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©rlc L10-16Feb20111 Ideal Junction Theory Assumptions E x = 0 in the chg neutral reg. (CNR) MB statistics are applicable Neglect gen/rec in depl reg (DR) Low level injections apply so that n p < p po for -x pc < x < -x p, and p n < n no for x n < x < x nc Steady State conditions

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©rlc L10-16Feb20112 Forward Bias Energy Bands EvEv EcEc E Fi xnxn x nc -x pc -x p 0 q(V bi -V a ) E FP E FN qV a x Imref, E Fn Imref, E Fp

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©rlc L10-16Feb20113 Law of the junction (follow the min. carr.)

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©rlc L10-16Feb20114 Law of the junction (cont.)

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©rlc L10-16Feb20115 Law of the junction (cont.)

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©rlc L10-16Feb20116 Injection Conditions

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©rlc L10-16Feb20117 Ideal Junction Theory (cont.) Apply the Continuity Eqn in CNR

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©rlc L10-16Feb20118 Ideal Junction Theory (cont.)

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©rlc L10-16Feb20119 Ideal Junction Theory (cont.)

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©rlc L10-16Feb Excess minority carrier distr fctn

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©rlc L10-16Feb Carrier Injection -x p xnxn -x pc 0 ln(carrier conc) ln N a ln N d ln n i ln n i 2 /N d ln n i 2 /N a x nc x ~V a /V t

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©rlc L10-16Feb Minority carrier currents

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©rlc L10-16Feb Evaluating the diode current

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©rlc L10-16Feb Special cases for the diode current

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©rlc L10-16Feb Ideal diode equation Assumptions: –low-level injection –Maxwell Boltzman statistics –Depletion approximation –Neglect gen/rec effects in DR –Steady-state solution only Current dens, J x = J s expd(V a /V t ) –where expd(x) = [exp(x) -1]

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©rlc L10-16Feb Ideal diode equation (cont.) J s = J s,p + J s,n = hole curr + ele curr J s,p = qn i 2 D p coth(W n /L p )/(N d L p ) = qn i 2 D p /(N d W n ), W n > L p, long J s,n = qn i 2 D n coth(W p /L n )/(N a L n ) = qn i 2 D n /(N a W p ), W p > L n, long J s,n > N d

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©rlc L10-16Feb Diffntl, one-sided diode conductance VaVa IDID Static (steady- state) diode I-V characteristic VQVQ IQIQ

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©rlc L10-16Feb Diffntl, one-sided diode cond. (cont.)

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©rlc L10-16Feb Charge distr in a (1- sided) short diode Assume N d << N a The sinh excess minority carrier distribution becomes linear for W n << L p p n (x n )=p n0 expd(V a /V t ) Total chg = Q p = Q p = q p n (x n )W n /2 xnxn x x nc p n (x n ) W n = x nc - x n QpQp p n

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20 Charge distr in a 1- sided short diode Assume Quasi-static charge distributions Q p = Q p = q p n (x n )W n /2 d p n (x n ) = (W/2)* { p n (x n,V a + V) - p n (x n,V a )} xnxn x x nc p n (x n,V a ) QpQp p n p n (x n,V a + V) Q p

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21 Cap. of a (1-sided) short diode (cont.)

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©rlc L10-16Feb General time- constant

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©rlc L10-16Feb General time- constant (cont.)

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©rlc L10-16Feb General time- constant (cont.)

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©rlc L10-16Feb References *Fundamentals of Semiconductor Theory and Device Physics, by Shyh Wang, Prentice Hall, **Semiconductor Physics & Devices, by Donald A. Neamen, 2nd ed., Irwin, Chicago. M&K = Device Electronics for Integrated Circuits, 3rd ed., by Richard S. Muller, Theodore I. Kamins, and Mansun Chan, John Wiley and Sons, New York, Device Electronics for Integrated Circuits, 2 ed., by Muller and Kamins, Wiley, New York, Physics of Semiconductor Devices, by S. M. Sze, Wiley, New York, Physics of Semiconductor Devices, Shur, Prentice- Hall, 1990.

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