Valence Band

Filled band with valence e-. Ex: Si at 0K. Relevance: Bound states. Debate: Thermal excitation. Expanded: Top EV; max occupancy 8N states.

Conduction Band

Empty band above Eg. Ex: Free e- motion. Relevance: Conduction path. Additional: Bottom EC; min energy for conduction.

Energy Band Gap (Eg)

Gap VB-CB. Ex: Si 1.1 eV. Relevance: Classifies materials (<3eV semi). Expanded: Direct/indirect affects optical properties.

Intrinsic Semiconductor

Pure semi, \( n_e = n_h = n_i \). Ex: Pure Si. Relevance: Thermal carriers only. Additional: Fermi level mid-gap.

Extrinsic Semiconductor

Doped semi. Ex: n-Si. Relevance: Enhanced conductivity. Expanded: Degenerate if Nd > ni.

Doping

Add impurities (ppm). Ex: As in Si. Relevance: Controls carriers. Additional: Diffusion or ion implantation methods.

Donor Impurity

Pentavalent, donates e-. Ex: P (+5). Relevance: n-type. Expanded: E_d near EC.

Acceptor Impurity

Trivalent, accepts e- (hole). Ex: B (+3). Relevance: p-type. Additional: E_a near EV.

Hole

VB vacancy, +q effective. Ex: Moves opposite e-. Relevance: p-current. Expanded: Wavefunction absence.

Covalent Bond

Shared e- pairs. Ex: Si-Si. Relevance: Lattice stability. Additional: sp3 hybrid in diamond.

Intrinsic Carrier Concentration (ni)

\( n_e = n_h \) at thermal eq. Ex: ↑ with T. Relevance: Pure conductivity. Expanded: \( n_i = 2 (2\pi m^* kT / h^2)^{3/2} \exp(-E_g / 2kT) \).

n-type Semiconductor

\( n_e \gg n_h \). Ex: Donor doped. Relevance: Majority e-. Additional: Electron mobility dominant.

p-type Semiconductor

\( n_h \gg n_e \). Ex: Acceptor doped. Relevance: Majority holes. Expanded: Used in p-n junctions.

Recombination

e- + hole → bond. Ex: Balances generation. Relevance: Equilibrium. Additional: Lifetime τ = 1 / recombination rate.

Generation

Thermal break bond → e-h. Ex: ↑ with T. Relevance: Carriers source. Expanded: Optical/thermal generation.

Diamond Lattice

Tetrahedral Si/Ge structure. Ex: a=5.43Å Si. Relevance: 4 bonds. Additional: FCC with basis.

Fermi Level

Probable e- energy at 0K. Ex: Mid-gap intrinsic. Advanced: Shifts to CB in n-type. Expanded: E_F = (E_c + E_v)/2 + (kT/2) ln(N_v / N_c).

Donor Level

Impurity state near CB. Ex: 0.05eV below CB. Relevance: Easy ionization. Additional: Hydrogen-like model.

Acceptor Level

Near VB. Ex: 0.01eV above. Relevance: Hole creation. Expanded: Similar to donors but for holes.

Band Theory

Atomic orbitals → bands. Ex: Overlap in solids. Relevance: Conductivity explain. Additional: Kronig-Penney model.

Resistivity (ρ)

1/σ. Ex: Metals low. Relevance: Material classify. Expanded: ρ = 1 / (n e μ).

Conductivity (σ)

1/ρ. Ex: Semis intermediate. Relevance: Device performance. Additional: Temperature dependence.

Elemental Semiconductor

Si, Ge. Ex: Group 14. Relevance: Common devices. Expanded: Si dominant in ICs.

Compound Semiconductor

GaAs, CdS. Ex: III-V. Relevance: LEDs, lasers. Additional: Tunable Eg.

Organic Semiconductor

Anthracene. Ex: Polymers post-1990. Relevance: Flexible electronics. Expanded: Conjugated π-bonds.

Vacuum Tube

Valve, e.g., diode. Ex: Heated cathode. Relevance: Pre-transistor. Additional: Space charge limited current.

Dopant

Impurity atom. Ex: Size ~ host. Relevance: Lattice undistorted. Expanded: Shallow/deep levels.

Majority Carrier

Dominant charge. Ex: e- in n-type. Relevance: Conduction type. Additional: Injection in junctions.

Minority Carrier

Minority charge. Ex: Holes in n-type. Relevance: Recombination. Expanded: Lifetime τ_min.

Stationary State

Bond intact low T. Ex: 0K all filled. Relevance: Insulator-like. Additional: Zero-point energy.

Thermal Ionization

Energy to free e-. Ex: kT ~0.025eV room. Relevance: Carrier gen. Expanded: Arrhenius form.

p-n Junction

p-type + n-type interface. Ex: Si diode. Relevance: Rectification. Additional: Abrupt/graded.

Depletion Region

Charge-free zone. Ex: Width W ~1μm. Relevance: Barrier formation.

Built-in Potential (V_bi)

Diffusion potential. Ex: 0.7V Si. Relevance: Equilibrium.

Forward Bias

V >0 reduces barrier. Ex: Exponential I. Relevance: Conduction.

Reverse Bias

V <0 increases barrier. Ex: Leakage I. Relevance: Blocking.

Zener Diode

Reverse breakdown. Ex: 5.1V. Relevance: Voltage regulation.

LED

Light emission diode. Ex: GaAsP red. Relevance: Display.

Bipolar Junction Transistor (BJT)

3-layer device. Ex: npn. Relevance: Amplification.

Current Gain (β)

I_c / I_b. Ex: 100. Relevance: Switching.

Logic Gate

Boolean function. Ex: AND. Relevance: Digital circuits.

Truth Table

Input-output map. Ex: OR gate. Relevance: Verification.

Boolean Algebra

Gate math. Ex: A + A = A. Relevance: Simplification.

Mobility (μ)

Drift speed / E. Ex: μ_e Si 1350 cm²/Vs. Relevance: σ.

Effective Mass (m*)

Curvature inverse. Ex: m_e* Si 0.26m. Relevance: Band structure.

Diffusion

Carrier spread. Ex: Junction formation. Relevance: Transport.

Drift

E-field motion. Ex: Current. Relevance: Ohmic.

Photodiode

Light to current. Ex: Solar cell base. Relevance: Optoelectronics.

Solar Cell

p-n photovoltaic. Ex: Efficiency 20%. Relevance: Renewable energy.

Band Formation (Qualitative)

• Step 1: Isolated atoms: Discrete levels (n=3 Si 4 e-).
• Step 2: Close atoms: Overlap outer orbits → continuous bands. \[ E(k) = E_0 - 2t \cos(ka) \] (tight-binding).
• Step 3: 4N valence e- fill lower 4N states (VB); upper 4N empty (CB).
• Step 4: Si/Ge spacing: Split by Eg ~1 eV. Expanded: Eg ∝ 1/d^2 (d interatomic).
• Depth: Bloch theorem waves; Pauli exclusion. Additional: Density of states g(E) ∝ sqrt(E).

Intrinsic Carrier ni

• Step 1: Thermal: e- excite if kT > Eg/2 avg.
• Step 2: Probability exp(-Eg/kT); density states ∝ T^{3/2}. \[ n = \int g(E) f(E) dE \approx N_c \exp(-(E_c - E_f)/kT) \]
• Step 3: \( n_i = \sqrt{N_c N_v} \exp(-E_g / 2kT) \), with \( N_c = 2 (2\pi m_e^* kT / h^2)^{3/2} \).
• Step 4: For Si Eg=1.1eV, room ni~10^{10} cm^{-3}. Expanded: Plot ln ni vs 1/T slope = -Eg/2k.
• Depth: Fermi-Dirac stats; mass effective. Additional: Non-parabolic bands correction.

Hole Motion

• Step 1: Hole at site 1 (vacancy).
• Step 2: Adjacent e- (site 2 bond) jumps to 1. Probability ∝ exp(-E_a / kT).
• Step 3: Vacancy now at 2; apparent hole move 1→2. \[ v_h = - \mu_h E \] (opposite to e-).
• Step 4: Under E-field, holes drift to -ve; current Ih = p e μ_h E. Expanded: μ_h = q τ / m_h* (τ scattering time).
• Depth: Equivalent to bound e- collective shift. Additional: Hopping conduction in disordered semis.

n-type Carrier Concentration

• Step 1: Donors Nd ionized: \( n_e \approx N_d \) (low T exhaust). Fraction ionized \( g_d / (1 + g_d \exp((E_d - E_f)/kT)) \).
• Step 2: \( n_h = n_i^2 / n_e \) (mass action law).
• Step 3: At room, ne >> ni; nh << ne. Charge neutrality: n_e + N_a^- = p + N_d^+.
• Step 4: Conductivity \( \sigma = e n_e \mu_e \). Expanded: Hall coefficient R_h = -1/(n e) for n-type.
• Depth: Freeze-out/intrinsic/exhaust regimes. Additional: High T: ni dominates.

Donor Ionization Energy

• Step 1: H-like impurity: \( E_d = (13.6 \mathrm{eV}) (m^*/m) / \epsilon_r^2 \).
• Step 2: Si ε_r=12, m*~0.3m → E_d ~0.045 eV.
• Step 3: kT room 0.025 eV; fraction ionized ≈1. \[ N_d^+ = N_d / (1 + g \exp((E_f - E_d)/kT)) \]
• Step 4: Ge lower ~0.01 eV. Expanded: g=2 spin degeneracy.
• Depth: Hydrogen atom analogy scaled. Additional: Screening effects at high doping.

Built-in Potential V_bi

• Step 1: Diffusion creates space charge: ρ = q (p - n + N_d - N_a).
• Step 2: Poisson: d²ψ/dx² = -ρ/ε; integrate for E, then V.
• Step 3: Equilibrium: Fermi levels align; ΔE_f = q V_bi = E_f^n - E_f^p.
• Step 4: \( V_{bi} = \frac{kT}{q} \ln \left( \frac{N_a N_d}{n_i^2} \right) \). Ex: Na=Nd=10^{16} cm^{-3}, V_bi≈0.7V.
• Depth: Boltzmann approx for carriers. Additional: Depletion approx W = sqrt(2ε V_bi / q N).

Diode Current I-V

• Step 1: Diffusion current ∝ exp(-qV/2kT) minority injection.
• Step 2: Drift balances in bulk; Shockley: Generation-recombination.
• Step 3: Ideal: \( I = I_0 [\exp(qV / \eta kT) - 1] \), η=1 diffusion, 2 recomb.
• Step 4: I_0 = q A (D_p p_n / L_p + D_n n_p / L_n) n_i^2 / N_d. Ex: Si I_0 ~10^{-12} A.
• Depth: Continuity eq. Additional: Series resistance, high injection.

Transistor β

• Step 1: Ebers-Moll: Ic = α I_e + I_co, Ib = (1-α) I_e + I_eo.
• Step 2: β = α / (1-α), α transport factor.
• Step 3: α ≈ sech(W_b / L_p) (base width W_b).
• Step 4: High β narrow base, high doping emitter. Ex: β=100 for W_b=1μm.
• Depth: Gummel-Poon model. Additional: Early effect voltage dependence.

Band Theory

Steps: 1. Atomic levels overlap. 2. VB filled, CB empty. 3. Eg determines type. Ex: Si Eg=1.1eV semi. Pitfall: Ignore T effect. Interlink: To quantum Ch11. Depth: k-space bands. Expanded: Reciprocal lattice, Brillouin zone.

Intrinsic Conduction

Steps: 1. Thermal gen e-h. 2. ne=nh. 3. σ ∝ ni (T). Ex: Ge more conductive. Pitfall: Forget recombination. Interlink: Ch3 Ohm. Depth: ni exp. Additional: Varshni Eg(T) = Eg0 - αT^2/(T+β).

Doping

Steps: 1. Add V-group (n) or III (p). 2. Impurity levels. 3. Majority carriers. Ex: 1ppm As → 10^{16} m^{-3} e-. Pitfall: Size mismatch defect. Interlink: Devices later. Expanded: Gettering impurities.

Hole Concept

Steps: 1. Vacancy +q. 2. e- jump = hole move. 3. Drift in E. Ex: p-type current. Pitfall: Real particle? No, effective. Depth: μ_h < μ_e. Additional: Valence band heavy/light holes.

Extrinsic vs Intrinsic

Steps: 1. Intrinsic T-dep. 2. Extrinsic doping-dep, weak T. Ex: Room doped >> pure. Pitfall: High T intrinsic dominates. Expanded: Cross-over T ~ Eg / k ln(Nd/ni).

p-n Junction Formation

Steps: 1. Diffusion majority. 2. Depletion ions. 3. V_bi equilibrium. Ex: Si 0.7V. Pitfall: Forget minorities. Depth: Quasi-Fermi levels.

Diode Biasing

Steps: 1. Forward: Inject minorities. 2. Reverse: Sweep out. Ex: I forward mA, reverse μA. Pitfall: Ideality η. Interlink: Rectifiers Ch3.

Zener Breakdown

Steps: 1. Tunneling in heavy doping. 2. V_z <5V. Ex: Regulation. Pitfall: Confuse avalanche.

LED Emission

Steps: 1. Forward recomb. 2. hν=Eg. Ex: Blue GaN. Pitfall: Efficiency droop.

Transistor Action

Steps: 1. Emitter inject. 2. Base transport. 3. Collector sweep. Ex: npn Ic=β Ib. Pitfall: Base width modulation.

Amplification

Steps: 1. Small Ib → large Ic. 2. Av= -β RL / r_in. Ex: Audio amp.

Switching

Steps: 1. Cutoff Vce=Vcc. 2. Sat Vce=0.2V. Ex: Digital logic.

Logic Gates

Steps: 1. Threshold ~2.4V. 2. Boolean. Ex: NAND low=high. Pitfall: Fan-out.

Solar Cell

Steps: 1. Photon gen e-h. 2. Field separates. Ex: Voc=V_bi. Depth: Fill factor.

Mobility

Steps: 1. μ= qτ/m*. 2. ↓ with T (phonon scatter). Ex: Si μ_e=1400 cm²/Vs.

Classification

• ρ: Metals Low, Semis Med, Ins High (LMI). Eg: Metals 0, Semis Small, Ins Large (0SL). Expanded: σ=1/ρ.

Bands

• VB filled, CB empty, Eg gap. Mnemonic: "Valence Filled, Conduction Empty Gap (VFCEG)". Additional: At 0K semi=ins.

Intrinsic

• \( n_e = n_h = n_i \); thermal e-h. "Equal Partners Thermal Dance (EPTD)". Expanded: ni ∝ exp(-Eg/2kT).

Doping

• n: +5 donors e-; p: +3 acceptors holes. "Pentavalent Gives e-, Trivalent Takes (PGT)". Additional: ne nh=ni^2.

Hole

• Jump e- = move hole opposite. "Electron Leap, Hole Creep (ELHC)". Expanded: Ih = p e μ_h E.

p-n Junction

• Depletion: Diffusion → V_bi. "Diff-Inj-Bi" (Diffusion Injection Barrier). Additional: Forward exp, reverse const.

Diode

• I = I0 (exp(qV/kT)-1). "Shockley Exponential".

Transistor

• β=Ic/Ib; CE high Av. "Base Controls Collector (BCC)".

Gates

• AND series, OR parallel diodes. "Series All, Parallel Any (SAPA)".