Carriers in Semiconductors MCQ Quiz - Objective Question with Answer for Carriers in Semiconductors - Download Free PDF

Explanation:

The mobility of a charge carrier in a semiconductor material is a measure of how quickly the carrier can move through the material when subjected to an electric field. It is typically denoted as μ.

Electrons and holes are the two types of charge carriers in a semiconductor. Electrons are negatively charged particles, while holes are the absence of an electron in the semiconductor lattice, effectively acting as positively charged particles.

In most semiconductor materials, the mobility of electrons (μ_e) is higher than the mobility of holes (μ_h). This is because electrons, being smaller and lighter particles, can move more easily through the crystal lattice compared to the relatively larger and heavier holes.

Thus, we generally have μ_e > μ_h.

∴ The correct answer is option 2.

The conductivity of an extrinsic semiconductor is considerably influenced by 1) Majority charge carriers originating from doping.

Explanation:

Extrinsic Semiconductors:

• These are semiconductors that have been doped with impurities to increase their conductivity.
• Doping introduces either an excess of electrons (n-type) or an excess of holes (p-type).

• Majority Carriers:
  • In n-type semiconductors, electrons are the majority carriers.
  • In p-type semiconductors, holes are the majority carriers.
  • The concentration of these majority carriers is significantly higher than the concentration of minority carriers.
• Conductivity:
  • Conductivity is directly proportional to the concentration of charge carriers.
  • Since doping greatly increases the concentration of majority carriers, they have a much greater influence on conductivity than minority carriers.
• Minority Carriers:
  • Minority carriers are generated by thermal agitation.
  • Although minority carriers contribute to the current, their number is very small compared to majority carriers.
  • Therefore, they have very little effect on the conductivity of an extrinsic semiconductor.

Therefore, the correct answer is:

• 1. Majority charge carriers originated from doping

Concept:

σ = q × nᵢ × (μₑ + μₕ)

• Intrinsic carrier density (nᵢ) in a semiconductor is related to resistivity and carrier mobility.
• Conductivity (σ) is given by: σ = 1 / ρ
• The relation between conductivity and carrier density is:
• Here, q = Charge of an electron = 1.6 × 10⁻¹⁹ C

Calculation:

Resistivity of Si, ρ = 3.16 × 10³ Ω·m

Electron mobility, μₑ = 0.14 m²/V·s

Hole mobility, μₕ = 0.06 m²/V·s

⇒ Conductivity, σ = 1 / ρ = 1 / (3.16 × 10³)

⇒ σ = 3.16 × 10⁻⁴ S/m

⇒ Using the formula,

nᵢ = σ / (q × (μₑ + μₕ))

⇒ nᵢ = (3.16 × 10⁻⁴) / (1.6 × 10⁻¹⁹ × (0.14 + 0.06))

⇒ nᵢ = (3.16 × 10⁻⁴) / (1.6 × 10⁻¹⁹ × 0.20)

⇒ nᵢ = (3.16 × 10⁻⁴) / (3.2 × 10⁻²⁰)

⇒ nᵢ = 0.987 × 10¹⁶

⇒ nᵢ ≈ 1.00 × 10¹⁶ m⁻³

∴ The intrinsic carrier density of Si is 1.00 × 10¹⁶ m⁻³.

Given:

The Fermi energy of silver is \(E_F = 5.52 \, \text{eV}\) . We are asked to find the velocity of the conduction electron in silver.

Concept:

• The velocity of conduction electrons can be calculated using the relation between kinetic energy and velocity. The kinetic energy of the conduction electron is given by:
• \( E_F = \frac{1}{2} m v^2 \), where:
  • E_F is the Fermi energy,
  • m is the mass of the electron ( \(m = 9.11 \times 10^{-31} \, \text{kg}\) ),
  • v is the velocity of the electron.

The velocity can be found by rearranging the above equation:

\( v = \sqrt{\frac{2 E_F}{m}} \)

Calculation:

Given\( E_F = 5.52 \, \text{eV}\) and \(1 \, \text{eV} = 1.602 \times 10^{-19} \, \text{J}\) , we can convert the Fermi energy into joules:

\(⇒ E_F = 5.52 \times 1.602 \times 10^{-19} \, \text{J} = 8.84 \times 10^{-19} \, \text{J} \).

Now, using the equation for velocity:

\(⇒ v = \sqrt{\frac{2 \times 8.84 \times 10^{-19}}{9.11 \times 10^{-31}}} \\ ⇒ v = \sqrt{1.94 \times 10^{12}} \\ ⇒ v = 1.39 \times 10^6 \, \text{m/s} .\)

∴ The velocity of conduction electrons in silver is \(1.39 \times 10^6 \, \text{m/s}\) .

The correct option is 3

Concept

The Fermi level is a crucial concept in semiconductor physics. It represents the energy level at which the probability of finding an electron is 50%. The position of the Fermi level in semiconductors can vary depending on the type of semiconductor and its doping level. 

In an intrinsic semiconductor at 0 Kelvin, the Fermi level lies exactly in the middle of the energy gap between the conduction band and the valence band. This is because there are equal numbers of electrons and holes.

At 0 Kelvin, the distribution of electrons is such that they occupy the lowest possible energy states.

Intrinsic carrier concentration depends on various factors defined by an expression

\(n_i^2 = {N_C}{N_V}{e^{ - \frac{{{E_g}}}{{KT}}}}\)

where K = Boltzmann constant

N_C = Effective density of states in the conduction band.

N_V = Effective density of states in the valence band

T = Temperature, E_g = Bandgap energy

The above equation increases exponentially with the decrease of the bandgap of the semiconductor and increases non-linearly with an increase of temperature.

The Fermi for a p-type semiconductor lies closer to the valence band as shown:

Similarly, the Fermi level for an n-type lies near the conduction band as shown:

• As the temperature increases above zero degrees, the extrinsic carriers in the conduction band and the valence band increases.
• Since the intrinsic concentration also depends on temperature, ni also increases. But for small values of temperature, the extrinsic concentration dominates in comparison to the intrinsic concentration.
• As the temperature continues to increase, the semiconductor starts to lose its extrinsic property and becomes intrinsic, as ni becomes comparable to the extrinsic concentration.

The Fermi-level in an intrinsic semiconductor is nearly midway between the conductive and valence band as shown:

​        

Concept: 

Extrinsic n-type semiconductors are formed when a pentavalent impurity is added to a pure semiconductor. Examples of pentavalent impurity are Phosphorus and Arsenic.

Also, the law of mass action is used to determine the minority carriers in a doped semiconductor.

According to law:

n.p = n_i²

n = concentration of electrons

p = concentration of holes

Also, if the doping concentration is greater than the intrinsic carrier concentration, the majority carrier concentration will be:

n = N_d

Calculation:

Given: n_i = 1.5 × 10¹⁰ /cm³

N_d = 10¹⁷/cm³

Since N_d >> n_i, the majority carrier electron concentration will be:

n = N_d = 10¹⁷/cm³

Now, the minority carrier holes concentration will be:

\(p=\frac{n_i^2}{N_d}=\frac{(1.5× 10^{10})^2}{10^{17}}\)

p = 2250 /cm³

p = 2.25 × 10³ /cm³

Concept:

Material	Property	Energy Band diagram
Conductors:	In conductors, the conduction band and the valence band overlap, which indicates that the valence electrons can easily move from the conduction band and are free to conduct
Insulators:	An insulator, there exists a large bandgap between the conduction band and valence band Eg (Eg > 3 eV), which results in no free electrons in the conduction band, and therefore no electrical conduction is possible.
Semiconductors:	In a semiconductor, there exists a finite but small band gap between the conduction band and valence band (Eg < 3 eV). Because of the small bandgap, at room temperature, some electrons from the valence band can acquire enough energy to cross the energy gap and enter the conduction band.

Explanation:

From the above explanation, we can see that, 

• The energy band gap is measured in eV or electron volt and it is the energy separation between the valence band and conduction band.
• The valence band lies below the conduction band.
• An insulator has the highest bandgap which is usually greater than 3 eV because the gap between the valence band and conduction band is large. Hence they cannot conduct electricity that well.
• The energy band gap of conductors is approximately zero because the valence band and conduction band overlap each other.
• The energy band gap of conductors is <3 eV, i.e. less than insulators and more than conductors because they lie somewhere in between these two.
• And the below fig represents the energy gap for all three types of material 
• 

In a semiconductor, the movement of charge carriers under the influence of an electric field is called drift.

The mobile charge can move in and out of the semiconductor, while the fixed charge does not move at all.

Holes and electrons are movable whereas ions are not movable hence they are immobile.

Intrinsic semiconductor:

• It is a crystal having all atoms of the same nature i.e. extremely pure semiconductor is called an intrinsic semiconductor.

          Ex: pure silicon, germanium.

• At room temperature (300 Kelvin), the electrons in the valence band are moved to the conduction band. When an electron leaves the valence band it creates a vacancy known as a hole. A hole attracts electrons as it is positively charged.
• In intrinsic semiconductor number of free electrons is equal to the number of holes. i.e. ne = nh
• Since there is an equal number of both the electrons and holes in an intrinsic semiconductor, the current contribution will be equal from both the charge carriers.
• The total current passing through intrinsic semiconductors is given by:

           I = Ie + Ih

          I_e = Electron Current

          I_h = Hole current

This is explained with the help of the following diagram:

For an extrinsic semiconductor the current will be because of majority carriers:

• For an n-type extrinsic semiconductor, the current will be because of the majority carrier electrons (I_e only)
• For a p-type extrinsic semiconductor, the current will be because of the majority carrier holes (I_h only)

CONCEPT:

• Forbidden energy gap (ΔEg): The energy gap between the conduction band and valence band is known as the forbidden energy gap i.e.,

ΔEg = (C.B)min - (V.B)max

• No free electron is present in the forbidden energy gap.
• The width of the forbidden energy gap depends upon the nature of the substance.
• As the temperature increases, the forbidden energy gap decreases very slightly.

• In a conductor, the conduction band is partially filled and the valanced band is partially empty or when the conduction and valance bands overlap. When there is overlap electrons from the valence band can easily move into the conduction band. 

• In an insulator, there exists a large bandgap between the conduction band and valence band Eg (Eg > 3 eV). There are no electrons in the conduction band, and therefore no electrical conduction is possible.

• In semiconductors, there exists a finite but small band gap between the conduction band and valence band (Eg < 3 eV). Because of the small bandgap, at room temperature, some electrons from the valence band can acquire enough energy to cross the energy gap and enter the conduction band.
• Therefore, the forbidden energy bandgap in conductors, semiconductors, and insulators are in the relation insulator > semiconductor > conductor.

Therefore, the correct order is Graphite, Silicon, Diamond

• Extrinsic conductors are those which have added impurities in them, like p-type and n-type semiconductors.
• The n-type conductors have electrons as major charge carriers.
• This is because n-type conductors have pentavalent (5 valence electrons) impurities like phosphorous, etc.
• Elements of Group 5 have five valence electrons, i.e. 1 extra from the Group 4 elements. 4 out of 5 electrons get bonded with the neighbouring Silicon atoms and 1 electron per atom remains extra with the Group 5 elements.
• Thus, electrons are the major charge carriers in n-type semiconductors.
• p-type semiconductors have impurities of elements from Group 3 and holes are majority charge carriers in them.

The concentration of minority carriers in an extrinsic semiconductor is given by the law of mass action, according to which:

n.p = n_i²

n = concentration of electrons in the conduction band

p = concentration of holes in the valence band

n_i = intrinsic carrier concentration

Cases:

In an n-type semiconductor, the minority hole concentration is given by:

\(p = \frac{{n_i^2}}{{{N_D}}}\)

N_D = Concentration of Donor impurity

In a p-type semiconductor, the minority electron concentration is given by:

\(n = \frac{{n_i^2}}{{{N_A}}}\)

N_A = Concentration of Acceptor impurity

Observations:

Thus the minority carriers concentration is:

1) inversely proportional to the doping concentration

2) directly proportional to the square of intrinsic concentration and not to the intrinsic concentration.