Glossary

11.5 Semiconductors and Doping

4 min read•august 16, 2024

Semiconductors are the backbone of modern electronics, bridging the gap between conductors and insulators. Their unique properties, controlled by doping, allow for the creation of various electronic devices that power our digital world.

Doping involves adding impurities to pure semiconductors, altering their electrical properties. This process creates n-type and p-type semiconductors, which form the basis for diodes, transistors, and solar cells. Understanding doping is crucial for grasping semiconductor behavior and applications.

Electronic Structure of Semiconductors

Band Structure and Energy Levels

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  • Intrinsic semiconductors consist of pure crystalline materials from groups IV, III-V, or II-VI of the periodic table (, )
  • Electronic band structure comprises:
    • Valence band (filled with at absolute zero)
    • Conduction band (empty at absolute zero)
    • Forbidden energy gap () separating the two bands
  • sits approximately in the middle of the band gap
  • Band gap energy typically ranges from 0.1 eV to 4 eV
    • Silicon band gap measures approximately 1.1 eV at room temperature

Thermal Excitation and Conductivity

  • Temperature increase excites electrons across the band gap
    • Creates electron-hole pairs
    • Enhances electrical
  • Conductivity falls between metals and insulators
    • Range: 10^-8 to 10^3 (Ω⋅m)^-1
  • Electron-hole pair generation follows the equation: ni=NcNve−Eg/2kTn_i = \sqrt{N_c N_v} e^{-E_g/2kT}
    • nin_i: intrinsic carrier concentration
    • NcN_c, NvN_v: effective density of states in conduction and valence bands
    • EgE_g: band gap energy
    • kk: Boltzmann constant
    • TT: absolute temperature

Doping and Semiconductor Properties

Doping Process and Impurities

  • Doping introduces impurity atoms into the semiconductor crystal lattice
  • Dopant atoms differ in valence electrons from host material
    • Donor impurities (n-type): one more valence electron (phosphorus in silicon)
    • Acceptor impurities (p-type): one fewer valence electron (boron in silicon)
  • Dopant concentration ranges from parts per million to parts per billion
  • Doping creates additional energy levels within the band gap
    • Donor levels near conduction band
    • Acceptor levels near valence band

Effects on Electrical Properties

  • Doping significantly increases semiconductor conductivity
    • Adds charge carriers (electrons or )
  • Shifts Fermi level position
    • N-type: closer to conduction band
    • P-type: closer to valence band
  • Enables precise control of electrical properties
    • Facilitates creation of various electronic devices (transistors, solar cells)
  • Doped semiconductor conductivity follows the equation: σ=q(nμn+pμp)\sigma = q(n\mu_n + p\mu_p)
    • σ\sigma: conductivity
    • qq: elementary charge
    • nn, pp: electron and hole concentrations
    • μn\mu_n, μp\mu_p: electron and hole mobilities

N-type vs P-type Semiconductors

N-type Semiconductors

  • Created by doping with donor impurities (phosphorus, arsenic)
  • Majority charge carriers electrons
  • Fermi level shifts closer to conduction band
  • Conductivity increases with temperature
    • Thermal excitation of electrons from donor levels to conduction band
  • Electron concentration in n-type semiconductor: n=ND+ni2NDn = N_D + \frac{n_i^2}{N_D}
    • NDN_D: donor concentration
    • nin_i: intrinsic carrier concentration

P-type Semiconductors

  • Created by doping with acceptor impurities (boron, gallium)
  • Majority charge carriers holes
  • Fermi level shifts closer to valence band
  • Conductivity increases with temperature
    • Thermal excitation of electrons from valence band to acceptor levels
  • Hole concentration in p-type semiconductor: p=NA+ni2NAp = N_A + \frac{n_i^2}{N_A}
    • NAN_A: acceptor concentration
    • nin_i: intrinsic carrier concentration

Semiconductor Junctions and Devices

  • Junction between n-type and p-type semiconductors forms basis for many devices
    • Diodes: allow current flow in one direction
    • Transistors: amplify or switch electronic signals
    • Solar cells: convert light into electrical energy
  • PN junction characteristics depend on doping levels and applied voltage
    • Built-in potential: Vbi=kTqln⁡(NANDni2)V_{bi} = \frac{kT}{q} \ln\left(\frac{N_A N_D}{n_i^2}\right)

Temperature Dependence of Carrier Concentration

Intrinsic Semiconductors

  • Carrier concentration strongly depends on temperature
  • Follows Arrhenius equation: ni∝e−Eg/2kTn_i \propto e^{-E_g/2kT}
    • nin_i: intrinsic carrier concentration
    • EgE_g: band gap energy
    • kk: Boltzmann constant
    • TT: absolute temperature
  • Low temperatures yield very low carrier concentration
    • Insufficient thermal energy to excite electrons across band gap
  • Increasing temperature exponentially increases carrier concentration
    • Thermal generation of electron-hole pairs

Doped Semiconductors

  • Carrier concentration shows less temperature dependence at low to moderate temperatures
    • Ionization of dopant atoms dominates
  • High temperatures cause intrinsic carrier concentration to approach or exceed dopant concentration
    • Semiconductor behaves more like intrinsic material
  • Temperature dependence affects device parameters
    • Reverse saturation current in diodes
    • gain
  • Carrier freeze-out occurs at very low temperatures
    • Dopant atoms become un-ionized
    • Carrier concentration decreases rapidly

Design Implications

  • Understanding temperature dependence crucial for reliable semiconductor devices
    • Operate over wide temperature ranges (automotive, aerospace applications)
  • Temperature compensation techniques employed
    • Bandgap reference circuits
    • Temperature-dependent biasing
  • Thermal management essential in high-power devices
    • Heat sinks, active cooling systems

Key Terms to Review (16)

Band gap: The band gap is the energy difference between the top of the valence band and the bottom of the conduction band in a solid material. This gap plays a critical role in determining the electrical conductivity of materials, as it dictates whether electrons can move freely under applied energy, such as thermal or light energy. Understanding the band gap is essential for analyzing how different materials behave as conductors, semiconductors, or insulators.
Band Theory: Band theory is a theoretical model that explains the electronic properties of solids by describing the range of energy levels that electrons can occupy. It helps in understanding how materials can conduct electricity, behave as insulators, or act as semiconductors based on the arrangement and energy of electrons in different bands, notably the valence band and conduction band.
Conductivity: Conductivity is the ability of a material to conduct electric current, which is influenced by the presence of charged particles that can move freely within the material. In semiconductors, conductivity can be manipulated through processes like doping, where impurities are introduced to enhance or modify the material's electrical properties. This characteristic plays a critical role in the functionality of electronic devices and components that rely on controlled flow of electricity.
Diode: A diode is a semiconductor device that allows current to flow in one direction while blocking it in the opposite direction. This unidirectional behavior is fundamental in various electronic applications, such as rectification, signal modulation, and voltage regulation. Diodes are typically made from semiconductor materials like silicon or germanium and can be engineered by introducing impurities through a process known as doping.
Drude Model: The Drude Model is a classical theory that describes the electrical and thermal properties of metals by treating conduction electrons as a gas of free particles that can move freely through a lattice of positively charged ions. This model provides insight into the behavior of electrons in conductive materials, linking their motion to properties such as electrical conductivity and heat capacity.
Electrons: Electrons are subatomic particles with a negative electric charge, fundamental to the structure of atoms and key players in chemical bonding and electrical conductivity. Their behavior is crucial in determining the electrical properties of materials, especially in semiconductors, where the movement and availability of electrons are manipulated through processes like doping to create materials with desired conductive properties.
Extrinsic Semiconductor: An extrinsic semiconductor is a type of semiconductor that has been intentionally doped with impurities to modify its electrical properties, enhancing its conductivity. This process introduces either donor or acceptor atoms, allowing the semiconductor to have more free charge carriers than pure intrinsic semiconductors, which significantly influences its performance in electronic devices.
Fermi Level: The Fermi level is the energy level at which the probability of finding an electron is 50% at absolute zero temperature. This concept is crucial for understanding the electronic properties of materials, especially in semiconductors and how they behave when doped with impurities.
Germanium: Germanium is a chemical element with the symbol Ge and atomic number 32, classified as a metalloid. It plays a vital role in electronics as a semiconductor, primarily used in transistors and diodes, which are essential for modern electronic devices. Its properties allow it to be doped with other elements to modify its electrical conductivity, making it fundamental in the development of various electronic components.
Holes: In semiconductor physics, holes are the absence of an electron in a crystal lattice, which acts as a positive charge carrier. They occur when electrons gain enough energy to leave their original positions, creating vacancies that can move through the lattice and facilitate electrical conduction. Holes are crucial in understanding p-type semiconductors, where they dominate the charge transport mechanism.
Intrinsic semiconductor: An intrinsic semiconductor is a pure semiconductor material that has no significant dopant atoms present, which means its electrical properties are determined solely by its own atomic structure. The behavior of intrinsic semiconductors is characterized by a balanced number of electrons and holes at absolute zero temperature, leading to low electrical conductivity. As the temperature increases, more charge carriers are generated, allowing for greater conductivity.
N-type doping: n-type doping is a process in which semiconductor materials are infused with elements that have more valence electrons than the semiconductor itself, typically three or four additional electrons. This addition increases the number of free electrons available for conduction, which enhances the electrical properties of the semiconductor. As a result, n-type semiconductors have an excess of negative charge carriers (electrons), making them crucial for various electronic devices like diodes and transistors.
P-type doping: P-type doping is a process in semiconductor physics where a semiconductor material is infused with acceptor impurities, typically from Group III of the periodic table, to create 'holes' in the material's electronic structure. This results in a material that has an abundance of positive charge carriers, or holes, which can move freely and contribute to electrical conduction.
Resistivity: Resistivity is a fundamental property of materials that quantifies how strongly a material opposes the flow of electric current. It is an intrinsic property, meaning it depends only on the material itself and not on its shape or size. In the context of semiconductors, resistivity plays a crucial role in determining how well a semiconductor can conduct electricity, which can be altered by the process of doping.
Silicon: Silicon is a chemical element with the symbol Si and atomic number 14, widely recognized as a fundamental material used in the production of semiconductors. This versatile element plays a critical role in electronics, particularly in integrated circuits and photovoltaic cells, by allowing precise control over electrical conductivity through doping processes that introduce impurities into its crystal structure.
Transistor: A transistor is a semiconductor device that can amplify and switch electronic signals, serving as a fundamental building block in modern electronic circuits. It can control the flow of current or voltage and is crucial in devices like computers, radios, and amplifiers. Transistors can be found in two main types: bipolar junction transistors (BJTs) and field-effect transistors (FETs), each with unique operational principles.
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