橡Taro11-卒業論文.PDF

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1 Recombination Generation Lifetime 13 9

2 Recombination Lifetime Si TEG 3 5. Recombination Lifetime Si TEG 6 6. Pulse Scanning C-V Generation Lifetime Appendix n p 3 31 Appendix 34 --

3 1. CPUHDD DRAM 1 Pulse Scanning C-V Generation Lifetime Recombination Lifeitime Recombination Generation Lifetime -3-

4 ..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-

5 E g E g a [K π/a] trap.1. Si n P E c G R E g E v p P, N.... G -5-

6 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-

7 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-

8 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-

9 P E c N E fn E fp E v.4. P N

10 .7. P N W Ec P N E v E fp E fn E c

11 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

12 * 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 ϕ bi kt N ln DNA ϕbi = ϕn ϕp = q n i.8 Si wp wn -1 -

13 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 d ψ qn A wp x < = * dx ε ε s.3 d ψ < x wn dx qnd = ε ε * s

14 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 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

15 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

16 ( ) 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 -

17 3. Recombination Lifetime a 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

18 Function Generator FunctionGenerator DC

19 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 -

20 I f I r t t τ r erf t If τ = I + I r f r I f I r t τ Appendix erf x r erf ( ) x = y dy π x exp 3. I f I r t

21 4. Si TEG 4.1. Si Si 3 4 V Si

22 E c E f E f E v 4.. E c E f E f E v

23 E c E f E f E v 4.4. E c E f E f E v TEG Metal SiO P N 4.6. TEG TEG 4.6. Metal -3 -

24 5. Recombination Lifetime 5.1. Si 4 Si 5 I f I r τ r ma τ r τ r.1µ Sec 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 -

25 5.. I f Recombination Lifetime τ r 5.3. Recombination Lifetime τ r 1-5 -

26 5.. TEG TEG Recombination Lifetime τ r TEG TEG R.L. R.L. -6 -

27 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

28 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 TEG ND 1. 1 cm n i cm τ r τ g τ r 9 µ sec τ g sec

29

30 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. :" " :" " :" " :" " :" " :" " A.S.Grove :" " :" " :" " B.G.Streetman :" " :" 3 " :" "

31 . 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 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 -

32 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 -

33 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

34 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 = , c, 1,, c1! c( c+ 1)!.4 x 1 x 3 erf( x) exp x F 1; ; x π = x 3 exp x 1F1 1; ; x a π = n= n

35 a x exp = x π x an = a 1 n + n = 1,, n 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 = π x x x x x.1 1.E 9 x 16 ( ) exp x erf( x) = π x x x

36 x.7 x 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 -

37 .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 =

38 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 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 -

39 14 X1= 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 -

40 4 E=S N IF 1/^Q-1 ^ -1 THEN GOTO IF Y-ETHEN GOTO IF Y-E1.E-11 THEN GOTO 5 Y E 1.E IF E-Y1.E-11 THEN GOTO 5 45 IF YETHEN GOTO IF YETHEN B= 47 GOTO B=1 49 GOTO 18 5 PRINT "X=",XQ 51 END > 1 q.3. erf x x erf x.4. erf x -4 -

5 36 5................................................... 36 5................................................... 36 5.3..............................

5 36 5................................................... 36 5................................................... 36 5.3.............................. 9 8 3............................................. 3.......................................... 4.3............................................ 4 5 3 6 3..................................................

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