143f2010-05-soln

143f2010-05-soln - EE143 Fall 2010 EE143 HW#5 Solutions...

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EE143, Fall 2010 EE143 HW#5 Solutions Problem 1 (a) C(x,t)=C S erfc( x 2 Dt ) 3.5 10 20 erfc[ x j 2 Dt ] = 10 16 x j 2 Dt = erfc -1 (2.9 10 -5 ) = 2.9 Since 2 Dt = 0.73 10 -5 cm , x j = 0.73 10 -5 2.9 = 0.21 m (b) Q = 2C S Dt = 0.73 10 -5 3.5 10 20 1.77 = 1.45 10 15 /cm 2 Problem 2 R s x j = 50 /square 1 m = 50 - m Using Irvin curve with half-gaussian profile ( p into n curve) and N B = 10 17 /cm 3 surface concentration C o = 5 10 19 /cm 3 Since C o e [ - x j 2 4D 2 t 2 ] = N B at x j = 1 m Drive-in Dt product D 2 t 2 = 4 10 -10 cm 2 Using D o =10.5 cm 2 /sec and E a =3.69 eV for Boron diffusion, D (Boron at 1100ーC) =10.5 exp [ - 3.69 (8.614 10 -5 1373) ] cm 2 /sec = 2.96 10 -13 cm 2 /sec t 2 = 1351 seconds = 0.375 hours = drive-in time Q predep = Q drive-in = C o D 2 t 2 = 1.772 10 15 /cm 2 Since solid solubility limit of boron at 1000ーC (predep temp) 2 10 20 /cm 3 = C s Q predep = C s 2 D 1 t 1 = 1.772 10 15 /cm 2 D 1 t 1 = 6.17 10 -11 cm 2 D 1 (boron at 1000 ーC) = 2.55 10 -14 cm 2 /sec t 1 = 2420 sec = 0.672 hours = predep time Problem 3 R s x j = 264  m N o = 10 19 / cm 3 from Irvins curve ( p gaussian into n, N B = 10 15 / cm 3 ) 10 15 = 10 19 exp [ -x j 2 4Dt ] Dt = 1 m 2 After additional drive-in: (Dt) total = 1 m 2 + 7.2 10 -13 6.5 3600 cm 2 = 1 m 2 + 1.68 m 2 = 2.68 m 2 10 15 = Q (Dt) total exp [ -x j 2 4(Dt) total ] However, Q can be found from original half-gaussian: Q = C s Dt = 1.1 10 15 / cm 3
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10 15 = 10 19 1 2.68 exp [ -x j 2 4(Dt) total ] x j 4 2.68 = 3.0 x j = 9.8 m Problem 4 a) To position the Gaussian peak exactly at the Si/SiO2 interface will split the dose evenly into Si and SiO2. For boron ions, R p (80 keV) = 0.1 m ΔR p (80 keV) = 0.04 m b) C p = 1 10 18 = 2   R p dose = 1 10 18 0.04 10 -4 2 = 1.0 10 13 /cm 2 c) The boron implant profile inside Si is a half-gaussian (characterized by Rp) is mathematically equivalent to a drive-in diffusion profile (characterized by Dt).
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This note was uploaded on 03/03/2012 for the course EECS 142 taught by Professor Ee142 during the Spring '04 term at Berkeley.

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143f2010-05-soln - EE143 Fall 2010 EE143 HW#5 Solutions...

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