2.1 Band theory and energy bands in semiconductors

Band theory is the backbone of semiconductor physics. It explains how electrons behave in solid materials, focusing on energy bands that determine electrical properties. Understanding these concepts is crucial for grasping how semiconductors work in electronic devices.

Energy bands, like valence and conduction bands, play a key role in semiconductor behavior. The gap between these bands, called the bandgap, affects how easily electrons can move and conduct electricity. This knowledge is essential for designing and optimizing semiconductor devices.

Band Structure

Energy Bands in Semiconductors

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• Valence band represents the highest occupied energy band in a semiconductor at absolute zero temperature
  • Consists of energy levels filled with electrons bound to individual atoms
  • Electrons in the valence band do not participate in conduction under normal conditions
• Conduction band is the lowest unoccupied energy band in a semiconductor
  • Electrons in the conduction band are free to move throughout the crystal, contributing to electrical conductivity
  • At absolute zero, the conduction band is empty, and the semiconductor behaves as an insulator
• Bandgap refers to the energy difference between the top of the valence band and the bottom of the conduction band
  • Determines the energy required for an electron to transition from the valence band to the conduction band
  • Bandgap energy varies depending on the semiconductor material (silicon: 1.12 eV, germanium: 0.67 eV)

Electron Transitions and Energy Levels

• Energy levels within the valence and conduction bands represent the allowed energy states for electrons in a semiconductor
• Electrons can transition from the valence band to the conduction band by absorbing energy greater than or equal to the bandgap
  • Absorption of photons with sufficient energy can excite electrons across the bandgap (photoelectric effect)
  • Thermal energy can also promote electrons to the conduction band, increasing conductivity at higher temperatures
• When an electron transitions to the conduction band, it leaves behind a positively charged vacancy called a hole in the valence band
  • Holes can be treated as positive charge carriers that contribute to electrical conductivity

Bandgap Properties

Direct and Indirect Bandgaps

• Direct bandgap semiconductors have the minimum of the conduction band and the maximum of the valence band at the same crystal momentum (k-value)
  • Examples of direct bandgap semiconductors include gallium arsenide (GaAs) and indium phosphide (InP)
  • Direct bandgap materials are more efficient for optical applications, such as light-emitting diodes (LEDs) and laser diodes
• Indirect bandgap semiconductors have the minimum of the conduction band and the maximum of the valence band at different crystal momenta
  • Examples of indirect bandgap semiconductors include silicon (Si) and germanium (Ge)
  • Indirect bandgap materials are less efficient for optical applications but are widely used in electronic devices

Density of States and Effective Mass

• Density of states (DOS) describes the number of electronic states per unit energy and volume in a semiconductor
  • DOS depends on the bandgap and the effective mass of charge carriers
  • Higher DOS near the band edges leads to more efficient absorption and emission of light
• Effective mass is a concept used to describe the behavior of charge carriers in a semiconductor as if they were free particles with a modified mass
  • Effective mass depends on the curvature of the energy bands near the band edges
  • Lighter effective mass results in higher carrier mobility and better transport properties

Fermi Level

Fermi Level and Carrier Concentrations

• Fermi level represents the energy level at which the probability of an electron occupying a state is 50% at thermal equilibrium
  • In intrinsic semiconductors, the Fermi level lies near the middle of the bandgap
  • Doping a semiconductor with impurities can shift the Fermi level closer to the conduction band (n-type) or valence band (p-type)
• The position of the Fermi level relative to the band edges determines the concentration of electrons in the conduction band and holes in the valence band
  • Carrier concentrations can be calculated using the Fermi-Dirac distribution function
  • Higher temperatures lead to more carriers being thermally excited across the bandgap, increasing the intrinsic carrier concentration

Fermi Level in Doped Semiconductors

• In n-type semiconductors, the Fermi level is closer to the conduction band, indicating a higher concentration of electrons than holes
  • Dopants such as phosphorus (P) or arsenic (As) introduce excess electrons, shifting the Fermi level upwards
• In p-type semiconductors, the Fermi level is closer to the valence band, indicating a higher concentration of holes than electrons
  • Dopants such as boron (B) or gallium (Ga) introduce excess holes, shifting the Fermi level downwards
• The position of the Fermi level in doped semiconductors affects the electrical properties, such as conductivity and carrier transport