PN Junction Diode: I-V Characteristics

Transcription

1 Chater 6. PN Juctio Diode : I-V Characteristics Chater 6. PN Juctio Diode: I-V Characteristics Sug Jue Kim kimsj@su.ac.kr htt://helios.su.ac.kr

2 Cotets Chater 6. PN Juctio Diode : I-V Characteristics q Qualitative Derivatio q Quatitative Solutio Strategy q Quasieutral Regio Cosideratios q Deletio Regio Cosideratios q Boudary Coditios

3 Chater 6. PN Juctio Diode : I-V Characteristics q The Ideal Diode Equatio ü The I-V characteristics of the ideal diode are modeled by the ideal diode equatio à qualitative ad quatitative derivatio Qualitative Derivatio ü Equilibrium situatio balace high-eergy carrier drift diffusio otetial hill E

4 Chater 6. PN Juctio Diode : I-V Characteristics ü Forward bias situatio à a lowerig of the otetial hill ü The same umber of miority carriers are beig swet ü More majority carriers ca surmout the hill à I N ad I P à I ü The umber of carriers that have sufficiet eergy to surmout the barrier goes u exoetially with V A à exoetial icrease of the forward curret

5 Chater 6. PN Juctio Diode : I-V Characteristics ü Reverse bias situatio à a icrease of the otetial hill ü The barrier icrease reduces the majority carrier diffusio to a egligible level ü The -side electros ad -side holes ca wader ito the deletio regio ad be swet to the other side à reverse I (à) ü Beig associated with miority carriers, the reverse bias curret is exected to be extremely small

6 Chater 6. PN Juctio Diode : I-V Characteristics ü The miority carrier drift currets are ot affected by the height of the hill (The situatio is similar to a waterfall) ü If the reverse bias saturatio curret is take to be I 0, the overall I-V deedece is I = I e - ( VA / Vref 1) 0 kt V ref = q Rectificatio I-V characteristic

7 Chater 6. PN Juctio Diode : I-V Characteristics ü Wheever a electro o the -side moves to the -side, it is relaced by a electro geerated through oe of the R-G ceters miority ohmic excess majority carriers à local E ohmic recombiatio excess majority carriers à local E Excess carriers move to the cotact with a relaxatio time à greatly fast miority ü Curret comoet Deletio regio : electros ad holes -regio (far) : holes -regio (far) : electros

8 Chater 6. PN Juctio Diode : I-V Characteristics Quatitative Solutio Strategy ü Basic assumtios (1) Steady state coditios () A odegeerately doed ste juctio (3) Oe-dimesioal (4) Low-level ijectio (5) G L =0 I = AJ J = J ( x) + J ( x) N J N = que + qdn dx JP = qu E + qdp dx P d d

9 Chater 6. PN Juctio Diode : I-V Characteristics 0 ad low-level ijectio à miority carrier diffusio equatios Quasieutral Regio Cosideratios D D D = - + G t DN x t D D D = - + G t DP x t L L N P d D D dx t 0 = D -... x -x d D D dx t 0 = D -... x ³ x

10 ü Sice 0 Chater 6. PN Juctio Diode : I-V Characteristics ad d 0 /dx=d 0 /dx=0 i the quasieutral regios dd J qd x x dx dd JP = - qdp... x ³ x dx N = N... - Q = + D 0 = + D 0 ü We ca oly determie J N (x) i the quasieutral -regio ad J P (x) i the quasieutral -regio Deletio Regio Cosideratios 1 = Ñ J N + t q t = - t 1 Ñ J q P + t thermal R-G thermal R-G + t + t other rocesses other rocesses 1 dj 1 dj N P 0 = +, 0 = - + q dx t thermal q dx t thermal R-G R-G

11 Chater 6. PN Juctio Diode : I-V Characteristics ü Suose that thermal recombiatio-geeratio is egligible throughout the deletio regio; ü dj / dx = 0 ad dj / dx = 0 N deletio regio J (- x x x ) = J (-x ) N N J (- x x x ) = J ( x ) P P P / t = / t = 0 thermal R-G thermal R-G à J N ad J P are costats iside the J = J (- x ) + J ( x ) N P

12 Chater 6. PN Juctio Diode : I-V Characteristics Boudary Coditios ü At the Ohmic Cotacts The ideal diode is usually take to be a wide-base diode The cotacts may effectively be viewed as beig ositioed at x= ± D D ( x - ) = 0 ( x + ) = 0 ü At the Deletio Regio Edges ( F ) ( E F ) kt N -Ei / kt i - / Uder oequilibrium coditios: = e, = e i i Equilibrium coditios Noequilibrium coditios

13 Chater 6. PN Juctio Diode : I-V Characteristics = e ( FN -FP )/ kt i L L F = N - qv F A P E F N - E F If the equal sigal is assumed to hold throughout the deletio regio qva / kt = e... - x x x i : law of juctio

14 Chater 6. PN Juctio Diode : I-V Characteristics ü Evaluatig the equatio at the -edge ( -x ) ( - x ) = ( - x ) N = e A i i ( - x ) = e N A qv A / kt qv A / kt D - x = e - N i qva / kt ( ) ( 1) A ü Similarly,

15 Chater 6. PN Juctio Diode : I-V Characteristics D x = e - N i qva / kt ( ) ( 1) D

16 Chater 6. PN Juctio Diode : I-V Characteristics Derivatio Proer ü The origi of coordiates is shifted to the -edge of the deletio regio d D D ' 0 = DP -... x ³ 0 ' dx t ü Boudary coditios D ( x ' ) = 0 ' i qva / kt x e ND D ( = 0) = ( -1) ü The geeral solutio D = + ' - x'/ LP ( x ) A e A e 1 x'/ L P '... x 0 ³ Q LP = DPt

17 Chater 6. PN Juctio Diode : I-V Characteristics ü A à 0 because ex(x /L ) à as x à ü With, A 1 =D (x =0) D x = e - e x ³ N ' i qva / kt - x'/ LP ' ( ) ( 1)... 0 D dd D JP x qdp q e e x ' dx L N ' P i qva / kt - x'/ LP ' ( ) = - = ( - 1)... ³ 0 ü O the -side of the juctio with the x -coordiate. P D D x = e - e x ³ N " i qva / kt - x"/ LN ( ) ( 1)... " 0 A dd D J x qd q e e x "/ N N " dx LN NA " N i qva / kt - x LN " ( ) = - = ( - 1)... ³ 0

18 Chater 6. PN Juctio Diode : I-V Characteristics ü The curret desities at the deletio regio edges, D J N x x J N x q e L N " N i A / ( = - ) = qv kt ( = 0) = ( - 1) D JP x x JP x q e L N ' P i A / ( = ) = ( = qv kt 0) = ( - 1) æ DN i DP ö i I = AJ = qaç + e - è LN NA LP ND ø P N D A qva / kt ( 1) I = I e - 0 qva ( / kt 1) æ D D ö ç è ø N i P i I0 º qa + L N N A L P N D Ideal diode equatio or Shockley equatio

19 Examiatio of Results Chater 6. PN Juctio Diode : I-V Characteristics

20 Chater 6. PN Juctio Diode : I-V Characteristics ü Carrier currets ü The total curret desity is costat ü The majority-carrier curret desities are obtaied by grahically subtractig the miority-carrier curret desities from the total curret desity

21 Chater 6. PN Juctio Diode : I-V Characteristics ü Carrier cocetratios ü Forward biasig icreases Reverse decreases the cocetratio ü Uder the low-level ijectio, the majority carrier cocetratios i these regios are everywhere aroximately equal to their equilibrium values

22 Chater 6. PN Juctio Diode : I-V Characteristics ü Uder reverse biasig the deletio regio acts like a sik for miority carriers ü Larger reverse biases have little effect N A > N D

23 6.. Reverse-Bias Breakdow Chater 6. PN Juctio Diode : I-V Characteristics

24 Chater 6. PN Juctio Diode : I-V Characteristics q Zeer Process Tuelig The article eergy remais costat durig the rocess. ü The article ad the barrier are ot damaged. (1) There must be filled states o oe side ad emty states o the other side at the same eergy. () d must be very thi.

25 Chater 6. PN Juctio Diode : I-V Characteristics Reverse bias # of filled valece electros laced oosite emty coductio-bad states curret 6..3 The R-G Curret ü A curret far i excess of that redicted by the ideal theory exists at small forward bias ad all reverse biases. thermal recombiatio-geeratio i the deletio regio

26 Chater 6. PN Juctio Diode : I-V Characteristics E c I R E c E f E f E v V R E v V R = 0 V (Equilibrium)

27 Chater 6. PN Juctio Diode : I-V Characteristics E c I R E c E f E f E v V R h e + - E v V R = < 0 V

28 Chater 6. PN Juctio Diode : I-V Characteristics E c I R E f E v e - e - e - e - e - E c E f V R E v V R << 0 V (Zeer Breakdow, V R = 0 V Tuelig)

29 Chater 6. PN Juctio Diode : I-V Characteristics < ü Reverse bias <, 0 0 thermal geeratio ü Forward bias, > recombiatio (1) The et R-G rate is the same for electros ad holes. () For every electro-hole air created or destroyed er secod, oe electro er secod flows ito or out of the diode cotacts. > 0 0

30 Chater 6. PN Juctio Diode : I-V Characteristics G R DIFF kt E E kt E E i i i G R x x i G R i G R thermal G R thermal x x G R I I I e e W qa I dx qa I t dx t qa I T i i T = + = + º = = = - = - ò ò ) ( 1 ) ( 1 0 0, ) ( ) ( ) ( ) ( )/ ( )/ ( t t t t t t t t t t kt E E i kt E E i T i i T e e )/ ( 1 )/ ( º º

31 Summary Chater 6. PN Juctio Diode : I-V Characteristics 31

32 Summary Chater 6. PN Juctio Diode : I-V Characteristics 3

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