EE105 - Fall 2006 Microelectronic Devices and Circuits. Your EECS105 Week

Transcription

1 EE15 - Fall 6 Mcroelectroc Devces a Crcuts Prof. Ja M. Rabaey (ja@eecs) Lecture : Semcouctor Bascs Your EECS15 Week Mo Tu We Th Fr 9am 1am Lab 353 Cory Lab 353 Cory Lab 353 Cory 11am Dscusso 93 Cory 1pm Offce Hour Rya Roberts 1pm Dscusso 93 Cory pm 3pm 4pm 5pm Offce Hour ate Pletcher Dscusso 93 Cory Offce Hour Geral Wag Lecture 3 McLaughl Offce Hours Prof. Rabaey 511 Cory Offce Hour Asako Toa Lab 353 Cory Lecture 3 McLaughl 6pm 1

2 Ths week Dscusso sessos a offce hours startg ths week Dscussos: 93 Cory Offce Hours TAs: 477 Cory Labs: 353 Cory Make-up Lecture: Fray September 8 3:3-5pm, 3 McLaughl 3 At a glace Last class Itro a some recap of crcut aalyss Toay: Revew of Semcouctor Bascs 4

3 Peroc Table of Elemets 5 Electroc Propertes of Slco Slco s Group IV (atomc umber 14) Atom electroc structure: 1s s p 6 3s 3p Crystal electroc structure: 1s s p 6 3(sp) 4 Damo lattce, wth.35 m bo legth Very poor couctor at room temperature: why? (1s) (s) (p) 6 (3sp) 4 Hybrze State 6 3

4 The Damo Structure 3sp tetraheral bo o.35a o 5.43A 7 States of a Atom Eergy. E 3 E Forbe Ba Gap Allowe Eergy Levels E 1 Atomc Spacg Lattce Costat Quatum Mechacs: The allowe eergy levels for a atom are screte ( electros wth opposte sp ca occupy a state) Whe atoms are brought to close cotact, these eergy levels splt If there are a large umber of atoms, the screte eergy levels form a cotuous ba 8 4

5 Eergy Ba Dagram The gap betwee the coucto a valece ba etermes the couctve propertes of the materal Metal Coucto Ba eglgble ba gap or overlap Valece Ba Isulator large ba gap, ~ 8 ev Coucto Ba ba gap Valece Ba Semcouctor meum sze gap, ~ 1 ev Electros ca ga eergy from lattce (phoo) or photo to become free e - e - 9 Moel for Goo Couctor The atoms are all oze a a sea of electros ca waer about crystal: The electros are the glue that hols the sol together Sce they are free, they respo to apple fels a gve rse to couctos O tme scale of electros, lattce looks statoary 1 5

6 Bo Moel for Slco (TK) Slco Io (+4 q) Four Valece Electros Cotrbute by each o (-4 q) electros each bo 11 Bo Moel for Slco (T>K) Some bo are broke: free electro Leave beh a postve o or trap (a hole)

7 Holes + - otce that the vacacy (hole) left beh ca be flle by a eghborg electro It looks lke there s a postve charge travelg arou! Treat holes as legtmate partcles. 13 More About Holes Whe a coucto ba electro ecouters a hole, the process s calle recombato The electro a hole ahlate oe aother thus epletg the supply of carrers I thermal equlbrum, a geerato process couterbalaces to prouce a steay stream of carrers 14 7

8 Thermal Equlbrum (Pure S) Balace betwee geerato a recombato etermes o p o Strog fucto of temperature: T 3 o K G G ( T ) + th G opt R k( p) G R k( p) G ( T ) th p Gth ( T ) / k ( T ) 1 cm 1 3 ( T ) at 3K Mass-acto law 15 Dopg wth Group V Elemets P, As (group 5): extra bog electro lost to crystal at room temperature Immoble Charge Left Beh

9 Door Accoutg Each oze oor wll cotrbute a extra free electro The materal s charge eutral, so the total charge cocetrato must sum to zero: ρ q + qp + q Free Electros By Mass-Acto Law: q q Free Holes Ios (Immoble) p ( T ) + q + q + q + q 17 Door Accoutg (cot) Solve quaratc: Oly postve root s physcally val: ± + 4 For most practcal stuatos: >>

10 Dopg wth Group III Elemets Boro: 3 bog electros oe bo s usaturate Oly free hole egatve o s mmoble! Mass Acto Law Balace betwee geerato a recombato: p -type case: o o ( T 3 K, + p 1 cm 1 3 ) P-type case: p a a a 1

11 11 1 Compesato Dope wth both oors a acceptors: Create free electro a hole! Compesato (cot.) More oors tha acceptors: > a a o >> a o p a o p >> a o More acceptors tha oors: a >

12 Dsturbg the Equlbrum Rap, raom moto of holes a electros at thermal velocty v th 1 7 cm/s wth collsos every τ c 1-13 s. Apply a electrc fel E a charge carrers accelerate for τ c secos zero E fel v th postve E 1 * m v 1 th aτ c kt λ v τ λ 1 cm / s 1 s 1 cm (mea free path - 1 m) th c (hole case) x v th 3 Drft Velocty a Moblty For holes: v r F a τ c m e p qe q c c c E mp m τ τ τ p v μ E p r For electros: v r F a τ c m e qe qτ c c c E m m τ τ v μ E r 4 1

13 Moblty vs. Dopg Slco at 3K efault values: μ 1 4 μ p 5 Spee Lmt: Velocty Saturato 1 c 3 1 m / s Thermal Velocty 4 V 4 V cm V cm cm 1 μm μm The fel stregth to cause velocty saturato may seem very large but t s oly a few volts a moer trasstor! 6 13

14 Drft Curret Desty (Holes) Hole case: rft velocty s same recto as E hole rft curret esty J p r v p E The hole rft curret esty s: x J p r q p μ p E 7 Drft Curret Desty (Electros) Electro case: rft velocty s opposte recto as E electro rft curret esty J r v E J r ( q) μ E qμ E x The electro rft curret esty s: J r (-q) v uts: C/s/cm A/cm r r J J p + J ( qpμ p + qμ )E 8 14

15 Resstvty Bulk slco: uform opg cocetrato, away from surfaces -type example: equlbrum, o Whe we apply a electrc fel, J qμ E qμ E Couctvty σ qμ, eff qμ( a ) Resstvty 1 1 ρ Ω cm σ q μ, eff 9 Ohm s Law V σ tw I JA J ( tw ) σ tw E σ tw V L L R 1 σ t L W ρ L t W V R 3 15

16 Sheet Resstace (R s ) IC resstors have a specfe thckess ot uer the cotrol of the crcut esger Elmate t by absorbg t to a ew parameter: the sheet resstace (R s ) ρl R Wt ρ t L W R sq L W umber of Squares 31 Usg Sheet Resstace (R s ) Io-mplate (or ffuse ) IC resstor 3 16

17 Iealzatos Why oes curret esty J tur? What s the thckess of the resstor? What s the effect of the cotact regos? 33 17