Semiconductor Materials

Unit IV: Semiconductor Materials

Duration: 3 Hours | Credit: ELX 133.3

Introduction to Semiconductors

Semiconductors are materials with electrical properties between conductors and insulators. They form the basis of all modern electronic devices including transistors, diodes, and integrated circuits.

Energy Band Theory

Energy band theory explains why some materials conduct electricity and others don't.

Electron Energy Levels

• Valence Band: Outermost electron shells (electrons involved in bonding)
• Conduction Band: Band where electrons are free to move
• Forbidden Gap (Band Gap): Energy difference between valence and conduction bands
• Fermi Level (E_F): Energy level where probability of electron occupancy is 50%

Band Gap Values

• Conductors: No band gap (conduction and valence bands overlap)
• Semiconductors: Small band gap (typically 1-3 eV at room temperature)
• Insulators: Large band gap (typically > 5 eV)

Common Semiconductors:

• Silicon (Si): Band gap = 1.12 eV at 25°C (most common)
• Germanium (Ge): Band gap = 0.67 eV at 25°C
• Gallium Arsenide (GaAs): Band gap = 1.42 eV at 25°C

Intrinsic Semiconductors

Intrinsic (pure) semiconductors have no impurities. At absolute zero (0 K), they act as insulators. As temperature increases, electrons gain energy and jump to the conduction band.

Intrinsic Carrier Concentration

n_i = √(N_c × N_v) × exp(-E_g/(2k_BT))

Where:

• N_c, N_v: Effective density of states in conduction and valence bands
• E_g: Band gap energy
• k_B: Boltzmann's constant = 1.38 × 10^-23 J/K
• T: Absolute temperature in Kelvin

Intrinsic Conductivity

σ_i = q × n_i × (μ_e + μ_h)

Where μ_e and μ_h are electron and hole mobilities respectively.

Extrinsic Semiconductors (Doped Semiconductors)

Extrinsic semiconductors are created by adding impurities (dopants) to intrinsic semiconductors in a controlled process called doping.

N-Type Semiconductors (Electron-Doped)

Created by adding pentavalent (5 valence electrons) donor impurities to silicon:

• Common Dopants: Phosphorus (P), Arsenic (As), Antimony (Sb)
• Majority Carriers: Electrons (negative charges)
• Minority Carriers: Holes (positive charges)
• Fermi Level Position: Closer to conduction band
• Conductivity: Higher than intrinsic silicon

P-Type Semiconductors (Hole-Doped)

Created by adding trivalent (3 valence electrons) acceptor impurities to silicon:

• Common Dopants: Boron (B), Aluminum (Al), Indium (In)
• Majority Carriers: Holes (positive charges)
• Minority Carriers: Electrons (negative charges)
• Fermi Level Position: Closer to valence band
• Conductivity: Higher than intrinsic silicon

Doping Levels and Conductivity

Compensation in Semiconductors

When both donors and acceptors are present in a semiconductor, they compensate each other:

• Excess electrons from donors neutralize the holes from acceptors
• The net carrier concentration determines the semiconductor type (n-type or p-type)
• The dopant that produces more carriers determines whether it's n-type or p-type

Conductivity Dependence on Doping

σ = σ₀ × (N_d or N_a) / n_i (approximately linear with dopant concentration)

Carrier Concentration and Fermi Level

Charge Neutrality Condition

p + N_d = n + N_a

This equation relates electron concentration (n), hole concentration (p), donor concentration (N_d), and acceptor concentration (N_a).

Fermi Level Position

The Fermi level position determines the ratio of electrons to holes:

n × p = n_i² (Mass Action Law)

Temperature Effects on Semiconductors

Temperature Dependence of Band Gap

E_g(T) = E_g(0) - (αT²)/(T + β)

For silicon: E_g decreases by approximately 2.3 mV per degree Celsius.

Temperature Dependence of Intrinsic Carrier Concentration

n_i approximately doubles for every 10-20°C increase in temperature.

Mobility and Conductivity

Carrier Mobility

μ = q × τ / m*

Where:

• q: Electron charge
• τ: Mean relaxation time (scattering time)
• m*: Effective mass of the carrier

Mobility vs. Temperature

• At low temperatures: Limited by ionized impurity scattering
• At high temperatures: Limited by lattice vibration scattering
• Silicon electron mobility at 300K: approximately 1350 cm²/V·s
• Silicon hole mobility at 300K: approximately 480 cm²/V·s

Summary Table: Semiconductor Properties

Key Takeaways

• Semiconductors have a small band gap (1-3 eV) between valence and conduction bands
• N-type semiconductors have excess electrons (negative charge carriers)
• P-type semiconductors have excess holes (positive charge carriers)
• Doping concentration controls the conductivity of semiconductors
• The Fermi level position indicates the majority carrier type
• Carrier mobility decreases with increasing temperature due to scattering
• Band gap and intrinsic carrier concentration decrease with increasing temperature