prelim107

# prelim107 - ECE 315 Prelim Exam 1 Fall 2007 The temperature...

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The temperature is 300K with V T = kT/q =26mV, while the semiconductor is silicon with E gap = 1.1eV, and the intrinsic concentration n i = 10 10 cm -3 . np = n i 2 can be used to estimate the minority concentration. For a semiconductor resistor with length l and cross section A , the resistance can be estimated as ( 29 p n qp qn A l A l R μ ρ + = = , where n and p are the electron and hole concentrations, n = 1000cm 2 /Vs and p = 400cm 2 /Vs are the electron and hole mobility. The minority diffusion length as: n n n D L τ = , where D n= n kT/q is the diffusivity and n = p =1 s is the minority recombination lifetime. Diode equations: W d = x n + x p bi D A si V N N q + = 1 1 2 0 ε , N A x p = N D x n , = 2 ln i D A T bi n N N V V 0 =8.85 × 10 -14 F/cm, si =11.7 is the relative dielectric constant of silicon, ox =3.9, q =1.6 × 10 -19 coul is the elemental charge, k the Boltzmann constant, and T the temperature. For a long-base bipolar junction diode, I D = I 0 (exp(qV D /kT) – 1) , with + = D i p p A i n n N n L D N n L D qA I 2 2 0 . The minority injection level at the edge of the depletion region can be approximated by p n = p n0 × exp( qV D /kT ), which is valid for both forward and reverse biases. Notice that the above equation needs to replace L n and L p with the geometrical length in the short-base case. For nMOSFET with the threshold voltage V th , the drain current I D in the linear and saturation regions above threshold ( V GS > V th ) are: (notice that C ox ch = k n and λ =1/V A . ( 29 ( 29 saturation ) 1 ( 2 linear 2 2 2 th GS Dsat DS DS th GS ch ox D th GS Dsat DS DS DS th GS ch ox D V V V V V λ V V μ C L W I V V V V V V V V μ C L W I - = + - = - = < - - = For nMOSFET below the threshold voltage, T ox si GS T DS V C C V V V n p D e e L D qWn I ) 1 /( / 0 ) 1 ( + - - - = and ox si C C m + 2245 1 1 κ Small-signal parameters R in g m R out BJT forward active (E at ground) r π = β /g m = V T /I B I C /V T r o =V A /I C MOSFET above-Vth saturation (S at ground) 2I D /V OV r o =V A /I D g mn v GS NMOSFET large/small- signal model for the saturation region. 1

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prelim107 - ECE 315 Prelim Exam 1 Fall 2007 The temperature...

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