Recombination Generation Lifetime 13 9
1. 3. 4.1. 4.. 9 3. Recombination Lifetime 17 3.1. 17 3.. 19 3.3. 4. 1 4.1. Si 1 4.1.1. 1 4.1.. 4.. TEG 3 5. Recombination Lifetime 4 5.1 Si 4 5.. TEG 6 6. Pulse Scanning C-V Generation Lifetime 7 7. 9 8. 9. Appendix n p 3 31 Appendix 34 --
1. CPUHDD DRAM 1 Pulse Scanning C-V Generation Lifetime Recombination Lifeitime Recombination Generation Lifetime -3-
..1. n p ( Efn Ei) n= n i exp kt ( Efp Ei) p= n i exp kt Appendix.1 Appendix. E fn Efp.1. np = n i.3 n p ni majority carrier minority carrier ( n) ( p) ( ).4 pn ni.4.3 GaAs Si Si -4-
.1. 4 3 1.85-1 E g E g a - -1 1 [K π/a] trap.1. Si n P E c G R E g E v p P, N.... G -5-
G = α N.5 α N n = G τ g.6 n τ g.. R dn dt dn n = R = dt τ r.7 τ r G R.3 pn ni R.3. R n.3. np p β R = β np.8 G R αn = βn p P P.9 n P, pp.. Na pp Na R = β n N P a.1-6-
n 1 [/Sec] n P n P E c G R E g E v p P, N.3. ( ) R= βn p = β n + n p P P P P.11 G G.1 n n n= n n P P.13 np np.13 n n P dn dt P n = R τ P r.14 n R = βnppp = τ P r.15-7-
τ r 1 β p P.16 τ r n G τ P g.17 np np G + n1 = R.18 n τ P i n τ p g r P.19 pp Na np ni τ τ r g ni N a. τ τ r g ni N d.1-8-
...4..5. P E c N E fn E fp E v.4. P N.5..6..6. -9-
.7. P N W.7..8. Ec P N E v E fp E fn E c.8. -1 -
Diffusion potential built in potential q ϕ bi ϕ bi.9. ϕ bi q ϕ bi = Efn E fp. ϕ bi P N qϕ bi E i E fp qϕ E bi fp E fn E i E v E fn E i E c.9. ψ ρ = = + d ψ de s q * * dx dx εs ε εs ε ( N N p n) D A.3-11 -
* ρ Ω cm q c ε ε s s -3-3 F/cm ND NA cm p n cm.3 d ψ = dx.4 N N + p n= D A.5 NA n.9. Efn Ei qϕn ϕn.5 ND n p NA.3 ϕ n 1 kt N ( Ei Ef) = ln q q n x wn D i.6 ϕ p 1 kt N ( Ei Ef) = ln q q n x wp i A.7.6.7 ϕ bi kt N ln DNA ϕbi = ϕn ϕp = q n i.8 Si.1..1. wp wn -1 -
p n.3 d ψ dx q = A ε ε * s ( N N ) D.9 q(n D N A ) qn D w p w n x qn A W.1..1..9 d ψ qn A wp x < = * dx ε ε s.3 d ψ < x wn dx qnd = ε ε * s.31-13 -
w p E w n x ϕ bi E max ψ (a) ϕ bi (b) W.11. a b x qn w = qn w A p D n.3 W W = w + w p n.33.11. a.3.31 ( ) E x ( + p) dψ qna x w = = dx ε ε * s p w x <.34 ( ) E x ( ) qn x qn x w = E + = D D max * * εs ε εs ε n < x wn.35 Emax x= E qn w qn w = = D n A p max * * εs ε εs ε.36-14 -
.34.35 ϕbi ϕ bi wn ( ) ( ) ( ) wn E x dx E x dx E x dx w p w p = = A p qndwn * * s s qn w = + = ε ε ε ε 1 E max W.37 ϕbi.11. a.3.37 W = * ε s ε N A + N D ϕbi q NAND.38 + NA ND wp wn wp W W w = n * ε s εϕ bi qn D.39 ( ) = Emax + * E x qn x ε s D ε.4 ND x W w n E qn W = D max * εs ε.41-15 -
( ) E x ( ) qnd W + x x = = Emax 1 ε ε W * s.4 ψ x x x = Edx= Emax x C C + W.43 ( ) -16 -
3. Recombination Lifetime 3.1. 3.1. 3.. a 3.1. 3.. b If Ir 3.1. P N P N Recombination E f p E v E f n Recombination Recombination E f p E v E c E f n Recombination E c (a) (b) 3.. a b 3.3. -17 -
3.3. 3.4. Function Generator FunctionGenerator DC 3.4. -18 -
3.. 3.5. 3.5. Recombination Lifetime 1 R 11 1kΩ R 1 1k Ω R3 1 1 Ω 3.6. TEG 3.6. Recombination Lifetime R 11 1kΩ R 1 1k Ω R3 1 1 Ω -19 -
3.3. 3.7. 3.7. I f I r t t τ r erf t If τ = I + I r f r 3.1 3.1 I f I r t τ Appendix erf x r erf ( ) x = y dy π x exp 3. I f I r t 3.7. - -
4. Si TEG 4.1. Si Si 3 4 V 4.1.1. ++ + 4.1. Si 1 3 5-1 -
4.1.. 4.. 4.3. E c E f E f E v 4.. E c E f E f E v 4.3. 4.4. - -
E c E f E f E v 4.4. E c E f E f E v 4.5. 4.. TEG Metal SiO P N 4.6. TEG TEG 4.6. Metal -3 -
5. Recombination Lifetime 5.1. Si 4 Si 5 I f I r τ r 5 5.1..5 7 ma 4.1.1. τ r τ r.1µ Sec 4.1.. 5.1. I f I r Recombination Lifetime τ r I f Recombination Lifetime R.L. 5.. I f I r τ r I I + I x τ r 5.3. I f I r τ r I f I r erf t τ r ( ) f f r -4 -
5.. I f Recombination Lifetime τ r 5.3. Recombination Lifetime τ r 1-5 -
5.. TEG TEG 5.3. 5.4. 5.4. Recombination Lifetime τ r TEG TEG 5.3. 5.4. R.L. R.L. -6 -
6. Pulse Scanning C-V Generation Lifetime MOS Generation Lifetime G.L. Pulse Scanning C-V Metal SiO N-Si (a) c d V b (b) C a V V a b c t (c) c d b a t 6.1. MOS a b Pulse Scanning C-V c 6.1. a MOS 6.1. c 6.1. b C V t V - n cm qn = Cox V 6.1 q - n t cm /Sec n = t Cox V q 6. 6.. -7 -
6.. 11-8. 1. 1 cm Sec [ ] G.L. Sec τ r τ g τ r τ g.1..1 τ τ r g ni N D 6.3 ND n i 15-3 -3 TEG ND 1. 1 cm n i 1.38 1 cm τ r τ g τ r 9 µ sec τ g sec. 1-8 -
7. 8. -9 -
1 S.Kawazu, T.Matsukawa and H.Nakata:"Pulse Scanning C-V Technique for The Analysis of Carrier Generation in Silicon", Electro-chamical Society Spring Meeting Extended Abstract pp6-633 R.H.Kingston, Associate member, IRE:"Switching Time in Junction Diodes and Junction Transistors" 3 W.shockley:"The Theory of p-n Junction in Semiconductors and p-n Junction Transistors" 4 S.M. :" " 1987 5 :" " 199 6 :" " 1988 7 :" " 1986 8 :" " 1995 9 :" " 1985 1 A.S.Grove :" " 1995 11 :" " 198 1 :" " 199 13 B.G.Streetman :" " 1991 14 :" 3 " 1978 15 :" " 199-3 -
. Appendix. n p N f E ( E) = N f.1 N f n E f p E 1 f n ( E) = E E 1 exp kt fn +. 1 1 f p ( E) = 1 = E Efp E Efp 1+ exp 1+ exp kt kt.3. E E fn 3kT E E E E fn ( ) fn f n E exp kt.4 E E E E fn ( ) fp f n E 1 exp kt.5 E fp n p -31 -
Ec ( E) n= N f de n E E = N exp Ec kt fn de E E fn E Efn = N exp exp kt kt E Efn = N ktexp kt Ec Efn Ec Efn = N ktexp ktexp kt kt Ec Efn = NkTexp kt Ec.6 Ev ( E) p = N f de p E Efp = N exp de E v kt E E fp E E fp = N exp exp kt kt E Efp = N ktexp kt Efp Ev Efp = N ktexp ktexp kt kt Ev Efp Efp Ev = NkTexp = NkTexp kt kt Ev Ev.7 n i E i -3 -
Ec Efn n= NkTexp kt E E c Ei fn Ei = NkTexp exp kt kt Efn Ei = ni exp kt.8 Efp Ev p = NkTexp kt Ei Efp Ei Efp = NkTexp exp kt kt Ei Efp = ni exp kt.9 E fn E fp pn ni Efn Ei Ei Efp n p = ni exp niexp kt kt Efn Efp = ni exp kt.1 E fn E fp n p= n i.11-33 -
Appendix. erf x t dt π ( ) = x exp.1 x x x 1 3 erf ( x) = xf 1 1 ; ; x π. d y dy + ( ) = x c x ay dx dx.3 ( ) = 1 1(, ; ) = (, ; ) ( ) y x F ac x M a c x ax a a+ 1 x = 1 + + +, c, 1,, c1! c( c+ 1)!.4 x 1 x 3 erf( x) exp x F 1; ; x π = 1 1.5 x 3 exp x 1F1 1; ; x a π = n= n.6-34 -
a x exp = x π x an = a 1 n + n = 1,, n 1.7.5 x.5 erf x x 5. erf x x 1 x sec x erfcx erf erfc ( x) = 1 erfc( x) x t dt x π ( ) = exp.8 erfc x F,1;, x ( ) exp x 1 1 π x x.9.9 x x erfc ( x) ( ) ( ) exp x 1 1 1 3 = + + + + + π x x x x x.1 1.E 9 x 16 ( ) exp x 1 1 8 erf( x) = 1 + + + π x x x.11.1.11-35 -
x.7 x.11.1. 1 1 sn = an, v= n+, mk = 8 k a exp x = π yes x? no a s n n x exp = x π = a 1 v = ; = n n 1 n ( n ) x an = an 1, ( n = n ) v + 1 s = s + a n = n v = v+ 1 ( ) m k = = 8 z = x m 8 zk = x+ = x+ k = z x 1 mk = mk 1 ( ) yes a > 1.E 1? n m >? no yes no erf ( x) = s n a erf ( x) = 1 z k.1. erf x BASIC -36 -
.1. BASIC x erf x erf1 erfx x erf 1!********************************************! ERROR FUNCTION PROGRAM 3! erf x :erf1 4!******************************************** 5 DIM A1 6 DIM S1 7 DIM M1 8 DIM Z1 9 PRINT "X=" 1 INPUT X 11 PRINT X 1 IF XTHEN GOTO 4 13 A = *X/SQR PI *EXP -X^ 14!PRINT "A =",A 15 N= 16 N=N+1 17 AN = X^/ N+ 1/ *A N-1 18!PRINT "N=",N,"AN =",A N 19 S =A x A = exp x π A S n x = A 1 n + = A n 1 SN =A N +SN-1 1!PRINT "SN =",S N IF AN 1.E-1 THEN GOTO 37 A n 1.E 1 3 IF AN 1.E-1 THEN GOTO 16 4 M =8 S = A + S n n n 1 x M = 8-37 -
5 Z =X 6 K= 7 K=K+1 8 ZK =X+ MK-1 /Z K-1 9 MK =M K-1-1/ 3!PRINT "K=",K,"MK =",M K,"ZK =",Z K 31 IF MK = THEN GOTO 33 M k 3 IF MK THEN GOTO 7 33 E=1-EXP -X^ /SQR PI /Z K 34!PRINT "E=",E 35 PRINT "erfx =",E 36 GOTO 38 37 PRINT "erfx =",S N-1 38 END Z Z k M = x k M = x+ Z Mk 1 k 1 k 1 = 1 exp x 1 π E = Z k.. erf x 1!*******************************************! ERROR FUNCTION PROGRAM 3! Y=erf X :erf 4!******************************************* 5 DIM X1 6 DIM A1 7 DIM S1 8 DIM M1 9 DIM Z1 1 PRINT "******** Y =1 ********" 11 PRINT "Y=" 1 INPUT Y 13 PRINT Y -38 -
14 X1=3.1965 15 X = 16 B= 17 Q= 18 Q=Q+1 b 1 19 XQ =X1* -1^ B * 1/^ Q-1 +X Q-1 Xq = X ( 1) X q 1 q + IF XQ THEN GOTO 9 X q X q 1 A = *X Q /SQR PI *EXP - X Q ^ A= exp X π N= 3 N=N+1 4 AN = X Q ^/ N+ 1/ *AN-1 5 S =A 6 SN =A N +SN-1 7 IF AN 1.E-1 THEN GOTO 4 A n 1.E 1 8 IF AN 1.E-1 THEN GOTO 3 9 M =8 3 Z =X Q 31 K= 3 K=K+1 33 ZK =X Q + M K-1 /Z K-1 34 MK =M K-1-1/ X q 35 IF MK= THEN GOTO 37 M k 36 IF MK THEN GOTO 3 37 F=1-EXP - X Q ^ /SQR PI /ZK 38 E=F 39 GOTO 41 A n 1 1 X q = A 1 n + M = 8 Z Z = X q k M M = Xq + Z k = Mk 1 n 1 k 1 k 1 1 q exp X 1 π F = Z k q -39 -
4 E=S N-1 1 1 41 IF 1/^Q-1 ^ -1 THEN GOTO 45 45 4 IF Y-ETHEN GOTO 44 43 IF Y-E1.E-11 THEN GOTO 5 Y E 1.E 11 44 IF E-Y1.E-11 THEN GOTO 5 45 IF YETHEN GOTO 48 46 IF YETHEN B= 47 GOTO 18 48 B=1 49 GOTO 18 5 PRINT "X=",XQ 51 END > 1 q.3. erf x x erf x.4. erf x -4 -