P-Type Semiconductor MCQ Quiz - Objective Question with Answer for P-Type Semiconductor - Download Free PDF

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.

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.

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.

EXPLANATION:

​EXPLANATION:

Conductors: 

• Conductors allow an electric current to flow through them. 
  • There is no forbidden gap between the valence band and conduction band which results in the overlapping of both the bands.
  • The number of free electrons available at room temperature is large. Ex. Gold, Aluminium, Silver, Copper, etc.

Insulators:

• These substances do not allow electricity to pass through them.
  • They have high resistivity and very low conductivity.
  • The energy gap in the insulator is very high up to 7eV.
  • The material cannot conduct because the movement of the electrons from the valence band to the conduction band is not possible. Ex. Glass, wood, etc.

Semiconductors: 

• Germanium and Silicon are the most preferable material whose electrical properties lie in between semiconductors and insulators. 
  • The energy band diagram of the semiconductor is shown where the conduction band is empty and the valence band is completely filled but the forbidden gap between the two bands is very small which is about 1eV.
• From the above explanation, it is clear that the forbidden energy gap in an intrinsic semiconductor is of the order of 1eV. Hence, option 1 is correct.

Semiconductor: 

Semiconductors are materials that have a conductivity between conductors and insulators.

Semiconductors are made of compounds such as gallium arsenide or pure elements, such as germanium or silicon.

There are two types of semiconductors:

​N-type Semiconductor

P-type Semiconductor

In a P-type semiconductor material, holes are generated because a trivalent impurity atom has one less electron than the surrounding silicon atom. Thus, leaving a vacancy in a covalent bond that acts as a hole. The presence of a hole does not make the semiconductor material positively charge because in an impurity atom, no. of electron and proton is equal before and after the doping, and the same applies for the silicon atom.

Thus, p-type semiconductor crystal remains neutral.

Important Points:

• Extrinsic P-type Semiconductor is formed when a trivalent impurity is added to a pure semiconductor.
• Example of trivalent impurity is Boron, Gallium, and Indium.
• Trivalent impurity like boron has 3 valence electrons.
• Each atom of the impurity fits in the silicon crystal by forming covalent bonds with the surrounding silicon atoms.
• The dopant boron atom has one less electron than surrounding silicon and thus vacancy is generated that acts as a hole.

In a P-type semiconductor material, holes are generated because trivalent impurity atom has one less electron than surrounding silicon atom. Thus, leaving a vacancy in a covalent bond that acts as a hole. Presence of hole does not make the semiconductor material positively charge because in an impurity atom, no. of electron and proton is equal before and after the doping, and the same applies for the silicon atom.

Thus, p-type semiconductor crystal remains neutral.

Important Points:

• Extrinsic P-type Semiconductor is formed when a trivalent impurity is added to a pure semiconductor
• Example of trivalent impurity are Boron, Gallium and Indium
• Trivalent impurity like boron, have 3 valence electrons
• Each atom of the impurity fits in the silicon crystal by forming covalent bonds with the surrounding silicon atoms
• The dopant boron atom has one less electron than surrounding silicon and thus vacancy is generated that acts as a hole

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.

EXPLANATION:

​EXPLANATION:

Conductors: 

• Conductors allow an electric current to flow through them. 
  • There is no forbidden gap between the valence band and conduction band which results in the overlapping of both the bands.
  • The number of free electrons available at room temperature is large. Ex. Gold, Aluminium, Silver, Copper, etc.

Insulators:

• These substances do not allow electricity to pass through them.
  • They have high resistivity and very low conductivity.
  • The energy gap in the insulator is very high up to 7eV.
  • The material cannot conduct because the movement of the electrons from the valence band to the conduction band is not possible. Ex. Glass, wood, etc.

Semiconductors: 

• Germanium and Silicon are the most preferable material whose electrical properties lie in between semiconductors and insulators. 
  • The energy band diagram of the semiconductor is shown where the conduction band is empty and the valence band is completely filled but the forbidden gap between the two bands is very small which is about 1eV.
• From the above explanation, it is clear that the forbidden energy gap in an intrinsic semiconductor is of the order of 1eV. Hence, option 1 is correct.

P-type semiconductor:

• Extrinsic P-type Semiconductor is formed when a trivalent impurity is added to a pure semiconductor
• Example of trivalent impurity are Boron, Gallium, and Indium
• Trivalent impurity like boron has 3 valence electrons.
• Each atom of the impurity fits in the silicon crystal by forming covalent bonds with the surrounding silicon atoms
• The dopant boron atom has one less electron than surrounding silicon and thus vacancy is generated that acts as a hole. 
• Therefore, holes are in majority in the p-type semiconductors. 

Pentavalent impurities:

Impurity atoms with 5 valence electrons produce n-type semiconductors by contributing an extra electron.

This is as explained in the figure:

In a P-type semiconductor material, holes are generated because trivalent impurity atom has one less electron than surrounding silicon atom. Thus, leaving a vacancy in a covalent bond that acts as a hole. Presence of hole does not make the semiconductor material positively charge because in an impurity atom, no. of electron and proton is equal before and after the doping, and the same applies for the silicon atom.

Thus, p-type semiconductor crystal remains neutral.

Important Points:

• Extrinsic P-type Semiconductor is formed when a trivalent impurity is added to a pure semiconductor
• Example of trivalent impurity are Boron, Gallium and Indium
• Trivalent impurity like boron, have 3 valence electrons
• Each atom of the impurity fits in the silicon crystal by forming covalent bonds with the surrounding silicon atoms
• The dopant boron atom has one less electron than surrounding silicon and thus vacancy is generated that acts as a hole

Semiconductor: 

Semiconductors are materials that have a conductivity between conductors and insulators.

Semiconductors are made of compounds such as gallium arsenide or pure elements, such as germanium or silicon.

There are two types of semiconductors:

​N-type Semiconductor

P-type Semiconductor

• Extrinsic p-Type Semiconductor is formed when a trivalent impurity is added to a pure semiconductor.
• Example of trivalent impurity are Boron, Gallium, and Indium
• Trivalent impurity like boron, have 3 valence electrons.
• Each atom of the impurity fits in the silicon crystal by forming covalent bonds with the surrounding silicon atoms.
• The dopant boron atom has one less electron than surrounding silicon and thus vacancy is generated that acts as a hole.

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.

EXPLANATION:

​EXPLANATION:

Conductors: 

• Conductors allow an electric current to flow through them. 
  • There is no forbidden gap between the valence band and conduction band which results in the overlapping of both the bands.
  • The number of free electrons available at room temperature is large. Ex. Gold, Aluminium, Silver, Copper, etc.

Insulators:

• These substances do not allow electricity to pass through them.
  • They have high resistivity and very low conductivity.
  • The energy gap in the insulator is very high up to 7eV.
  • The material cannot conduct because the movement of the electrons from the valence band to the conduction band is not possible. Ex. Glass, wood, etc.

Semiconductors: 

• Germanium and Silicon are the most preferable material whose electrical properties lie in between semiconductors and insulators. 
  • The energy band diagram of the semiconductor is shown where the conduction band is empty and the valence band is completely filled but the forbidden gap between the two bands is very small which is about 1eV.
• From the above explanation, it is clear that the forbidden energy gap in an intrinsic semiconductor is of the order of 1eV. Hence, option 1 is correct.

Concept:

The conductivity for a doped semiconductor is obtained as:

σ = q n₀ μ_n = q p₀ μ_p

where,

n_i = Intrinsic carrier concentration.

μ_n = electron mobility

μ_p = Hole mobility

When a semiconductor crystal is optically excited, one hole is created for every electron, i.e. electron-hole pass are created.  

Application:

When the light is ON, excess electron and holes are generated in pairs, i.e.

Δp = Δn = 10¹⁶ cm³

Before Illumination:

N_A = 10¹⁷ cm^-3 and n_i = 2.2 × 10⁶ cm^-3

Since N_A ≫ n_i, the excess hole concentration at thermal equilibrium will be:

p₀ = N_A = 10¹⁷ cm^-3

The electron concentration using mass-action law is obtained as:

\({n_0} = \frac{{n_i^2}}{{{p_0}}}\)

\({n_0} = \frac{{{{\left( {2.2 \times {{10}^6}} \right)}^2}}}{{{{10}^{17}}}} = 4.8 \times {10^{ - 5}}c{m^{ - 3}}\)

The electron concentration before illumination is negligible.

After illumination:

When an electron is generated optically, one hole is also created, i.e. they always occur in pairs.

∴ The excess hole concentration and excess electron concentration will be the same, i.e.

Δp = Δn = 10¹⁶ cm^-3

Now, the electron and hole concentration after illumination will be:

n = n₀ + Δn

n = 4.8 × 10^-5 + 10¹⁶

n = 10¹⁶

Similarly,

p = p₀ + Δp

p = 10¹⁷ + 10¹⁶ cm^-3

p = 11 × 10¹⁶ cm^-3

∴ the conductivity of the given sample when the light is ON will be:

σ = q(n₀ + Δ_n)μ_n + q(p₀ + Δ_p)μ_p

σ = q[(10¹⁶)μ_n + (11 × 10¹⁶)μ_p]

= (1.6 × 10^-19) (10¹⁶ × 5300 + (11 × 10¹⁶) (230))

= 1.6 × 10^-19 (5.3 × 10¹⁹ + 2.53 × 10¹⁹)

= 1.6 × (5.3 + 2.53)

σ = 12.528 (Ω-cm)^-1         

P-type semiconductor:

• Extrinsic P-type Semiconductor is formed when a trivalent impurity is added to a pure semiconductor
• Example of trivalent impurity are Boron, Gallium, and Indium
• Trivalent impurity like boron has 3 valence electrons.
• Each atom of the impurity fits in the silicon crystal by forming covalent bonds with the surrounding silicon atoms
• The dopant boron atom has one less electron than surrounding silicon and thus vacancy is generated that acts as a hole. 
• Therefore, holes are in majority in the p-type semiconductors. 

Pentavalent impurities:

Impurity atoms with 5 valence electrons produce n-type semiconductors by contributing an extra electron.

This is as explained in the figure:

Common ambipolar transport equation simplifications are as shown below. In achieving the simplifications the complete term (along with constant) has been shown equated to zero.