6.1 Intrinsic and extrinsic semiconductors

Semiconductors are the backbone of modern electronics, bridging the gap between conductors and insulators. Their unique properties allow for precise control of electrical conductivity through doping, enabling the creation of various electronic devices that power our digital world.

This section explores intrinsic and extrinsic semiconductors, delving into their properties, charge transport mechanisms, and applications. Understanding these concepts is crucial for grasping how semiconductors function in devices like transistors, solar cells, and LEDs that shape our technological landscape.

Semiconductor materials

• Semiconductor materials are essential components in modern electronic devices and have unique electrical properties that allow them to conduct electricity under certain conditions
• The electrical conductivity of semiconductors falls between that of conductors and insulators, and can be precisely controlled through doping and other techniques
• Semiconductors are used in a wide range of applications, including computers, smartphones, solar cells, and LED lighting

Elemental semiconductors

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• Consist of a single element, typically from group IV of the periodic table (silicon, germanium)
• Silicon is the most widely used elemental semiconductor due to its abundance, low cost, and favorable electronic properties
• Elemental semiconductors have a diamond cubic crystal structure, which contributes to their unique electronic properties

Compound semiconductors

• Formed by combining elements from groups III and V (GaAs, InP) or groups II and VI (CdTe, ZnSe) of the periodic table
• Offer a wider range of electronic and optical properties compared to elemental semiconductors
• Compound semiconductors are used in specialized applications such as high-speed electronics, optoelectronics, and solar cells

Intrinsic semiconductors

• Intrinsic semiconductors are pure semiconductor materials without any intentional doping
• The electrical properties of intrinsic semiconductors are determined by the material's inherent crystal structure and electronic band structure
• Understanding the behavior of intrinsic semiconductors is crucial for designing and optimizing semiconductor devices

Properties of intrinsic semiconductors

• Have an equal number of electrons and holes, which are the charge carriers responsible for electrical conduction
• Exhibit relatively low electrical conductivity compared to metals
• The concentration of charge carriers is strongly dependent on temperature

Energy band structure

• Semiconductors have a band gap between the valence band and the conduction band
• The band gap represents the minimum energy required for an electron to move from the valence band to the conduction band
• The size of the band gap determines the electrical and optical properties of the semiconductor (silicon: 1.1 eV, germanium: 0.67 eV)

Charge carrier generation

• Electrons can be excited from the valence band to the conduction band by absorbing energy (thermal, optical, or electrical)
• When an electron is excited to the conduction band, it leaves behind a positively charged hole in the valence band
• The generation of electron-hole pairs is crucial for the operation of semiconductor devices

Intrinsic carrier concentration

• Denoted by $n_i$, represents the number of electrons (or holes) per unit volume in an intrinsic semiconductor
• Intrinsic carrier concentration is determined by the band gap and temperature of the semiconductor
• For silicon at room temperature, $n_i \approx 1.5 \times 10^{10} cm^{-3}$

Temperature dependence of carrier concentration

• The intrinsic carrier concentration increases exponentially with temperature
• This is because more thermal energy is available to excite electrons across the band gap at higher temperatures
• The temperature dependence is described by the equation: $n_i = A T^{3/2} e^{-E_g/2k_BT}$, where $A$ is a constant, $T$ is the absolute temperature, $E_g$ is the band gap, and $k_B$ is the Boltzmann constant

Fermi level in intrinsic semiconductors

• The Fermi level represents the energy at which the probability of finding an electron is 0.5
• In intrinsic semiconductors, the Fermi level lies approximately in the middle of the band gap
• The position of the Fermi level relative to the band edges determines the electrical properties of the semiconductor

Extrinsic semiconductors

• Extrinsic semiconductors are created by intentionally introducing impurities (dopants) into an intrinsic semiconductor
• Doping allows for precise control over the electrical properties of semiconductors, enabling the fabrication of various electronic devices
• The type and concentration of dopants determine the majority charge carriers and the conductivity of the semiconductor

N-type vs P-type doping

• N-type doping involves introducing impurities with extra valence electrons (donors) into the semiconductor (phosphorus, arsenic)
• P-type doping involves introducing impurities with fewer valence electrons (acceptors) into the semiconductor (boron, gallium)
• N-type semiconductors have electrons as the majority charge carriers, while P-type semiconductors have holes as the majority charge carriers

Donor and acceptor impurities

• Donor impurities have one more valence electron than the host semiconductor atom
• Acceptor impurities have one fewer valence electron than the host semiconductor atom
• Donor impurities create energy levels near the conduction band, while acceptor impurities create energy levels near the valence band

Energy levels of dopants

• Donor energy levels are typically a few meV below the conduction band (phosphorus in silicon: 45 meV)
• Acceptor energy levels are typically a few meV above the valence band (boron in silicon: 45 meV)
• The small energy difference between the dopant levels and the respective bands allows for easy thermal ionization of the dopants

Carrier concentration in extrinsic semiconductors

• The majority carrier concentration in extrinsic semiconductors is approximately equal to the dopant concentration
• For example, if the donor concentration is $N_D = 10^{16} cm^{-3}$, then the electron concentration in the n-type semiconductor will be $n \approx N_D$
• The minority carrier concentration is much lower than the majority carrier concentration and is determined by the law of mass action: $n_0 p_0 = n_i^2$

Majority vs minority carriers

• Majority carriers are the charge carriers (electrons or holes) that are most abundant in the semiconductor
• Minority carriers are the charge carriers that are less abundant in the semiconductor
• The type of majority carrier depends on the type of doping (electrons for n-type, holes for p-type)

Fermi level shifts in extrinsic semiconductors

• Doping shifts the Fermi level towards the conduction band (n-type) or valence band (p-type)
• The Fermi level in an n-type semiconductor is closer to the conduction band, while in a p-type semiconductor, it is closer to the valence band
• The shift in the Fermi level is determined by the doping concentration and temperature

Temperature dependence of extrinsic carrier concentration

• At low temperatures, the majority carrier concentration is approximately equal to the dopant concentration
• As temperature increases, the dopants become fully ionized, and the majority carrier concentration remains constant
• At high temperatures, intrinsic carrier generation becomes significant, and the semiconductor behaves like an intrinsic semiconductor

Heavy vs light doping

• Heavy doping refers to high dopant concentrations (typically > $10^{18} cm^{-3}$), while light doping refers to lower dopant concentrations
• Heavily doped semiconductors have a higher conductivity and a smaller depletion region in p-n junctions
• Lightly doped semiconductors have a lower conductivity and a larger depletion region in p-n junctions

Degeneracy and Fermi level

• In heavily doped semiconductors, the Fermi level can move into the conduction band (n-type) or valence band (p-type)
• When the Fermi level is within the bands, the semiconductor is said to be degenerate
• Degenerate semiconductors have a higher conductivity and exhibit metallic behavior

Compensation doping

• Compensation doping involves the introduction of both donor and acceptor impurities into the semiconductor
• The net doping concentration is determined by the difference between the donor and acceptor concentrations
• Compensation doping can be used to fine-tune the electrical properties of semiconductors

Charge transport in semiconductors

• Charge transport in semiconductors is governed by two main mechanisms: drift and diffusion
• Understanding charge transport is essential for designing and optimizing semiconductor devices, such as transistors and solar cells
• The electrical properties of semiconductors, such as conductivity and mobility, are determined by the characteristics of charge transport

Drift current

• Drift current is the flow of charge carriers (electrons or holes) in response to an applied electric field
• The drift velocity of charge carriers is proportional to the electric field strength and the carrier mobility
• The drift current density is given by $J_{drift} = q(n\mu_n + p\mu_p)E$, where $q$ is the elementary charge, $n$ and $p$ are the electron and hole concentrations, $\mu_n$ and $\mu_p$ are the electron and hole mobilities, and $E$ is the electric field strength

Diffusion current

• Diffusion current is the flow of charge carriers due to a concentration gradient
• Charge carriers tend to move from regions of high concentration to regions of low concentration
• The diffusion current density is given by $J_{diffusion} = qD_n\frac{dn}{dx} + qD_p\frac{dp}{dx}$, where $D_n$ and $D_p$ are the electron and hole diffusion coefficients, and $\frac{dn}{dx}$ and $\frac{dp}{dx}$ are the electron and hole concentration gradients

Carrier mobility

• Carrier mobility is a measure of how easily charge carriers can move through a semiconductor under the influence of an electric field
• Mobility depends on factors such as temperature, doping concentration, and scattering mechanisms (lattice vibrations, ionized impurities)
• Electron mobility is generally higher than hole mobility in semiconductors (silicon: $\mu_n \approx 1400 cm^2/Vs$, $\mu_p \approx 450 cm^2/Vs$ at room temperature)

Conductivity in intrinsic vs extrinsic semiconductors

• Conductivity is a measure of a material's ability to conduct electric current
• In intrinsic semiconductors, conductivity is determined by the intrinsic carrier concentration and the carrier mobilities: $\sigma = q(n_i\mu_n + n_i\mu_p)$
• In extrinsic semiconductors, conductivity is primarily determined by the majority carrier concentration and mobility: $\sigma \approx q(N_D\mu_n)$ for n-type and $\sigma \approx q(N_A\mu_p)$ for p-type

Hall effect in semiconductors

• The Hall effect is used to characterize the electrical properties of semiconductors, such as carrier concentration, mobility, and conductivity type (n-type or p-type)
• When a magnetic field is applied perpendicular to the current flow in a semiconductor, a transverse voltage (Hall voltage) develops due to the deflection of charge carriers
• The Hall coefficient, $R_H$, is defined as the ratio of the Hall voltage to the product of the current density and the magnetic field strength: $R_H = \frac{E_H}{JB}$
• The sign of the Hall coefficient indicates the type of majority carriers (negative for n-type, positive for p-type), and its magnitude is inversely proportional to the carrier concentration

Applications of semiconductors

• Semiconductors are the foundation of modern electronics and have revolutionized various fields, including computing, communication, and energy
• The unique properties of semiconductors, such as the ability to control their electrical conductivity and the presence of a band gap, enable the fabrication of a wide range of electronic devices
• Advances in semiconductor technology have led to the development of smaller, faster, and more efficient devices

PN junction diodes

• A p-n junction diode is formed by joining a p-type and an n-type semiconductor
• P-n junctions are the building blocks of many semiconductor devices, such as solar cells, LEDs, and transistors
• When a p-n junction is forward-biased, it allows current to flow, while under reverse bias, it blocks current (rectification)

Bipolar junction transistors (BJTs)

• BJTs are three-terminal devices consisting of two p-n junctions (npn or pnp)
• BJTs can be used as amplifiers or switches, controlling a large output current with a small input current
• The three terminals of a BJT are the emitter, base, and collector, and the current flow is controlled by the base-emitter and base-collector voltages

Field-effect transistors (FETs)

• FETs are three-terminal devices that use an electric field to control the conductivity of a semiconductor channel
• The two main types of FETs are junction field-effect transistors (JFETs) and metal-oxide-semiconductor field-effect transistors (MOSFETs)
• FETs are widely used in integrated circuits, such as microprocessors and memory devices, due to their low power consumption and scalability

Light-emitting diodes (LEDs)

• LEDs are p-n junction diodes that emit light when forward-biased
• The wavelength (color) of the emitted light depends on the band gap of the semiconductor material (GaAs, GaN, InGaN)
• LEDs are energy-efficient, long-lasting, and widely used in lighting, displays, and indicators

Solar cells and photovoltaics

• Solar cells are p-n junction devices that convert sunlight into electricity through the photovoltaic effect
• When light is absorbed in a solar cell, electron-hole pairs are generated, and the electric field at the p-n junction separates the charges, creating a current
• Solar cells are made from various semiconductor materials, such as silicon, GaAs, and perovskites, and are used in renewable energy applications

Semiconductor lasers

• Semiconductor lasers are p-n junction devices that emit coherent light through stimulated emission
• Common semiconductor laser materials include GaAs, InGaAs, and GaN
• Semiconductor lasers are compact, efficient, and widely used in fiber-optic communication, barcode scanners, and laser pointers

Integrated circuits and microelectronics

• Integrated circuits (ICs) are miniaturized electronic circuits fabricated on a semiconductor substrate, typically silicon
• ICs consist of numerous transistors, diodes, resistors, and capacitors interconnected to perform specific functions
• Advances in semiconductor processing and miniaturization have led to the development of complex ICs, such as microprocessors, memory chips, and system-on-chip (SoC) devices
• Microelectronics has enabled the proliferation of compact, high-performance electronic devices, such as smartphones, computers, and wearables