2 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 CHoles are positively charged, p = 10–19 CThe 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 fieldChanging the temperatureIrradiation
3 Bond Model of Electrons and Holes 2-D RepresentationHoleWhen an electron breaks loose and becomes a conduction electron, then a hole is created.SiConduction electron
4 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.
5 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 concentrationni ≈ 1010 cm–3 at room temperature
6 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.
7 Energy Band Diagram Ec EG, band gap energy Ev Electron energyEcEG, band gap energyEvFor Silicon at 300 K, EG = 1.12 eV1 eV = 1.6 x 10–19 JSimplified 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.
8 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.Photonphoton energy: hn = EGEcEvElectronHoleBand gap energies
9 CarriersCompletely 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.
10 Band Gap and Material Classification =~8 eVSiO2vEcvEcvG=1.12 eVSiMetalEvcInsulators 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, Ev > Ec.
11 Carrier Numbers in Intrinsic Material More new notations are presented now:n : number of electrons/cm3p : number of holes/cm3ni : intrinsic carrier concentrationIn 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
12 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, AlDonors: P, As, Sb
13 Doping Silicon with Acceptors Example: Aluminium atom is doped into the Si crystal.Al– is immobileThe 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.
14 Doping Silicon with Donors Example: Phosphor atom is doped into the Si crystal.P+ is immobileThe 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.
15 Donor / Acceptor Levels (Band Model) ▬EcDonor LevelEDDonor ionization energy+EvAcceptor LevelAAcceptor ionization energy▬+Ionization energy of selected donors and acceptors in SiliconAcceptorsIonization energy of dopantSbPAsBAlInEC – ED or EA – EV (meV)39455467160Donors
17 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 = ni. Extrinsic semiconductor: doped semiconductor.
18 Density of States g(E) is the number of states per cm3 per eV. EcEvDEEEcEvgc(E)gv(E)density of states g(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).
19 Density of States Near the band edges: E DE gc(E) Ec Ec EvDEEEcEvgc(E)gv(E)density of states g(E)Near the band edges:E EcE Evmo: electron rest mass
20 Fermi Function EF is called the Fermi energy or the Fermi level. The probability that an available state at an energy E will be occupied by an electron is specified by the following probability distribution function:k : Boltzmann constantT : temperature in KelvinEF is called the Fermi energy or the Fermi level.
23 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 materialEnergy banddiagramDensity ofstatesProbabilityof occupancyCarrierdistribution
24 Equilibrium Distribution of Carriers n-type semiconductor materialEnergy banddiagramDensity ofStatesProbabilityof occupancyCarrierdistribution
25 Equilibrium Distribution of Carriers p-type semiconductor materialEnergy banddiagramDensity ofStatesProbabilityof occupancyCarrierdistribution
26 Important Constants Electronic charge, q = 1.610–19 C Permittivity of free space, εo = 8.85410–12 F/mBoltzmann constant, k = 8.6210–5 eV/KPlanck constant, h = 4.1410–15 eVsFree electron mass, mo = 9.110–31 kgThermal energy, kT = eV (at 300 K)Thermal voltage, kT/q = V (at 300 K)