Institute of Solid State Physics Technische Universität Graz Extrinsic semiconductors The introduction of impurity atoms that can add electrons or holes is called doping. n-type : donor atoms contribute electrons to the conduction band. Examples: P, As in Si. p-type : acceptor atoms contribute holes to the valence band. Examples: B, Ga, Al in Si. Institute of Solid State Physics Technische Universität Graz n and p The electron density and hole density are: EE EEFc vF nN exp pN v exp c kT kTB B The law of mass action: 2 Eg np nivc N N exp kTB Ionization of dopants Easier to ionize a P atom in Si than a free P atom me4 En 222 8 0 hn 2 m* Ionization energy is smaller by a factor: 0 m r 0 Ionization energy ~ 25 meV acceptors in Si donors in Si Crystal growth Czochralski Process add dopants to the melt images from wikipedia Crystal growth Float zone Process Neutron transmutation 30Si + n 31Si + 31Si 31P + image from wikipedia Gas phase diffusion AsH3 (Arsine) or PH3 (phosphine) for n-doping B2H6 (diborane) for p-doping. http://www.microfab.de/foundry/services/diffusion/index.html Chemical vapor deposition Epitaxial silicon CVD SiH4 (silane) or SiH2Cl2 (dichlorosilane) PH3 (phosphine) for n-doping or B2H6 (diborane) for p-doping. image from wikipedia Ion implantation Implant at 7º to avoid channeling http://www.synopsys.com Donors Five valence electrons: P, As States are added in the band gap just below the conduction band E c EF(T=0) ED Eg Ev D(E) n-type: n ~ ND Many more electrons in the conduction band than holes in the valence band. majority carriers: electrons; minority carriers: holes Acceptors Three valence electrons: B, Al, Ga States are added in the band gap just above the valence band Ec Eg E A E (T=0) Ev F D(E) p-type: p ~ NA Many more holes in the valence band than electrons in the conduction band. majority carriers: holes; minority carriers: electrons Donor and Acceptor Energies Energy below the conduction band Energy above the valence band Temperature dependence Intrinsic Extrinsic p NA kTBD E Freeze-out 200 K 1000 K Eg nNNivcexp kTB n-type n-type ND > NA, p ~ 0 EEF c nNDc Nexp kTB Nc EEkTFcB ln ND For n-type, n ~ density of donors, 2 p = ni /n p-type p-type NA > ND, n ~ 0 EEvF pNAv Nexp kTB Nv EEkTFvB ln N A For p-type, p ~ density of acceptors, 2 n = ni /p Intrinsic / Extrinsic Intrinsic: n = p Conductivity strongly temperature dependent near room temperature Extrinsic: n ≠ p Conductivity almost temperature independent at room temperature Intrinsic semiconductors Extrinsic semiconductors intrinsic extrinsic -3 Ge ) cm ) i n ( Si freeze-out 10 log GaAs At high temperatures, extrinsic 1/T semiconductors have the same 300 K temperature dependence as intrinsic semiconductors. Eg nNNivcexp 2kTB Why dope with donors AND acceptors? Bipolar transistor collector base emitter n+ p n lightly doped p substrate MOSFET Bipolar Junction Transistor Ionized donors and acceptors For Ev + 3kBT < EF < Ec-3kBT Boltzmann approximation N D N ND A EE N A FD EE 12exp 14exp AF kTB kTB 4 for materials with light holes and heavy holes (Si) 2 otherwise -3 + -3 ND = donor density cm ND = ionized donor density cm -3 - -3 NA = donor density cm NA = ionized donor density cm + - Mostly, ND = ND and NA = NA Charge neutrality Carrier concentration vs. Fermi energy - + n + NA = p + ND Calculating EF(T) numerically http://lamp.tu-graz.ac.at/~hadley/psd/L4/eftplot.html degenerately doped semiconductor Degenerate semiconductor Heavily doped semiconductors are called degenerately doped ND > 0.1 Nc -> EF in the conduction band NA > 0.1 Nv -> EF in the valence band Heavy doping narrows the band gap The Boltzmann approximation is not valid Degenerate semiconductors = metal Institute of Solid State Physics Technische Universität Graz Carrier Transport Ballistic transport Drift Diffusion Generation and recombination The continuity equation High field effects Ballistic transport dv FmaeEm dt eEt vv m 0 eEt 2 xvtx 2m 00 Electrons moving in an electric field follow parabolic trajectories like a ball in a gravitational field. .