Semiconductors and doping | Solid State Physics Class Notes

Semiconductors are materials with unique electrical properties that bridge the gap between conductors and insulators. They form the foundation of modern electronics, enabling the creation of devices like transistors, diodes, and solar cells. Their conductivity can be controlled through temperature, light, or doping. The study of semiconductors involves understanding their crystal structure, energy bands, and carrier concentrations. Doping, the intentional introduction of impurities, allows for precise control of electrical properties. This knowledge is crucial for designing and optimizing electronic devices used in various applications.

6.1

Intrinsic and extrinsic semiconductors

6.2

n-type and p-type doping

6.3

Carrier concentration and mobility

6.4

p-n junctions

6.5

Semiconductor devices

unit 6 review

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 ( $n_i$ $n_{i}$ ) 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 ( $\sigma$ $σ$ ) 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

Solid State Physics Unit 6 ReviewSemiconductors and doping