Doping In Semiconductors - Electron And Hole System In Silicon Crystal

Slide 1: Introduction to Doping in Semiconductors

Doping is the process of deliberately adding impurities to a semiconductor material.
It is done to alter the electrical properties of the material and create desirable characteristics.
In this lecture, we will focus on the electron and hole system in a silicon crystal.
Understanding the behavior of these charge carriers is crucial in understanding semiconductor devices.

Slide 2: Silicon Crystal Structure

Silicon is a common semiconductor material with a crystal structure.
It has a diamond lattice structure formed by covalent bonds between silicon atoms.
Each silicon atom is surrounded by four neighboring atoms, creating a stable structure.
This structure allows silicon to have unique electrical properties when doped.

Slide 3: Intrinsic Silicon

In its pure form, silicon is an insulator and does not conduct electricity.
This is known as intrinsic silicon, where there are an equal number of electrons and holes.
At room temperature, a small number of electrons and holes are thermally generated.
The concentration of electrons and holes in intrinsic silicon is quite low.

Slide 4: Doping with Donor Impurities

Doping with donor impurities introduces additional electrons into the silicon crystal.
These impurities have one extra valence electron compared to silicon.
Common donor impurities include phosphorus (P), arsenic (As), and antimony (Sb).
When a donor impurity atom replaces a silicon atom, an extra electron is loosely bound to the atom.

Slide 5: Electron System in N-type Silicon

When doped with donor impurities, the resulting silicon is called N-type silicon.
The extra electrons from the donor impurities become the majority charge carriers.
The majority carriers contribute to the conduction of electricity.
The concentration of electrons in N-type silicon is much higher than in intrinsic silicon.

Slide 6: Doping with Acceptor Impurities

Doping with acceptor impurities creates additional holes in the silicon crystal.
These impurities have one less valence electron compared to silicon.
Common acceptor impurities include boron (B), aluminum (Al), and gallium (Ga).
When an acceptor impurity atom replaces a silicon atom, it creates a hole in the crystal lattice.

Slide 7: Hole System in P-type Silicon

When doped with acceptor impurities, the resulting silicon is called P-type silicon.
The holes created by the acceptor impurities become the majority charge carriers.
The majority carriers contribute to the conduction of electricity.
The concentration of holes in P-type silicon is much higher than in intrinsic silicon.

Slide 8: Electron-hole Recombination

In both N-type and P-type silicon, there are still a small number of minority charge carriers.
Electrons and holes can combine, or recombine, resulting in neutral atoms.
This process of recombination reduces the number of charge carriers in the material.
Recombination can be spontaneous or can be induced by adding energy to the system.

Slide 9: Formation of a pn Junction

When N-type and P-type silicon are brought into contact, a pn junction is formed.
The region near the junction is depleted of majority charge carriers, creating a depletion region.
This depletion region acts as an insulator, preventing current flow between the N and P regions.
The pn junction forms the basis of many electronic devices, including diodes and transistors.

Slide 10: Summary

Doping is the process of adding impurities to a semiconductor to alter its electrical properties.
Donor impurities introduce extra electrons, creating N-type silicon.
Acceptor impurities create holes, creating P-type silicon.
Electron and hole recombination reduces the number of charge carriers.
The pn junction formed by N-type and P-type silicon is a key component in semiconductor devices.

Carrier Concentration in N-type Silicon:

The concentration of electrons in N-type silicon is given by the equation: n = Nd + ni, where Nd is the donor impurity concentration and ni is the intrinsic carrier concentration.
The intrinsic carrier concentration depends on the temperature and is given by the equation: ni = sqrt(Nc * Nv) * exp(-Eg / 2kT), where Nc and Nv are the effective densities of states in the conduction and valence bands respectively, Eg is the energy band gap, k is Boltzmann’s constant, and T is the temperature in Kelvin.
For example, if Nd = 1 x 10^17/cm^3 and T = 300 K, the carrier concentration can be calculated using the above equations.

The Concept of Majority and Minority Carriers:

In N-type silicon, electrons are the majority carriers and holes are the minority carriers.
Majority carriers have a higher concentration than minority carriers.
Minority carriers can contribute to conduction, but their concentration is much lower than the majority carriers.
In P-type silicon, the majority carriers are holes, while electrons are the minority carriers.

Carrier Mobility:

Carrier mobility is a measure of how quickly charge carriers move through a material when subjected to an electric field.
It is denoted by the symbol μ and is expressed in units of cm^2/Vs.
The mobility of electrons and holes in silicon is typically in the range of 300-1500 cm^2/Vs.
It depends on various factors such as temperature, impurity concentration, and scattering mechanisms.

Conductivity of N-type Silicon:

The conductivity of a material is a measure of its ability to conduct electric current.
In N-type silicon, the conductivity is mainly due to the movement of electrons.
The conductivity (σ) is given by the equation: σ = n * μ * e, where n is the electron concentration, μ is the electron mobility, and e is the charge of an electron.
The conductivity of N-type silicon is higher compared to intrinsic silicon due to the high concentration of electrons.

Conductivity of P-type Silicon:

In P-type silicon, the conductivity is mainly due to the movement of holes.
The conductivity (σ) is given by the equation: σ = p * μ * e, where p is the hole concentration, μ is the hole mobility, and e is the charge of an electron.
The conductivity of P-type silicon is lower compared to intrinsic silicon due to the low concentration of holes.

Doping Concentration and Carrier Mobility:

The choice of dopant concentration in N-type and P-type silicon influences the carrier mobility.
Higher doping concentrations can lead to a decrease in carrier mobility due to increased scattering of electrons or holes.
Optimizing the doping concentration is crucial to maximize the overall conductivity and performance of semiconductor devices.

Doping Efficiency:

Doping efficiency is a measure of how effectively the dopant atoms are incorporated into the semiconductor crystal lattice.
It is denoted by the symbol η and is expressed as a percentage.
Doping efficiency depends on factors such as the purity of the dopant source, the crystal quality, and the doping process.
Higher doping efficiency leads to a higher concentration of charge carriers and improved device performance.

Temperature Dependence of Carrier Concentration:

The carrier concentration in N-type and P-type silicon depends on temperature.
As the temperature increases, more electron-hole pairs are thermally generated, leading to an increase in carrier concentration.
The temperature dependence can be described using the equation: n(T) = n0 * exp((Eg - E)/kT), where n0 is the carrier concentration at a reference temperature, E is the activation energy, and T is the absolute temperature.
The activation energy reflects the energy required to generate an electron-hole pair.

Impact of Doping on Energy Bands:

Doping introduces impurity energy levels within the energy band gap of the semiconductor.
Donor impurities create energy levels just below the conduction band, while acceptor impurities create energy levels just above the valence band.
These impurity energy levels influence the behavior of electrons and holes, affecting the electrical properties of the semiconductor material.
The position and concentration of these impurity energy levels depend on the choice of dopants.

Summary:

Doping in semiconductors alters their electrical properties by introducing impurities.
N-type silicon has a higher concentration of electrons as majority carriers.
P-type silicon has a higher concentration of holes as majority carriers.
Carrier concentration, mobility, conductivity, and temperature dependence are important factors in determining the behavior of charge carriers in doped semiconductors.
Optimizing doping concentration and efficiency is crucial for semiconductor device performance.

Slide 21: Band Diagram of N-type Silicon

The band diagram of N-type silicon shows the energy levels of the conduction and valence bands.
The Fermi level, given by Ef, represents the energy level at which electrons have a 50% probability of being occupied.
In N-type silicon, the Fermi level rises closer to the conduction band due to the extra electrons from the donor impurities.
The energy gap, denoted by Eg, is the difference between the conduction and valence band energies.
The band diagram helps visualize the behavior of charge carriers in the material.

Slide 22: Band Diagram of P-type Silicon

The band diagram of P-type silicon also shows the energy levels of the conduction and valence bands.
In P-type silicon, the Fermi level drops closer to the valence band due to the presence of acceptor impurities creating holes.
The energy levels of the impurity energy states are shown between the valence band and the Fermi level.
The band diagram aids in understanding the behavior of holes in the material.

Slide 23: Charge Neutralization in Intrinsic Silicon

In intrinsic silicon, where there are no impurities, the Fermi level is centered within the energy gap.
This balance ensures an equal number of electrons and holes.
According to the principle of charge neutrality, the positive charges (from ionized donor impurities) in N-type silicon are balanced by the negative charges (from free electrons).
Similarly, the negative charges (from ionized acceptor impurities) in P-type silicon are balanced by the positive charges (from free holes).
The overall charge neutrality is maintained in doped semiconductors.

Slide 24: Forward Bias in a pn Junction

Applying a forward bias to a pn junction allows electric current to flow.
In N-type silicon, the extra electrons are repelled by the negative terminal of the battery, while holes are attracted by the positive terminal.
In P-type silicon, the holes are repelled by the positive terminal, while electrons are attracted by the negative terminal.
This results in the majority charge carriers crossing the depletion region and allowing current flow through the junction.

Slide 25: Reverse Bias in a pn Junction

Applying a reverse bias to a pn junction prevents electric current flow.
In N-type silicon, the extra electrons are attracted to the positive terminal of the battery, while holes are attracted to the negative terminal.
In P-type silicon, the holes are attracted to the negative terminal, while electrons are attracted to the positive terminal.
This widens the depletion region, creating a barrier to current flow.
Reverse biasing is commonly used to control the behavior of diodes and other semiconductor devices.

Slide 26: Diode Characteristics

A diode is a two-terminal device formed by a pn junction.
When forward biased, a diode allows current to flow.
When reverse biased, a diode blocks current flow.
The curve showing the relationship between the voltage across a diode and the current flowing through it is called the diode characteristic curve.
The shape of the curve is determined by the properties of the pn junction and the material used.

Slide 27: Equations for Diode Current

The current flowing through a forward-biased diode can be approximated using the Shockley diode equation: I = Is * (exp(V / (n * Vt)) - 1), where I is the diode current, Is is the reverse saturation current, V is the voltage across the diode, n is the ideality factor, and Vt is the thermal voltage.
The reverse saturation current is a parameter that depends on the characteristics of the diode and the temperature.
The ideality factor accounts for non-ideal behavior of the diode, such as recombination processes.
The thermal voltage is given by Vt = (k * T) / q, where k is Boltzmann’s constant, T is the temperature in Kelvin, and q is the charge of an electron.

Slide 28: Breakdown Voltage

Breakdown voltage is the voltage at which a pn junction breaks down and allows a large amount of current to flow.
There are two types of breakdown: Zener breakdown and avalanche breakdown.
Zener breakdown occurs in heavily doped junctions, while avalanche breakdown occurs in lightly doped junctions.
This breakdown phenomenon is utilized in Zener diodes and avalanche diodes, which are designed to operate in the breakdown region for specific applications.

Slide 29: Bipolar Junction Transistor (BJT)

The bipolar junction transistor (BJT) is a three-layer semiconductor device formed by two pn junctions.
It consists of two types: NPN and PNP transistors.
The NPN transistor is formed by sandwiching a thin P-type region between two N-type regions, while the PNP transistor is formed by sandwiching a thin N-type region between two P-type regions.
The BJT functions as an amplifier or a switch in electronic circuits.
It operates based on the control of current flow through the transistor by varying the voltage applied to its three terminals: the emitter, base, and collector.

Slide 30: Field-Effect Transistor (FET)

The field-effect transistor (FET) is another type of three-terminal semiconductor device.
It comes in two primary forms: the metal-oxide-semiconductor field-effect transistor (MOSFET) and the junction field-effect transistor (JFET).
The FET operates by controlling the flow of charge carriers through an electric field.
The MOSFET utilizes a voltage applied to a gate electrode to create an electric field to control the flow of majority charge carriers.
The JFET uses a voltage applied across a pn junction to control the flow of majority charge carriers.
FETs are commonly used in amplifiers, switches, and integrated circuits.