⚛️Solid State Physics Unit 6 – Semiconductors and doping

What are Semiconductors?

• Materials with electrical conductivity between conductors (metals) and insulators
• Conductivity can be controlled by temperature, light, or impurities (doping)
• Most commonly used semiconductors are silicon (Si) and germanium (Ge)
• Semiconductors form the basis of modern electronics (transistors, diodes, solar cells)
• Conductivity increases with temperature, unlike metals
• Have a small energy gap between valence and conduction bands
• Electrons can be excited from valence to conduction band by thermal energy or light
  • Creates mobile charge carriers (electrons and holes)

Crystal Structure of Semiconductors

• Most semiconductors have a diamond cubic crystal structure
  • Each atom is covalently bonded to four nearest neighbors
  • Examples: silicon (Si), germanium (Ge)
• Some semiconductors have a zincblende structure (GaAs, InP)
  • Similar to diamond cubic, but with alternating types of atoms
• Crystal structure determines the electronic properties
  • Affects the energy band structure and bandgap
• Lattice vibrations (phonons) play a role in carrier scattering and mobility
• Defects and impurities in the crystal structure can alter the electronic properties
  • Introduces energy levels within the bandgap
  • Can be used for doping to control conductivity

Energy Bands and Band Gaps

• Electronic states in a semiconductor form energy bands
  • Valence band: highest occupied energy band at 0 K
  • Conduction band: lowest unoccupied energy band at 0 K
• Energy gap (bandgap) separates valence and conduction bands
  • Determines the electrical and optical properties
  • Examples: Si (1.1 eV), Ge (0.67 eV), GaAs (1.42 eV)
• Electrons can be excited from valence to conduction band
  • Requires energy greater than the bandgap
  • Creates mobile charge carriers (electrons and holes)
• Direct and indirect bandgaps
  • Direct: minimum of conduction band aligns with maximum of valence band in k-space
    • Examples: GaAs, InP
  • Indirect: minimum and maximum do not align in k-space
    • Examples: Si, Ge
  • Affects optical properties and device applications

Intrinsic Semiconductors

• Pure semiconductor without intentional doping
• Charge carriers are generated by thermal excitation
  • Electrons excited from valence to conduction band
  • Leaves behind positively charged holes in valence band
• Intrinsic carrier concentration ($n_i$) depends on temperature and bandgap
  • $n_i = \sqrt{N_c N_v} \exp(-E_g/2k_BT)$
  • $N_c$, $N_v$: effective density of states in conduction and valence bands
  • $E_g$: bandgap energy
  • $k_B$: Boltzmann constant, $T$: temperature
• Equal concentration of electrons and holes ($n = p = n_i$)
• Intrinsic Fermi level lies near the middle of the bandgap
• Conductivity is low compared to doped semiconductors

Doping: N-type and P-type

• Intentional introduction of impurities to control conductivity
• N-type doping: introduces donor impurities
  • Donate electrons to the conduction band
  • Examples: phosphorus (P), arsenic (As) in silicon
  • Creates mobile negative charge carriers (electrons)
• P-type doping: introduces acceptor impurities
  • Accept electrons from the valence band, creating holes
  • Examples: boron (B), gallium (Ga) in silicon
  • Creates mobile positive charge carriers (holes)
• Doping concentration determines the majority carrier type and concentration
  • N-type: electrons are majority carriers, holes are minority carriers
  • P-type: holes are majority carriers, electrons are minority carriers
• Doping shifts the Fermi level towards the conduction band (n-type) or valence band (p-type)

Carrier Concentration and Fermi Level

• Carrier concentration: number of mobile charge carriers per unit volume
  • Electrons in conduction band, holes in valence band
• In intrinsic semiconductors, electron and hole concentrations are equal ($n = p = n_i$)
• Doping changes the carrier concentrations
  • N-type: $n \gg p$, electron concentration increases
  • P-type: $p \gg n$, hole concentration increases
• Fermi level: energy level with 50% probability of occupation at thermal equilibrium
  • Intrinsic: near the middle of the bandgap
  • N-type: shifts towards the conduction band
  • P-type: shifts towards the valence band
• Carrier concentrations and Fermi level depend on doping concentration and temperature
  • Increasing temperature increases intrinsic carrier concentration
  • High doping concentrations can lead to degenerate semiconductors
    • Fermi level moves into the conduction band (n-type) or valence band (p-type)

Electrical Properties and Conductivity

• Conductivity ($\sigma$) depends on carrier concentrations and mobilities
  • $\sigma = q(n\mu_n + p\mu_p)$
  • $q$: elementary charge
  • $n$, $p$: electron and hole concentrations
  • $\mu_n$, $\mu_p$: electron and hole mobilities
• Mobility: ease of carrier movement in the presence of an electric field
  • Depends on scattering mechanisms (lattice vibrations, impurities, defects)
  • Generally decreases with increasing temperature and doping concentration
• Resistivity ($\rho$): inverse of conductivity ($\rho = 1/\sigma$)
• Doping increases conductivity by increasing the majority carrier concentration
  • N-type: increased electron concentration
  • P-type: increased hole concentration
• Temperature dependence of conductivity
  • Intrinsic: increases with temperature due to increased carrier generation
  • Extrinsic (doped): decreases with temperature due to reduced mobility

Applications in Electronics

• Semiconductors are the foundation of modern electronics
• PN junction: interface between p-type and n-type regions
  • Basis for diodes, solar cells, LEDs
  • Rectification: allows current flow in one direction
• Bipolar junction transistor (BJT): three-layer device (npn or pnp)
  • Amplification and switching applications
• Field-effect transistor (FET): controls current with an electric field
  • Examples: MOSFET, JFET, HEMT
  • Low power consumption, high input impedance
• Integrated circuits (ICs): miniaturized electronic circuits on a semiconductor substrate
  • Enables complex digital and analog systems on a single chip
  • Examples: microprocessors, memory chips, sensors
• Optoelectronic devices: convert between light and electrical signals
  • Examples: solar cells, photodiodes, LEDs, lasers
• Power electronics: high-power, high-efficiency switching devices
  • Examples: power diodes, thyristors, IGBTs
  • Used in power conversion, motor control, and renewable energy systems