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ECE5360_HW_5_and_6_soln

# ECE5360_HW_5_and_6_soln - ECE 536 Homework 6 Solutions(Rev...

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Unformatted text preview: November 29, 2006 ECE 536 Homework # 6 Solutions (Rev. 0) Fall 2006 1. Show that the ideality factor of a diode can be calculated from measured forward IV curve according to: η = kT q- 1 dI dV- 1 I . (6 . 1) → Starting with the diode equation which relates diode terminal characteristics ( V,I ) in slight forward bias V a > kT/q : I = I exp qV ηkT- 1 ≈ I exp qV ηkT . we take the derivative: dI dV = q ηkT I exp qV ηkT ≈ q ηkT I . Solving this equation for η yields equation (6.1). 2. Based on Table 1 given below, compute the expected reverse saturation current for each of the 4 pn junction diodes ( D1 - D4 ). Use numbers appropriate for your implanted n + p or p + n diodes. Clearly state which dimensions you are using. Table 1. Mask dimensions (microns) for the diodes, capacitors and TLM patterns. We will take parameters for junction diodes similar to those in Tables 1a and 1b below. ECE536 November 29, 2006 Page 2 Table 1a. p + n junction diode Parameters. Parameter Symbol Value (300 K) Acceptor Doping (p +-side) N a 10 19 cm- 3 Donor Doping (n-side) N d 9(10 14 ) cm- 3 Electron Diffusion Const. (p +-side) D n 2.5 cm 2 /sec Hole Diffusion Const. (n -side) D p 10.0 cm 2 /sec Electron Lifetime (p +-side) τ n 100 psec Hole Lifetime (n -side) τ p 1.0 μ sec p + region thickness W p 1 μ m n region thickness W n > 100 μ m • The minority carrier diffusion lengths for the p + n diode are ... L p = p D p τ p = p (10)(10- 6 ) = 31 . 6 μm , L n = p D n τ n = p (2 . 5)100(10- 12 ) = 0 . 158 μm So L p < W n and L n < W p so we will use long base assumptions on both sides of the diode... • The reverse saturation current is given as (in lecture notes) I = A q D n n p L n + q D p p n L p = qAn 2 i D n N a L n + D p N d L p . • So an example calculation for D1 , A = π [(380 + 1)(10- 4 )] 2 = 4 . 56(10- 4 ) cm 2 I = 1 . 602(10- 19 )4 . 56(10- 3 )[1 . 45(10 10 )] 2 2 . 5 (10 19 )0 . 158(10- 4 ) + 10 9(10 14 )31 . 6(10- 4 ) = 0 . 542 ( pA ) . As you can see the second term in brackets dominates the first, hole diffusion into n-type substrate dominates. Table 1b. n + p junction diode Parameters. Parameter Symbol Value (300 K) Donor Doping (n +-side) N d 10 19 cm- 3 Acceptor Doping (p-side) N a 3(10 15 ) cm- 3 Hole Diffusion Const. (n +-side) D p 2.0 cm 2 /sec Electron Diffusion Const. (p -side) D n 20.0 cm 2 /sec Hole Lifetime (n +-side) τ p 100 psec Electron Lifetime (p -side) τ n 1.0 μ sec n + region thickness W n 1 μ m p region thickness W p > 100 μ m • The minority carrier diffusion lengths are for the n + p diode are ... L n = p D n τ n = p (20)(10- 6 ) = 44 . 7 μm , L p = p D p τ p = p (2)100(10- 12 ) = 0 . 141 μm ECE536 November 29, 2006 Page 3 So L n < W p and L p < W n so we will use long base assumptions on both sides of the diode......
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ECE5360_HW_5_and_6_soln - ECE 536 Homework 6 Solutions(Rev...

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