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Semiconductor Device Physics Lecture 2 Dr. Gaurav Trivedi, EEE Department, IIT Guwahati Electronic Properties of Si Silicon is a semiconductor material. Pure Si has a relatively high electrical resistivity at room temperature. There are 2 types of mobile charge-carriers in Si: Conduction electrons are negatively charged, e = –1.602 10–19 C Holes are positively charged, p = +1.602 10–19 C The concentration (number of atom/cm3) of conduction electrons & holes in a semiconductor can be influenced in several ways: Adding special impurity atoms (dopants) Applying an electric field Changing the temperature Irradiation Bond Model of Electrons and Holes 2-D Representation Si Si Si Si Si Si Si Si Si Hole When an electron breaks loose and becomes a conduction electron, then a hole is created. Si Si Si Si Si Si Si Si Si Conduction electron What is a Hole? A hole is a positive charge associated with a half-filled covalent bond. A hole is treated as a positively charged mobile particle in the semiconductor. Conduction Electron and Hole of Pure Si • Covalent (shared e–) bonds exists between Si atoms in a crystal. • Since the e– are loosely bound, some will be free at any T, creating hole-electron pairs. ni = intrinsic carrier concentration ni ≈ 1010 cm–3 at room temperature Si: From Atom to Crystal Energy states (in Si atom) Energy bands (in Si crystal) • The highest mostly-filled band is the valence band. • The lowest mostly-empty band is the conduction band. Electron energy Energy Band Diagram Ec EG, band gap energy Ev • For Silicon at 300 K, EG = 1.12 eV • 1 eV = 1.6 x 10–19 J Simplified version of energy band model, indicating: Lowest possible conduction band energy (Ec) Highest possible valence band energy (Ev) Ec and Ev are separated by the band gap energy EG. Measuring Band Gap Energy EG can be determined from the minimum energy (hn) of photons that can be absorbed by the semiconductor. This amount of energy equals the energy required to move a single electron from valence band to conduction band. Electron Ec Photon photon energy: hn = EG Ev Hole Band gap energies Semiconductor Band gap (eV) Ge 0.66 Si 1.12 GaAs 1.42 Diamond 6.0 Carriers Completely filled or empty bands do not allow current flow, because no carriers available. Broken covalent bonds produce carriers (electrons and holes) and make current flow possible. The excited electron moves from valence band to conduction band. Conduction band is not completely empty anymore. Valence band is not completely filled anymore. Band Gap and Material Classification Ec Ev Ec E G = ~8 eV Ec Ev SiO2 EG = 1.12 eV Si Ec Ev Ev Metal Insulators have large band gap EG. Semiconductors have relatively small band gap EG. Metals have very narrow band gap EG . Even, in some cases conduction band is partially filled, E v > E c. Carrier Numbers in Intrinsic Material More new notations are presented now: n : number of electrons/cm3 p : number of holes/cm3 ni : intrinsic carrier concentration In a pure semiconductor, n = p = ni. At room temperature, ni = 2 106 /cm3 in GaAs ni = 1 1010 /cm3 in Si ni = 2 1013 /cm3 in Ge Manipulation of Carrier Numbers – Doping By substituting a Si atom with a special impurity atom (elements from Group III or Group V), a hole or conduction electron can be created. Acceptors: B, Ga, In, Al Donors: P, As, Sb Doping Silicon with Acceptors Example: Aluminium atom is doped into the Si crystal. Al– is immobile The Al atom accepts an electron from a neighboring Si atom, resulting in a missing bonding electron, or “hole”. The hole is free to roam around the Si lattice, and as a moving positive charge, the hole carries current. Doping Silicon with Donors Example: Phosphor atom is doped into the Si crystal. P is immobile The loosely bounded fifth valence electron of the P atom can “break free” easily and becomes a mobile conducting electron. This electron contributes in current conduction. Donor / Acceptor Levels (Band Model) ▬ + Donor Level Ec ED Donor ionization energy Acceptor ionization energy ▬ Acceptor Level EA Ev + Ionization energy of selected donors and acceptors in Silicon Donors Ionization energy of dopant EC – ED or EA – EV (meV) Sb 39 P 45 Acceptors As 54 B 45 Al In 67 160 Dopant Ionization (Band Model) Donor atoms Acceptor atoms Carrier-Related Terminology Donor: impurity atom that increases n (conducting electron). Acceptor: impurity atom that increases p (hole). n-type material: contains more electrons than holes. p-type material: contains more holes than electrons. Majority carrier: the most abundant carrier. Minority carrier: the least abundant carrier. Intrinsic semiconductor: undoped semiconductor n = p = n i. Extrinsic semiconductor: doped semiconductor. Density of States E DE Ec gc(E) Ec Ev Ev density of states g(E) gv(E) g(E) is the number of states per cm3 per eV. g(E)dE is the number of states per cm3 in the energy range between E and E+dE). Density of States DE Ec E Ec Ev Ev gc(E) density of states g(E) gv(E) Near the band edges: g c (E ) g v (E ) mn* 2mn* E Ec 2h3 mp* 2mp* Ev E h 2 3 E Ec E Ev mn* : effective mass of electron For Silicon at 300 K, mn* 1.18mo mp* 0.81mo mo 9.1 10 31kg mo: electron rest mass Fermi Function The probability that an available state at an energy E will be occupied by an electron is specified by the following probability distribution function: f (E) 1 1 e ( E EF ) / kT k : Boltzmann constant T : temperature in Kelvin EF is called the Fermi energy or the Fermi level. If E EF , f ( E ) 0 If E EF , f ( E ) 1 If E EF , f (E) 1 2 Effect of Temperature on f(E) Effect of Temperature on f(E) Equilibrium Distribution of Carriers n(E) is obtained by multiplying gc(E) and f(E), p(E) is obtained by multiplying gv(E) and 1–f(E). Intrinsic semiconductor material Energy band diagram Density of states Probability of occupancy Carrier distribution Equilibrium Distribution of Carriers n-type semiconductor material Energy band diagram Density of States Probability of occupancy Carrier distribution Equilibrium Distribution of Carriers p-type semiconductor material Energy band diagram Density of States Probability of occupancy Carrier distribution Important Constants Electronic charge, q = 1.610–19 C Permittivity of free space, εo = 8.85410–12 F/m Boltzmann constant, k = 8.6210–5 eV/K Planck constant, h = 4.1410–15 eVs Free electron mass, mo = 9.110–31 kg Thermal energy, kT = 0.02586 eV (at 300 K) Thermal voltage, kT/q = 0.02586 V (at 300 K)