Lecture 7: Properties of Materials for Integrated Circuits Context

Transcription

1 Lecture 7: Propertes of Materals for Itegrate Crcuts Cotext Over the last two weeks, we revewe: Basc passve compoets Capactors Resstors Iuctors Lear crcut moels Phasor otato Trasfer fuctos Boe plots 1

2 Cotext Over the ext couple of weeks, we wll cover: The relevat basc physcs of materals How electros move through materals How semcouctor evces are mae Moels of semcouctor evces Cotext I ths lecture, we wll cover: How atoms jo up to form materals The ffereces betwee: Metals Isulators Semcouctors How the propertes of semcouctors ca be mofe to form electroc evces

3 Itegrate crcuts A tegrate crcut s mostly a arragemet of just a few elemets: Slco Alumum Oxyge troge A traces of: Boro Phosphorus Arsec Etc. What gves these materals ther propertes? Atoms cosst of: A ucleus cotag protos a eutros A clou of electros The fferece betwee fferet atoms: the umber of protos, a cosequetly the umber of electros eee to mata eutralty 3

4 Ferm excluso Sce o two electros ca be og exactly the same thg, a there are two types of sp each spatal orbtal ca oly hol two electros. Orbtals As electros are ae to the potetal well of a postvely charge ucleus, they go to orbtals whch are smlar to the resoaces of a rum hea. The rate of chage of phase e ωt correspos to the eergy of the orbtal Eħω 4

5 Eergy levels We ca agram the levels as a fucto of ther eergy: Molecules If two or more ucle are close together, electros arou them wll have ew orbtals, wth ew shapes a fferet eerges 5

6 Bog The orbtals close to each of the ucle o t chage much, but the outer orbtals jo together a have fferet shapes. If electros occupy these orbtals, a they have a lower eergy whe the molecules are close together, the t requres eergy to separate the atoms. Ths s calle bog Elemets The cofguratos of bos that wll form betwee atoms wth fferet umbers of protos ther ucle epe o the bleg of ther outer orbtals to molecular orbtals. The patter of the fllg of orbtals of fferet agular shapes yels a patter of smlarty of the types of bos that wll be observe betwee atoms. Ths patter s mae explct the peroc table 6

7 Peroc Table of Elemets Groups of atoms As atoms come close together: the umber of electros stays the same (to mata eutralty) The umber of orbtals stay the same Each orbtal from each atom s trasforme a blee to a ew orbtal, over may atoms 7

8 Lots of atoms close together: sol As more a more atoms come together a clump, the orbtals from the atoms become early cotuous bas of states Ba b { Ba a { } Ba gap I geeral, there wll be may bas of states, but the lower oes wll be all flle completely wth electros, a grlocke, a the hgher oes wll be empty. Electroc states crystals The electros are states whch exte through the sol as waves We moel them as cely as ths But they mostly look lke ths 8

9 Metals So we wll mostly be tereste the top few states whch are occupe, a the bottom few of those that are uoccupe. Ba b { Ba a { Electros up to here If the electros fll the lower states up to the mle of a ba, the materal wll be a metal The eergy that the electros are flle to s calle the Ferm eergy Sce the electros ca chage ther eerges a orbtals a lttle bt at a tme, they ca move freely a the materal s a goo couctor of heat a electrcty, a ther stregth comes from metallc bog Isulators a Semcouctors If the electros fll the bas up to a gap, a the states above are empty, the materal wll ot couct Ba b { Ba a { Electros up to here If the materal s very uform a pure, f there are a few electros the ba above the gap, they wll be able to move freely. I ths case, the materal s calle a semcouctor 9

10 type Semcouctor If we a a few atoms wth a extra proto, the the orbtals wll be the same, but there wll be a few more electros, a they wll go to the upper ba. Coucto ba { A few Electros here Valace ba { Stll completely full These few electros wll have lots of elbow room, a so the materal wll couct, ot as well as a metal, but pretty well P type Semcouctor If we a a few atoms wth oe less proto, each the the orbtals wll be the same, but there wll be a few less electros, a the lower ba wll have a few empty orbtals Coucto ba { Stll empty Coucto ba { A few empty orbtals here All flle wth electros There are a lot of electros the lower ba, but they oly have a lttle elbow room, so they wll couct, but ot as well as a metal 1

11 Carrers A couple of mportat parameters are (r,t) the umber of electros the coucto ba at a partcular tme a place, A p(r,t) the umber of empty states the valece ba (the umber of holes) P s for postve, because surprsgly eough, the empty states the valece ba act lke postvely charge partcles. Resstvty for a Few Materals Pure copper, 73K ohm-cm Pure copper, 373 K ohm-cm Pure germaum, 73 K ohm-cm Pure germaum, 5 K.1 ohm-cm Pure water, 91 K ohm-cm Seawater 5 ohm-cm The fferece the cofgurato of the orbtals makes a very large fferece couctvty Why the strog temp epeece? 11

12 Thermal occupato At temperatures above absolute zero, a pure semcouctor, there wll be a few electros excte from the valace ba to the coucto ba. Coucto ba { Stll empty A very few electros here Valece ba { A very few empty orbtals here All flle wth electros Ths gves us the three basc materals for tegrate crcuts: Metals to couct currets arou wth low voltage rops Alumum Copper Isulators to keep currets where we wat them: Slco oxe Slco tre A the easly chage semcouctors to gve us cotrol: Trasstors Does Etc. 1

13 Electroc Propertes of Slco Slco s Group IV 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 (1s) (s) (p) 6 (3sp) 4 Hybrze State The Damo Structure 3sp tetraheral bo o.35a o 5.43A 13

14 Slco Slco ba agram 14

15 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 (ther eergy a mometum ca chage by cremetal amouts), they respo to apple fels a gve rse to couctos O tme scale of electros, lattce looks statoary Bo Moel for Slco (TK) Slco Io (+4 q) Four Valece Electros Cotrbute by each o (-4 q) electros each bo 15

16 Bo Moel for Slco (T>K) Some bo are broke: free electro Leave beh a postve o or a hole + - 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. 16

17 Yes, Holes! The hole represets the vo after a bo s broke Sce t s eergetcally favorable for earby electros to fll ths vo, the hole s quckly flle But ths leaves a ew vo sce t s more lkely that a valece ba electro flls the vo (much larger esty that coucto ba electros) The et moto of may electros the valece ba ca be equvaletly represete as the moto of a hole J ( q) v ( q) v ( q) v vb vb Flle Ba Empty States J vb ( q) v Empty States qv Empty States More About Holes Whe a coucto ba electro falls back ow to a hole (a empty state the valece ba), 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 17

18 Thermal equlbrum Oe very mportat cocept from Physcs s the cocept of thermal equlbrum. Thermal equlbrum s whe somethg s left solato log eough so that t stops chagg. Ths meas that every process s exactly balace by the reverse process Ths s calle etale balace Ths has sometmes surprsg mplcatos: for example, the velocty strbuto for water molecules that are jostle out of the lqu s exactly the same as the velocty strbuto for the gas! (the atoms httg the surface, for example) Usg thermal equlbrum results Almost always, the materals we use are so early thermal equlbrum that we ca use formato about the thermal equlbrum to fgure out what they wll o. For example, thermal equlbrum, geerato (electros jumpg from the valece ba to the coucto ba resultg a electro a a hole) must equal recombato (a electro fallg to a hole, freeg some eergy). 18

19 Thermal Equlbrum Balace betwee geerato a recombato etermes o p o Geerato s a fucto of temperature G(T), but recombato oly epes o the umber of electros a holes (r,t) p(r,t), because electros a holes are rare. G G ( T ) + th G opt R k( p) Thermal Equlbrum But at thermal equlbrum, geerato a recombato must be equal: G R k( p) G ( T ) Ths hols true for ope as well as trsc slco, a we kow: th p Gth ( T ) / k ( T ) 1 cm 1 3 ( T ) at 3K 19

20 Dopg wth Group V Elemets P, As (group 5): extra bog electro lost to crystal at room temperature Immoble Charge Left Beh + 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 Free Holes By Mass-Acto Law: q + q q Ios (Immoble) p ( T) + q + q + q

21 Door Accoutg (cot) Solve quaratc: Oly postve root s physcally val: For most practcal stuatos: + ± >> Dopg wth Group III Elemets Boro: 3 bog electros oe bo s usaturate Oly free hole egatve o s mmoble! - 1

22 Mass Acto Law Balace betwee geerato a recombato: p -type case: o o ( T + 3 K, 1 cm 1 3 ) P-type case: p a a p a Compesato Dope wth both oors a acceptors: Create free electro a hole!

23 3 Compesato (cot.) More oors tha acceptors: > a a o >> More acceptors tha oors: a > a o p a o p >> a o