Lecture #18Effect of R-G in Depletion RegionSlide 3Slide 4Effect of Series ResistanceHigh-Level Injection EffectSummary: Deviations from Ideal I-VDerivation of Narrow-Base Diode I-VSlide 9Excess Carrier Profiles: Limiting CasesSlide 11Slide 12Slide 13Narrow (Short) Base Diode I-V EquationSummary: Current Flow in pn JunctionsEE130 Lecture 18, Slide 1Spring 2007Lecture #18OUTLINE• pn junctions (cont’d)– Deviations from the ideal I -V R-G current series resistance high-level injection– Narrow-base diodeReading: Chapter 6.2, 6.3EE130 Lecture 18, Slide 2Spring 2007Effect of R-G in Depletion Region•The net generation rate is given by•R-G in the depletion region contributes an additional component of diode current IR-Glevelenergy state- trap and where)(τ)(τ/)(1/)(1112TkTEEikTEEinpiEenpennppnnnpntntpTiiTdxtpqAIGRxxGRnpEE130 Lecture 18, Slide 3Spring 2007•For reverse bias greater than several kT/q, inipiGRnpnnWqAnI1100ττ21 τ whereτ2IpInEE130 Lecture 18, Slide 4Spring 2007•For forward biases, kTqViGRAWeqAnI2/IpInEE130 Lecture 18, Slide 5Spring 2007Effect of Series ResistanceEE130 Lecture 18, Slide 6Spring 2007High-Level Injection Effect•As VA increases, the side of the junction which is more lightly doped will eventually reach HLI: significant gradient in majority-carrier profileMajority-carrier diffusion current reduces the diode current from the idealpopnonppnnor(p+n junction)(n+p junction)EE130 Lecture 18, Slide 7Spring 2007Summary: Deviations from Ideal I-VForward-bias current Reverse-bias currentEE130 Lecture 18, Slide 8Spring 2007Derivation of Narrow-Base Diode I-V•We have the following boundary conditions:•With the following coordinate system:•Then, the solution is of the form:0)''( cnxxp)1()(/kTqVnonnAepxpppLxLxeAeAxp/2/1)(NEW:x' 0 0 x' 'x' cEE130 Lecture 18, Slide 9Spring 2007Applying the boundary conditions, we have:ThereforeNote that so that '///'/'/0'0 ,)1()'(''''cLxLxLxxLxxkTqVnnxxeeeeepxpPcPcPcPcApcpcLxLxneAeAAAp/2/121''0)0( 2sinhee '''/0'0 ,/sinh/'sinh)1()'(cPcPckTqVnnxxLxLxxepxpAEE130 Lecture 18, Slide 10Spring 2007Excess Carrier Profiles: Limiting CasesLong base (xc’): pAPcPcpPcpPcAPcPcPcPcALxkTqVnLxLxLxLxLxLxkTqVnLxLxLxxLxxkTqVnneepeeeeeeepeeeeepxp/'/0///'//'//0///'/'/0)1( )1( )1()'(''''''''EE130 Lecture 18, Slide 11Spring 2007Narrow base (xc’0):pn is a linear function of x Jp is constant (no recombination) '/0''/0''/0'1)1(//')1(/sinh/'sinh)1()'(AAckTqVnPcPckTqVnPcPckTqVnnxxepLxLxxepLxLxxepxpAEE130 Lecture 18, Slide 12Spring 2007•For a p+n junction, then:where )1(/sinh/cosh)1(020kTVqPcPckTVqDiPpxPAAeILxLxeNnLDqAJAI PcPcDiPPLxLxNnLDqAI/sinh/cosh'0''2 PcPcPkTqVnpPnpPLxLxxLepqDJxxpqDJA/sinh/cosh11 )(/0 2cosheeEE130 Lecture 18, Slide 13Spring 2007 0 as sinh Note: 0 as 1cosh2•If xc’ << LP:and DicpcPDiPpcPPcPcPcPcNnxDqAxLNnLDqAIxLLxLxLxLx2202//1/sinh/coshEE130 Lecture 18, Slide 14Spring 2007Narrow (Short) Base Diode I-V EquationLetandThen,region type-p of width region type-n of width PNWWNpPPPnNNLxWWLxWW 11/0/2kTqVkTqVAPNDNPiAAeIeNWDNWDqAnIEE130 Lecture 18, Slide 15Spring 2007Summary: Current Flow in pn Junctions•The diode current is dominated by the term associated with the more lightly doped side:p+n diode:pn+ diode:i.e. current flowing across junction is dominated by carriers injected from the more heavily doped side sidenshort siden long )( 220DNPiDPPinPNWDqAnNLDqAnxII sidepshort sidep long )(220APNiANNipNNWDqA
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