EE40 Lecture 32 Prof. Chang-HasnainElectron and Hole Densities in Doped SiPowerPoint PresentationJunctions of n- and p-type RegionsThe pn Junction DiodeDepletion Region ApproximationSummary: pn-Junction Diode I-VCharge Density DistributionTwo Governing LawsDepletion Approximation 1Depletion Approximation 2EE40 Lecture 33 Prof. Chang-HasnainDepletion Approximation 3Effect of Applied VoltageDepletion Approx. – with VD<0 reverse biasDepletion Approx. – with VD>0 forward biasForward BiasReverse BiasOptoelectronic DiodesExample: PhotodiodePlanck ConstantBandgap Versus Lattice ConstantSlide 1EE40 Fall 2007 Prof. Chang-HasnainEE40Lecture 32Prof. Chang-Hasnain11/21/07Reading: Supplementary ReaderSlide 2EE40 Fall 2007 Prof. Chang-HasnainElectron and Hole Densities in Doped Si( )2v fE E kTa vi ap N N ep n N−= ==•Instrinsic (undoped) Si•N-doped Si–Assume each dopant contribute to one electron•p-doped Si–Assume each dopant contribute to one hole( )2f cE E kTd ci dn N N ep n N−= ==2iin p nnp n= ==Slide 3EE40 Fall 2007 Prof. Chang-HasnainSummary of n- and p-type siliconPure silicon is an insulator. At high temperatures it conducts weakly. If we add an impurity with extra electrons (e.g. arsenic, phosphorus) these extra electrons are set free and we have a pretty good conductor (n-type silicon).If we add an impurity with a deficit of electrons (e.g. boron) then bonding electrons are missing (holes), and the resulting holes can move around … again a pretty good conductor (p-type silicon) Now what is really interesting is when we join n-type and p-type silicon, that is make a pn junction. It has interesting electrical properties.Slide 4EE40 Fall 2007 Prof. Chang-HasnainJunctions of n- and p-type RegionsA silicon chip may have 108 to 109 p-n junctions today.p-n junctions form the essential basis of all semiconductor devices.How do they behave*? What happens to the electrons and holes?What is the electrical circuit model for such junctions?n and p regions are brought into contact :*Note that the textbook has a very good explanation.Slide 5EE40 Fall 2007 Prof. Chang-HasnainThe pn Junction DiodeSchematic diagramp-type n-typeID+ VD –Circuit symbolPhysical structure:(an example)p-type Sin-type SiSiO2SiO2metalmetalID+VD –net donorconcentration NDnet acceptorconcentration NAFor simplicity, assume thatthe doping profile changes abruptly at the junction.cross-sectional area ADSlide 6EE40 Fall 2007 Prof. Chang-Hasnain•When the junction is first formed, mobile carriers diffuse across the junction (due to the concentration gradients)–Holes diffuse from the p side to the n side, leaving behind negatively charged immobile acceptor ions–Electrons diffuse from the n side to the p side, leaving behind positively charged immobile donor ionsA region depleted of mobile carriers is formed at the junction.•The space charge due to immobile ions in the depletion region establishes an electric field that opposes carrier diffusion.Depletion Region Approximation+++++–––––p nacceptor ionsdonor ionsSlide 7EE40 Fall 2007 Prof. Chang-HasnainSummary: pn-Junction Diode I-V•Under forward bias, the potential barrier is reduced, so that carriers flow (by diffusion) across the junction–Current increases exponentially with increasing forward bias–The carriers become minority carriers once they cross the junction; as they diffuse in the quasi-neutral regions, they recombine with majority carriers (supplied by the metal contacts)“injection” of minority carriers•Under reverse bias, the potential barrier is increased, so that negligible carriers flow across the junction–If a minority carrier enters the depletion region (by thermal generation or diffusion from the quasi-neutral regions), it will be swept across the junction by the built-in electric field“collection” of minority carriers reverse currentID (A)VD (V)Slide 8EE40 Fall 2007 Prof. Chang-Hasnainquasi-neutral p regionCharge Density Distribution+++++–––––p nacceptor ionsdonor ionsdepletion region quasi-neutral n regioncharge density (C/cm3)distanceCharge is stored in the depletion region.Slide 9EE40 Fall 2007 Prof. Chang-HasnainTwo Governing Laws22( ) ( ) ( )d x dE x xdx dxφ ρε=− =−001( ) ( ) ( )xxE x E x x dxρε− =∫dEdxρε=1enclS VQE dA dVρε ε⋅ = ⋅ =∫ ∫rrÑ ÑGauss’s Law describes the relationship of charge (density) and electric field.Poisson’s Equation describes the relationship between electric field distribution and electric potential00( ) ( ) ( )xxx x E x dxφ φ− = −∫Slide 10EE40 Fall 2007 Prof. Chang-HasnainDepletion Approximation 10( ) ( ) ( 0)apo posqNE x x x x xε−= + − < <( )( )( )( )( )000000 , 0 and 0 0 npndpaxxxxxxxqNxxqNx >−<=⎩⎨⎧≤≤≤≤−−≈ ρρ xno x x -xpo _o(x) -qNa qNd xno x x -xpo E0(x) snodspoaxqNxqNEεε−=−=)0(000 00( )( ) ( ) ( ) 0( ) ( )(0 )noxdno noxs sdnosnox qNE x dx E x x xqNE x x xx xρε εε−= − = − −= −< <∫Gauss’s LawpnpnSlide 11EE40 Fall 2007 Prof. Chang-HasnainDepletion Approximation 2pnP=1018n=104n=1017p=105 xE0(x)snodspoaxqNxqNE)0(0xno-xpo2222posanosdxqNxqN0(x)xxno-xpoPoisson’s EquationSlide 12EE40 Fall 2007 Prof. Chang-HasnainEE40Lecture 33Prof. Chang-Hasnain11/26/07Reading: Supplementary ReaderSlide 13EE40 Fall 2007 Prof. Chang-HasnainDepletion Approximation 3 0 0 0( ) ( ) ( ) ( ) 0po popo pox xapo pox xsx xapox xsqNx E x dx x x x dxqNx dx x dxφ φεε− −− −= − + − = + +⎛ ⎞= +⎜ ⎟⎝ ⎠∫ ∫∫ ∫20( ) ( ) ( 0)2apo posqNx x x x xφε= + − < <()20 0 00 020 0( ) ( ) (0) ( ) (0 )22x xd ano pos sx xd ano pos sqN qNx E x dx x x dx xqN qNx dx x dx xφ φε εε ε= − + = − − + += − + +∫ ∫∫ ∫2 20( ) (2 ) (0 )2 2d ano po nos sqN qNx x x x x x xφε ε= − + < <Slide 14EE40 Fall 2007 Prof. Chang-HasnainEffect of Applied Voltage•The quasi-neutral p and n regions have low resistivity, whereas the depletion region has high resistivity. Thus, when an external voltage VD is applied across the diode, almost all of this voltage is dropped across the depletion region. (Think of a voltage divider circuit.)•If VD > 0 (forward bias), the potential barrier to carrier diffusion is reduced by the applied voltage.•If VD < 0 (reverse bias), the potential barrier to carrier diffusion is increased by the applied voltage.p n+++++–––––VDSlide 15EE40 Fall 2007 Prof. Chang-HasnainDepletion Approx.
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