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Numerical Differentiation of Ideal Diode Equation in Semiconductor Device Theory

This lecture by Professor Ronald L. Carter focuses on the numerical differentiation of the ideal diode equation, addressing both hole and electron current densities. It covers the equation for saturation current (Js) components and their behavior under high-level injection conditions. The discussion includes the effects of carrier recombination, the ideality factor, and other key parameters influencing current density equations in semiconductor devices. Additionally, the impact of series resistance on the external voltage and current density is also explored with relevant calculations and SPICE modeling considerations.

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Numerical Differentiation of Ideal Diode Equation in Semiconductor Device Theory

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  1. EE 5340Semiconductor Device TheoryLecture 26 – Spring 2011 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc

  2. dy/dx - Numerical Differentiation

  3. Ideal diodeequation (cont.) • Js = Js,p + Js,n = hole curr + elecurr Js,p = qni2Dpcoth(Wn/Lp)/(NdLp) = qni2Dp/(NdWn), Wn<< Lp, “short” = qni2Dp/(NdLp), Wn>> Lp, “long” Js,n = qni2Dncoth(Wp/Ln)/(NaLn) = qni2Dn/(NaWp), Wp<< Ln, “short” = qni2Dn/(NaLn), Wp>> Ln, “long” Js,n<< Js,p when Na >> Nd

  4. Effect of carrierrec. in DR (cont.)

  5. High level injeffects (cont.)

  6. Summary of Va > 0 current density eqns. • Ideal diode, Jsexpd(Va/(hVt)) • ideality factor, h • Recombination, Js,recexp(Va/(2hVt)) • appears in parallel with ideal term • High-level injection, (Js*JKF)1/2exp(Va/(2hVt)) • SPICE model by modulating ideal Js term • Va = Vext - J*A*Rs = Vext - Idiode*Rs

  7. ln(J) Plot of typical Va > 0 current density equations data Effect of Rs Vext VKF

  8. Calculating k/q For Vt = kT/q = 0.025852 V, (T=300K) Then k/q = Vt/300K = 8.6173E-5 V/K

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