type electrons are majority carriers.
- When a material is subjected to an electric field, electrons move in a particular direction with steady speed called
**drift speed**and current**drift current**.

**Negative Temperature Coefficient: **Those parameters decreasing with the temperature have a negative temperature coefficient, e.g., an energy gap (E_{g}).

where, constant β_{0} = 2.2 × 10^{–4} (for Ge)

= 3.6 × 10^{–4} (for Si)

Mobility (μ), μ ∝ T^{–m}

**Positive Temperature Coefficient: **Those parameters increasing with temperature have a positive temperature coefficient.

** Important terms**

- Drift velocity V
_{d}= μE - Current density J = nq μE
- Conductivity σ = nq μ
- Concentration of free electrons per unit volume
- Semiconductor conductivity σ = (nμ
_{n}+ pμ_{p})q - In intrinsic semiconductor, n = p = n
_{i}Hence, conductivity σ_{i}= n_{i}(μ_{n}+ μ_{p})q Intrinsic concentration - In
**extrinsic semiconductor**, the conductivity is given by, For n-type, σ_{n}= (n_{n}μ_{n}+ p_{n}μ_{p})q For p-type, σ_{n}= (n_{p}μ_{n}+ p_{p}μ_{p})q But in n-type p_{n}< < n_{n }N_{D}= Concentration of donor impurity N_{A}= Concentration of acceptor impurity n_{p}= Number of electrons (concentration) in p-type P_{p}= Number of holes (concentration) in p-type and n_{n}≅ N_{D}while in p-type n_{p}< < p_{p}and p_{p}≅ N_{A }Hence, conductivity can be calculated as, σ_{n}= N_{D}μ_{n}q and σ_{p}= N_{A}μ_{p}q - Mass-action law np = n
_{i}^{2}

In n-type, n_{n}p_{n} = n_{i}^{2} , hence

In p-type, p_{p}n_{p} = n_{i}^{2}, hence

** Hall Effect **

When a magnetic field is applied to a current-carrying conductor in a direction perpendicular to that of the flow of current, a potential difference or transverse electric field is created across a conductor. This phenomenon is known as the Hall Effect.

According to this effect the statements are:

If a specimen (metal or semiconductor) carrying a current I is placed in a transverse magnetic field B, an electric field E is induced in the direction perpendicular to both I and B. This phenomenon, known as the Hall effect, is used to determine whether a semiconductor is n- or p-type and to find the carrier concentration. Also, by simultaneously measuring the conductivity σ, the mobility μ can be calculated.

Consider the figure shown below. Here current l is in +x-direction, magnetic field B is in +z direction then induced electric field will be in negative y-direction.

Hence a force will be exerted in the negative y-direction on the current carriers.

The current l may be due to holes moving from left to right or to free electrons travelling from right to left in the semiconductor specimen. Hence, independently of whether the carriers are holes or electrons, they will be forced downward toward side 1 of above figure.

If the semiconductor is n-type material, so that the current is carried by the electrons, these electrons will accumulate on side 1, and this surface becomes negativity charged with respect to side 2. Hence a potential, called the **Hall voltage**, appears between surface 1 and 2.

Now under the equilibrium condition

Where ρ is the charge density, w is the width of the specimen and d is the distance between surfaces 1 and 2.

It is customary to introduce the **Hall coefficient** R_{H} defined by

By hall experiment mobility of charge carriers is given as

⇒ Hall coefficient, R_{H} Temperature coefficient of resistance of given specimen.

⇒ For metals, σ is larger, V_{H} is small.

⇒For semiconductors, σ is small, V_{H} is large.

**1 Hall Effect in an n-type semiconductor:**

- If the magnetic field is applied to an n-type semiconductor, both free electrons and holes are pushed down towards the bottom surface of the n-type semiconductor. Since the holes are negligible in n-type semiconductor, so free electrons are mostly accumulated at the bottom surface of the n-type semiconductor.
- This produces a negative charge on the bottom surface with an equal amount of positive charge on the upper surface. So in n-type semiconductor, the bottom surface is negatively charged and the upper surface is positively charged.
- As a result, the potential difference is developed between the upper and bottom surface of the n-type semiconductor. In the n-type semiconductor, the electric field is primarily produced due to the negatively charged free electrons. So the hall voltage produced in the n-type semiconductor is negative.

**2 Hall Effect in a p-type semiconductor:**

- If the magnetic field is applied to a p-type semiconductor, the majority carriers (holes) and the minority carriers (free electrons) are pushed down towards the bottom surface of the p-type semiconductor. In the p-type semiconductor, free electrons are negligible. So holes are mostly accumulated at the bottom surface of the p-type semiconductor.
- So in the p-type semiconductor, the bottom surface is positively charged and the upper surface is negatively charged.
- As a result, the potential difference is developed between the upper and bottom surface of the p-type semiconductor. In the p-type semiconductor, the electric field is primarily produced due to the positively charged holes. So the hall voltage produced in the p-type semiconductor is positive. This leads to the fact that the produced electric field is having a direction in the positive y-direction.

**3 Hall voltage**

- The expression for the Hall voltage is given by:

**4 Applications of Hall Effect**

- Measurement of magnetic flux density.
- Measurement of displacement.
- Measurement of current.
- Measurement of power in Electro-Magnetic waves.
- Determination of mobility of semiconductor material.
Hall effect is used in many applications as following:

**[Note:**Minority carrier mobility (μ) and diffusion coefficient(D) can be measured independently with the help of**Haynes-Shockley experiment**.**]**

### Fermi Level in Intrinsic and Extrinsic Semiconductors

- Electrons in solids obey Fermi-Dirac statistics. The distribution of electrons over a range of allowed energy levels at thermal equilibrium is:

Where k s Boltzmann’s constant (k = 8.62 × 10^{–5} eV/K = 1.38 × 10^{–23} J/K).

- The function f(E), the Fermi-Dirac distribution function, gives the probability that an available energy state of E will be occupied by an electron at absolute temperature T. The quantity E
_{F}is called the**Fermi level**. - If E = E
_{F}then = 0.5 or 50%

If E > E_{F} then f(E) < ½

If E > E_{F} then f(E) > ½

- A closer examination of f(E) indicates that at 0 K the distribution takes the simple rectangular form shown in figure. At temperature higher than 0K, some probability exists for states above the Fermi level to be filled.

**1 Fermi Level in Intrinsic Semiconductor**

In intrinsic semiconductor Fermi level E_{F} is given by

where, N_{C} = density of states in conduction band

N_{v} = density of states in valence band

In pure Semiconductor at T = 0K, Fermi level lies in the middle of bandgap.

**2 Fermi Level in n-type Semiconductor**

Fermi level in n-type semiconductor is given by

Where, N_{D} = doping concentration.

- Fermi level in n-type semiconductor depends on temperature as well as on doping concentration.
- At 0K Fermi level coincides with that of lowest energy level of conduction band.
- As doping increases Fermi level moves towards conduction band.
- Shift in Fermi level in n-type semiconductor with respect to Fermi level of intrinsic semiconductor is

shift = kT

shift ≅ kT

**3 Fermi Level in p-type Semiconductor**

Fermi level in p-type semiconductor is given by

- In p-type semiconductor Fermi level depends on both temperature as well as on doping concentration N
_{A}. - As temperature increases Fermi level moves away from E
_{V}i.e. towards middle of band gap. - As 0K Fermi level coincides with highest energy level E
_{V}of valence band. - As doping concentration increases Fermi level moves toward E
_{V}or away of middle of band gap - Shift in Fermi level in p-type semiconductor with respect to Fermi level of intrinsic semiconductor as

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