Doping In Semiconductors – An Introduction

Doping in Semiconductors – An introduction

Definition of doping in semiconductors
Role of impurity atoms in doping
Two types of impurity atoms used in doping:
- Donor impurities
- Acceptor impurities
Concept of majority and minority charge carriers
Effect of doping on conductivity

Donor Impurities

Definition of donor impurities
Example of donor impurity: Phosphorus (P) in Silicon (Si)
Process of adding donor impurities (n-type doping)
Resulting effect on conductivity
Equation: n-type doping equation

Acceptor Impurities

Definition of acceptor impurities
Example of acceptor impurity: Boron (B) in Silicon (Si)
Process of adding acceptor impurities (p-type doping)
Resulting effect on conductivity
Equation: p-type doping equation
Comparison of donor and acceptor impurities

Majority and Minority Charge Carriers

Explanation of majority and minority charge carriers
Donor impurity effect on majority and minority carriers
Acceptor impurity effect on majority and minority carriers
Concentration of majority and minority carriers in doped semiconductors
Relation between majority and minority carrier concentrations

Effect of Doping on Conductivity

Change in conductivity due to doping
Increase in conductivity with n-type doping
Increase in conductivity with p-type doping
Relation between conductivity and carrier concentration
Equation: Conductivity equation

Types of Doping

Intrinsic semiconductor vs extrinsic semiconductor
n-type doping vs p-type doping
Comparison of n and p-type semiconductors
Applications of n and p-type semiconductors
Importance of understanding doping in semiconductor devices

Donor Impurities

Donor impurities are atoms that have excess electrons compared to the host semiconductor material.
Example: Phosphorus (P) in Silicon (Si)
The process of adding donor impurities to a semiconductor is called n-type doping.
Donor impurities increase the concentration of free electrons in the semiconductor.
This creates an excess of negative charges and results in the formation of an n-type semiconductor.
Equation: $ N_d = N_{c0} \cdot e^{-\frac{E_d}{kT}} $

Acceptor Impurities

Acceptor impurities are atoms that have fewer electrons compared to the host semiconductor material.
Example: Boron (B) in Silicon (Si)
The process of adding acceptor impurities to a semiconductor is called p-type doping.
Acceptor impurities create “holes” in the valence band of the semiconductor, which act as positive charge carriers.
This results in the formation of a p-type semiconductor.
Equation: $ N_a = N_{v0} \cdot e^{-\frac{E_a}{kT}} $

Majority and Minority Charge Carriers

Majority charge carriers are the dominant type of charge carriers in a doped semiconductor.
For n-type doped semiconductors, the majority carriers are electrons.
For p-type doped semiconductors, the majority carriers are holes.
Minority charge carriers are the less dominant type of charge carriers.
For n-type doped semiconductors, the minority carriers are holes.
For p-type doped semiconductors, the minority carriers are electrons.

Donor Impurity Effect on Majority and Minority Carriers

In an n-type doped semiconductor, the donor impurities provide excess electrons.
These excess electrons become the majority charge carriers.
The original host semiconductor holes become the minority charge carriers.
The concentration of majority electrons is significantly higher than the concentration of minority holes.

Acceptor Impurity Effect on Majority and Minority Carriers

In a p-type doped semiconductor, the acceptor impurities create holes in the valence band.
These holes become the majority charge carriers.
The original host semiconductor electrons become the minority charge carriers.
The concentration of majority holes is significantly higher than the concentration of minority electrons.

Concentration of Majority and Minority Carriers

The concentration of majority carriers is determined by the dopant impurity concentration.
Higher dopant impurity concentration leads to a higher concentration of majority carriers.
The concentration of minority carriers is determined by the intrinsic carrier concentration and the temperature.

Relation between Majority and Minority Carrier Concentrations

The ratio of the majority carrier concentration (n or p) to the minority carrier concentration (p or n) is related to the intrinsic carrier concentration (n_i) and temperature (T).
For n-type doped semiconductors: $ \frac{n}{p} = e^{\frac{E_g}{2kT}} $
For p-type doped semiconductors: $ \frac{p}{n} = e^{-\frac{E_g}{2kT}} $
$ E_g $ is the energy gap between the valence and conduction bands.

Change in Conductivity due to Doping

Doping significantly affects the conductivity of a semiconductor.
For an n-type doped semiconductor, the conductivity increases due to the presence of excess electrons.
For a p-type doped semiconductor, the conductivity increases due to the presence of excess holes.
Doping introduces additional charge carriers, enhancing the conductivity.

Increase in Conductivity with n-type Doping

In n-type doped semiconductors, the conductivity is primarily due to the excess electrons provided by the donor impurities.
The higher the concentration of donor impurities, the higher the conductivity of the semiconductor.
The conductivity can be further increased by increasing the temperature, which promotes more electrons to the conduction band.

Increase in Conductivity with p-type Doping

In p-type doped semiconductors, the conductivity is primarily due to the excess holes created by the acceptor impurities.
The higher the concentration of acceptor impurities, the higher the conductivity of the semiconductor.
The conductivity can be further increased by increasing the temperature, which promotes more electrons to fill the holes and create more holes.

Applications of n and p-Type Semiconductors

n-type semiconductors are commonly used in:
- Electronic devices such as diodes, transistors, and integrated circuits
- Solar cells
- Light-emitting diodes (LEDs)
- Sensors and detectors
p-type semiconductors are commonly used in:
- Electronic devices such as diodes, transistors, and integrated circuits
- Light-emitting diodes (LEDs)
- Photovoltaic cells
- Semiconducting devices for energy harvesting
The combination of n and p-type semiconductors forms the basis of many electronic devices and circuits.

Comparison of n and p-Type Semiconductors

Conductivity:
- n-type semiconductors have higher conductivity due to the presence of excess electrons.
- p-type semiconductors have lower conductivity compared to n-type semiconductors due to the presence of fewer charge carriers.
Majority and Minority Charge Carriers:
- In n-type semiconductors, electrons are the majority charge carriers while holes are the minority charge carriers.
- In p-type semiconductors, holes are the majority charge carriers while electrons are the minority charge carriers.
Doping:
- n-type doping involves adding donor impurities with excess electrons.
- p-type doping involves adding acceptor impurities with fewer electrons.
Energy Band Gap:
- The energy band gap of n-type semiconductors is slightly larger than p-type semiconductors.

Importance of Understanding Doping in Semiconductor Devices

Doping plays a crucial role in the design and operation of semiconductor devices.
Proper doping is necessary to control the conductivity, carrier concentrations, and behavior of electronic circuits.
Understanding doping allows engineers to optimize the performance of electronic devices.
Doping enables the creation of different types of semiconductors and facilitates the development of advanced technologies.

Intrinsic Semiconductor vs Extrinsic Semiconductor

Intrinsic Semiconductor:
- Pure form of the semiconductor material without intentional doping.
- The number of electrons and holes is equal due to thermal excitation.
- The conductivity of intrinsic semiconductors is relatively low.
Extrinsic Semiconductor:
- Doped form of the semiconductor material with intentional impurities.
- Donor or acceptor impurities are added to modify the carrier concentrations.
- The conductivity of extrinsic semiconductors is significantly higher than intrinsic semiconductors.

n-Type Doping vs p-Type Doping

n-Type Doping:
- Involves adding donor impurities with excess electrons.
- Creates an abundance of free electrons, increasing the conductivity.
- Produces an n-type semiconductor with majority electrons as the charge carriers.
p-Type Doping:
- Involves adding acceptor impurities with fewer electrons.
- Creates holes in the valence band, increasing the conductivity.
- Produces a p-type semiconductor with majority holes as the charge carriers.

Comparison between Donor and Acceptor Impurities

Donor Impurities:
- Have excess electrons compared to the host semiconductor material.
- Donate electrons to the conduction band, increasing the conductivity.
- Examples: Phosphorus (P) in Silicon (Si).
Acceptor Impurities:
- Have fewer electrons compared to the host semiconductor material.
- Create holes in the valence band, increasing the conductivity.
- Examples: Boron (B) in Silicon (Si).

Equation: n-Type Doping Equation

The concentration of donor impurities (Nd) in an n-type doped semiconductor can be calculated using the equation:
- $ N_d = N_{c0} \cdot e^{-\frac{E_d}{kT}} $
- Nd: Concentration of donor impurities
- Nc0: Effective density of states in the conduction band
- Ed: Energy level of donor impurity with respect to the conduction band
- k: Boltzmann constant
- T: Temperature in Kelvin

Equation: p-Type Doping Equation

The concentration of acceptor impurities (Na) in a p-type doped semiconductor can be calculated using the equation:
- $ N_a = N_{v0} \cdot e^{-\frac{E_a}{kT}} $
- Na: Concentration of acceptor impurities
- Nv0: Effective density of states in the valence band
- Ea: Energy level of acceptor impurity with respect to the valence band
- k: Boltzmann constant
- T: Temperature in Kelvin

Equation: Conductivity Equation

The conductivity (σ) of a doped semiconductor is related to the carrier concentration (n or p) by the equation:
- $ \sigma = q \cdot \mu \cdot n $
- σ: Conductivity
- q: Charge of a carrier (electron charge)
- μ: Carrier mobility
- n: Concentration of majority charge carriers (electrons for n-type, holes for p-type)

Conclusion

Doping is a crucial process in semiconductor technology.
Donor impurities create n-type semiconductors with excess electrons.
Acceptor impurities create p-type semiconductors with excess holes.
Doping significantly affects the conductivity, carrier concentrations, and behavior of semiconductors.
Understanding doping is essential for designing and optimizing electronic devices and circuits.
The combination of n and p-type semiconductors enables the development of advanced technologies.