semiconductor physics unit 5 study guides

Basics of Semiconductors

• Semiconductors are materials with electrical conductivity between insulators and conductors
• Their conductivity can be controlled by doping with impurities (phosphorus, boron)
• Intrinsic semiconductors are pure materials without any added impurities
• Extrinsic semiconductors contain added impurities that change their electrical properties
• The most common semiconductors are silicon (Si) and germanium (Ge)
• Semiconductors have a band gap between the valence band and conduction band
• Electrons can be excited from the valence band to the conduction band by applying energy (heat, light)
  • This creates electron-hole pairs, which are responsible for electrical conduction

P-Type and N-Type Materials

• P-type semiconductors are doped with acceptor impurities (boron, gallium)
  • Acceptor impurities create holes in the valence band, which are the majority carriers
• N-type semiconductors are doped with donor impurities (phosphorus, arsenic)
  • Donor impurities provide extra electrons in the conduction band, which are the majority carriers
• The doping concentration determines the conductivity of the semiconductor
• Minority carriers are electrons in P-type and holes in N-type semiconductors
• The Fermi level in P-type semiconductors is closer to the valence band, while in N-type it is closer to the conduction band
• The majority carrier concentration is much higher than the minority carrier concentration
• The mobility of electrons is higher than that of holes due to their smaller effective mass

Formation of P-N Junctions

• A P-N junction is formed by bringing P-type and N-type semiconductors into contact
• Diffusion of majority carriers occurs across the junction due to the concentration gradient
  • Electrons diffuse from the N-type to the P-type region
  • Holes diffuse from the P-type to the N-type region
• Diffusion creates a depletion region near the junction, which is depleted of free carriers
• The diffusion of carriers leaves behind fixed ionized impurities (acceptors and donors)
• The fixed charges create an electric field that opposes further diffusion
• Drift current is generated by the electric field, which balances the diffusion current at equilibrium
• The P-N junction reaches thermal equilibrium when the Fermi levels align on both sides

Energy Band Diagrams

• Energy band diagrams represent the energy levels of the conduction and valence bands in a semiconductor
• In a P-N junction, the energy bands bend near the junction due to the built-in potential
• The built-in potential is caused by the electric field created by the fixed charges in the depletion region
• The Fermi level is constant throughout the P-N junction at thermal equilibrium
• The conduction and valence bands are shifted by the built-in potential
• The potential barrier prevents the flow of majority carriers across the junction at equilibrium
• The width of the depletion region depends on the doping concentrations and the applied voltage
• Under forward bias, the potential barrier is reduced, allowing current to flow

Depletion Region and Built-in Potential

• The depletion region is a space charge region formed near the P-N junction
• It is depleted of free carriers due to the diffusion of majority carriers
• The width of the depletion region depends on the doping concentrations and the applied voltage
• The built-in potential ($V_{bi}$) is the potential difference across the depletion region at equilibrium
• $V_{bi}$ is caused by the electric field created by the fixed charges in the depletion region
• The magnitude of $V_{bi}$ depends on the doping concentrations and the semiconductor material
• The depletion region acts as a potential barrier, preventing the flow of majority carriers at equilibrium
• The capacitance of the depletion region is important in various applications (varactor diodes)

Biasing P-N Junctions

• Forward bias is applied when the P-type region is connected to the positive terminal and the N-type to the negative terminal
  • Forward bias reduces the potential barrier and allows current to flow
• Reverse bias is applied when the P-type region is connected to the negative terminal and the N-type to the positive terminal
  • Reverse bias increases the potential barrier and the depletion region width
• Under forward bias, the diffusion current dominates, and the junction conducts
• Under reverse bias, the drift current dominates, and the junction acts as an insulator
• The applied voltage affects the width of the depletion region and the magnitude of the current
• The current-voltage relationship of a P-N junction is described by the Shockley diode equation
• Breakdown occurs under high reverse bias due to impact ionization or tunneling (Zener breakdown)

Current-Voltage Characteristics

• The current-voltage (I-V) characteristics of a P-N junction are described by the Shockley diode equation:
  • $I = I_s(e^{qV/kT} - 1)$, where $I_s$ is the reverse saturation current, $q$ is the electron charge, $V$ is the applied voltage, $k$ is Boltzmann's constant, and $T$ is the absolute temperature
• Under forward bias, the current increases exponentially with the applied voltage
• The forward bias current is mainly due to the diffusion of majority carriers
• Under reverse bias, the current is small and saturates at $-I_s$
• The reverse saturation current depends on the doping concentrations and the minority carrier lifetimes
• The ideal diode equation assumes negligible recombination and generation in the depletion region
• Real diodes deviate from the ideal behavior due to series resistance, leakage current, and high injection effects
• The I-V characteristics are temperature-dependent, with the current increasing with temperature

Applications and Devices

• P-N junctions are the building blocks of various semiconductor devices
• Diodes are the simplest P-N junction devices, used for rectification, switching, and protection
• Solar cells are P-N junctions that convert light energy into electrical energy (photovoltaic effect)
• Light-emitting diodes (LEDs) emit light when forward-biased, used for displays and lighting
• Bipolar junction transistors (BJTs) consist of two P-N junctions, used for amplification and switching
• Photodiodes are P-N junctions that generate current when exposed to light, used for detection and sensing
• Zener diodes are designed to operate in the reverse breakdown region, used for voltage regulation and reference
• Varactor diodes have a voltage-dependent capacitance, used for tuning and variable capacitance applications
• Schottky diodes are formed by a metal-semiconductor junction, having lower forward voltage drop and faster switching compared to P-N diodes