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.

Trivalent Impurities in Semiconductors

Definition: Trivalent impurities are elements from group III of the periodic table that have three valence electrons. These impurities are introduced into an intrinsic semiconductor (pure semiconductor) to create a p-type semiconductor. When a trivalent impurity is added to a semiconductor, it creates "holes" (positive charge carriers), making the semiconductor conducive to electrical current primarily through hole movement.

Working Principle: In a pure semiconductor like silicon or germanium, each atom forms covalent bonds with four neighboring atoms. When a trivalent impurity (e.g., gallium) is added, it has only three valence electrons, which are insufficient to form four covalent bonds. The absence of the fourth electron creates a "hole" in the crystal lattice. This hole acts as a positive charge carrier, and the movement of these holes constitutes electric current in a p-type semiconductor.

Examples of Trivalent Impurities:

• Gallium (Ga): A commonly used trivalent impurity for doping semiconductors to create p-type materials.
• Boron (B): Another widely used trivalent impurity for the same purpose.
• Indium (In): Occasionally used for specific semiconductor applications.

Advantages of Doping with Trivalent Impurities:

• Increases the conductivity of the semiconductor by providing positive charge carriers.
• Enables the creation of p-n junctions, which are the basis of many electronic devices like diodes and transistors.
• Facilitates the customization of semiconductor properties for specific applications.

Correct Option Analysis:

The correct option is:

Option 3: Gallium

Gallium is a trivalent impurity, meaning it has three valence electrons. When introduced into a semiconductor, it creates holes by leaving a bond incomplete, which facilitates the formation of a p-type semiconductor. This is a classic example of a trivalent impurity used for doping semiconductors.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: Phosphorus

Phosphorus is a pentavalent impurity, meaning it has five valence electrons. When added to a semiconductor, it donates an extra electron, creating an n-type semiconductor. This makes phosphorus unsuitable as a trivalent impurity.

Option 2: Antimony

Antimony is also a pentavalent impurity. Like phosphorus, it donates an extra electron when introduced into a semiconductor, leading to the formation of an n-type semiconductor. Therefore, it cannot be classified as a trivalent impurity.

Option 4: Arsenic

Arsenic is another pentavalent impurity. It behaves similarly to phosphorus and antimony by contributing an extra electron to the semiconductor lattice, creating an n-type semiconductor. It is not a trivalent impurity.

Option 5: None

This option is incorrect because Gallium (Option 3) is indeed a valid example of a trivalent impurity, as explained above.

Conclusion:

Among the options provided, Gallium is the correct example of a trivalent impurity. Trivalent impurities like Gallium play a crucial role in the semiconductor industry by enabling the creation of p-type semiconductors. Understanding the behavior of trivalent and pentavalent impurities is essential for designing and optimizing electronic devices such as diodes, transistors, and integrated circuits.

Explanation:

Fermi Level and Its Significance

Definition: The Fermi level is a concept in quantum mechanics that represents the energy level at which the probability of finding an electron is 50% at absolute zero temperature. It serves as a reference energy level, separating occupied energy states from unoccupied energy states in a material. The position of the Fermi level is crucial in determining the electrical and thermal properties of a material.

Working Principle: The Fermi level is not a fixed energy level but rather an indicator of the energy distribution of electrons within a material. In metals, the Fermi level lies within the conduction band, allowing free movement of electrons and making them good conductors. In semiconductors, the Fermi level lies between the valence and conduction bands, and its position can shift based on doping. In insulators, the Fermi level is typically far from the conduction band, making electron movement difficult.

Correct Option Analysis:

The correct answer is:

Option 2: Probability of occupancy of electrons or holes

This option accurately describes the Fermi level. The Fermi level is a measure of the probability that an electron or hole will occupy a given energy state at a specific temperature. This probability is governed by the Fermi-Dirac distribution function, which is given by:

F(E) = 1 / [1 + exp((E - Ef) / (k × T))]

Where:

• F(E): Probability of occupancy of an energy state with energy E
• Ef: Fermi level (energy)
• k: Boltzmann constant
• T: Absolute temperature

At absolute zero (T = 0 K), all energy states below the Fermi level are completely filled, and those above are empty. As the temperature increases, electrons gain thermal energy and can occupy higher energy states, leading to a distribution of electrons and holes around the Fermi level.

The position of the Fermi level in a material determines its conductivity and other electronic properties:

• In metals, the Fermi level resides within the conduction band, allowing for free electron movement and high conductivity.
• In semiconductors, the Fermi level lies in the band gap and shifts with doping. For n-type semiconductors, it moves closer to the conduction band, while for p-type, it moves closer to the valence band.
• In insulators, the Fermi level is far from the conduction band, making electron excitation difficult and reducing conductivity.

Importance in Semiconductors: In semiconductors, the Fermi level provides valuable insights into the type of doping (n-type or p-type) and the carrier concentration. It plays a crucial role in determining the behavior of devices like diodes, transistors, and solar cells.

Additional Information:

To further understand the analysis, let’s evaluate the other options:

Option 1: Doping of electrons

This option is incorrect because doping refers to the process of intentionally introducing impurities into a semiconductor to modify its electrical properties. While doping does affect the position of the Fermi level, the Fermi level itself is not a measure of doping. Instead, it represents the probability of electron or hole occupancy in energy states.

Option 3: Probability of occupancy of photons

This option is incorrect because the Fermi level specifically deals with the energy states of electrons (or holes) in a material. Photons, being quanta of light, do not have a Fermi level associated with them. Their behavior is described by other principles, such as Planck's law and the photon energy equation (E = h × ν).

Option 4: Probability of occupancy of wavelength

This option is incorrect because wavelength is a property of waves, including light and sound, and does not directly relate to the Fermi level. The Fermi level is concerned with electron or hole energy states, not with the occupancy of wavelengths.

Option 5: (No provided content for Option 5)

Since no information is provided for Option 5, we can conclude that it is not relevant to the question.

Conclusion:

The Fermi level is a fundamental concept in understanding the electronic properties of materials. It provides a probabilistic measure of electron and hole occupancy in energy states, which is critical for analyzing the behavior of conductors, semiconductors, and insulators. The correct answer, Option 2, highlights its role as a measure of the probability of occupancy of electrons or holes, distinguishing it from other unrelated concepts such as doping, photons, or wavelengths. By understanding the Fermi level, we can gain deeper insights into the operation of electronic devices and the design of advanced materials.

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.

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.