Semiconductor Device Physics

Transcription

1 1 Semcoductor evce Physcs Lecture 7 htt://ztomul.wordress.com 0 1 3

2 Semcoductor evce Physcs Chater 6 Jucto odes: I-V Characterstcs

3 3 Chater 6 Jucto odes: I-V Characterstcs Qualtatve ervato Majorty carrers Majorty carrers

4 Chater 6 Jucto odes: I-V Characterstcs Curret Flow a Jucto ode Whe a forward bas (V A > 0) s aled, the otetal barrer to dffuso across the jucto s reduced. Morty carrers are jected to the quas-eutral regos Δ > 0, Δ > 0. Morty carrers dffuse the quas-eutral regos, recombg wth majorty carrers. 4

5 5 Chater 6 Jucto odes: I-V Characterstcs Ideal ode: Assumtos Steady-state codtos. o-degeerately doed ste jucto. Oe-dmesoal dode. Low-level jecto codtos reval the quas-eutral regos. o rocesses other tha drft, dffuso, ad thermal R G take lace sde the dode.

6 6 Chater 6 Jucto odes: I-V Characterstcs Curret Flow a Jucto ode Curret desty J = J (x) + J P (x) d d( ) J( x) qe q qe q dx dx d d( ) JP( x) q E qp q E qp dx dx J (x) ad J P (x) may vary wth osto, but J s costat throughout the dode. Yet a addtoal assumto s ow made, that thermal recombato-geerato s eglgble throughout the deleto rego J ad J P are therefore determed to be costats deedet of osto sde the deleto rego.

7 7 Chater 6 Jucto odes: I-V Characterstcs Carrer Cocetratos at x, +x Cosder the equlbrum carrer cocetratos at V A = 0: -sde ( x ) 0 A 0 ( x ) A -sde ( x ) 0 0 ( x ) If low-level jecto codtos reval the quas-eutral regos whe V A 0, the: ( x ) A ( x )

8 8 Chater 6 Jucto odes: I-V Characterstcs Law of the Jucto The voltage V A aled to a jucto falls mostly across the deleto rego (assumg that low-level jecto codtos reval the quas-eutral regos). Two quas-ferm levels s draw the deleto rego: e e ( E F ) P ( F E ) ( EFP) e e e ( F F ) P ( F E ) e qv A for x x x

9 Chater 6 Jucto odes: I-V Characterstcs Excess Carrer Cocetratos at x, x 9 -sde -sde ( x ) A ( x ) e e 0 qv A A qv A ( x ) ( x ) e e 0 qv A qv A qva qva ( x ) ( e 1) A ( x) ( e 1)

10 10 ( x ) e 100 e cm 0 Chater 6 Jucto odes: I-V Characterstcs Examle: Carrer Ijecto A jucto has A =10 18 cm 3 ad =10 16 cm 3. The aled voltage s 0.6 V. a) What are the morty carrer cocetratos at the deleto-rego edges? 0 qva ( x ) e 10 e cm qva b) What are the excess morty carrer cocetratos? ( x ) ( x ) cm ( x ) ( x ) cm

11 11 Chater 6 From the morty carrer dffuso equato, d P dx 0, x 0 Jucto odes: I-V Characterstcs Excess Carrer strbuto For smlcty, we develo a ew coordate system: x 0 0 x We have the followg boudary codtos: x e qva ( ) ( 1) 0 ( ) 0 The, the soluto s gve by: for x 0 x LP ( x ) Ae A e 1 x L P L P P L P : hole morty carrer dffuso legth

12 1 Chater 6 Jucto odes: I-V Characterstcs Excess Carrer strbuto x e qva ( 0) ( 1) ( x ) 0 ew boudary codtos From the x, From the x 0, x'/ LP ( x ) Ae A e 1 0 A 0 A e ( qva / 1) 1 0 x'/ L P Therefore x e e x qva x LP ( ) ( 1), 0 0 Smlarly, x e e x qva x L ( ) ( 1), 0 0

13 13 Chater 6 Jucto odes: I-V Characterstcs ode I V Characterstc -sde J d ( x) x q q e e P A ( ) ( 1) P P 0 dx LP qv x L P -sde J d ( x) x q q e e qva ( ) ( 1) 0 dx L x L J J J J J xx P xx x 0 P x0 J P q L A LP qva ( e 1)

14 14 Chater 6 Jucto odes: I-V Characterstcs ode I V Characterstc I AJ P Aq L A LP qva ( e 1) I I I e 0 qva ( 1) Aq P 0 L A LP Shockley Equato, for deal dode I 0 ca be vewed as the drft curret due to morty carrers geerated wth the dffuso legths of the deleto rego

15 Chater 6 Jucto odes: I-V Characterstcs I Aq P 0 LP L A I 0 ca vary by orders of magtude, deedg o the semcoductor materal, due to factor. I a asymmetrcally doed jucto, the term assocated wth the more heavly doed sde s eglgble. If the sde s much more heavly doed, I Aq P 0 L P If the sde s much more heavly doed, I Aq 0 L A ode Saturato Curret I 0 15

16 16 Chater 6 Jucto odes: I-V Characterstcs ode Carrer Currets Total curret desty s costat sde the dode J J J P eglgble thermal R-G throughout deleto rego dj /dx = dj P /dx = 0 J ( x x x ) J ( x ) J ( x x x ) J ( x ) P P

17 17 e qv Chater 6 Law of the Jucto A Carrer Cocetrato: Forward Bas Jucto odes: I-V Characterstcs Low level jecto codtos A Excess morty carrers qva ( x ) ( e 1) e 0 x L Excess morty carrers A ( x ) ( e 1) e 0 qv x L P

18 Chater 6 Jucto odes: I-V Characterstcs Carrer Cocetrato: Reverse Bas efct of morty carrers ear the deleto rego. eleto rego acts lke a sk, drag carrers from the adjacet quaseutral regos 18

19 Chater 6 Jucto odes: I-V Characterstcs 1 Breakdow Voltage, V BR If the reverse bas voltage ( V A ) s so large that the eak electrc feld exceeds a crtcal value E CR, the the jucto wll break dow ad large reverse curret wll flow. E q A CR b BR S A V V At breakdow, V A = V BR Thus, the reverse bas at whch breakdow occurs s V BR SE CR A V q A b

20 Chater 6 Jucto odes: I-V Characterstcs Breakdow Mechasm: Avalachg Hgh E-feld: Hgh eergy, eablg mact ozato whch causg avalache, at dog level < cm 3 Small E-feld: E q V A CR S A BR E CR : crtcal electrc feld the deleto rego Low eergy, causg lattce vbrato ad localzed heatg oly V BR s q CR

21 Chater 6 Jucto odes: I-V Characterstcs Breakdow Mechasm: Zeer Process Zeer rocess s the tuelg mechasm a reverse-based dode. Eergy barrer s hgher tha the ketc eergy of the artcle. The artcle eergy remas costat durg the tuelg rocess. Barrer must be th domat breakdow mechasm whe both jucto sdes are heavly doed. Tycally, Zeer rocess domates whe V BR < 4.5V S at 300K ad > cm 3. 3

22 Semcoductor evce Physcs 4 Chater 7 Jucto odes: Small-Sgal Admttace

23 Chater 7 Jucto odes: Small-Sgal Admttace Small-Sgal ode Basg Whe reversed-based, a jucto dode becomes fuctoally equvalet to a caactor, whose caactace decreases as the reverse bas creases. Basg addtoal a.c. sgal v a ca be vewed as a small oscllato of the deleto wdth about the steady state value. V 0 << V A RS : seral resstace Y G jc C G Y : caactace : coductace : admttace 5

24 6 Chater 7 Jucto odes: Small-Sgal Admttace Total Jucto Caactace v a R 1 G C C C J Morty carrer lfetme CJ C s A W I C q Jucto / deleto caactace, due to varato of deleto charges ffuso caactace, due to varato of stored morty charges the quaseutral regos C J domates at low forward bases, reverse bases. C domates at moderate to hgh forward bases.

25 Chater 7 Jucto odes: Small-Sgal Admttace 7 For asymmetrcal ste jucto, s W Vb VA qb Relato Betwee C J ad V A B : bulk semcoductor dog, A or as arorate. Therefore, 1 W ( Vb VA ) C A q A J s B S A lot of 1/C J versus V A s lear. The sloe s versely roortoal to B. A extraolated 1/C J = 0 tercet s equal to V b.