Semiconductor Study Guide

📖 Core Concepts Semiconductor – Material with conductivity between a conductor and an insulator; can be tuned by doping (adding impurity atoms). Charge carriers – Electrons (negative, in the conduction band) and holes (positive, absence of an electron in the valence band). Band structure – Filled valence band, empty conduction band, separated by the band gap \(Eg\). Fermi level – Energy where the probability of occupation is ½; its position relative to the bands determines whether a material is n‑type (near conduction band) or p‑type (near valence band). Temperature effect – Raising temperature promotes electrons across \(Eg\), increasing carrier pairs and conductivity (opposite of most metals). p‑n junction (homojunction) – Interface of p‑type and n‑type regions of the same material; diffusion creates a depletion region with an internal electric field. Generation vs. Recombination – Generation creates electron‑hole pairs (thermal, photon, radiation); recombination destroys them (radiative → photon, non‑radiative → phonon). Carrier mobility (\(\mu\)) – How fast carriers move under an electric field; higher \(\mu\) → higher conductivity. Key materials – Silicon (Si) and Germanium (Ge) (elemental); Gallium Arsenide (GaAs) and Silicon Carbide (SiC) (compound). --- 📌 Must Remember Doping purpose: Introduce donors (group V) → extra electrons (n‑type); acceptors (group III) → extra holes (p‑type). Majority carriers: n‑type → electrons; p‑type → holes. Charge neutrality: \[ n + NA^- = p + ND^+ \] Electron density ≈ donor concentration when donors are fully ionized; hole density ≈ acceptor concentration when acceptors are fully ionized. Depletion width grows until diffusion current balances drift current → built‑in electric field. Hot‑point probe test: Voltage polarity tells you n‑type (negative probe on n side) vs. p‑type. Intrinsic carrier concentration \((ni)\) depends exponentially on \(-Eg/2kT\); much larger for Ge than Si. Fabrication sequence (key steps): Crystal growth → Oxidation → Photolithography → Plasma etching → Diffusion (doping). --- 🔄 Key Processes Doping (substitutional) Replace a host Si/Ge atom with donor (P, As, Sb) or acceptor (B, Al, Ga). p‑n Junction Formation Bring p‑type and n‑type regions together → carrier diffusion → depletion region → built‑in potential. Carrier Generation Thermal: \(kT\) provides energy \(\ge Eg\). Optical: Photon energy \(h\nu \ge Eg\). Radiation: Ionizing particles excite electrons. Carrier Recombination Radiative: electron drops to valence band → photon emitted (LEDs). Non‑radiative: energy released as lattice vibrations (phonons). Photolithography Coat wafer → expose UV through mask → develop photoresist → pattern for etching/doping. --- 🔍 Key Comparisons n‑type vs. p‑type Donor vs. Acceptor dopants (group V vs. group III). Majority carrier: electrons vs. holes. Fermi level: closer to conduction band vs. valence band. Intrinsic vs. Extrinsic Intrinsic: pure crystal, carrier pairs from thermal excitation only. Extrinsic: doped, carrier concentration ≫ intrinsic. Direct‑gap vs. Indirect‑gap semiconductors Direct‑gap (e.g., GaAs): electrons can recombine radiatively → efficient LEDs/lasers. Indirect‑gap (e.g., Si, Ge): recombination mainly non‑radiative → poor light emission. Substitutional vs. Interstitial Doping Substitutional: dopant replaces host atom (common for donors/acceptors). Interstitial: dopant sits in lattice gaps (less common, can cause strain). --- ⚠️ Common Misunderstandings “Higher temperature always lowers conductivity.” False for semiconductors; conductivity increases with temperature. “All holes are actual particles.” Holes are quasiparticles—absence of an electron, but they behave like positive charge carriers. “Doping only adds carriers, not affect band structure.” Doping creates impurity states near the band edges, moving the Fermi level. “A p‑n junction conducts equally in both directions.” It conducts readily forward‑biased; reverse bias widens depletion, blocking current. --- 🧠 Mental Models / Intuition “Semiconductor as a highway”: Valence band = parked cars (no movement); conduction band = open highway. Doping adds “extra lanes” (electrons or holes) that let traffic flow. “Depletion region as a sandbag”: Diffusing carriers fill the sandbag (neutralize charge) until the bag (electric field) is strong enough to stop further flow. “Hot‑point probe as a compass”: The probe’s voltage direction points toward the “north” (majority carrier type). --- 🚩 Exceptions & Edge Cases Incomplete ionization: At low temperatures, dopants may not be fully ionized → carrier density < dopant concentration. Compensated doping: Simultaneous donor and acceptor dopants can partially cancel each other, shifting the Fermi level toward intrinsic. Band‑gap narrowing: Heavy doping can shrink \(Eg\), altering intrinsic carrier concentration. High‑frequency operation: Materials like GaAs (high electron mobility) outperform Si despite Si’s superior thermal properties. --- 📍 When to Use Which Choose Si for most digital ICs (cost‑effective, good oxide). Choose GaAs for high‑frequency or optoelectronic devices (direct gap, high electron mobility). Use hot‑point probe for quick, qualitative doping identification; use Hall effect for quantitative carrier concentration. Apply diffusion doping when deep, uniform dopant profiles are needed; use ion implantation for precise, shallow doping. --- 👀 Patterns to Recognize Temperature ↑ → Conductivity ↑ (semiconductor vs. metal). Doping type ↔ Majority carrier ↔ Fermi level location (donor → electrons → near conduction band). Direct‑gap material + forward bias → light emission (LED behavior). p‑n junction I‑V curve: Sharp turn‑on at forward voltage (0.6 V for Si, 0.3 V for Ge). --- 🗂️ Exam Traps Mistaking intrinsic carrier concentration for doped carrier density. Remember \(n \approx ND\) only when donors are fully ionized. Confusing depletion width with physical thickness of the crystal. Depletion is a narrow region at the junction, not the whole wafer. Assuming all semiconductors emit light. Only direct‑gap materials (e.g., GaAs) do so efficiently. Choosing the wrong dopant group: Group V → donors (n‑type), Group III → acceptors (p‑type). Over‑applying the charge neutrality equation without accounting for ionization fractions at low temperature. ---