Voicu, Dolocan - Fizica jonctiunilor cu semiconductoare

TS

,a3-----ernooro.auqr$lJd"osllrcrllouscora1.r*n+rulBonuepoadrcoopoatxmsr;1urrd+drsalaonroq{d4quJ;'(rsaaa1Fz".tullrsrfa€ral;aliirr€o;lxups'1IaB€nlqec,6+trn.ornnrrasr1dlrp}n+)ugto3lsiro)r.ans'tnosaoJllrndnK€n.{(rdlltr€cnrrooocaglrsrpplluJJdlnJr?naIrp'ou.euopronJ€lr+Erl,rlao€EusuonJzalaorarnr.n++tpllqroar4unaoepracoirrl,aaJdGdiiror1zra;l'u8occuauo4delfpaltruslsiurraaoooozo4cJrcpoc{rdn{ddluIutoO'rueur1€pnnSus4r1lot1Jnuumun1urm-ed*t+rgaucqr4(n(Xaosvsl1rarrqao,rmurnr'u+nnoossc'?uIul€ouIarnrrJaarraFdo.siedeoaduo;ppue''gapeIeIazolpldK+I€cnot€o4€'rrspulJJI;l

os a.r€c ecl p1u.r1sc1ns no 1ctsluoc uI Tsnpe olso ufl 'nrmuml€ ep rrfrzodmoc

p!q3!1

'nldncour

/ --(-'Rt1ru*nadlr1On}a8t--pn'J(e:lud1p:!ufl-)cl.l:dI.nu'Lir.ll:ierurpFr'"l(nllrllglsruJrrnd)luts-y.rIFz,,)af*puI1uJs'e10.rp1u!I:)B^ntpu-.anZ..rrcrralF.glFx's-lciuly.llp,IiliI

e1a,s.ur,n,rraFaaur;lap$un{lrolEnK+r€zl€t,s18arrzaarpzlJa+aldnrainlolosaslssoFVIT(gIrfy,€afisCna)rulIunnaqrudrKafcl,scrutcsltplr+uEe}1uin{eoc1druy1q's(umo1,-'{rtUlSrr)?l o-'r[g€gI?nl]lcaTOlo.f{u'afrl

aloclosp,J nc urxnlrde l* (A.qg) r.rodes dp FztsJ urp erxtlrda '(.f,fg) Fpirp11
'gztsJ ulp tlxulrda : a1€rls ollnru ltru nc rolal€lsrJc u o.rolia.rc ep aledrcul.rd

apoloru ro.r? !rlsr-{g 'olqrlcnpoJda.r rS ourlorrun 'o1ca;.rad r€ru +[o ol€+sr.rc
.{o[m €arJlia"rc olsa lndoas '.rasr1 rrnlcrt.r],s ap op.rndrl r)+€o? rLrlu?d

a.rnredard op opolol[ '9'6

'(ts:) svul) - rr :(o.L:)svel)-rr
: syc'1/syt-r1yrr:1;-6 :'-1.1us1rug-P
rsyca-f i svu-r1111 ui)-r : u.1t-rsyuiy-9
d.1eci,),_1-'-69i(.r:.:(Iu),It*t'trr,)-F-; (O 'vZ :
: : :.\r:D - \
t
: rlltnuro 1n[1oo 1* nlcrlls rrrp 'nluoJ.]s
Snuur:Ipd)u.ar-olrcuJlllolsrrlollru!nlq)pro!oslu0r)rop;lr)cslurrurl(Ji?oJs^r1lranl1u,(r$[rl1ruru'd*1luJe'r.qttoit'lagZrufgrno'lttulur.rn,nlI)

-tirtsduoc (nrctlrs'nrualos trlp Jolr.rolJalop uoas'cles6lal1'uzroqeulwmroa8sIunrlun*lIqm'cInloronol€w,rodnd1cr.urea^se+p1

.rolrir.ra;rp € alslurJ op Innroruop g1mza.rdor

1lr'til cu o precizie dc 0,01 grado .qi in gazul (hich'ogen) care curge prin incinti,
cr'ttttitatt'n de oxigen treltu.ie sii fie redusX pini,la0,03 pprn. (iratlientul de
lernpelatur:i poate ti controlat prin folosirea efectuluf Peltier. in timpul
cle;lelii cste nece-qri,r'si, se asigure protec.tia suprafelei atunci cind substra-
tui t,ste tntntinut lil temperaturii inaltii,. Deteriorarea suprafelei cristalului
in lirrrprrl incd,lzirii estc cvitatl daczi se yealizeazd, o presiune dc vapori de
-\s. lletoth epitaxia,Li din stare c1e r-apori [47] nu se lutilizeaz5, pentru creq-
telt'it cornpusului ((iaAl) As dar este util5, pentru creqterea altor compu;i
car'(' r11r se oxid.eazS, ugol culn sint (InGa) (AlP). Totuqi, folosind. surse
olgano-rnetalicrr, & fost anunfatri l18l creqterea de cristal de (GaAl) As
1.rrin aceastd, tnetorl5.
O trltir rrietodir, care c1il po;ibilitatozl sX se facii un contlol precis al
gtosimii stt'atului depus este meto(la erpitaxiei cu fascicole moleculare
i+9.50]. Este o rnetodii r1e evapolrlle carre difer:i de metocla obi,lnuitX
tleoalece sc, folosesc lzrscicole focalizate ale fiecXrui element car.e intr5 in
crlootlltipt.lrsS.eAlcuecsleteaazhc,atilnpeviltinl tualtlsauibnsatllat.,tOunintlestaselncfioerntibpinici [focrsmtcinredpcreozmepnutasutil
ltl fiwl':t 2.11. Est'eu rnetodri rnult utilizatil in realizare?l srlperrelelelor f12,j.

\-J

Iiig. 2.71. f-asIcnicsotalelarfniaolcdccnlaerpei-;
taxic
cu
spcctrornetnr dc masl EAI,
rr11-- frrreastrir- ,'11 -- bloc cle in-
cdlzirt' din rnolibrlcn. S - sub-
strat, I -ccr:rrr fluorcscenl,
Obr.lrion--ccluoalb.tilutcn,irr(a,a't-ozorctcrlnlicuehlicidad,ne'i1c' ,-cmAties-ric'-
-F cu iucirlzirc individuali, T -

tun clectonic de llkc\'. IiI{ ..
Irscicol irrolccular, 1 tun tlc
U^ ;rArrlv..c' raiznoetl'i,zo(st'ptArttur:grienrg)cidlin{,driiocn.i,

Pc:1{1'11 rnodificalctr oorlductiviti,!,ii cristalelol exist5, mai multe
rnt'tirr1e. Clea inai obi;irniid, este clifuzia rrtr:milor qle Zn sati alt element
tlin glupa a fl-a pentru a ct'elt<: conductivilatea dr: tip p a cristaiului cle
GaAs. frn;nlitiitile caio apal'tin eletnerrtelol' din grupa a Vf-a sint mai
pulin rnobile .si intt'odricerea l{)r nccer"it5, uri tratarnent Ia temperaturi inalte
{:eea, ce nu este de clcrit tlin r:.auzia degradi,rii termice. Impurificarea se
poate face, de asemenea, folosincl ntetcda iitplantilii de ioni. Pentru rea-
liza,rera regiunilor semiizolarite irnplanteazd, Oprr[in51f]olqoispirreoatodneia[l5ia2j]e.
(.lotrtactele ohmice st: fac se rnod obignuit pe

in

ita,zri' cle aur. trloalizal'ea heterojoncliunilor depinde cle paramel,rii ctre relea
ai sir-bstratului ;i si'ia.tului care se depune, de drferenla intre coeficienlii
de dilatare ryi de disloczaliile induse cle tensiunile mecanice cale ac\ioneazil
ca c,erltle cle recombinale neladiairte. Pentru alegelea compugilor ternari
important este rrolubilitalea aceiioril intr-una din componente. in ficura
2.12 [53] r clei,ermind, ternpei'atura la oar.e axe loc saturalia; de exemplu,

E'

t9

'€0f .8',Ig:e0T. -T - (r-urc)cr ortsruq ir{uaolsrp ap tso+ts+rsrrep r* n61 "
.€'g: (r_ruc)61
oul{qo os,r_gf :Lt .4up-41y rnlnura+srs {nztsc uT

'y irl S tsr0l ._9On-: nrOf .?,8-(z_urr)O

elsa rr{ecoISIp dp plercry"redns Eo+'B+rsuoe

aa''inor]?r'ef+t9ssscero'Jlgltanlel"o'rup'pr'.3ieotJc1pEocJeIns.ir?rJapu+l.saoeourcurp€rlTJopuop,drc_€_(9rau1.+6r1si'ouuusno1orpa{narqo;lecuro1ro)Vgepeuo:ongo{ehee.},;lurrraecso+lupupseiuurpaon.lco6t,.l+ru.uE6lcoErng+ul"osJn-prldarcqigoucv'Iieta-tar-JsurIoi1aou"pr.lidp4uoxeq.bunluiTrirarprAa"nla"-riprr.aB++iilIebrraflfJ;rr,
t1ir{I-gquarl-urrrorc r*ncTuloa nledrcur.r6 'all3rclo.rde ralaiae e,rn1cn.r1s'r3 rr,r,larirra,rrd
pluorroduroc o nts oJ€J r,rturq rrinduror rSele ornqoJ+ {.re{r"ra

Je) .m9 t-o I

<-N--.rz-'t--_AT-O_-Z_TI 000t.

-l

dDC sv Do l-l

I -:l

dsDc 'rr-c t
t

tl I

I -.1 'nr1uS ui cIE3 l!
'(lSB{) B ri
II runel:eX

:ui I j
:I

qSUI

1t-ot

-lI svl?.|)
unarilrEu:lrJlu]qJnidoustr,'s\.JzfLitr'7'qS'nu-lX:n
_l
I
ll
f
-1)lz-vn' t
I
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s
j
r
-Jll
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1It-ua, t
0
I
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o
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v
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v

;opAnduroa Eo"rr3zrl,BoJ n.r+uod 'E+tsp flu,rnltz"- er{n1or' o-J{rrp g1urrelrda
a.reiia.rc ep e,rn1t;.radruol +ca.roc ozayr; as KS pp r.rolul J(ilsoJli
ea.reliuounC 'O.g,cg tsI oIuI t?Jl1lts 'r3a JoJSoJ j.lt,r1 o
"oop?erllrqrroqlresoz d-0I: r ounr

'fcbela !.2 I'cnrperlt- Tabela 2.,j

Unelc caracterisl-ici ale colnpu$ilor I I I- V tura dc Difercnla dintrr col-
top.{irl e,
I n",ro" lconrtanra stantelc dc rcfca 4tn pra-
cente) alc unor coftlpllsi
l-nlAConrpusul I interzisS, I rcfelei,
bins ri

Sistemul

-{lrls 2, 1t; 5, 661 in<lircclc 5,2 2 013 .\|P-GaP i,,01
1 ,,13 5 ,653 directcr 5,8 1 511 AiAs .'-GaAs r),14
GaAs 5, ,151 indire ctc 5,:l
GaP 0,73 6,09i.r dirccte 6,9 I 73u (,ia Sb - AlSli lJ . {)f,
(la Sh 0,35 directr: 4,5(5.3) (Ini;ArAs s-* In P 'r r)
InAs 7,34 6,058 dirccte $85
InP 2,4 5,87 indirecte 1 210 (ir P ii,6
AIP 5, 451 1 3.13 l],8
2 823 ijl.nn)SSPbb-'r--\AGt.ldaSsSbb
InAs- 4"7
trnAs * InSb
GaAs .4" r
InP--AlP
In]) * Ga P {;,6
6.9

7, "'l2

: in 1c0a1z2u;lisiDst(ecmmu-il)ui:In1P'-2G.a1P0,6."4 : 7,2 . 10-2 sc oblrine O(cm ''1 -
1r5 '
Ilrin urrnare, in <,:azul cind cristir, o diferentd, mai mill'e intte corrsta,n-
estp mai mal'e. Degr:aclzl,reil la;serilol'
tele re!,elei ryi clensitatea dtl clisloca!,ii dincristal. Criskr,lele crescute,s(i cet!
depinde qi cornportarea defectelor
de
cetean\, la, inceput ou ochiul liber penl,rti a obselva oxistenta, nclegulali-
tfr,lilor pe suprafa,ti,. Structurilc mai liine, nurnite in motl rrzual morfologii,
se observii pe suprafala cristalin[ prin nretoda Nomarski [54]. Nelegu]a-
rit5,lile cle la suprafatd, sau interfn'{d, se datoreaztl in rnod obiqnuit, la citevrl,
tipuri de defecte. llorfologiile, caro se manifest[ ca regiuni cle intrinelic
irniliafotuorluiomr indcesfeccetne{rpi,oast-earfidaintoldr,itLuriamtdp,udriatcil[,,liicorre;[t5er5e]a.,Se-paitoabxsiearlrfralitchcli1dda,pa(a-
compngilor III-V) se facc in prezenla, vaporilor unui elemont din gl'rpa a,
V-a [56.]. ]forfologia este afectati], cle
101e oontrolul
pr:rlcis al satura{,iei qi tempe-
raturii, de orientarea cristalini, de cre$-
lentd, ;i de ad5,ugarer
../---\ terea de impul'i-
,/b Dcfectele terrnice ale suprafelei
tifi.
substra,tului precuur ;i varia,fia, lxustd
Iv"nrI
a nivelului cle dopaj pot deolan$il gene-
u- rarea rle dcfcctc in sl,raiul cpitaxi:r,I. fn

"^t7
b I tatrela 2.4 sint prezenta,te ilefectcle sirn-
ple c:i,re apar in GaAs ryi energin lor tle
I f,orrnarc. Nu se cunoaqte inc5, sigru <lare
din aceste defecte joaci, rol in degrada,-
la rea laserilor $i nici chiar care exr'st5 in
realitate. ln figura 2.13 sint reprezentate
l 0,8 concentratiile de vacanle de As tqi de
1
I Ga in GaAs in funclie de tcrnperatula

I

1A'5 a6

10"/T, K-, de creqtere. Ele au fost, crrlculate pre-

F'ig. 2.1:1. -* Oonccntraiii cle vacarile dc supunind cd, in material existd, num?]i
Gr 5i dc i.s ln {ia:\s in funcfie dc
t.crnprratur{ : * lnrbogi}irc ln Ga ; acesteforrne sirnple [5?]. Densitatea de
r.r defecte din cristal poate fi determiuatd

D -- lnrbogrifirs ln As.

54

99

n----e-ooicopJpi€.u"1riore.rneorqpo1n*lraeaou{d.oqqct!IouuSo+uq+opcfs;!ftqo€er'eua4pnnu1r1usulriso1{rn'qcra{qoouqolclpmpbserauleeFaoasluaus-ltu€p.au5rgruac€groEnuluuupJqnoonltoqsorcqruurpu]rooqclutJsrsoraou€ulmoolrrro*ouJ{cerqt(oroeIrorrr€eltrr_o's{uXa+uuporsIqrir}u€;J{utcqsnuKuouoslr^u.€cnrc;n+eooOOfc.q'renFsFp'r'aa+?+(+tsptusrqsrel-lFxxc9ir?3la{oJcI+u'€pl6osetpsptppIwoun'ouc5qJu€ptnno1o€J.)uJutg+aosrglrloJ-gldruq'ruuJ(putnoqocurJ"+epls}r9'gtuious+I€uo+e'J6ooecs.nropuuadr'nnF*ptJ?rlIpEo{1J{olcca)rs".nuruJoruaoot-coulrd?'Yfrirr,
1rou---.aeIiilc4,AcIrfrotcaeu€sJ'uupuD[€aorzooclfnfrsIaort]ouasrp"uu1rsgoel'ra:rvlaqaufaucr,rrn{qEe{ncu."puc15ro.aeg8rigaa4ryaia(;oucrlu."Inruors-lrg"od{pro+asp;aspuaey€olole€ooocofuclolcpopp€n.rcrqpreorau{rupgccgrrun+uerprcrnqoaauful(uro€rIn{e:Loueurrau-r{ntildpcovrlJFtuuEtn$te.Joo.ql"dqfs,r{can€Junsnop-uorJJe.io+urllasudpsnuun'rdlaJr8(ne51-J,eragAauu{.ut.qcroTlrl1uuuoue'oa'nIizqzI€fTeooI"g'-luF;rouTtaddc-_ocKo?ZI..nJorrzao€Jtpq.pa+a+runsslouosnP€Frcg1rl,llf'gdat'€d9lo'uodot1pJouauu,'fl6-a?tcatldrs"luresrTtnoeo.vrrJolspneoF€?w5uurott'?grmtnn;g1?l'

ai"u erF.roua op rzuoq ap alorrrrlFl;lp o+€?lroza.rda.r 1u.rs p1'6 e.rnfty u1

t 1 l{ fr*--\ \F-d d
'rolIunllJuo lilJ
-JJaq E e18.rauo Jp lzrlJq ')p u'iticrfil]l(I 'l,t'f i;-!ri

f\-

'^'/ u

t'mt4clx"t?s ap t,mdt,6 .Y

pnliouo[o;ralaq n;] Iraserf '9'6

i.IBITI (rsV,tu.r) (J*IvEArll?,s"cra,tli)r! alraJO(l
ojuucerl
(gu.rag 1np,r,1u ap cpuldap)g.; (t)s'v'sveg) Eoiar-rluv
cqca.rod o nlluad 4.9 urppurp$iu1 Jp ;lrJloq
paru 1lqer1o.rd
(p1u:1ds
(.ro1;j glr.rndutr u1J c.rluocuor
'd ')c) rrcrJrrnlu rp !ltrucolsr(t
.IS IndJl ap apurd;p) q'1-1

{a 'arEurJoJ Ji) or:rJJ{r? J}JJJ J(I

sVEr) u! oldurrs aJu.urlcn.r?s i)l)il.;)( [

P.A TjlaqDl,

---r-Jcunro0lq'ql+lToylt.s.ru.0ndrzrcI,;+eu?ooc1l?lzroSJu{urolaouruul?o€lr+lJuo$uusrsaaaoru?as+sIjlsoup.'ngssgvty'a{LFE?ilisO;,O.urreIq^rceey.opitap'{siutrIrrrry.rrnruccdl/;nnlrnd6d;sn1su'1surr('+r,g(pI.cJprr?orsud,Iyrr*ut)sa;ImI(lrsiuFaqa,Itur.eIudrIogIpr.r{e)rao.llrun5uniiact]pp{'w}pt,aouoE.pgrxz€oeoJqn}oqors:dlpE5'+lati,nr.s1lair/.uuuIrFnourr;+qp+ur

pamclleaealgit_fehlbuicuqxlnaiutr-itellueaeiapsrltulteeartirn5aagt,ojurolsrinaitl5cgti,{e"ipudco9rxtiiiassr,(tpi,fxrXicgrione.XaZp, cr.-olL(ofbuiig5ac,.b)2eiIlfitete6ic.x,ttie&es)tn.fr,cTncraolleoitura,i'qisreaie,,m":de(ee1nto)ieaelaraed, cvieseartclrroguerrgugiiefiilrnrnn,ielear,:rrarrI

r ,,clt5 !c I
:-Jii-s I

- )L_
I

I

--r+-;

I
I

P'Al"Gc, -,:.:
-) a., L<
^
F
NGClAS
, ,,,,f) --- >,za.r-
/ // / / // /a

r^larerxu,rf-i_.45 -d . -.--+:- '-.-_
P^-r-U: U 1^5:-:--
u) 2rm
n AlrGor-" As

c)

.r+Alx Go,_*As \NF .-<pOU _
:-->
i
+PP,GAI "oGAc,s--As __ru
i ld ----4

d'

I

+ !4y--9s!/l1

nAlr Go1_,As itm

d) u) I

lrig. 2,15. .. Structura si indicelc de -lIii!{. 2.16. -dc (lonfinare:r
refrac{ic pcutnr : a-.ioncfiunea purlitorilor. sarcinit in
p-n: h. heteroiotrc{iunea sintpli; hetcrojoncliunea simpli
hce-tcrhoejotenrco!ijuonnecaliudnuebalSducbulrci;avditat*e ra) li iir helcrc.iorrctirrrr.a
dubl:i (b).
Iargi.

isdmtirfbiucueuntlutS5rtiliii,l5i-rsiee(2af)olpdoeisrr.eefosrcrgmesnatlnrau.tcefltluourxriulalcusuiecdmaelyvuiiintaesteemooabrplcitn.icepi,ealnatutrmgicdi,a(bfiniigidl.ituzcor.atnitifni,dac,elr.settaej
purt'i,torilor este separatS de confinarea radiaiiei. un asemenea lilser se
numeryte laser cu heterostructuri, cu confinare psueiptia,troatrxil.ocroensfitneasreuafissieep;tai-r
{l.eoarece penfuu confinar,ea
rati, este posibil5,

noi.4ldrii-cfecer)etencfdlile,e^crnrietafiprmaecicnldiet,m)i.ntorceoanirsefeinnmaaeirlneeeaiantresartzlcuislcieatul1riredyi ,idee(csreitezuunreltspaartreltazd,eednpiianott[ensi!na,iaitttriugrlunalirar-il
2.tr5, unde,regiunea cu trandd, ingustd, (GaAs) se afl6 situatx intxr tloux
pmAdre-es([gerGeri'urgxnaneieAni,nmiseAtei(prl0rluGsd,1tear:5pnrn,dcrGpotAuruasnrdAi),-scpmru-oepAtk+glroIAallu,nlro{gcGl",5!,a,coGi:nu,nateNAobr,sarzuA(ni.0sd*s,#d4q.,5?p-0ui,.nrpltiPmenpirr)nzm--yrisoap-dAim",lopmsa,AarrGlaeuo,a,i-Go}crIira,,,r1'r-aAeors,-e,l}.a[.oh&rAsi-nI(elc0i,nlG,u_4li.*oblFnn1,_i:o,rilr,r"-nrsAp)incs,"L{,.',
Iaserul cu cavitate optic5, largd, construit inilial diferE pulin d.e aceasta,,
care este numit cu confinare.scpar?_t5, (ryi are qi cavitate olticil, larrqir), prin
&ceeffr e*i este o stnlctu-rir, de tipul N-n-p-pllfi1 in care c6nfinarea'rmiste

56

L9

'(q) pt8:rorlrrr.\

-uol rS (D) F1liElFun(ttul E,illul?ld l?puuq rp EJL]lrulq - '8I'e '6-lC

-+ua.mc €crJsrra+cu€c o+Sa+K+?unqurl @ gf'Z '5rr) g;rn+cn;r+s ,EnoI{ 'rulp'ts
rwlr yzaoznlrp as Incuz pq.r{plpunqrrrJ €rn+crl.r+s ul oc durrl
q 'p{u;u.rdns
€I lnlncmz ulznJlp r4tcI pzvazrlual os €llu€q pleuor{"uarruoc €Jn+cn4s utr
ne's-t-[sT.Olryipnu8gpg8u81rgr]tyt;s0-6rpq-tluyrnfa-al,arr{(encp2pJaot+f)srrnulf0;uaiggrl"nuul-rend.qrIlublu?(on'g4?l.rr){p?:ug'sups:a.tyerrs,uursqpuur0oelo'lT(\lcyrcpJ.-tle:(sule6JfrprpBnr'c0etu+surtus€ocrufuOenqlr-4drfdusos'oqr.p,dC(praCFu€tp0suJl()nyn0pq,_ter]Inc-:r:aulnduolp.lcrrttlpr.]trsBa1ga.sfFLmq:'+r.lo+,get_sc'yus?rn'rspuiJtcy?o-K'sz€a1ra+-rSi?r.gsr+r(-drlrgtdxasc.o)}.ru(fiaraigo€uiz)gl(uos(ril1.rior.tr.O1:Tg.qrraftl€ZsSl ?qg-a'uAn(llsa'osea:g))t

'runrimoiio.r.t:1.ttJ ltJ rnlnJJsEI

u l-rEluoJ-PpuBq Jp ;lulrruoJ8 rlJ r-r.!nlJn.r'l\^'l,I'a'ilrl

(la4sgnsi. =. - sV x'--llpg*lv-N
sv 'Dc'lv-d
svDc-u-l_

-fsnr.1ro1+'ciJEcJrrrl?rrc3+aaIaiuJIBno?:cl€€u?rurnoco.r(tsf),R'it(?f+fu'AarnurltnodFxrel atl sol uI s{n?saueap{uoas1tsr1grc)'i,ggl.s.]nFtcut1f

ts.rn?cnJ+s
gpueq o ad ulnlcnJJs nc +ce+uoc oct?J InpoJ+c'Jla acoJ€oop ("rpuuq-1,Jt?+uoc
ap p.rn+cn"r+s nc Jos€I alSarunu os 1,1'5 u"rn8r; uI +ts+uozo.rde,r 1n;resu1 'a{a s.r1sg

a1e3o acluo"rdu lugs ounricuof e d g;rupcrpuacl:rod or{ao.lrp u; rS gialr.reil
ar{carrp ug rar{cu"r;rp o?tsJo?€p g{uaF"ralrp ap ap,rnrqFun ecaJt?oilp pimlo;r
Itsur a+sa lnlorrcsrs] '€ouaruasts aO 'aJts?uo{ri€lr} op rn1 uiurpua+ purJnpa.r
uJ5-'-FuuartT"srtlry.tdrsd?)dI Ig(eIlennurpcuI€llnorq;uIrrzo1oiacosJ)rrl€cnugosalItlEps€rruJa?,tucrsqioeuel?lrlsaoceeiaupuldqlro?{o,ruprnrEncqdll?anss;cn?'t,rtn8KusrurJrlor1n€icJ?so}xncuarcnool€u.eltSrrof}{afro.rur?'proiruur1;JKnre*la€pus;r"rJarrrono{trss..?gOqnc€lpcIn+oSuJs-€.tnurcso,qo1plu"ucrgqtyi.Jlqrdri'{slia€+orrtnodus?lcIntsoanr+rflpJslugaaIaons{;cuot€+nlJIeu€c€i"I.}nnrrJ?dilr{Jsan}dJ,s{K'rpJ{clrtossa+f-'nJ.e'rrar:+S:a1i

-rcrJns p,ieyu"rdns nc tsJnlcnJ+s o-Jlnl 'loruoFz ,ra1 eleliuu €op ,FS rS alrqulsur
pq+ o?uoru€IrJ o?sacv '8u;rd op ui{rpuoc qns gcrq p1;,e as prrof
fur^ap KS uaunrFa"r ac durl ul k+ltua rs adecul (rr;rn1cn.r1s
oc .ropiggueForlroau
-uocur o

vzttwc mp 'a.rec arfcafur nc rnlruosts1 u glsn5ul Il€IoJ ounr8e;r o o]sa Jas€X
luoulr€F; u11 'arfurp"eJ ap JJnpow Jo?Inur ruur ur{r,recle r* er{urpuJ ap rn{nlo"
-Ics€J ,l? oJ€luorrrulrg ap u{urpuo+ a?sa or{calur nc rrJas€I ur a.rud,rz oJ€o
O 'arurrr (?1uupoJ8nuc;r:iloa,rpuc?uoa..4rnmc.rudn(rn.r-n4du1o+do)Xrlnr?lind^1xBanI{rrgrJnrecp
euralqo.rd ourr8lel reru a"ralnd o rS
Kclru n?ur
o 'Seld ap crur
ar{eleduroc ur afr1ue,ru olorrn a"re rltludas oJt;urJrroc nc Imssr?T 'r1'u.r,edas

rilclialitr li stabilizeazd, rriotlul t[r. usciLltie olizontitl, rleoal'roe ziucul estr:
riifuzat, ;i irr regiunea activir', t'eaiizintlu-se un auurnit pnrfi! al irrriicelni
dc refi'ac;ficr: zincul difirzat rfeopt:tr'rerzeeanztiziro,tiilcigtrirmtigeul1a.,r'.2A.1I9terrs,tlsntnctructrui ldaeirlracnarlrier,

sint: st,r'uctura ruesa 1611,
iianda este realizati prin borrrba,rc.lilre cu prrrtoni 162 l, i:upla,ntarc de (J,
[63], tlifuzi* sulfului 1641, r'epltrzentalii, ilr figura 2.18 b, s1r'uetlrra c'u jorrr:-
lriunc tla'nsversalii, [65], r'ept't,zentl,iii, fignla ?.1.1] c,
il e1 c. Intnitlucelerr,
prrrlonilot', rn Oesa,u a,S, forrnettzir,un s1t'it1, srlniizoltiru'cil,rt'separi. o lrantl:i
licrtlm l,recerea cruentului clcclt'ic. ln st,trrclrrt'iltr tle ha,ndii,. eii aru llt ulod
ol:istruit lS,rgitnea rlrr 13 i-rrn.

B. Cu,rentu,l tla ,prug ;i eJ'icienla,

Funcliona,rea laserilot' ou inir:cl,irr r'ste czu'ztct.triza,lti tlc ulr cluent (.le
1ua'.9 la Lrare apale efectul lirset'. furtulnl tlr pla,{ bt }ioale riett-'rn;ina, tiilt
in l'nnc{ic rle t.,rllentul tlertlie
tlependt'nlir, intensilit,ii radiafit:i de it:sire
din laser. Un exetrtpltr esto repl'ezen1:1,t itr fisula, 9.20 1lt'1l rrr tyei la,:*eri cu

M etal

'

Celectcr

Metol n= $alQl7gn- 3

prota^i 10,a1 \;.9
J
qtrdqi R

Metat j',r,

:.= -.:- -(ol--asaGso Al As

f-*1* r-GoAs
l* ,+GoAt As
n.GoAs

cl

ljig. 1.1$. Strrrr:tlli dc banrli : l - l;ir'. 12.l{}. Ittlcttsitlilr':l ltttlti;lii r ttlist itl 1 Liltt'Iir"
rr.rrstr : ir J1-irr borrrl.11'tll!1rs1t (.u ltrolqrri ; tlt ctlli'tttttl t llt ti ir: iiitt l:tsi'r.

. (u iorrctitrrrc tlirrrstt:rsirli.

heterojonc!,iuno dubli, rle rliftritc hirrgirrri [66 l. St, ol)set'r-ri' r:a' intert-itit1t'it,
Iuntinii ie;ite cstc funclie ([e (.,ur(nrtul t'lcctt'ic, p()ntl'tt va,ior"i lLle i],('('-{t,uia'
pesl,o valoarea de prag. Radialia la,sel cste drrtccla,tii crr ii,jturul unui delt'e'-
tor din siliciu. Din panta cur])olor clin figrrr'l str tlt-.tct'rninti eficienta, trttilllticii.
tlifet't:n{,iali a ia,serului.

't,tl : ,, Jl.r 1 r !.I-l)

J JI' ri

un(le ri' estti eficienla ycrutraialttliicaii,caruednetteuchtiritrdtrilturi,ltrI,1s4cr'.- r'arla!,iar' cul't'Ltului
tletcctolulni ;i l/, -
S-a rta,bilit t'\]lt'l'i-

58

6S

J'-[opgJgJBl]airtqssr'nrnZcl :aIIrJ{acuSut'nqr1urto+llus'8oadn+Tu+T5r:llspriurluoncraiucpuouocnfo'Ir"?{r"ri[lnloc*lqo6rulon)l,rurDrrJrs{aqsoorS?lBrua-nl''FlEt1rit;Tl,crqtornuopapFoIuuntlIun'aicJuno']r

'9'6 ,utoqu+

p3.re1 pr13do u-r altp +qs 8,Brd op rnln+uarnr ols
e.lrdp r.rol,u1 'p{uorcr;a uI a.rtsolpzurid
009 'JI!;IIAUJ n3 r^lqnr)
-:.-+.sr1tougeJogo_tJoJO.1arIoJu.o11Josf*:qa,rt.,rrnoJ:lit)so-fr{rn.l.Do,rrol_rV-suo/trirl),it.l}utc'lJF(a+l_'qlfrtg;llpnl i":'irtmgunoll+rfi:
00t r aungfcuo[o.r11o1 I
000 0I
arrn"r"fr-u;^oil?[;oli.;qr"on1p,r11

r,,nyiruoio.ralr;1
ounlJcuo[ouro;] -oJo]oq ItD rr.rast?I u] +tlztltsor,u-s $u.r[t
-rucly66g 6y

y00g et svc") ror1tuprrl1JdrJ1rsrr.iloJlu.1 ;)p rnlu+iTiJnJ l: HIqBJOplsuoc ,I-rir.l,Bro*
-]rur rJop 1! rc 1n1 ,BoruJoiclm
rrl sqBrd op |rtn:Frarnr l+loe.r-aOlSIa..r;ljt.g6 n.quictv/tuD a*01 I...F6.d{[._iu:-[

s'?; DIaqDJ I* 7' n,rlrl3d r--ru;) z6+rtr

alatilrJd ',0 InI uaJuJoSJIur IS d iul Inruoruop uI r+?u'zl,sBd[z9rl9u.]].ra3lnswo{i)q,ot?.)rJ.r,){rdlul-or.;
,BoJa?io.rJ ur.rd
€d-o-fr,sut€oxDreic,BopJfuznt?rsuanJ+ceJdsItslrJ.laroo}+s€u€IrI€ugafq.Iu'rd?pncpofu1egi.,rrcul"xr-4aoururilloc5),lcuu.or,dr.?rougpru'rrd.nralnJlallrullrrcolu.3rrrni?))o?co'{[?paosJa'l]osJopn(u&2nD1ru/aIip)]u{{.lngriindarlJ{,in])6

;polp ul rrfplr.ru:r 'svui] !p1l J as 'irIp lrrr.rrJ Jp rllllrsurp
couliiunl irp ic.rd
1rr{rraptr.rdap e.lrlnsu ;t;r;ltrcutrl;dxc .}lDll}rz..rl.l - ' le'a i i.,t

**{u> 3!r

,d6ro-r il]t 0 ill" f,01 il

g0l. x xzb [t/.t,-+r a+
U, e otxs
sItrx) ,/ /*
/*" tOaFl -:
la

/n

x96L 3 1

Talxs !P* )4964 N J
I
,o,i" v s0tx(
d
,alx stt /" 0 tx2
p
Satxz __'":o--j
1:
p+u,Bd lor9r 1r ulp '(f6'A 'fi3) piduo.rp o o+so ,IlT ap arfaung ul df, IntrJ,Brl)
t?
(srz) '(u/r)*,lI;d+; F) -o[
t-')l
K"u8rlrr,,l4.erdnnolalepowlIincpluuta'o4Jyn.4roo1p"-.aals+prscroFl rdnqt*co1clptzmsFyalpra,{du)ldrnror:pp0rpu-8ro-rdrl.*orgcuocn'orFs{oulu;fruoldgtfiqu]nlocSf.crelr"retiot]lsmJ€oo{ippqorI4orn!.??'u.uor,sl)l,srl!]]utuuZoal"aouZyI]})
A,I
t?r

Fr
{}ll

l-ig. L.22. - Dep,,rrtl rrlr
rrirlA r lrri ij'E a" t 'L iri i","r'ii
cu hetcrojonctiuno dubIS re-

p|czcntrrfi in f igurn 2.2f1.

!0

I L, Cil

L-,kAtct,z

FiS-. 2d.e23g.ro-sirXirtl:capreengdiuclllIiai cureni-ultri cir '1 2
prag active in i.rsc- i7

Eul cu hcttr*structuri sintplil.

9

I

v

d" fm

o-bsertf..ilit fi4ga 2.22 este reprezentat acest rezrltat experimental unrte .qe
prag clepincle r1e grosi-
ci, j'r't estc fnnclie tiniar5 de 1i-t. curentul de
t\ea) d) a regiunii active. ln fiSrra 2.3i,i este
Jp,kA/cm2 reprezentatti dependenla curentului de prag cle

grosimea regiunii aotive in iaseml cu h{rtelo-
structuni sirnpld, ial in figura 2.24, in laser-nl crr
heterostructur5, clrrbl5. fn gencral se poate scrie

t': ur(ft)':' f 2.16 )

u, !m undo I este frac],iunea clin luruina stilnulatd,

l.ig. 2.2,.1. - tr)t:pcndenta eare iese in fascicol din interiorul regirrnii acti-
curentului de prag ele
grosimea rcgiunii activc in I'e, gr-cirstigut la lrrag Di r;" - efieienla radiantd
lastnri cu heterojoncfiunc
}"]-:__r:- 1
drrlrtri.
rrfr,

60

T9

(e ra) '{ttlt) Ir.TIT-: Eoz

(i1e.,rrr"xu1,g [Og] nc leuor{.rod

agtiunce urp au1{qo as 19
qo
-o.rcl 1ole4-f.rql:g : *o+€+ral?c n"r1uod rn1

,Qf !ilqi7l I) + ?o fr ,19 'aurrFunl op €o+€?run au-npurroJog

(sra) '(1g/,1g) lll - ett

a,elsopd.'rurnrallelsn"r.ar,lds{uorJa-al lcoPqphucT1iSr3r.ae,qp.rud-aadpr!qhru-lenal'rSl3ZeJ'Zrne:)p.o.,crr,ur IolIuTpdluuaappe,u1tfrsuun1urru,i.ulgreco1lnupr1.lllr.rr,(*rn;nurd1pccoaeu.dr[udlptrruruosooolllpool lOJaa;IJln€eoCdppcS
r>l'J
001 InJ?runu 1g na (rn1n-rastsI 'fKttu'JZo+)
-ur e{uarcr;a 3Le nc pul+oN
=--- tr'O u-'-.rusonr{lr1.perrtor1lc.orlaae,J"gsqr€u--nu1gqru?tpp{ruuqoKeJcr,unaprrrcul;uqoJJl-oNan.+'rXpdos9pg€a9.pZ"mIsu?t:r:ct,orsuJJl0?nts,Jscc

', .-r

0r<;:-''uoTrr,t-jlInr11qq?4:ncrprgnup'r,g?l)qs:"o!nroJynpo5Ol+J.puAanJtqrtrq1-la:s,J6or€:rou,qpalJrsl(anpocqi'Jdu-lud8ylnzlgo{s32qq-pr--1n:Fe,p.)l

:o,T,-f tsqmc: [6] Elqnp aunr{c

-uo[o;re1aq nc rS gldrurs aunr{auof

00r -oJal.oq nJ JasBI lJn?JILI?s uI llz'I
o;-uarur.radxe g1nu1f qo g{uapuedep

'cauaruasts o ,r??t?uaza.rda.r a:1se 96'6 eln5r; {rJ '?lu€?suot o olsa apun

(n'a) :'(o nla) dxa o"f u.l'

"qar.rrd
-uia ulnur.rog uird grur"rdxa es Su;rd ap rnln+{ralnc {? pl.rn+ts.radrue1 ap e{uap
'^V nr elia.rc df, rS rurilu:toduroi; ea.ragie.rc nc ag.Sa.rc auu';uods
-uadaq tarurFrpl 'arfae.r;a;r op rnlaltlpur uolaq*a.rc na ToISIuo
rarurl r* ny ag.*a.rc df,
r* e"rng.
ra--auts,rqaE?caofuoOrca1'(IaJanonqc1clI,"Brro.rroirnu1nea1rg8;Iiraorrd.rauoadarruu{rc{suqo.".rrr;o8a.sraqlouiap,ur1oo.rl1dorclnrp1r;uerel;pa'u;dietr$utdIoeolop.rraaI.n1r+o*uloSa.arrcclcrJtsna{ococ 'c€rniopurucooaupct
+rsrloncluYlo'4dlnu1rte;.lreedam.raail,Sau.ar,lran1cSa'.1ra11nuc1
1! r,raqg JolrJo+B+.rnd er{u"rquaruoc a'1ie.rc u) gpun
'azrratl o?Inru rtsru €[ KztsoJo1t?p os uoruorral Jolopun
a3.-ia.r.r Su.rd ap +ua:rnc ap Ba+B+ISuag '(.ro1gur.rn 1n;u.rFe"r'ud eapa,r as

ap uorur5unl nc pgqu.rutluroa aurrtap car+cts rrunr8ar saurrso;rF pulc
r o.rrprqF ep .rop{p1er.rrlo"rd rr.rap,rerd g?rro+€p p rnl €arapgrs no J InI llrap
rrna-'glgi"rpyrrnIse+iF1Jl.'erI(r(autpc."rahrrr1c.icrrsr1lSu{cuunre-.1arr.adifdsueuuueeungprpnrlFudrKI8oannzaldr+csrauoopaJ-aFJo+lln??iosrruca3uo[pntqrcp€ouosIInln'1tauaI'nlruJs?{u€uqc{KronJ'pTcJodrug6s+oJ€I',6'dorIac1uaIna*ro+gJp€cctgasa€Z€o"Jrr'lZort'sesrJuaueponJ.aocrqrunFlrq1Funanroll;VsncruJ+arrtorcrluepynrz(sq"r.tglorrvaacl"ou1rrlo81aicmosdte+qals;mougioee.{owourtsoJ4urS€sTlacocug.lenuur)5pcrI
lndurrl-"r, J€r K?uurp€r €a.rtsulqruooo.r n-4uad p{url ap 1ndur1 alsa 'r apun

'iinde c') e.qte pulsatin, c cste vileza lrrrninii qi fu este coeficienlnl de extinc-
f,ie. Sc oblino
1- t["+*, I'rt,! 'n, L
ln(LtJ?; J ezo)

l'firsurincl 1u da,t de {2.1a) se pot clt'termina rIliniarecinuafilgiaur(a2.22.02)6, ba Ei E. In
figrira' 2.26a sr reprezint:i 1/1nin funcfie de
s-e repre-

I Ttl

5 tI I

I 0,61
i

I I

L osf gPro---q.
owitt,{\\\/l\.F
I

I

I '"..

JL

I

i

2 I

t-
I
I
I
A.2l
lrt I- \ rti .6so7, t.6x!0'7cm-3

d -- 0,1+ Stm rI

I I Lt l- L !- 0,1
I 8AC t zt.!t,
tffia L f,._-r1.6! , , r-
0 I I l,- L.,tt^
d,p^

o) b,

lllicitrria rlittrontial:'i irt Itnrclit'dl ii:rrginrcl cavitilii (c) si irr lLrrrclic rlc grosirlca
trgiLrrrii :rctir',. (l),

zirrlii, 1o irr firnc!,ic rle glosirnol, r/ l lt'giunii ilctir.e" Eficien{a r:rrantic[ (ex-
Lcrnil
) se poiltt scrie

,j?',u{"t_e1lecan.tldecinietfriraer_e,=.
:,' Pl!!:
,,._ Pflryl , (2.21)
rin
It'(W)

it,r cf it'r'ernt,il ltm rrticir rliferentizr,lir

(2.22)

preunte{'rae'zVsleirdr'iseerrirnlilntrdaarpcerl,ilstesperoepzaoitt*ivlttouliudeei;,itrer.:erem,lacinluiaa:r(',24ju.r2.to2rr)),auscleiiu,mnseoediiaisfifcieniLreccoiunnstepidguertearartoereaarrepez,ieisqr--i

'rlrrti, 12n.

(1. llocluri tle un,tld,. t)istribu,lia spectral,d, u, rad,ial,i.ei

in rnotl oltiqnuit litsernl se constmieqte sub forma, unri cavitS,{,i rezo-

xtilrrlLr Fa,hry-Perot care este un paralelipipecl cu o pereche de fele opuse

ii2

89

--aIs"a-F'trps€,1ssd)nr{1,:parpn'g":?.E"lr'pa-r'rIoTurJlriopllusa1rrlelgplp:soutr?'e't+onIeea1'r0up;o1?boro,rd?-".u{urao-qEdusT'plonleogDJrslr'lr8rriu€o)ga.al33.aI€darJ.rir,oofpJronnlrJlsus€r.oatr.nr.pEJlraJ-ur,runuBc'La.rloolurlipa1arp(dcruplc{+"uoi''ur",r(!ufnrgcltJooirrZ(r;;o,nrli.r"'pc.rtZ--r,ss]\urreuiuDzlllJqr'ras3',,0(JlBorcE1n+5llnorIios)rrir.aararrttrtrrr?.,urrsopi/Jnoze1nupJtriO'lt{,€5su.oaaO:a€11lpt;aIcozr'{:c.ptrrrcrtz0;nrp1ia,Iuiunur.losltJI'(ratEpoozto-fcJu,cud3t+r,sprr,csJnu-,rrtonrprlu-si.u,gnmro)re1nln,.c4[lrrndL)i€ln-,eysr.xrc:-a"lyoririusaualpeBodrayJugolIxpSu6uruae:,reruipfI1oa+drKurpr.fqneunq;ur,c8r]oooFouJpupaiauoJarnpgncu€{s
: , LL: J-'-l,c-ELuiauorfoO,Eugar+fonqiiJJrd.otstu€'ogNI.ru'ua,n.ro,BnJ€,!4JJ'ut?rap{roI1u6nir5rlJ}d'r5i-r{rureiior.grsrnTreFrArrrugaaOuproI'lclr+rroo,mrJJ3r+nBrDorac:]zpsuaau.nrnc0{qne.ipa,+rap"tglsus1cncarpe-(rs,nJeyaporuu+pnesoqlSu11annpgo;rlaocuuenndrgi{l,.
-auofouroq nr InJastsI ur o1usJaa,qrlr.r+ olrJnpour nrluocl aurriqo as (ar{n1oza.r)
a,rururlas Trrnq IBur ra3 '(ursleclsrp ror a.rtslaplsrTor ur tzr e,rmc)
er{.cu.rye.r
€aa'papcuJlu)rozpl:orrnletcsllrronp8ocuJrutpoueola?pcst,pa{r.iurlgaaracd.clrauTtrprs€iasra..urr.ormua(rs)jo,u&aoqu(l?t€.roru1ofi.u]lsJnnrouollierDa.irudn1opufnolcsrnu1c0a)fe1rlluoai.,riruc0cd;,rrr.ruu'gidn{puplu1€+1qs.u"nrr,IaauSacrpsbtuu^sI€ao.+dJuf)u?{ora.dJt.3adt(,aunr3ualurlrrorfdr+arcsppauueoTn.lr

,q,!t6l"y - r-ib,1!'ttrY _ tiu'*\: ,(VV)

{v['6) :(0fr,U,u6f b'I+x!,il\ - b,u'u.{: "(VV)

",,t

atto;-:t1f "y - rlu't+w\{ o'tt'wr: "r(tv)

-

161] .;,trs.lcJns t,rrrpou{ .enop oJ}ul Fpun op auir8unl ap
,u'.!.ua.royrp n.rguacl rrirla.r i)IaJ'eo?r?ur.rn nr.rcs t;S 'ol€sJalsuts.r+ t'pun op rJnpom

IarD-TnnJssna[Ia,-r,rE.rrtarrau?a1Jn+ruIr,pusrro.orpcedal1€lrse1{aanrrdl'qa(arua(rlg..d.arsrpsal.asr,']+eZrJapruy{iJllunn'glq'r€i.nurrrac.llroneiJ,llJgJs.lprotzr)rpu+egnr€r.Jprriuulelustoalarolzloa.JrarcoairrurCplnrennrx'por1€vuni}€raa:ar5u-Joqd€uil1pDunl'uunnlruslJaroBTl5paz?leuplssrroor{uxupl€ourKx.eo(Eqp(up1uru1ann+uncoofrulpspou1rurl1puJ1dnsinS8,pruaura.o?orr,r11wsrsuarugxpru5cgo..s;4rrragaurruu)uroenr_ur7usugr

t tt'z) {\,?rp^,' - a)rz :YV

a-a{+ppsaaullloJ'rlJlrpopolf.i}rrnup-ro{.qor+;rIlNri{upearspluuu1enlrsoarrp,pluur'pE;ruJr:urIro5€rr+rTsnelpr-1ln ursa.rdxo aI) g?tsp
c1r ar{curJ a}-qa oricc;qa". dp blab
ap earcrr$unl alsa tr./,1 : ar{au.rya"r

1 .*,ea.r1rrl J,Rrunu un a+so J.4- opun

\ I, t. (,., "r:iw'll'(,

ar,rcs as ar{rp
-{roD €}suace 7 earmffunl nD o+tslraec o nlgrrad'?pun ap r{p1pmn[ ep Fa"rgug
.r'r?mnu un euliuoo tsa+r1ra€J rJo a+Io all rJo eluuor{etrs opun
d+saJti ad .rulnirrpuad.rad p5rdo.rd Kz€aru"roy a{ey
as a.rsJ rr{urprg 'a1a1u.rrcl ri
auqcl lcal.rad

{rlis;r, d^c unde pealanuengc_hai]u'er)i:leeplio0p,aigniirreagpiuronexaimdaetiyin, dinicedidreecileiafraacxlieei"gmhaidr.eu,-
face cl1
lui_qi

;i r1e uncle care descresc e\ponenlial ;i se propagi, in regiunea de inctice de
:'trfraclic mic (fig. 2.28 a). findele plane sufer*, fenomenulc1ereflexie totald,
la marginile ghidului (cu indice mic de
rcfraclie ,si forrneazd, unde sta,tionare in
tiireegia perpendieularl pe asi ghidului
de undii. Tn figura 2.28 a estereprezen-
stalionari cu un sin-
tatl o singrlr5 unc1d,
gur rnaxim al cirnpului optic inghid.utrcle
nrrcl5. Cu creqterea lui d, pentriL acelaqi
dijilgl *.m2i .t2ir;.l:r- i irclltxit tr,lal'1 a t'azti
ir uslii 0. sc poat e oht ine o u nrlX staf ionard
rterla t:,r GaAs.'.\1-,. i lri,,..:\s ;
rr cii'rei inbcnsitale a,rt' rlouli maxime
tl) ''a t1'.. (fig. 2.28 }). Prin valiati:r, lui0 ln interio-
rui linritelor pelmise, sau a lui rJ, se poate
obtine o succesiune tle rnodsri trans-
versale. in cazul cind c.rist[ un singur
maxim, rnodul transrrersal se numenste
de ordinul zct'o sau fundarneutal, in ca-
zul clnd. existi, douf rn:rrime se numes-

te c1e ordinul intii, q.a.m.d. tn laserii
A.. C. cu heterojonctiune dubki modurile per-
piierngcelicnuelraarleTpEe(ptrlaannsuvel rjsoanlcellieucntriiics)inqti
I
nu TM (transrersal magnetic), deoarcce
Fn/

tt1\,

!t morlurile TE suferS, o reflexie neai puter-

nici, 14, capeiele cavitXfii, au pierderi
'I mai mici qi deci clensitate mai rnicX de

curent de prag. I)atolit5 limitS,rilor

ltig. 2.2s. I)ropag:tt'ta ttncicilrr irnpusc de 0 moclurile de ordin lnai mare
inir-un glliil ilt rtnde : ri trllrclul sint elirninri,te. Moclurile TE de ordin mai
inn<ltnicril.al: ir rnotirtl dt: olditlui
inlii : -1{, - lllnplitll(ii;lc:r cimptrini. maxe zlu unghi de incidenfir, rnai mare $i
piertlei'i mai rnici la capetele cavitdlii in
compaliltie cu modurile TE de ordin nlai
rnic. Totu;i elo avird 0 nrai nrare p5,truncl mai ad.inc in regirrnile cu ind ice de re-

fCraicl !nir,-lrtetlicrL,iur-ninicte, irincaocetifvicei,e;nitsuulfeIrt=slcpadieerdcertrcimreasitemreaarioirndvinoululurnimuol dduislpuoidzeituivnudlSui,..
Prol;a,bi1 din accst rnotiv in laserii crr heterojoncliune dublir dinGaAs-A1,Gar-,

As, eru gosinrca, regiunii active tlqlpm, se obline numai modul funtlamental.
tn rlispozitivele practice esto tle clorit sd, se menlini moclul de ordin cel mai
nric, aclici fundarnental. Din fericire a,ceastd dorin{X coincide cu cerinla
rivclu.lui mic cle injeclie, rlin cauz5, cL amJrele conAilii necesitd, o regiurie
:r,ctiv.i subt,irc. tn stlucturile cu legiunea activd, suficient de groasd,, pragul
clc culenl pentru rnodurile de ordin mai rnare d.evine comparabil cu cei
pentru ruorlul fu^ndamental astfel cd, laserrri funclioneazd pe mai nulte
nrotluri cle und.i. fn aceste situalii mentinerea unui singur mod qi eliminarea
celorlalte rnoduri se face prin controiul profiiului ciqtigului astfel ca sd,
fie fa,vorizat rnod.u.l clolit. Un asemenea control se poate reallza in laserul

cu confinar"e separat5, rrnde se selecteazi, modul transversal fundarnental.
MentionX,m c[ c].atoritir, eonfirdrii slabe in laserii cu homojoncliuni qi in

laserii cu heterojonc.tiune sirnpl5, se selecteazX, nrrmai moclul transversal
{unda,mental. S-n, ar.itat [29 | cn htr-o structuri asimetricd, pentru ca s5,

99 61 6re .c-s

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.

-I

sale se ia in considerare presupunlndu-se cd, constanta dielectrici e(n,A)
a,r'e valoarea maxim5, d"e-a lungul liniei ce coincide cu axa oa si descreqte
cu deptirtarea de aceast5, axil, cu creqterea lui r
asadueryp.roCpoangsataren,tapotlriertieecf-i
tricd, e(r, y) tlrbitrari,, ind.ependenti de d.ireclia
dezvoltatfl in serie in julul tylx.eiI:n. Datorit5, simetriei, constanta
este funcliepard de dielectric5,
r ;i structura men{ionatI, s-a considerat
urmd,toarea rtependenfi, spalialii a constantei clielectrice l72l

'e(.r,. ",)' I.o - 4212, pentru y in stratul actir'.
e, pentra y in afara strat'ului ar:tivr
t

uji:onnndd0c..eil;rieuarcnel;iisiai.teyre.ionsneNgumoeteniilsnestordcaalpcroieu, rcdEmoenoi-tsaicvtaoiltunmatn5tpeg,oaucnloevmn;iitd,dpu,lreelcuxsiaiip,tfcecl,icaactrieovcn,icmsaptrpeazunrlcpltutaeeinrciezdlileeiecalceuztcllra'ti'crrficopc5coe,al'llpeaizlsaapr,rnue:unal-

z[,tor unui mod d.e unc1d,, ea' este solulie a ecualiei scalare

V2E+e/i:2E:9, /r) .)t \

und"e k : Zrlt,. Solulia se scric

6 : 6 ("")E(u) exp(-ip:). (e.28)

rnult mDeaoiairnecceet ecsuterde(dae;-taeplutantgcual constanta dielectricil, e(r, y) sX yarieze

planului jonc,tiunii), deeit cu y' presu-
punem cd, distribulia, lui E- (y) nu este afectatS, apreciabil de c5,tve confi-
narea de-a, lungul axei r. In acest caz E 19it satisface ecua'!,ia

-qTl.g *r1it(y)- o. (2.2e)
0!1" (9.;10)

Substituind (2.28) ,si (2.29) in ecualia undelor, sg obline

iTP - :0.atyt
r'lrz
+ (,1,, p? _ g\a @)6(y)

Pentrr a obline o ecualie numai pentru 6(r) se rntrltiplicri ecualirr,

rle mai sus cu E*(y) li se integreazd, pe y

qqg) {1ftfi*a2tP)k'l + -e1to2(1 f) - p; - :p2l6{;r) Q, (?.31)
CI,If

unde factorul de focalizare (confinare) I este definit de relatia

,:\loo' ays*{u)s(y), (2.32)'

L9

r-oo+1ro3;clrldSr+r1nnlrrtu"ro+loaJruoorr+lgacecalsp1+n.ouo+1cau+o;p?'+gr{gsol1lsouJea1-urT,-dIngIIpJoorrpdo?'ronJ lonnroclul€cilcqotlalrplpur (
{+-E-?r€sJ+IootIsJn+(oorIusu+sFlooauu+rlrr€ao+poJropsr+uuiqr€1r5+u1o€n{ngllcolcr1osenluIoceu1s,lrluvzrprzru{pvnInaudn,slnIzIJlJunaluorgp,ogricdroae.aur'l.csrarr{opF(,JgluuErmrnarn.lrtarl4ddor,
un'J^IlrB l.runlpear ucruls {
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(fr.':,
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0W

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-e.rucl ur{ururxolcls uI 'n xalduroc Inln+uarcrJaoc € pIEoJ uol"rud also 'ri apun

, ztrJtlt:L :

6" "(ot)

op F+tsp alsa nfplrsua+m Is ,af 1 pcund Iug eerur5;rppuras rS : 0H ,0 : tu.
'lu1ueurupunJ
Inporu ru+uod '?{, InurpJo op a+rurJalJ lnruourlod alse u'g- apun

- +- :'(,*o ry
(ee'a) ) u'" lru..(fln)1*H (r)''s

11nnF1e.nr1uu;qdad1n. 5i(uf).g1l*u-"rnp",ro1un.nrfina#lu;rilrf,iae]:lr,gffctu*1p3ultnTrF.?a#l JuailrTur#so*.,rJFJoI-+"s;a::?Hr ialtp:un

sau fotod iod.[, este expus lpuienmrueingniiosistircnailtolousrcnogIp-uIl,..sjioinncafnlciue[ln7ai;2ii ]liinsmt-rap-urpnneiisluaunsreainrttcienugrasacitreoasr-t
dLe unde este trecut la un

fel distribulia spalial5, a

E -dT. - i

-Jntx)_^1lr-f\-i'1-1-'-.---'^..= I C{b

I b)

Io

s 'l

o)

Fig. 2.:]1. - Profilul indicelui tlc rclrac!ia (o) si al cirtigului (I)i.

75iAs05iCi5
. pozitio, ym

h)

dIrieSu-.n2Ia.3s2c.rc-ri Schcna iusLal:l!ici rrtilizatc pcntru rlisurrllca rlistlibuIiti spaliak: r irt[r'rtsiiirLii emisc
jonc{iune.cll g-comctri{r do.b:rnclir: a}-:1'- alimcr.rtator',011 cbict'lii,{/1l--o':lindi
rotitoarc"F-fant5, P-polarizor,l--]entili. S-spcctrofotonlohu. li.\l iotornrritii.rlicator.
Pl3L*prcanrplilicator dc l;anclit".*llr1]1.;:;:'jig:"I).-intogrator. INH-inrceistmtoi'.

tul activ, p-Al0,0'Ga0,orAs cu gro"simea de 0,12pm, cuplins intre tk;uil
strate p li n din Alo.ruGa0.64As. Lasem} considerat are factolul t1e foctllizare
inlcnsila,tcil, erttisiei sl)onl ane rrriisu-
I':0,3. irr figrrra2.32 este reprezeutntrr
ratir,, in funclie de distan!:i c1e-a lungul jonc{innii. }lezultiltele cxpcrirnen-
cele l.eoretice f?al. In figura 2.33 este
ta,le coincid. d.estul de bine cu l5,rgnrrea tlis1,r'ibuliei intensitilii de-a r{-.pre-
zentatl, varia!,ia obseri.ati
in lurigul
planului joncliunii pentr-u emisia total[ T]tr polarizatd, paralel cn planul
joncliunii ;i pentru emisia corespunzfitoare lungimilor de und"ii ir tlou[,
rnoduri Fabry-Perot ale cavit5!ii iaserului. Pentru crerytereil preciziei miisu-
rd,torilor ld,rgimea total[ s-a m5,surat peri.tru jumi,tatea puterii {]rl}ise.
Pcntru un morl de formi, ga,ussianir, lii,rgirnea totalir in punctul tie!, 2w,
este de 1,? ori mai mare rlecit Lirgirnea, pentru puterea pe jumitntc dat'.i
in figurS. Menlioni,m c5, in figut{, cercurile goale li ,,X" reprezintd, -r;alorile
mXsurate ale intensitd,lii emise pentru lungirnile de und5, a clouil uroduri
longitudinale TE iar cercurile pline reprezinti, valorile pentru intenlita,tea

68

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5 g ra,ulsoeled1*ra{.urco.rnnoc'gtq1er1Ss,}?I€ArroilsJqoupas(r'n1nln1png1ou;er.drtt,'u;

]o )e1r"" 'c o.ru1sn5u1 '(sns op tl.rlcs 1i eaptl,r as
rl
3

r."j . atL I Fu.rd ap rtqnq.uoJnc €aJ€ol€a fr€a?rrmlop
'gFgq'€6rIoIrpnrFsIu;oIna.rcozr"rraatluslnu5rupl gl€cr+ra^ €IrlT)
l|Ii:'!x.l1c I -ualq os oslruo
-*a,r; II+g+IS
-l-a.L p1;o.rd'rn1n1uo.rno na.ro1
n1ec1e'8rr{e"rdds ap €a,ruol,r?A qus rnlnrl[i),r
rI l**,1I"' ).!
---nsIJc+lounIz€I oorgJ1ou'l'T€luasarzrnai"l.arrldu'oogJ1c{eozrlrcu"rqt?r.1u,}oo3cJul€r"gr9ei9ld'x6FaIu€e"+1iona?51
Z,L I Bbtt 9,C T,O ZA
/;

Se observ[ cil degradarea cre,,ste cu crelterea
gcrualcelnirttiui.lulni dle76inl j'se-caiiue folosit in timpul tle-
t'ealiz:tt rlefccte prin
lrombarclarea cu electroni de energie 1lIeY.
Defectele ap;rute prin iracliere sint vacanle'
intersi!,ii sau cornplexe. S-a observa,t c5, in
COnpU[ii ternari Sau Ctl inai mU]te
suFdituiiigolnir.iralri2"t:n.ipe,JLceal-ntriucccSil;aiicrphrarleilclrm.atrnrraueriaaic'cup.unrao"ei*lirctttu.lp,.t.:uor-i nent,e fata de degradale a laSerilOr d,CeOpminpd-Oe-

Jc'::,r-pmciah-enlsotiiacnrdtrrrrs:ai icdtaicllcldpet,oartl.rilit;,titmrt,a-.rerrtJ:rn"tti..anlo,rOrcr.,, de compozilie [77] gi de lir,rgimea benzii inter-
zise lZg l. l)efCr,lCle (,e se (.aIAC-
letizeazii. p,rint'r'-o DLf, dCfeCte
"l'i-te1i,- lnare de Cl'eltere
dciareleCldieepdielidCered$etenleivperleufledleeneliaxlciti,tasliielt;icadreago-
ieristice struct'urilor de tipul (GaAl)As' De-
grad:Lrea in laserii cu hetel'ojonctriune dnb15, din (InGa) (AsP) nu
,ie cl*toreazf' acestui tip cle dcerefe$ctetere1a79]d. eOnsaitl,tSir,lioi bdsiesrlvoacta,ieli-iloers)toesct;e,

ploceliul de degradare (cle

rt--0, o B i --tJr,-:")(-t,rf+r;;;;1

2kA /cn? 1

|a,a6

0,2kA,/cmz ] iS>ealoo0'o4hIF\ 6:^ t0odyn/cm1
i"r{",rdyn,cm2
0'0'?1 /,r-,=,

0 6 12 ' l,kA.zcm?

p, x108dyn/cmz Fig. 2.:'ic61. c- Depcnclt:nla ratei dc dcglaclarc
tlegradare.
F-ig. 2.35. -- Depenclcnta curctttttlui rlt culentul dc

prag frtnclic dr tcnsiunea nccatlicS..

activat telmic clu o energ'ie cle activare (fol'rnale) in jur de leY sau mai
rniczi. ScS,derea tirnpului c1e via!5, a tliverselor dispozibive cu temperatura
de hrclu este reprezentatd in figura 2.37. Energia cle activare pentru laserii
cg heterojoncliune clublii clin AlGaAs es,te de 0,7qJ. Pentru imbun*tXli-
re1 pelforrnantelor qi creqlrelea timpului cle via!5, a laserului este,important
Ass"ip,'faasrcli!,rtirnuri,ce;io-xlrlto,reIzrepirodta1eetnerisnfitiualettelvagitacr1itjei[i.d{eianfceifc,igtepurrdoacine2s.se3ul8ebesdstetreaclter;epi $rdet.ezinerenstta,srtia5ct,Iuedlpeergepllaiutdacarxariaereal'
plinortaer-itpuenalralairpsiieidrtillci,supphionezXteitritovajuo2lnu0ci",fCiu/inmnein,fsaiimmzpablSud,nui[n,p1f55u,,!nercqeltiaoeliztdiaemrerpaauta-l de rficire d.intimpui

elitaxiei. Ricirea

de via!i,. a dispozi-
tivului, aleen cu rata de 0,2'C/min. duce la deglaclatea cu 50 fi3 dispozi'
tivului riupi 200 ore de functionare, iar cu O,8"C/min. duce la deg_radarea
cb/maxpi5nh0.c/na"ualia-adiisntlpuflsuoezlanitilnveiuiclriuaoiteddieudgpela[rdd5a,0cr0eireoinraestiiumnpprtaiumld,pdeegcrefaudr_din,,rcciiilrieocanonac$rue15rd,aeitna1fo40r90r?n0Oaor"reCea.i
de centie neracliabive. Rf,cirea rapicli micgoreazi, concentralia de vacan!'e

v0

IL

-{-enruuznBrJrnu)rIrlllraJ-earrldsB'olrupoaouBllJrla3aEuulornlJrJesdl]eslllBurpJrJrdalIu:onllcd-Eut.Inl6l[n.oIeBpls.."rqcJl,lJ.lI 'cIJ+coIo rnlnq.ualna €oJocoJl r?I o'}€+
-InzoJ IIJnpIgC s nBs ocru€cour runrsua?
roun €{uongu.r qns ?}Io^zop os runri
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]
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'sVB9 ulp laun:I aporp-, :syIVES -t
Flqnp atrnrfcrro[o.ra1aq n:r
ulp 0

'u!uI/ IJJSBI-!, : SVe,I] urp aluJJsau.rtunl O
epop-f : dsvBt ulp alucrsourun[
!ul)l.".OrZ2o'O,,\-I-ltByIa::r(uqnl)iupolrr3Bu"u7nol-iucfuln3l:aulellerpurp1/3ned""gur r(1B03r-laB;plIsaur:iraa{luIuwnr.)/l OpoJp*f; :sv€c urp uun5 epolp-a -
or-r)FJ ap IJnlcIr esJc.\lp nlluad ua.repel8cp,(,r) u: s5V1EuSurur^lprdxJaJV,e4.rIiqlgIzoedps;oprpro-lras:Jai)JAo
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ul
-u T*,{st 3"7 -a
€a
-e -w) .P)
trY +!N

2.?. Tirnpul de intirziere ;i contutarea intetnfi in laserii eu

semieonduetoare

A. Timpul tle i,nltrziere

Laserii cru semiconcluctoare prezintf,, un tirrip de intilziere intle incre-
(t,urcnf, fascicol de electt'oni, etc.) ;i int'cpttlul
Irulul l;ulsului cle excitat'e
emisiei stirnulate. normal acest tirnp de intirzielc este tle arrlinul
fn rnocl nsei,ceesgaarl&peenptriuerar,lereriiileliz. aininavefar'sr'iaa clc popula!,ie

nsaunfiocsieecn,tuiinpdeelnortrruyi estc t'irnpul tr,cestui timp
ca ciqtig'ul
laserii cu homojoncliuni ui cu helcrojonc!,iune sirnpki
normal de intirziere,
prezintir, in anurnite conililii un timp tle intirziele mult rna.i
din (laAs
rnale (50-i00 ns) [S2-Sir]. ln alte cazuri timtjul tle intirzicre este cgal
c1 lungirnea pulsului qi efectul laser apare irneilja,t clupir tcltniualea pulsu-
Iui ; acesta e.ste efectul tle contutilre interni, Q. In fi.qut'ti 2.40 este lcpt'c-

.ljii- fAr(t;l liltt,dtAlo)b) -fi-c)
ritl
LI -----i.1-rI--
-l--t\-
I
t

(

Irig. 2.{{). lrrtirzierea in laserii ctr semicorl-
ductolt'c : a timp de intirzierc seurt ;
timp dc inttlzierc lung ; comutarea
D- intetni Q. c-

zerrta,t schernfttic tirnpulde intirziere in la,scrii ciu semiconductoare. Con-
centrnlia plrlfltorilol tle sarcinti in funclie t1e timp e.cte determin:rt'i do

ecua.t ia

tl'rr_i _tr,
dt qd, r

unde t' este tlensitatea de curent de injeclier d - lirgimea regiunii active,
contlifia la iimit5,
l:a-t :t0irn,pusol ltuleliaviaatc5esatcpi uerctuitzorrliiiloerstede sarcind,. Cu n:A

?r(l)--;l--tL - c-t/').

qd

Concentralia purtltorilol qtlie, inti.meopnsdeecicnfi,ldiv,,acitg.tifgnulacaet,ainsgtei, valoarea sa de
echilibru intr'lun interval situalie emisia

la.ser are loc dup[ uu timp scurb de intirziere

t6:aln i
.*t
J - Jp

72

o,

-srs altsc ul tpJ1nail oJ€1s o olsa g uaJ€+S 'Jos€[ rorcruro er8"reua nc uo?oJ rnun
vriq"iosqe nc oc€J os oJtsc giue1u.r. op
tspu€q mp'uo.r1ca1o rtrun u.rnqdro ur"rd
g tsa;r€?s ul Kc€oJ+ es egeod 6 tsar€+s u1p zA
nc el*a.rc uirzuwtl ra+sac€ piaAIN 'rrlngu.radruog ra"raq.So.rc
acaJ] Irr;t+uoc piuele,t ap
€ale+rlrq€qofl, d dl+ ep InlerJa+€tu ur i 6 ea.rels u;
€putsq urp uo.rq.colo rnun e"rnldnc urJd .o+€zruol

eE-ns1nllqpto[nape;pt8nao+cpuJielsgo;rroinnl1aood,pref+caurraroirccpneepols;la4ge.ucorafa?crpl]nrnrqrcone]llIa€encdplarrpurpauno?rlnurqsnlllpuTnildru'r;uoe1o;zJnr?addauldarr1rua,elpl ronqr;lrlsnlJuoloraaTidrd?ro.aA+lruiKeo;iuqrrnn.rdn5doarc;aucu;arrdiIron(.lq1o[gr1a.g6rlru]]l
glufe8ap olnof €.rnplgr oJ+Kc op rS g,r.r1ce eaunrFa.r ug r{rlcatur rr;ro1g1.rnrl
oJ+?? op ar{cul;al ep Inlac1pur rrJpqrn?Jod pzua;ro1ep as 106l rnpfeprq$
'r€-[ad:uoaJuaolsa?zcp.r]uBTr.tueEeianra+r+tdrrlr'fslqtr.c3aJ?runaJnor'sd+fuupqs1uilltraor(rrg+qr-uuaioe)r.parpr'zfiol{rtgroscl;lupJlguurnza;llr?ryrlraBoraorirolpp.qqrr.deIrauonolrlnrsdrJ.?ccrruoplrdqlrlrecrr?ou?ecaooporpc?;?pr.,oIra€(o+JepcalcrgJ)aar?acacJ'ulpraredr{Jtcqrpesn';irala?ru?lo.osalrrs-os?l?otqcfnDazr+ea{Jc{pauKrrraip+l{rrdnirn.a?rrxqonollaonro+l;rpadrBu1arropnuuul?uco€rooaolaaJJdJzlI+rau(l€r?rdaaz{rcrqarJzaro;cr:rnJ1oopco;ulsrupplq(lzsp'eCuua)rnpa;(;rcuircSy1I)l
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-de.r ur.rd Bzrl"a,r oluorl as arielndod op rars;o,rul ri,roFur,lu to,rarzJr+rrl -I

or'o+ nc .rnlnreprq5 uara5uncrprtl*T3'H?;l"il;*.dt+"*::tt"*:"lli,:j;::"t#t#,: -a.
r.roiluolo; rerfq.rosqe E+IJol€p 'Sr1igc oJ+FO op .rolr,rap.rord rr"rgzqr5a €o.rorz.rilur -I1
o(6le) o1d*,aJleosseqaernirina?rc{e?iJn3dorad.eIoprrza.rlsr.+roqa'uIrzgrr-.lge.g8u]r1o,cir€roo,l{qoorzr'drr.gr.oulrs(a1c)r: ur.rd psnpo;rd rJ
e,rdnsr gzolrlrs Fr
o tluazald rrroa Tz€ourrn oc a15c uI 'rnln+cora rorir.iudr olc ozt]Ec €alrlt? 1o1 lur
g1u1zo,rde,r 1de; op aJEc oloporu a:llnirr rrur snclolr{ n€-s T{ourouoJ rni}soce rr.rfc
-r1dra lndocs u1 'Sr.rd ep €oJ€oI€^ elsocl ar{ooftn o{} rnln,JrroJnr €are?ia.rc no 9l
apuJs 1enpcfatulnr.5re'osaqr??crtnsJrlsruunorc5eo.rlsroauar.rr€.8D.rgu1rpoIpnlr€irJra:?a,uI?rrrr5{ uonpi ep 'o,rl:c d
-iJqEJ o;rorz,q1u1-op eprrrdolr oti
ap Inopaco,icl ln
inl
'ftro]oJ J({.ruos([B J,il1) r]JJt:ls als) ;: .ritr
(l.ros(lu nlr JJUJ IJllls girrs 1' r( l: .'J,)\1r t:1!rl) -o
r.lJ J.rBoJdoJJr? Jrlr-rJ) t1) lntJpol\ -'It.a '.i;-1,,i

t 'a I i-
-.-t,
--'=- J
(J
IJ kJ'
=--
z- -J
:J -- -

fo-uTea'l.+s8oelr.drldrreuaJnptdu,rBn"ltnalJ{ar'o1rzJ1lnl?.o0Trtrlge-a0pr6e5l*uaInnJr1cualonrrdrFoAupJrrouSs1q'o-5ersozr.snrd.urda€np}cInI.ngu.?rrnug1o'ur.nE.raac{d?uarr.lorsc+opfdl.rrlrn'u,1anep{.iulatsnd

temul nu rnai absoarbe fotoni. Astfel, ciqtigul r5,mine rnai mic decit pier-
derile
pin5, se satureaz5, toate nivelele Er. Acesta este timpuilun_g de intir-

ziere d apariliei efectglui laser. DupX, cum am menlionat 186l' _intirzie-
condiliile in care este realizatS, inversia de qo1u-
rea efectului laser, chiar in
lalie, se mai poate datora pierderilor prin difraclie qi strf,pungerii.ghid.a-
-jnciiturei d.in cauZa perturb5rii indicelui cle refraclie clin regiunea activd,, de
variatia concentraliei purti,torilor injectali qide
degajatS,. Pentru modul fundamental TE pierderile pcdr,itrne cd,Idura Joule

diffraclie sint

rlate de expresia [92]

(oif : u11. nt us

unde a1 este coeficientul de a2b.4s2o)rbia.trie! dgini G-resginiut tfeuanc1li1i .c*a.re- coeticientul d.e
absorb.fie din regiunea 3 (fig. depind de,para-

metrii gniAajutul. tn figura 2.43 este reprezentati, deponclenla pierd"eriior
iapergliuniui nAde,ifasrua1bc-lciiAal iidle:entudlif,mer-aeinferls,arb)e.ADp,oisdnib.ifitiidtgr,uergSihn,iddracicrieeiisae.deOcXirnereflrxAaistctlsi:eei din regiunea 2 osi
o valoare minim5,

apropie de aceastX
valoar6 minim[, c{dir clegte abrupt. In cele ce ur:meazd, vom discuta Tarialia
indicelui de refraclie in regiunea activ[. Bl variazii in timlul curgerii culen-
tului electric clatorit5, puitd,toriior injectali ;i ci,Iclurii Joule clegajate, de
asemenea, cu localizarea truminii in ghit1. Cu varia.tia concentraliei purtX,-
torilor de s.'l,rcin.i,, marginea de absorblie se deplaseazd, spre, energii mai
mari sau mai mici. Deoarece indicele de l'efraclie este dependent de coefi-
oientql de absorblie (prin intermediul relaliilor l(ramers-tr(ronig)' orice
varialie a marginii'benzii d"e absorblie este inso-litd c1e o varia{ie_corespu!-
ziatoare a indicelui de refracfie. S-a ard,tat l93l cir, r'arialia indicelui de
refraclie depinde aproximativ liniar d,e concentralia purtd,torilor liberi clupi

expresia

A,n x -lt!n. (2.35)

constanta fu d.e proporlionalitate poatefi cuprinsi, in domeniul10-20-10*21
Tcfrfei-c3e,redae-pciunrzeinntiul ludieprci6nnrcelliiluiilneeadeacfutinvcd!,,ido.negaarejd, (dgqai, temperatur6, etc.).
cre6-
cX,ldurd, care.duc,e la
terea ternperaturii acestei regiuni. Se poate presupune ci, incillzirea este

Ar lfrriKz=iz nt+ il(t= nt 60 t-r4o6co,r<(,a'1'-qo._i4:?llll4]*Ao+oz

nf iKr=n n4o
*30
iEFdsnaesidlgetuei.nc:dri2eiAe.p4d,;r2-ee.Az-ernrenz$tSfaliactAhcng,el1iicr,spniAnral2oat fu:silanurnlfultiazuimrr-gilogeindhfiuillinedt-. h420
lui de undi fundametal. *I

74 1A

0 /, x 10-r L,5x 1A-3 5x iA-

At

Falieg.gh2i.d43u.lu-i Picrderile prin difracJie
de undi in funclie de A..

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-(r'' t)tt - r' \
Its
e tt (naqvlrr-uap grsa;rdxa ap p1€p alsa .7:rati;nrac1ku*arl.i3nc.rrX-i cuu-olcra.la,:mlnxluaaJpnucn -'Rl
nc'rr,rnle,radiu6+'"
'nV op
-u
{se'z) ';[v*: !!v
ul
qalnloloccrpmmuloJu+am"rap1e*a{u;re3;rr'raos;rarnp.cradarx.l_isaJoloclprugnK,frm+8tacs;pers1oue+ospaocrrrJirniapaarlruq?.lcac€aaprr+r.mr€orJg8uoan?ir€F1pee;raarei{iac?pe..sqgizaa...rrreoeluppl
ap€€'EpAuITn€+uqor€paJupoougni€rFIae.'reliauag.rrtc"ugsfaar8plsaKpaAa+Is+ucaKts"rrnnepoalugoncprFaarp.nr lonu+qr€pn+rdo?sur€ezcarour1,rFrm8e.ar1gillzul ug+oIqaodneel+-oer.u4rrdr8e,g"rlcg$lgl,,ustauq+O+usiO1fe1f F+.c

FiU

lct

JOI
-tsJ

op

+uI
sIn
ap
-€p
-nd
-el

{!}

-JAI

I

t

rreilar l:i1a/2 (curba 1) ryi r :114 icurba 2). Parametlul r e-qte tlefinit de

r

-ttnT1 I-ro

oL
1 iI ") , (2.3e)

f, '(rto

unde oc este gradientui impuritS,lilor de dopaj, in regiunea p-GaAs, m,por-

tat la concentralia acestora (s-a presupus o tlependenli, exponenfial* a
pcvo-iaGn!ac[,Ae,nsttrr;a-lEiel:iunim&guipmu-erai&tX,d.l.ieloindr ifcfuiguzuiedraiast2ae.nl4ef6acb)e,nsrpnteil-orremipaorerbzipleitnraetatzetiXsat,ivdrietap-tceiatridmcrnepig,uaiul nddeeii

j,l. '-t/ 2 Irig. 2.15. l)is{riirrrril rr,rr(1.r)lrii.
tici prtrlltoril6r rtc s:tr.cirrir iir lt.qi-
a,a uncr p-{ilr\:;.

-tor
L J.U

a'1
n"(

t r-
5?ri\t \
,-;, / 3

roi l- \- \'

"^".," I

I

I

oo.fr 250 300

T,X

i.'ig. 2p..c1n6.tr-u n(0) ln i uncfic {lrc'img.pc2r.i4tt7u.li--r I)cpcndenfe dc
constant, a lui r in rci4^inr
cie ,- Jo -

tlc curcnt constant (curbclc
i, ;i , (i\ si in rclj-lm de citnp
constant (cnrbelc 1, 2, 4).

r a concentra1,iei electronilor la u :0 pentru Jo : constant. Se observi,
r qi ln consecinlri, cregte indiceie de
ci, m(0) descre;te cu cre$terea lui

rcfraclie. Dependenlaiui r de tempera,turd, este determinatd, de dependenla

de ternperaturX a mobilitd,lii ,si timputui de vialX, a purthtorilor de sarcin5,
precum qi a celorla$i parametrii care intervin in relalia (2.39). Citeva exeill-
ple sint reprezentate in
situalii: (1) p- fttzi figura 2.47, curbele corespunzind urmd,toarelor

jop:constant; (2) fr - Tstz, jop:constant;

/t)

LL

'luulsuoJ Curlc op /a€mqtrasnqocJpn0Bc':Brau€rtrcsq,4qJI.uJonn+pccu6(oo9[d1ulv^'u(aeqq;ptrirnluc{oz?qao'9lrP€r7iqasJev^npqI?ctcr/rtrI3e* a. -
ora1rl-luouruqnlucrl6napcazga'Ilf.irI:dr?OaJrla:cuoonl?aFeJqnluJurn+oIoudoopud+urnrp14d{ss4oas+(;0tI(ana9cuf-r-ar'Ii€€l/u\c}ri
rut8ar 1* luelsuor uluiJr(n7c)zaupy r-ur8.so.lr,.ne.rl.u5atCd J
alicunJ
JV rp -
Y
x 1ll
v
z g't z'L 8'O ''0 0
o
.U U-
!
tt r.o'0 -
sp
tt
a!Iupn
a olac 'pplqc{ arxelrcle ur.rd uliqo
I zoa'o- os oluaca.r alrJn+clr"I+s mp a+lnru r€ur 3E

oloc ocar€ootl '9'6 €Ioq€+ q o?ts+uaz -.rod
:!00'0- 3 ]i-.i1aug0"lr0'cdg2a1:f:mm0sJu.rool'pIdp"Gu.rrorna1f1gxt.,e'rp9enad[dulour'agrui1ige'.plr'lgeu.-asouc€lcouaaqocr"a0r€nTc'il.3)*I
(os'
U! \
op
cd

100'c a7-9::F06p,r':rg0:rJ)"r:ntn,,?+:+lu.un((€ro1s+:qzos@pnu-l:ooidru/a;,r'1n6:cIrunol'u'z-zldsartrl'ucJ['aI4oLperp1luoi1'Jtucrruu10l"ro'Irt5n€dcaa$)al'ur(la1ua€'oluqr]or,a"-rlru:r€.nrroaonc+dca).r

200'o
,0

11un1dsu4iio1srqnc?uotlsat1;rsauuorcnu: .rots.rf)'(?run€ln+squnodc
a+gIuata-Jr6onucIonolNopqu'rrrn,tz8cafIS"-r n;quod rr-d4sr'"i{,orU5stlUg-.rrap)dy

d 'r ,t
zlr-J -
nlluacl l€s€.r+ n€-s 0a ii; 6/ J'gV- f
oloqrnC '0 : I €I (0h, rntr €or€oltsa
a+n-o 0,1{, ! oti, u1 plulroder (O)& lnt .e nc
ur{er.rel elurze.rclo.r os gt'6 u.rn5q uI 'auJo+xa oiu{rpuoc ep ri rnlnlur.ra+tsur
pllarne,rud ep oricun; ui cglrlu5au n€s p.trllzod aJr?ol€a t;a,tt aleod t1,)tuy

ftr'z) '(t)tw1tt - tyx: (,f )gV

I?tr+s r+IJu€oa++uIn€r.zprooJ-ol r,r,uioccup+:quaaou;Jrrn{couopacpr?nrnuloloncJqrnpncudar plnnrdr{n.runlnr1lqenq.tdtl(e1OnJ)rdllsur14or1'ie'u"rrrqrrunralrtaJuunoo+cdcnurJre}ars{len1r..orrrrr:z{,irngguJuelr!lr

-o1up ar{cuJ}oJ ap rnlecrpul €r{rr;ru,r arntrr?suoc (l)orwtL- InuaruJaf,

$v'z) !Q *0)nuv:t-fivx{uy:l- tv: }v

',fd i

1an"drururr,i1}qypou?r,+laupaupr{ouuer.reugnrp glsuor€ tp,rnlcnrls ad 1,rn11cle +ualnc op
EoJ€o{€:r
rcun1t 'ry etrsa (syeg-d) K.^.r?o{B q?Jun
qrnlnqnd
li-rFa,r
: qg 1 allurp
pd(suyuelg-rr.g) c^tesaOrs'nrd"rnu1auu.rnerdFuara.rqu. rrparaarq{.icaa;rrc;enJ cepopo€loascrnpums riu.t,rapp
a1*(a.rc .l cale"rap

-rsuoc rliunlrs olasJoarp op orfoun;u('LT'(, u"rn8g mp osaror irinc eiy ',pplqcli
.?t(rsgzo-€ps)J{pI'2rlutrJ"crr.pn,.,-dtreur-rxrdreirrla"rrrd{.luau".,rtrgml7us"aur-cduooprcci,1:6dIn€;muolu{ufqlsao(urtpor)Jucnl8l:}ro.rranouulf;sn-o(gJua\,diu?!a'a;""qu'nc1uJr€alsg-uucnedoer€"aput.:01nn,df:,sluo',,€J_ot+r1cs€uJ,oa-oap';ir(€s:tuo)oooc6}

Tabela 2.6

Citiva paranrctri si variafia tentperaturii tlatorit:i cdldurii Joule

llil'r r l7", li $. nr:.\'.r :.s L, rrr

1i,J,.\.t'rnl ':l. f)nr '

,lz.ru n
I , Lo:r,i.r0slI|r.osri ...,tluror---,i'l1rlr.,.ror, I lrr.ro-o
| ;.roor i ;'. r,r-r Il..1.trr,oo,--u,u
2,s.108 r).25 | ;. r0ci J rr:-, l:.1.r0-o
lr,r.ro.r I Z.tO-o
I s.ro'l ut ;.ro-'l:11.01(rls
j.r.ru.

Efectul l:lsel incepe cincl este incleplinitii, relalia (2.12), adic[ ci;tigul
tergairllresaruziilspiciesrttl'erliirlcli.ctPi elinl trr-uillol?ar:r0:a,3(21/I)[i 1,:2 .10-2cm, pierderile prin
ln(lin):57,,it cnl-1. Pentrl-r p:
rrg:p.nr1rri:iin0nl1ui-i,rr.6i8uJdi9i.7."iri.n:1l1p, 00l-lur-P/aa"(i,OlQJio\a2imacrd'2tliu';rr(ept=n?2(oy=er)tc2o:1ic'u22:s2-a5i{1),rclA'i,r.sin,r1iicrr0(,t.9.t1I1:ss'P20ict41,cint0p8n.oc1)3tamr)0lutaXs'43e,)asicons=ebotr=faAeoisp0/nLtce.5gln{,Pe,ris,\nzr4erne:'tnis:slo2qietir.ra7',uor:lec1aiasr,r2sfnie:,an25re1c,e2.rlsurn5troeai-f,u1l(oiqr1tIllsriSnri:r,€.-zealr)ckt1leeucl,an5ta\er8ttferriia,au--.
(:2.7I2).))1t0l-t5S0-r1nc. mI)-irncifnigdurFa,:12,.643 .1() 4() llr 1Si ao,,:37,5 crrr-i pcrntl'rr c:

rezultd, cr.i, ernisia laser. incepc cincl Ai
devine {2,1 . 10'a si, r'espocti\-, +2;l .10-4. Pentru }.: 0,83pm, rrltimul
rlin t'elaf i:r, (2.40) tler.irre ega,l ctl -31,1s.e1o0-b4tiinAer /:,'A.l0r, ,:0165,6i
tAer:t'ru1t'0n r0crn'r rji pentr'lr
Ari := '7116; : 6,6 . 101?ern
. 10-'.
Cn iuce'ste dale rezullit tlin (2.40) c:i {in'1t0irnpau;iipruelssupleucitittl.e,
hli Alr, este clatd, de curent trebuie sir,
se lealizeze o cLe;terc a lui ,lr cu
a cilt{int'act'iuncil ltr,str. Cle$telea 4e,c2u.a1li0i}-4(:.J4)r1.)n) tl;ui
intirzielca so obtine din aceast:i lel:r,-tie folosind, datele din tabela 2.6. Luind
in consitlera,r't, datele rcprezentate in figura 2.48 st-r obl;in pt'ntru tirnpul rle
intilziele r-:llorile leprezentater in ta,beltl 2.7.

7'altela 2,?

\:alorilc tirnpului de intirzicrc in citeva cazuri

Rcgimul dc lucnt A?'

J: constant 1,1-107t 63(66) 78(91 )
[i - constant 7 .706t 13 5(140) 1 60(193)

7,4.7A?I 61(6e) 70(82)
7. 108t
128(1.13) 150( 1 71)

pti(I:aorcuerorli0l-ilecnosl(ercDpTcoiutanerlnetl2eteezi'sr1lilsznae.paidlAuetrpcncclrecizeencuiazriaiirnd,sezbtnluaecactrlauaoisnzrterdebuee:(il1inslnVo7ct0ritrrp+'epnacq21-rpr5t0apeeln)f-;;(ttecce1d?zul1e6iSn/rco2b,qau,feraiigeelcue7sc.rtee;fe12oq8.i5rtn4s)en;.8trapeP)1iera6riimvmai)amt.areluAutracelnaepdtocldeeoaebeluzrsapcaaeleicttterunoovirntnbsariicsuitnceiee(atnrcewztueptu-a'rsealblti\neepe1iat0lcrse-arpirslu7ctte?armi;tr5nc:-8,5r1--),,
in ambele c zLl.ri prezenla unui cimp retarclat (clatele inscrise intre paran-

78

6Z

Kirpg-Sy+ddnInrfcnrouspp?cs€(d6prrpu4ceEre'qg-pou0.l,reorrIneppK8.u.rrdl8on;tsnrdu^:dpJnlporsd*a+sgpm'rfl€rdlnncu'11ezsnnloefceirp1lqp;1t+quu?is1drcnlnoouxdclorsporoqsufIuJc3nnroe+zc4Poulu;a^rorrrdgorocanrdserclqlpouo''.[s1ra9auo.T9rerSd9n];r'6cn'a.truclouaicele.rpr6.*nprpzaomd-ptlg;nreelTulnprnd1q'qpni'6nf"(&tdda1'lrf:/n€u€lop-ocJ):JdS€sauudrrrtilx€'nruiu'er1c;JJrooz-ur?+ruI
.uro{u1trc;[email protected]
aJ€x€IaJ ap rtrad"urarrFl uonJd+gm.4psrer{iuoa.rre{c;rep.r€;rpK+ucoilJdtp
t1n1n[up1qF

'T1 t'{:' 'g1i
e--unc1ular;rroipcpdguromrp{ludraoupleduoe"rdna.rarJgcuKooSJd€+qoul{o€pJaunc(o1a3upa.'JrrnnacisnqesplInndr+nc1lannJqqot"na€.drz;yuspodE^€IruJ€1crlcooq?psot+ioIcr8rauJp.ardoluJerepu}€rll'JtIe€qcu+'ur
o!?J$tsxool€a(mo1Jn€qnKcturr€cJa€Js€ualuprrJoo+IIJuo1+Ko?p;rrn,d1u(r6{u: r?luIaicLuoTc0'a0r:ts?c u1 glur{uds ountFar o

nlluad Kc f^.rasqo og
LrIr'/(nrgJ+:u?gtIrsr0uoaqt?r;0rrrmuquu.osJ:Crauau?r+p{'qnrIJlnIq,no-lrudu;llrruarqJ{asoronuur?qupo?nroup;?rru{rlrlusncrtrrduszpqIoauuprfdrlpmfn?on{uecrzqliarcf,Jr.rJrodtle€sssepsqr€JpJ1Inoggnucpld'unru€ri-zlqqo4ai1Jn1.unrulendlcqraqo,sd..1narruegcaGrr1ll)1rr€vnnrocdnclrnLl€pnlseurqrlrJonc{nu?'dn1rduJquo€aerusolra.rJlroJsEn€rtrsuIcupu_orerurpaturpzr"s"lorurJla?ltna+tz0ldan€€"rrspII:d1poae€dpp;}rI
gurcrtss op .rolrro+Kpnd tr{nqu?slp E+ulzs;tde,r as [Sg] Oq'a u.rnFq u1

'nps lndrurl ul +Icap oJ€rr l€rr ouraop +€pJE+oJ rnlndu4c In+caro iS esnpa;r luis
o+caJa a+soo,r? D+ugaC;tInJc+CoOpIOrnrlnnlqnndcful iuoorEtsqul.rIuor+Jtsop+

'U.J 'lf,cqCIU
€'qldurrs ounriorrofo.rcl:r1[ nc rasul
un-rlul 8.r1r..rrcel iariprptnulnalud3r.rqnr'6c1-'r6:r'nnt-B!dr at;r€d ,g+Ie Op OcI .rer elterl o Ap OrI aiznJlp
-;rdurcl
"oo(itpl,'sl',aZrrn1d'1Fln,(,l1silL)upiroqcr.grlnruic1..rnrao3dl?up.i.romr,rr3ncr.lnnugisn'-1.1drnor'ud81leculn;prIydn1i4uecy;aprsolo.r.a,cn(xi,*1leiu'oraorl:uurfnir,bccr
x'1 -rus oIJ ,roplo1p1rnd rer{u.rluacuoc ,RIB}

a,f c)c€ csa.tt

OZ -r[ogn1gln]uquan".rrdealliu1arn.r1crrn"rlu;nrr,d;qrrsduqrpcc{trnifcllo'lxpIan(}1reunslq;f,lr[iue'+outlae.lLrnrripucrrdocropJ

# a].r€ol Ed,rr{ooe ur.ril gcqdxa as ErrJo+rn €alts}
;
as

!' ut 'KuJo+ur ff o.rulnuroc op uaunr$ar elso I
g{e.rnSuq ou+asuonrIFJaluaJBunr rF8rall;?r?(u"roocslus1 orsrure ep
1:, uaunrFa.r alsmro i
a1.r I

uaunrFa.r s+sa I uaunrFag 'pldrurs aulrr{cuof
-oJoloq nD Jasul un-J+ul fl gulalur aJ,BJnur

-oc ri a.rarz.rl+q op 5un1 durrl op aputrlFal
eltluoza;rdal +uIS 6t'6 u;rnFrr uI 'fuJa+m fr
-seaJv 'lud,rnc a1r a;etrnruoa ap Inuauroual olsa €+
rnlnslncl uo,ru-urru.ra;" qdnp gupaurr rds€J Jrsrurc y.ltrclt-l 1s ri
luoJnc ap mlnspd eeun8unl nc lr8a ery gs eluocl oJorzJr+ur op pclurr;

(1 ptt,nyu, Da.(,nln"ur.oC 'g

rnlocrpu € a"I€rf,r r€ru o+€+rnTrl+uocsrp o €l (al€ur.tn ulnt;drdru(ltc"&o0ca:'Jetsrfioicou€p.Ir;(Ja0o"Ir:IJaoFp+
-ggnd rar{r4uacuoc ralalie"rc RurruJa+op +€pr€}ar
ur{unys nc er{truduroc u1) oralzrl1uI oll rnlndurr; ua.raliola EI dcnp (dzJl

pierderilor prin absolblia pe purtd,tori liberi, acest interr,-al creEte cll creD-

terea rezistiviti,lii substratului. De asemenea acela;i efect il are lunginrea

pulsului clatoriti, reducerii pielderilor prin inc[lzire Joule.

4,8 130
o 124

\ * 100
I
E
$80
trl
60

a,L 0,8 1,2 1'6 2 0,/" a,B 1,2 !,6
X+
r, ns
I'ig-. 2.i)0. (ionccrttmlie
purtirtorilor cle sarcini l:r Fig. 2.ir1. llclr:rrrea cis-
(iivcrse irltcrlalc tlc 1.irn1r I i trr lrri si 1lir.t'tl,.r'i)oI rr ilui
dt' la l, rtttirrirrr'.r pttlsttltti Iaser tiupl lcrrnirtrlt'n pul-
suirri tlc curcirl, indicind
d,.: cutelit, reg.itrnrn tkr conrrtt.:tro a,
Lrndc cistigttl tlcp15t:stc i:iu-

dcri l e.

2.E. Oscilnfii in Iaseri. Modttlaretr

in aplicaliile practice tlin tlotneniul comunica{,ii}or in clistani,ii este
necesa,r5, lllodlrlarea lurninii laser. llotlularea la, inalt[ frecven!5, poate fi
afectat:i de uneler efecte tle oscila!,ie atit ale intensitii,lii lurninii clt ,1i ale
intensitii,l;ii curentului electt'ic cdael'aeli1rnloetnatalarereaddaiotodreitii,iain,saeir rntlltor (zi-LZ(';
a[91,e5i]n. teLnasiitnl-cr.h{iiiciluermeainciii,rccuariteulsnei
nir,rii,. in figula arnortizeazir, pinti so ajungc ia a,par oscila-tii
diocie lasel in uletp] rre'ezzeinsitaotr.rln'aoitrc:0uit starea stalio-

2.52 este sirnplu dd rr,limentar.' a unei

seric' crl se deschicle comutatot'ul I{
;i st-. cle la generatorul de ellt'ent. Culentul aplicat pe
a,1imenteazii.' rliocla
<tiotlri arat5, ca o funclie treapti lzt, i:0((fig. 2.52b), iar intensitatea lumi-
nii cmise este o func!,ie crscilant.i, arnortizati', in jurul r'alorii metlii J,,,.
itirlefilreoiscrtti.uc,riilleesxeaiscdteeirsn,ttlooerri:eouasnzcuiiiiliantlitimei rcpctelefpipnineidtndpdeeinnll[aepsi eocoartjnuucnlegdneitnrlatar,eti'"ilo;otaurlreeeanletsuctltarclciaonrnielaotrrr5eE.ceCi afporartoicn--
de prag gi t1e tinipii de via![ ai purtXtorilor de sarcin5,,
diod:i Ei curentul [96]. Oscilaliile se intintl pe o perioadir, cle timp egald, cu
fotonilor c, purt';torilor de sarcind,, r. (mil-
t., qi
aproximativ de dou5, ori timpul de via!5, a
suratf cle la inchiderea circuitului). In afara acestor oscilalii, care se ate-
nueazd, intr-un tirnp foarte scurt, numite qi oscilalii tranzitorii, care apar
la aplicarea c.urentului electric funct,ie ti'eaptd', exist5 qi oscilalii continue,
autointrelinute, cate apar in laserii ce funclioneazra in unde continue (cle
exemplu in curent alternatir'). Acestea sint cscilalii atit ale eurentului elec-
tric cit si ale intensitllii radialiei emise ;i se ilatoreazi, efectului zgrrmo-

80

T8 099'c-9

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- --)n.rts
nr ."apr'' 91,., .^tq^.a .*F. irt .:ffrtril\tiiiE i#,"j"-e"T,1hi"fi1Littr#
_IFJ?I q q:au1epbn.1re1i1ucal1urqe uu1"mo.ar,dB"y
-rrser i.rporir lt (anlludourdoxoas
'r,rns1nd
a1r 'erniqo as oJ€c .r,ms1ncl u5 ua;rqnpolq
'aJq?luautqu ep In+ueJnc rS esrtua gquml
:-N_=> Ba}ts+rsua+ug at{{o}W,tsFlsrB,)ciu€qu€.)[r,ie.s1al{"Ir:-ouBftrJ-}riqJop

JS rs rrnqJJl

llIltiunrJS n,) t?[puor i,rodord ilsa asrursuuil
rrraJrd'uenqs;ulnl d_rrmrI Lnuunil p8oleur ea.re1npc,ru
,pie11"Fp ra;relnpoiu ri
g5o1eu,e Eara?lnportr : o.r,Blnpou
ap cruoqcs
r[nop Ir]JauoF uJ csoi.olor og .pslursuurl

a{nqaJ} ac eriunr"ioJur nD pJo}B ul FztsJlnporil as Jastsl emtunf,raiitstll.rolm

q?J,ra+rrusu'RJ'1 nJ+uod 'Jas€[ rruJurnl rr{gFsrralul aIB irfeircso ;ruile ariulnclocl op
rirars.rs.rur r eua5ouroou ar{nc[.r1srp

"311.riis 'r?Juauros€ o (oJuru.rn ur.r4
o-J]ur.rd '.rasB[ Turruni ap r.rnEnd afllro g:rn1
.pladoJ as Inlcl? 6 uaunr5a.r rn rfrc1.rosc1,r?

+lns I 'll.)Lrnr5a.r ui titure rtuoloJ nou uq) ror gz€alacul rrururnl Ersrtlro ,arfe4nclocT
lloll srs,rJrur n,rluad urtssaaau EaJ€oI€r qns JollJo+'p1rnd
urier uaDuor acnp
-ar "rorluo+{)r 'r?a"rts.rrlrJ{) 'F}tsInLuIt'J*il,-T,jru;:$#"#:
m::rl1[.L:rlrirrir;lilu'1'1ri;p'rl)j:i1.l,"nrs'1lrir,ir,,r,,,rr'.-l,.",;l/;i.{.'l;\ti.:_;a,.".'_"]t.,;.t_i,"..l.li. t;,t;".:t*"n*ol'i,i,of5
K:]uirarrns o},t?+r+utsc ul J.uJn 5 eaunroqo;r u;
,. (, 0 liurarras tt"rolq;1;no 1up l1,ouroul Trn Br
-'1.roo-isl-quuo.r+1cuai1saorpquana,r5ad,nalluznur5aar.er u1e45punriu,]l+plcql
,--f I Y|II -,
V/-\n\// | €aunr$a,r ug rirrue rruolod 'T+EInIlIIls
a-'l16'i:"nlcrr1sTrtn,Earauu.+rnrirrnunn.onrar?orlFf:€o[ittaaBnsslle.ca^rlJudurtuusure€o,rprerl(-tccT1s,.rrrlr.rlrrocsI?autr{reJs-uaJr"oelSuI)rtuT.rd?urcaFrltSJrunu]ran.u?lrerratFs"clq-ua;n,zlp'I7dtit.znne1Iur.s'onrnLaua1prl]1nrruuoduraroru.;iTrcgudnneug3.c"tI
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I
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orsrura ep ounr8a.r o no eJnlcn;r?s o-Jlur

tq-o:a*f-ir-"zaq-rxduIo|a.remle-p-un-u-l[qodJr€u"xrfytu'rJ1'Kau+.sroc.rE€(tYsfa)a!prferdorluraaro"na.opqrppc.doitqcloB2KF.pcBa,izrfJlpotnud€orJuc.rurri€or.Iaoo€targllIua.atparss'rp^plraooc.rulorgnaarnalru{ps,1s{rcta,auieoruqrd".i-pr.q'tia(?oc;md.rr5srqnoucoelonrg;cln?uren1Zd?out{sIqouaIoa.OioJopappin"1l,ecc1cqrrs1*na6ailulr.nzf6rinu1atlIutlI"11nltea.urSc+F\'.srouJroeoo.nerutudacdsrl

ap ra+tsJ € rcasmJ?m rei{tntrcng € a.rtsulrn tc e.rrilu Ig 'cllu€nc ,,,q1u,, 1n1n1

in modularea poziliei, deplasarea pulsuiui fal[ de un timp de referinli, este
proporlional5, cu semnalul infonnaliei. Ilodularea codificatd in pulsuri se
se poate face: (a) prin eqantionarea semnalului cle bazd, (de alirnentare),
(b) prin cuantificarea amplitudinii eqantioanelor (c) prin aranjarea eqanti-
oanelor codificate intr-o succesiune binara. In suecesiu:rea binard, se folo-
unt fiind reprezentati,, de exemplu, printr-u:r
sesc sltu5m,rilienousnuiarryi zero, statea prin absenla acestuia. Datoriti, neliniariti,lii
starea zero dorit
puls
t, mari a caracteristicii tte
diodei last-'r este s5, se utilizeze modularea
cotli{ieati' in pulsuri.

2.9. Laseri cu reaelie distribuitir

in laserii cu reaclie clistribuiti amplificarea luminii nu se obline ca
rezultat, :r,i reflexiei ei Ia felele cavit5,lii ca in cavitatea Fabry-Perot ci ca
rezultat al sumririi unol itnpri,qtieri Bragg cale reflectir, lumina in mod
vinarsiaenl,sieinpre.erirosclciceirl,uai dientplircoeplaugi acrlee.reAfcraecsttiefeninornct:linrescelioabdlieneprionpsatgraurce-
continuu
turile cu
tl unclelor luminoase. Laserii cu leac.tie distribuitii, se folosesc in circuitele
optice iltegrate unde nu ma,i este posibil sii se realizeze laseri cu felele
clivate cleoarece acqtia fornteazt-r, ul circuit monr.rlitic cu alte elernente,
curn ar fi ghidurile cle lumin5,, rttodulatori, cornutatori etc. O asemenea
structurX, cu heterojoncliune dublii, este reprezentat5, in figura 2.54 l97l
unde se obsen S, structura ontlulati, a granilei p-GaAs-p-Gao,, Alo,rAs ceezl
ce corespunde unei varialii periodice a inclicelui de refraclie ai cavitXlii.
Perioada de 'r.ariatie estc de 0,3-0,4 plr. Deza\-antajul structurii repre-
zentatd, in figura 2.54 este posibilitatea prezenlei rc'combind,rii neradiante
pe defectele introduse in tirlpul ,,siip:irii" ;anlurilor de onclulare. Pentru
inl[,turarea acestui neajuns se utilizeazX o c1ior15 mesa cu satrcuticvt5u,r..'ifndeabcaenacsl[t'l,
regiunea
in care regiunea ond.ulatii, este separatX, de
structur[', reprezentatl in figura 2.5i, regiunea p-GaAs (care are grosimea
cle 0,2 pm) constituie atit ghiclul optic cit qi stratul activ. Ondularea este
construitS, intre stratele p-Alo,orGao,nuAs qi p-Aio,trGao,ruAs, ultimul strat
fiind destul de sublile (aproximativ 0,1prm). Stratele n-Alo,3Gao,rAs qi p-

hy p-Ao As g. j

l-Ga 9,, Ai As l.'ig. 2.54. * Secfiunc intr-un
p-6c lascr ctr reaclie distribuitd cu
"1s
n-Gt g,7Al 9,3 As hcterojonc!iune dublit.

p - Oa g.z ),! p,j As Fig. 2.55. * Secliune intr-un
u-Aog.93A!g.g7 .r,s laser cu reacfie distribuitd cu

p -{}c 6,63 t.i (,fi A s geometrie de bandX mesa.

'an--G0ao rAs
g,, A! 6.j As

n-Ga 'As

,Au- Gt- N i
82

f8

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1egu.r6o1oq 1n1d1ou1.rg .0I.6

'iU,Ol ar€lnpuo Trfr

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rc.uindtrehiodloigmtaemnsaiu;nio. bAsceeravasttforimularg.eincelesoebniuemcteursl tenevcilritsutoarlsi,iocnl,eaota,reilce_sppeantlriuul

fonnarea, ei este necesari o 1entili,, in cazul de fzllX lentila ochiului observa-
forului. frnaginea rea,li, se formeazfl cle cXtre undele ]uminoase car.e se pl'o-

OBSERVATOR

c0Li|lA'ioq
I

$tr;sr':o

Irig. 2.5;. - Sistlmul pentru citirca holo3-ramei.

-rpn.iac,czgeuistia[nritr,rde.oibveulerisenctpiclriloliriepececltniiatItriu,eapfoepromuaDatereefcairapenrio).(iehMcnetaangtlii,oinndefiira,cmcrfecap[eli upneenctrrau,na;ipnuuteeastfei

o parte tlin lurnina
proiecbaili, pe htlograni, se transmite direcb, in tlireclia fascicrlului de citire'
iir; si fie hifractalS,. in proc:sul dc integistrare a hrlogramei exist5, tliverse
posibilibir,li d.e arania,le a elemeubelor schstnei din figLrra 2.1:p'. c71e po?r-!?
ih*ii,tvfue1gr1suce1a1n.dra1ei3npugI"rnfri.ihnrine1nl,9rl3iof1o. ntDr:ga:rtaieaiixlciet,mfotrlpcmlcuea,atzgeSec,o:minceetbrleeriadeolreeupiuir,nefzauesnnctgiachtczili.e^Iinncafiplgelulrpsar,hr2do.-l5uo6c-
graia reali?a,llr c-r sch:-n.a din figlra 2.56 se_numeqte hologrami,.Frestel;
nIgnisftiarencae:szcitei,cshaarzrliopbglalre,acn.nlteifl5obinpt:gntrrb-;lrrf,uincsoittbernliitnzere,brpeelaaFrhalrutlicirgireerar'lanoteiavir.eaInpsleouanppeoeletdcoeab,ozlblilnrieiecsben,ui.nrfn|r,aer,-[i
pentru obiecte plane [99].
Pentru a inlelege in ce constX procesul t1e hologratie consiclerX,m intii
ca obiect o surs,i-punctua1d,. Se cunoalte c:1, atunci cind o untlri plani, coe-
renti este clifracbatil de citre un oriticiu punctual se obline o und5, sferic5,.
AtUnci cinil o unil[, sfericl interfers, ou o undX plan5, (uncla de referinli,)
se obline un specbru de interferenlri inelar cu zone alternative luminoase qi
intunec*te, care se aselmd,nl cu o structurX cle zone Fhrirebsinee,l_c(lefisge. n^i2nd_5iqn)e. l-eO
asemenea, strncburX se poate
clnltr[i cu creionul pe
iacnolttnreecrgeiaintLtirv,ic.2e1Scb3rui'L. r,rcat.uzr'e-'salieidnepcerzopopinnoe,rlfFicoruneasplnereimlcsauezrcoisdnmzii,ipcioinnreatil,aprcXia,atorcaetrsie,telceatainsedaeirnaduqimufrraeearcezlildee,
cu proprietLli t1e focalizare. Ea acgioneazzi ca o lentild,,si focaiizeazd, o und5,
p1ai5, intr-uir puncl, care replezint5, imaginea rcali, a ol:iectului punctual
ionsiderat. Aceasti irnagine se princle pe un ectan qezat in focar (!ig. 2.591.
In afara acesl,ui farciccfcrnvergent, structura de zone Fresnel produce ;i al
sferice, ca,re pa,Ie
rloilea fascicol de luminX,, d.e unde ci dive,rge din orifi-
ciul punctual otiginal. Acearta este imaginea virtualX a obiectului pulctual.
Iln oibiect, mai ccmplicat, poate fi crnsiderat ca o surn5, de asemene& obiecte
punctuale. Fiecare punct va produce structura sa zonal5, prin interferenla
iascicclului ctifracbat cu fascicllul de referin![,. Structurile zonale ale punc-
telor obiectului se suprapun, alcituind o structurl de interferen!5,, complexS,.
Pentru citire se foloieqte acelali flux d'e referinld' pentru a reproduce toate
punctele conlinute de obiectul original. Apare astfel imaginea tridimensi-

84

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oaut6outl

9) tlar6olo !

otD !d

=::>11 opt4y

28. Ii. \\'eiscr'. .J. Ir. \Vootl, Appl. Phvs. Lctt.,2,225 (1965).

29. l). l;. Nelson, .J. \ic Iienna, J. Appl. l)h-vs., 30, .1t)ri7 (1967);
T. Iiaurcjinra ot al,.lap..J..\ppl. Phys.. 16.2:JJ (1577).

:10. I'. l). Southgatr. .1. r\ppl. Ph;-s.. il8, 6580 (1tl{;;).
:11. .1. I. I)nnliovc. ()pticu.l Processes. itt Scnticon(lu(lors, Prt'tttice IIall Irrc., \. J., 1!l;l.
i]2. \-. 1li)roclsoscral,n.l;I.n-tl..I.l1a.rIv')rlc;'clotr.on.I..,
lllJ. IL 35. 121 (1973). 205 (1g{}lJ).
r\ppl. Irhys.. 39.
It1. .Nl1r...IIIBi..e\Irc'gIielrtrr.pncc(lri..,;\'\\.\pr.pC.ioJ.u. dlI'l:|cr3sr',tsraS. roIn-li.ccllItSI.t.tIa,9Llic.i
3o. 1-l'tr1-an(1s9. toi0tr). I'llcclrott I)t'r'iccs, Ill.l-I6.6.11 (196!tt.

:J6. lilcclron.. lf, j19 (196ti).

37. II. Ir. l{atalt.. Liolt aniLlittyl tluticcs. Pat't. l. \[cthercls, in lrlactnccs itt eletlrottics anrL tl:tlrctn
physics. lcaclenric l)tcss. r-rtl. 12. 197ii.

::18. .I. lr. Ilcadr'. Ituluslrial eppliculiots ol' Iastrs' r\.crrit:trtit: Plt'ss, 1978'
:|9. (;. A. O\\-pxtr..b1ll,;.'\1p6p5l3. Opt., ll. 1;tli (l9lS).
It. I). 'I\lninthcllcilrf-t.', .1. S.
10. ,\pp|. (11)76).

.41. I. trlttnqailis. IlillIi Tratts. (icosci. I'llcctrorr.. filt-10. 7 (107!).
-12. J. I1. Ilessort ct al. Appl. I'h1's. Lt:tt..7,2t)$ (190it).
.tri1. I. l)etlcscu-!)t'alrorl.'l'czii dc cloctot'r'.t, Btrctircsti, 1li7i.
.,41t(51i...*1i)t..* tllsi*h..a1I)i.alon('tils'livchsi.. lI.'.ll.(ltai:rzloiai lsltilerh.i2c,,7lo\p,cpIolt)r.cact.S..1Io]9tlrit?cl 1rSr.rtta'sttci.
1979. (1971).

Sei'.4.21|;
4?. A. (iolrlerr[]rrui. i1 Itroblcnu: ut:tutie tL[t'fi:it:ii st:rttit'ortrlrtc!orilor, I]clit. r!catlelrtiei, 11r7i)..
4ti. li. l)upuis el a1..,\ppl. l)h5's. Lttl.. iit. l(;li (1077).
.lf). ,r. 1't,,r ct el., r\ppl. I)h1's. Lttt., 'Jtl, J01 (i97$).
i{)- A. (iossartl ct al.. Appl, I'hys. iicr'. L':tt.- 29, :}23 (1!]}7(i).
51 . l]. \krnt'nrot'. J. Bluiu., .i.;\ppl. l)l-t5r;..411, 1:r?$ (1{)77).
.ir. .I. Dynrcnt ct al., J. ^'lppl. i)h-r's.. /r4.207 (1{i;:j).
5iJ. il. N. llall...J. l'llcclt'ochetl. St;c.. 110.38; (19ti3)
51. I). ltock'ct al." r\ppl. Pirvs. Lctt..30.;; (1977).
55.'f. Iiuiirnura t'l lr1..,\p-trl. I)h,v's. l-ctt..30. o2ti (1{}77)'
56..I. \ishizarv:r cl al.,,i. Or'1-s[. Cit'orvth.,31.2i5 (11]75]
5?-. ll. [,ogari. i). I ftir"lc, J. i)hys. C]rtn.r. Solitls. :]S. 17:lS (1971).
53. II. iircsscl ct 4i...\ppl. i)trrs. I-t'tt.,18, l3 (1971).
i:-t11. I'..\. I{.ir:kbv tt 41.. IIllifl .l. r.rl (lrtarttrtt:r Iilcctt'oti.. QE-fi}' 70ir (i1}77).
0O. Ii. iiobar':rshi cL ai.. lil{rIl .l. ol Qttttrttt;tt l'llt'cIr<itt..0l:-f3' 659 (1t;7)-

61. 1-.'fsukada et al., Pr.oc. .1 tir Conl. on Solid Stale l)evices,'fokyo, O;9o Butnri,'12 (1S73),
Suppl., p. 251;
F. C. Prince, N. B. Patel, D. J. Rull, IEEE J. of Quantnnr Hlectron., Qtri-16'

103.r (1980).

62. J. l)yment et al., Proc. IEEE, 60; 726 (1972).
63. J. Blum et al., IEEE J. of Quanturn Eiectron., QE ff , 41:l (1975)'
6.1. H. Nishi et al., Tech. Digest IOOOC,1977, p.73.
ti5. T. Kobayshi et a1., J. Appl. Phys., 16, 601 (1977).
66. E. Pinkas et al., J. Appl. Phys., 43,2857 (1572).
67. lI. Pilkuhn, H. lluppreclrt, Trans. AIME, 230, 282 (1964)'
68. II. I-I. Pitkuhn, H. Ilupprecht, J. Appl. Phys., 3{1, 5 (1967).
69. J. Il. Baird et al., 'frans. AINIE, 230, 286 (1964).
70. T. L. I)aoli et al., IEEE J. Quantum Elcctron', QE-5, 271 (1969).
71. N. Marsumoto, IEEE J. of Quanturn. Electron., QE-fB, 561 (1977).
72. '1. L, Paoli, IEIIE J. of Quanturn Elcctrou., QE-f :i, 663 (1977).
?3. D. D. Cook, F. ll. Nash, J. Appl. Phys., 46, 1660 (1975).

74. B. N. IIakhi, J. Appl. Phys., 44,5027 (7973).
?5. P. Petrofl, P'. llartman, Appl. Ph5rs. Lett., 23, 469 (1973)
?6. D. V. Lang, L. C. Kilnmerling, Phys. Rev. Lett.' Bl|, 489 (1074).
??. R. Polirnadei et al., IEEE Trans. Nuclear Sci., NS-PI, 96 (1971)'
78. I. Ettenberg, C. Nuese, .I. Appl. Phys., 46, 2737 (1975).

79. C. Shen et al., Appl. Phys. Lett., 30, 353 (1977);
II. Suyama et ai., .lap. J. Appl. Phys., 20' L395 1981).
80. A. al., Appl. Phys. Lctt., 30, 87 (1977).
81 . K, Ladany et al., IEEE J. of Quantum Electron', QE f i' 819 (1978)-
l\Iettler et
82. Ii. Iionnerth, IEEE Trans. Electron Devices, ED-l:l' 5t)6 (1965).
83. J. C. Dyment ct al., J. Appl. Phys.' 2!3, 452 (1972).
84. I1. O. Carlson, J. Appl. Phys., ll8, 661 (1967).
85. G. E. Fenner, Solid-State Electron', 10, 753 (1967).

86

L8

'uEIrolS 'E 'd 'eu'6oJtE'.I,Irg'{r)luq.ner]s€erlsnllrl3p.'q('gcIS'r.oOJ1f)r,a]OrslcetjElq.faro7'hptFitltJ'iiat.1clStgTl.dByp.co.no.rdrcdf.eI,{d.run.\lr10.,1nlclos.1el'ldod.:l.I.lNi ..I.0.0686
'(osor) sr'![ "]1c'l's.{q;r'1ddy
'(ssor) 8tI'p-tio "uo'r(iSrafOlgf)rCunOlIu'uIAn$''lJliro:"t'(rfS'fs.O,:iIrig1).g1LIL'1'1.Lcrl11d's1I6lt.El'l1r'('r'13{'ru?aos.pr-nL.t_rE.1nrsNr,1N11u'1rr1uo1.8qs;l;ii1ur1.\ .at '96
'26
.I{ .[5,
.j,

'ssaJd cILrrJ'p(.UV)\^/tr)s'(.C(U]'.t-(:,AIgt?r?.i(o'uS(IrS-SoS)gftOiOlOgstfu'e)('f8rn)sz'g'ff,reoZ,O!r-6taoffgag-r)|t!olarIrS.o-go?q.gl.Igg.u$p.-uo'tu'Qougf,rtJf'r)'tful.(1tcn,(ZsSrooe,la'J.ufrua1lfiOrlgOelsor-rgDoa.fntrru).rSl])$J:u:lr:]rfZncJlSrae1JnolAlruioiall1?u){u'uni?.n}ru,alfn,][n]f.ur.riiuge$?rln(oeou-?l:lJs)ung)rIloulofe,rg,li.tre..snofIilfiIoi.oSiro{]s,oglrS!l..lsJlggiJfdr-.oae]-.-6sEc,gotc.'sl.tl]lfg{lldoSn.ur.Ad.g,T3\.o.'rl\lsuIu3s-..d,]dISrpl1.rt{rn.{fatrrdrr.o,,of.ssssr..q.rauuoruu{,o;dBsluuucepdEnrpp.rSu5rooNNUvvy1sJlaoo........H:(({.{{]A-1JI-I,l:It'.......I!\.1.]C,..,1..r\lI\11[I '96

rb

l.tt
at)

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'0rl
'6S
'88

'98'

Capitolul 3

ST;"}U I]E SLTPRAFATA

Ira suprafa,la nrrui clistai a,ptlr stI,ri loca,liza,ta in banda ilrttrrzisli ni,Lrnite
sti,ri de suprafa{,d,. Ilxistri stiri cle supr:a,fzl{ii, intrinseci, tltr,toril,te inlt'r-'luperii
periodicitir,!,ii leleiei cristaline la suprafala, cristaluiui-a citror tlensitatt trsitt
propurlionillir, cu clensitatea atontilor pe suprilfa,!';"l-;i r:xisti, stiiri tlt silpL:I,-
fu;ain!a,c[tol,i,stentaxi tlarirdnlsisro,etr,.cbiini"{s,i.ciilaIdlteeonrrrassitilet,azltpteceaartdtuleclrbssili,,trriiiuriiicc,li,euinrstpuriupnllsaue{iactcr,l:t:i'isettlatsttlecinr' mocoilre}it:slcttaiirtrtLlttt1i'tctpLtteettonetctlltiueii
rr,clsorbili ;i cle defectele relelei clepinrlcr ele tra,tatnentul supraftr{ei i5li:fuirtr
tlecapar.e etc.) S;itritr1ioienrteleclisuui pnr,lurfrtbr,iafrni tjo(aa,tcn:ri,ousrfrellio, lgainzlo1:,t'',oslit,,anutr,itiirtllitflrltlnecl..iottntt:rlrpee:u-
raturri etc.).

tlispozitir:elol',st-'r n j cr,ind uct oarc.

i3.1" (ionsitleralii ttrcretiee

faaoitcnloiulmiltairzicti'ii.iIe.n:riil,rnniSitnmcr1nh[1itriiint-dir|,ic1telie)ill1n,us'geiltrnce:Itr"irrrczoieu:nnttpriopgar,e-icezPensrzet-ntrlnc,uslnlt-ilrpsetttsy1imri,ltuuis,p:ra;ifcr,t,lifnoecieultlauir.,[uliiitr,,culu{corfnornoitdstrltiaitgtltilna-n:tP!ltdgttnceeirsenrcttt'li'1iillctal'oiiliio:ilciitriieBitatnclloctt1erceus.hu,Shpo'lony'r{lgiLu?ta{i'}tr)ltinicir:2l,ee,lr
:u,(.,t") exp(ilcr), unclc tr,(r) este depentlentti tle Ii: si este peritttlicil cu pt'l'irttl'tlit
SpectrLll rie encrgie beestnt,zci oinrntepluzsistd-rin(cboei'nez,sipl)urn-lz'Iiritloisiltlr'llr)l1u1i.n/-;
relelei cristaline. real) separate prin

punzltoare lui i;
iornplt'x). Tamtl :l arifuit cX, spcctrul energetic str ruoditicil in-1;rtzr:nt:t,
supra,felelol clterioitl'e, in sensul ot"l anpal sti,ri cua:rtice perrnise chiar pen-
/i tonrpicr. in figura il.1a se lcprezintri energia poten1;ialii a clctrtfillltl-
trrr intr-o re,fea
Iui lnicliiirensionaLi seu-riinfirritii, in aproxinra,lia F'ott'rLtiaiului
in figura lJ.trD se leprezintt"r' o siluatie rria,i t'ealist:i. Fiupra-
rectangulal [3"], ia,r aflS"in planui ltu, c-riual .tleinieviiitlel, ttlin< 0i energ'ia potenlial:i
?o); qro este
fala cr:istalllui se solit:l. Solu!,itt, ctualiei
esie constitnt:i (ir:

Schrcirlinger

lt' (rtt-uI '' LE- l'-('t)17- tr

,t,,,:;,;

pentru ; { 0 tste d{l forma (3.1)
* : ceY',

uncle 6*\t2'n tE,

(:3.2)

88

68

#e(r'e) '(or1) soc'=:'(*r*) soc +

[l] utp (ff'Z'V) urienca uro]rcsatT

nn

(s's) 'oE\Q: l))ogo0+ -0-i romS

.€p aruc orjrpuoc tzralnus as rnlnru?+sr$

lfnntoruprialrlpu;rtou+ao+p$sTu.cnup?,KtrlIunrzaarrJ+(ga'ug)arq{'n1oorsitlooJ;r€ Jo"tr?c I"& }r u-l aua8ouro llflsnca

Trrrrlln ljl,quaae pr4cnporlrrT

(c'e) T-aiq-l-p)r-O _Y* --- lI

- 1- 'fiff

Kllnzo.r 0 <- q rA oo <- 0r1 1u;x;rlliurr lnzec rrl

ffi*.,-r.EI---:.?(r'e) + -nn,a{(qd)qcd (s€l)qs"l} a(1l.r;,-rg

am,irlo os It] (Ca'i-) ,rrir1.r.r m1J

(x) AlI

'lsllllJ.r Il}rtr lllIJl]orlr rlr
- q : ,hrru;r.1-F1lro.iy lnlilporu lT - i)
: ;!urJUJIUIOS IUUOrSUir.illllltrn ,J-l?.lt5.1t.:lJ.n^r1i.l.l1-
-J:lirl rnlnJurluolotl rrintgr.rlsrll

(s'g) 'c'.cL::g(g+- v)",t

v

q?llnzoJ 0 : 'u r1I irpl4p r* ri: nrluad e,1utrrnur1uoc ap a1n{rpuoc urg

' "rr-o{ * *"tey : lp

0 <- +. eqls{arp;urac5cusrccsAJqs'cr+s€sraar{r",frnnlcoes e1{n1os 0 < ,r nfrllrrrnainduo.o:ro1o-a1o<-errfi.nre"4uueard*
g?st?ocy
.0d >

Eliminincl k intre aceste doui, ultirne ecualii se obline (3.s)

a-act"s2Pa-&,: Jv.-T.. -V -*"'z-r,'t o"3 ,'' ,

unde

,elr2m9o (3.e)
'
ttz

I Ecuafia (3.8) are 6 gingurd, -qolutie pentru energie in intervalu! (nr,
eE(nne:)r-g(ileh)znlpZ)e,rnrmr)aaizsf)idi.n,,Ddcaourrnels1npluuinmnz55f,,irteoicanartrereelguinit(eEkr,nvearerlga(inla.nAe, s;('attred-aler1g,)airnt)[t,redexeisdtfao,,.upodr,lib:naenrreidzl[ai ldtilaee
energie, pexmise, adicX, in banda interzis5', limitarea lan{ului de atcrni la
un cap[,t introduce o stare localizatzi, nurnit5, stare de suprafati,. DacX,
lan!,ul de atomi este limitat la ambele capete apar doui stlri de suprafald,,
cite una la fiecare cap5,t. Aceste stXri se numesc st6ri Tamtn. Se poate ard,ta
c5, la suprafa!,i, funcliile de undit, sint localizate. Funclia de undi' (care
descrie starea localizatd,) scade exponenlial cu depd,rtarea de la suprafa!5,
spre exteriorrrl cristalului qi se prezintS, ca o undi, oscilant:i amortizati, cu
dep5,rtarea de la suprafalii, c5,tre interiorrrl cristalului. Astfel, o condifiede
existenld, a std,rilor de suprafafX este ca \raloatea lui li sai fie
k:n(nfu) f o refea, corarplexir',
i[y (,,"nr >0 l4].Shockle;'a considelat
unidiuren-
sionalS, finitd, in care potenlialul la suprafrr,!5 se terrnini' simetric {fig.3.2)
qi nu asimetric ca in figura 3.1. Bezultateie teorctice oblinutt' tle Schcckley
sint urm'),toarele:
a) Pentru clistan!,ir, mare intre atomi, a,stfel cii brrnzile llermis€ nu s{)

,,intretaie", nu exist:i stziri cle supraftL'1ti.

r\r\f\ l;'iij-. 1i.2. - Iinclgic poten!iali a clecti'o-
rluhri pcn[ru o rclea uttidirncnsionalX.
ox scnriinliniti cu tcrrninatic sitneNrici la
,supral'at:i : linia lntrcrupti corcspnndc

I t'rrni na tici asinrctricc.

------> Distan!a interof omicfr F-ig. 3.3. -- Renzile cle cnergie qi stirile
de suprafa[ir (notatc cu s) calculatc
pentru un cristal unitiitnensioltal care:

colt!ine R olonri.

90

T6

tncolllru o]saasloz:r1}lu: rFJllzousouqlrl.xJ JrinqlJl -?'g €JnoqrJ uJ a+€+uozaJd tuls lcasrrrJ+ul
::-n-sr/-rz,lpleDuuaSJgq:d"ilIRqJIrzrnrssluororpaprdloqJ-louu--grI-pJF: eJlE?,:lJ:aroBrrllJrl.sIrr)udrupno-n-s1r)'rIlJtJzpz,u\rtrrueJiicq[F[Ir'n,--FiolClpsa7 p{uyrerdns ap alrrf+s nlluad alapow as

-JojlrO' OSrzJO+Ur rrzrr"q vrvlv u[ a?iBn?rs

oIJ HS g{,t:yu.rdns op rrp}s o+ru{n{rr3 €}
u1du41ug o1"eod og '(a.ruoldora/B Joloc

ra.rprlunnsurerpcual?p€en+ursrf+nuIdS o.rl?ouop otroXo.rru

c.reoldaacr nrs

aJ€orrop g,ip11.rnclu4 op Jololar\ru {nlnz

t-3 -?c rsJaaur e1"'a l3l:i.un1rs Kc rn{nJ0xr+r}
urrlurury) '(tln1o.d urluad adt.rl) aJrou
t-J -op JoIaI;;lru u.rrlnsre p a+un+rt ,llralca;r;
6- rlllJlr3 on' (ruo.r1ca1a n;1uad o1adr.q) a"r

-uolder.re elolarrrrr ya (rcao'ur.r1rq) gieg

-u"rdils 31) JolrJ'H+s 13 lJr+-slJo1D€;r€c o
aln-U 'ola od r.rnlooe nB pulc ,rrlrzocl oluc
-rpculr! e1a od r,m1o5 nu nu pulr a,n?nau
+rqs aJ€c (r,m1o8 u,rluorI olauu.tclea 1u.rs
;ul'ruo;r1
,TW41 a-r.rsuloouonpc.roalr1Jug1dsnc{no}T+ruolsllrnp{uclac
a,u,:tr?5ou

T l'; r"l o1a arl ruo"r+roJa nE nrr pul;) o"iq.rrou
!u[r' oJ,l]c 'ruo.r1ao1a n.r1u+cI {anadurl)
'tl olauts.)cluc ]rrJr' o.reoldecct ,{r)[r.rg+s

'.t Fr+ualtrrqca : or5olorrrut,rol fllu Vz'voz
-r{r}n a:'(o.ruo1,r:1ozr) ,tla1{6ff nc olai€+
=ld -srJ.,) UI 'UO,llC.)[J UII ll.)
pu1.r -1ts]a]ttrllii.Txrr.rtd1n5J3
- -rr1u5cu Fl1l,),rUJor e

-oou a?Sa pulD fJ rlau o+s^o oJ€fi?doccr?
a.rB+D' O 'uoJ+cola un nc g4udnco a+so pulc ;uJlnou o'g,t.sr1oat"e&cllrslrazl o(nrrls%,?g'zil!')e.nafucouJp
oJr?J.s O 'rrroJ+cale pldacce
also gledncoou o,leouop

-ucup oJ'€o+clacct n€s ar€ouop ?uIS ?c BJoprsuoc os q,i"egu.rclns ap alrry?S

gie;u.rdns op rollrpls eginqptsltl .z'e

'p{uyu.rdns BI op rolruro+€ olt olnc,F}srg.€sau
ap.rn1p8o1 op o+\3p 1qs plqe.rclns op ollry+s rgc Baapr gluldacc'e o,1".9 '(r*uro
-sr0T ) g,iuye;rdns op rolrwo+ts rrfpqrsuap InurpJo op o+sa pfu;e.rdns ap .{olrrp+s
e€oc+uq+urldsuaaqp.SuEcolopJ+os+tssog{le€yuuo.rrdsnusooupnopJiull+sporfutsdapsXuS 1p{u'royu,ie;rtdrun;srdEnIsalpnuurrol+c'lE or€ool}
uJ r{nu

-r{uoc aIJ KS a. rS trr ruor lIqmu uc er{rpuoc nc (f{ua1e,r) ardcnpuoc a]l {xzuocl
r(lel+.idonpsueefptl)uq.rndsnAsaooppornuen+csozO{3'aaoc+pIcor€Ip{fsiurgzurald+rrw"' €putsq uI B?un}rs alsa {g) ;r
-a.racl u1" o+mqrJ+slp 1u1s p{,uyu;rclns op oIIJK+S op rrp?s cr-oturu es rbr g({aqc
'trit+aruau Inuorur3 a1s; r"&

crlts+arrrlnuor+tsc a+sof epun'pJy nstsIc urp o1.red cu; aIB+sr.rJ a+D'scy'reatm{J+ur
p'Aiu-;rf;"frldnrsindouprorco)IrJoEc?rusoreporlfirnecdlr.n4stsrpocrSru,uoaraacuialK€+qsI€rJECS'oruu{de+(s1r1Jc1,.1ro-1fo{'aI3Ae.-rdIn1,-
ra{.ua1srxo e p{,urcasuoc o €c .rude p{eyu.rdns ap aIIrl??S 'a+uoctsrpe al{uuoq
urp orucorJ u; (psrur.red 'epuuq wp) urnlo,t op oJ€+s o a+Io o.t'tzd'(ser11'r '3s)

na'(rs.arllz1uJeao{c+el;mru€rrmzuTo'cKqriutsrroJ€JppJqccuIanursJlsoIunpoJcor).rrJgIor+u+som?prnu?oIopar++Jtutss.ndr+tFsrsc{(ar,rrgutfsu+p;oaiu4rcuulnllssars€pIanolr,przgtruuarooq4+XE(qaa.I{a'uJ??so'lr?}

Functi ile 11 e di""1,ribu!ie a purt[torilor r]e sarcinli, pe stririle tle srrprafil!&
sint analogt' cu cele pc' nivelele de impurit.i!i :

.f.,i(I,) : 1 t + ;l -o, (g';q ) 1 _ s"*r, (, ;ru,)

pentru stirilt' rle supt'a,fa,fi donoale 1i

:.1..(E,) r ';,,*r,(",,,-rt.)

pentru stii'rile a,cceptoare, untle Zr, este erre.r'git-t stilii tle sripr':rfa!i, f' * nir.t'-
lul l-ermi ii f*ctonrl rle ponclcle statisticli cart, in setnic,onrluct,oLi ciir
Sar-e valoare 2 pt.ntru. stiir:ile donoa,re si .{ pentru stirile ltccLrll-
Ge, Si, GaAs
toarc. I)en,qitrr,tea de stlri cte suprafa{,5, se nrir,soar'[ in stiri]crn2.e]'. Cle]
rnai sirnphr tnodel cle clistribulie a sttiril<;r tle suprafa,{ir r-ste morlelul cu
rlouir, nivele tliscrete prezenta,t in fierrr';r,3..[ a. Notzim nilelulrlonor d:,t-tr)o,
nivelnl acceirtor ctt. E,r, concentra,lia, si n
acceptoarr: cu -}i,,. Sarcina locra,lizatii npier-elirle-eloler lcelortlreoislru'eltl{a,,uftr-,tY,L, cclor
este

0... : (]p -7 Q., : e-Y,
I -; g(l'- - El4it:r

S-a t-.tinsicleltlt pentlu sitnpiit'ate rl: l.
Oonsiderin<l -}-,, - ^V, : i. ;i rlefininrl

E^ - *8" '' E' .11.'- r-" - I L,,, - ri., - r'o - f. -- 8,,,

') -8-r,r,', .)

turde,Eo es1,c ettet'giil petltlu ctrle ff,,. == 0 fi se ntiltleltt'etlelgi(i lterttt:1"t, se

Jl(lt.te "Ct"e

-rl", [ra -r' .[ r e ,\ll{[1 tt . ,- rl')/r," ]-' -
I 'l

- "'n(lft r '- -'Lt| n)[,,r] 'i,

0"" : - rilish (AI'/lif),'[ch{-81n,?/ir?) -; ch(l}',4'f)], 1.3.10}

J- se mi.qoir,rri -in\?,stplrei;nctrrunt.A-SFe<ol:(s7er2r..)irn, $c,iafQi ,.s-ees-qteatourefrai.znfc, fpieensitnrrtu,<,:A.riFdir,I>ii,
AI perrtru trei
hiperlroiicri^cle
> (1- 12)E$. In figura ll00 Ii {r,nrba
temperaturi rliferite i:l.5Tes:te leprezent,at (l""l,V in functtie c:le

TirK {curba lrunctati,). ?

92

r6

"'.f * irp[(g)"-f i- (g)u'.r] (.t - @-i _- :

n[ *),

- ::ar,(r.r)o-r tu -.rlJ?-lr + an(a)nr(a - ell*-tr "'0

'f'tuI?r.rDr' af€od as lra.raua5 FrzBr 'or-Bo[ I,l]ttl r.rn+?JJckual e1 IJo+FJnD'Jiur gctsJ
ar- !s ornea"q rrinqr,rlsrp alos.ra.irp o,r']uJ auJacr'Ip ts ,nu.lrlKuJJc?frr'.o'l.rIc'sltou,m.)Srr'JIJ].crJ.raJrp
e.m8r; rrp .{?Jc rrc 'L?rrprrr€asn os uriucluislp 14006
I
i,rnl€.raclrual ra.rleggll/"'fi qvluaza"nli),I aln-a 9'ge.rn8ry ul'rv-tsJ,rr?ol,u:r'J,rts 1* rzuarl
JI.lqurB ul Kluulstroc a?n'o or$.IottJ ap IJf]s ap l:oll?]Isuoi y;r n'rtclnn-J,r([ t?-S

laryalQtv + zi's)lttt
ug'"1rgD5
-lr:tzlEv
zi'ct))qc

,,fv)tTxo * 1 tti({\ - f54)clxa T I t!tr-,-
I
.,,,,\-"u
: 4:1!!
I"o{

ar trfl nc IIZri.)q uaurrF.r,pl pullol{ ',ry'g t.rn5rt u! +u+rrJzJJcl.t.t autiqo
o;.s.-r urna uSt

1,cp'.r4)t'r;outg,rrrrJi5re'lFt.rrorlurms;'draclJItnutussgJlcorrazapuppo.ra+(olcrlarTJrJn-aprolaspops,F?uuZrar,|Bnlnedq)lurrrg.lJrrolcqsJolrnptauq.rKeo"o'rrp,tarr.d+pmail)sa1i);u.'luu'uop,)r1a,a3pil1su.ul.t3(r;a'rlurl1o.urueaaoc.1tpl".a'ra;pa.ielaarl,luruail'ttn{d.r;rr'rFB.Itp1r1qus*Brslo.aJr,)nrItns:aFzf.rEu'ttc{J:

lfitLzi''g)qc -F rli (;.ri.gb) - : o''(t{vpl"0o)

og ul tzlrirtl auriclo cs (gl't) 'ut1t1a.r ur11

z'o- 7'0-

Z,O 'JlrJilJrp J.rnlu.rlrl
-ruJ] raJJ rI rrrui),J rn1n1;.r1rr u1i
n -tzod ap ati:xrrtr rr1 -r],)rJslp .r[Jrlrr
- -s^'Fr5n pnop ll) lJndlJpuouulJr .ruaJs l:-iut'rq:.r'tt;lns'31:r.p1

9'0- ,)[rJJAru

r-reur
uri,nqrJJr'rp ur,rd garlrha 'giu.gwdns (oapla"oralaslreparroularlrocal rrruur{o?..rre€Js€ Eut3rlla..lt
as aJ 't;aat
uI or5.rauo

ap nruaruop rrn ecl !?+rnqr.T+srp t?Ilq€Jnsgrrr piuyu.rc{ns op ?urc,r€s Fg.srxa ?c
op g.u'B,.{a.Ia+fl o?-qg 'e.m1.u.radura+ op a+so EJ sndns
Tluapuadapur
IS Ac A6'0 o![f +€nI "-S '(p1dnra.rqu5 eq,tna) 14 006 fr '(FuIId
: I :l€r\JosQo

-c.rd 'B-s

itnde

:l-,, !]*rv,te)a E; f(n, T) : f o(n,, O) { fr(r1, T);

fo(q, o): {l; I <0, E-n''f
>0, =- l;T

i,a r I

i- -c,2 a

,,u [- AF

r FiS^. ::i.6. Sarcina pc uilclcle dc
suprnfzr{i in rnodclul in care ben-
qtt c,o, Ir - zilc se continu:i la tlei ternperaturi
t't I clileritc. in Iunclic de pozi{ia

It nir,eirrlrri ]i'crnri.

-"1

I z-

-L

1,0

A;zr,dar,

:o-.., - .@ []..,(E) + f.,,(D)l -t1D I_*t," - !, T) [t',(n) -r

o\:_

j r,(E)ltil,'+ rv,,

si

otarltl :- _ tr-.,(tr) | r,,(r)' -l:_ !f'@-J't{l pr",qer -}-r-,,(rr)lrtu.

(3.11)

La,, zero absolut ultimul terrnen se anu-
leazir,; el reprezint[ de fapl, contribu-tia cozii
distributiei lfa-xrvell. Primul termen din ecu-
alia (3.11) raecpcreopztionat[r'ecsointutraibteulliaa stX,rilor
donoarc si
nivelul
Fernri. in figura 3.7 este reprezentati, tlia-

glarna de benzi c1e energie la suprafala nnui
iemiconcluctor t1e tipp. Potenlialul este astfel
stya definit incit are valoarea zero in volumul se-

miconductorului qi se mi,sozlri, fa,!i, de nivelui
Fermi intrinsec, Eu.l-'a suprafald,, t,|.r: *'; r.lr"
se numeqte poten{ial de suprafa{,i'. Astfel, con-
centraliile electronilor ;i golurilor au valorile

Fenigc"rg3i.c?.la- Diag-rarla de benzi dc flp - hro exp (B{.i), (3.12)
sttprafa[a tttttti
semicon-

cdlrerccttorrondeictiipap.sqetZniccsotncclaufcintoitmatlenia. ?tt:Ppo exp (-P+)

g4

g6

:(srs) - -'dpt(r +ao)onu- (r -- oo-e)oudr"5; (#)r(#).,,.:!

gzrer8alul as ri rp nc gldea.rp eal.rnad r"& gfiq1s eol"rucl ag*a,fyrurul ag

'r\/+*pp\l *p : zrp rp
p
,i'.t, op 6

uri'ela.r qzuazrlrgn .r"' rS

,frIl

nc ri.rBd al.renrr osa'flnruug a-s alitnce 'E1s€ac€ tsLlozal € n;t+uocT

QP

{!'f'g) 'l(f - -66a)odu. (f -+o-a)o' ud-lb=, - ::y

lz0

ar.rcs aluot{ os (g'g) er{e1el o.rapoa uI puIAT-

0=_r+'0E'0.-? t@'-,t'

s..ln.prturo(gricEunczTprpuureoorJ(orluotar1ozrs;rtsolalnd.rra€urornln€lAo.larr1uaua-cdI-rs4a'r.cnr oln.lrario"glrno.cd1nur;prro;uauoocIp*rue0rpa{ps,o1€orsa<ul€a*+1rrirrqrrluuTiulsur."araldfcl'KI*oao+Ip,sq€o-

{tre) ,(ort,- 'l[ -_ od j- fl;.)b : (r)C

piuj'ucls !url.r,rh' ap ?o+u+r.quop a?sa (.r,)C apuu

(sre) 3 "ra
h"0
6--(_ r)d __-

-

-troza,r as piur:1o'ip ap arriorrnl u1 rir rninpriuaSod IIoSr'Io.f EilunCa TA

tso.Rlol,B^ rsp5 r nJ+uod
'arlonpuoc ap rn1ndr,1 't;rsJo:lur <,ulj. "+

.uiit,rluocuo;;r)("r.!(o?-st1n-ru- 1u'dio+a-'elurr'rurtlaDpul'or+oral-urrgzzru1sJ'oe.atc1Lllr1)rluzrEru"rrpinlrqulzo)uu5qaaa,qr.prrzppcrJnrrtacrsliolornpluf,rr0mrror<crJe,n",,6i+0 :'(r:ao-4.t-ur.r1ur
<:
"+

"+
) "f

'd qI11 : rriunqrs
I! oou,
alaJ€o+FrrrJn B+srro +o9od4 aJpTr;n,7ln:J1olb?J:5njpu.ron,lpruuroaqscInnpuunollrorrr{rrousI eniJuqlurl.rrqdcnas ap
oyrd,rrluaauoc luIS
r,1

(,zre) (",it€j-) dxo odd: sd
(("f $)dxa :o:t11 s7{

rS ttmlc I ug

Rezuit[, pontrn r.tr,loarea cirnpului electric

e: - d'l : :'!- t'(l v, y), (rJ.17)

d,t' - QL,,

r r tttlc : - - -1r'(9 {,r) l(c-i:'! -1- 9'.i, 1) 1 vlso+ p+ 1)11/' > 0, (3.18)

',''':_Y1[zpl' n?q,. . .,=ut,9 (3.1e)
'
'- r,on

i{rlci,r,retrs.tre+lu>ng0irn;eia,seDrnen|ru'ci rlrrreinnutrsnpgeonltlrr'ui).+in< rclalia s(3u.p1r?a)fase!fnl r*uu:l plus este
0. f:a
'i'"

: - ;-6. -Lqflu, '41 1"( 3?", T). (:1.20)

Qf,r

iar tlin lcrgca 1gi Ga.lss st, ol-r!i1e sarcrina spaliafui la suprafaf,x pe ulitatea
rle aric

i3.21)

P6rntr.r t!, : 0rsetrzreauztlutddlt,c,r0ia"0c,-un:teux0lzp.lrPe(qe. inCYtirn"uld/h*,.",!"){). 0, in funcfia -i? tlominil
Q" arc valoare pozitii'it
qlriricnorruclspteurnmtlecnunqlii 0, 0" atc valoare neg?'
ntp{istevetnr[rar.t,rtPuQde*gon-et\r.pruelulxoirztaJlarlre(req))a,.{!,,Pp>l2oe0htn,eZtnirlnu{('isfatut"lrnuac}ltu!,ici,a11de,"ef,iin'idsnvuoepfmrusraniiunfcanilrfierai)a.-llIadndovoielemrsaiinatie, pramulteepnlanlEircui h0le' "a:r-,[pte*a"rrc-

{"(inv) = 2 *r' "'(-'r) t3.22)

Pentru capacitatea diferenlialir, a regiunii de sarcinit spatin'lil tlin
*otrl'iss1fl11ctot rltl olttine expresiir,

$:-:-o'N,cn = 1 _ s-llcrr -y-.1(e3+s-1) (3.23)

r',, .F(9 ,1,,, i')

PentrtL ,lr" : 0 (conclilia dc bandir,'platX), dezr.oltind telrnenii expo-
nentia,li in sclie rezult[

Cr(barxlil plati,) :lfi elt,o, farad/crn2. (3.24)

3.ii, Suprafefe reale. St[ri de suprafali extrinsec'ri
c:rrtiroamtzlio,i scesaurp^poe'r.,are,ttxaci!.o5s1,talcluiunreiantpirip,inleascutelir'rl.s"uraerpesrpa,sefaacultiplirr'c,inairnel:iolnimaubltcli,onrdnalvirnoeelucamu1.i!oi 0an,itotstimuipniradcfeialczltitii

96

t6 et 0t;'r*1

1u(-o[3u'r.tF)id+llr'uiJp]+J]Ir+alurApqtporourlprolol3cl1lglla{aFwuol;'srri.arJrxJod+o+n.E-say..rotenopslrr,lcrt'ouel,ix1uuaoer-ulloctrnrpgp'cuf+..poro+iJr.':c';uru+.or.rllrrrodlsot*rliuaiuoroiu'.11rrc.or.ri;+orJ1J?rot"rrradprsJ[>ui.l-re1.,frirr+l]auurqofp;l1iul.inllrrpr;.-rlularrrp,irlrluiir).pruo.)c+l)l

giu;u.rdns op rollJBts- Iu nqlnls op olElrroutuarlx;r opolotr[ .f,.g

uunrilp+o+.lup 'ytc(1+ur.a;crru+apcdrroeoTJclo)aesp-gop.n+rlla0suqossrlr'trnBi{l{.ppni'.;Bll,Brrrr.ulnrs;1drrc,urrlrroursrBrfIa€usotI.rrpe.or._rlIrcd)r1rnauls1r,-0]rpD11rue'ra,rplrrlurr,ioyorlunlsrili]i}rrrIiootriiinelnrlu'.u1i;,r1I:"l1rlpi,r_i3lr\i11riiri)
op lBrgs un ltD
qc ruguor{n3lf

tt--.arntr;prcraJ1h,?s1or.iartLio;rJop;rIpap-iDardc.relto.lrrrrpullrrclyola+J'B.rrscta-{llual+nosstopolal'iarponJ){ri-ll.(nart1sld."cnenit;l1lor(1t:rrldd,rura;rtscaruo,llrrnro..ro1ril+lasxari:1l,r.rr,;r1roror?ii1iicar,rur3lolsJl.;srrrpr,rrru.drlonJtlo"f.-uilururoa.lro-liirt1icp,aoglp,arr;ip.,rrr1"rr",ll1ortiluo.tr1rl.rliir,',...riit.,yr.1airoror,ri-ri
(-,orJorlIa] nopsurzoro.lrltu{rrorsz-ullro}{:loltct:_itryJo,r+aclnrrprlrorJrrT.rtr'FasurrollpJ
*o,r}urp rnr ,ro+Jrrpuo?rtr;ls_J,tr}Jl{i

prlos.pryrs ,t1uy;ro1uJ

+',\Dilurl+uIJr.o'),}riutl o.rsunzclenpyluturoc.:St.rr\cc;pr-1(pn1itip,r1tt1ln..*r ri prlo-r rrn o.rl{rl nr
;i'*u.|rj.rtlli"-tt1r'
i)T) slrurolllortr)trr r.rn+'u,rls tl;l iti;lrlrr-
o'-uuoptOlforqorl'loBrxi+olrnio.Jrl.+lprl:8so.ororl1ltttl-Drruoiipoolr+si!lt,n?I/iiulo:Jtr.rrri-noorir11ul?l?rrr1rrrrJun.nr+uPo'B1rcrjlJs,I,)nns rcrcrlln+rar1isrnrqiuti,trrlioart-uslr)put1n,ru'au'n(-or-1gqupnr',dl,orr.-rrl'ulurpnoo1l);nuairn.oc[rl5ltrtiaulrliiJ.iuarer'ailJi:r,csurtlar.lrcrri1afzhnn.prrs3s,irr)_.*rr_1xrc,idrlli,rr:-aot\xl{r;}

ruIiJ1'rr1r.\ig'r0,rr1lir!qo'utDtor-.usrrrrztcrl'llD'.ouuuris'{u"Lar3J1ruJrsr,rir'ztcllri'it,rrtrc"rn'rr.?rgiJ*)irrpur,rir)ionrr'rurio]r,5,rro..rrraluu,rrin*rr..iDirlr.rrloouns.orpl'rrl,]ripn:iJJgr3rricullu;,i1.ri3oluptqi.irnurufi(ill;r.rro.trrloida(fiitr,xutH:u.a;rrr,r1i:iJ,sr,l1r,Ji1ilrnial]rr-irprli)Ir.-artixllu.1il
_--.."
-i)}r]J JJIlll'II ruur al) .|rrir'rJt)r'r.rlJ1ra p,iBlu,rrllrrJ op oTIJRls .rJJs[r,rirrr,p:irrlu",r{dLn,ltsr.(,

ao'upg+sr't.i?r:!iJe+tgs\,cr;'BFrducnoils..{lrrrrrglJoI+uoruerirulrpo?i,1cus;ruc..rrJadtnro.-'r,r1(1oa;ir.p.rr.cr1rIa1_1ul).nig'prlri1olr'lpr.r|o.rron.1roan,*ce;lrisugr;inl;or,yrbdr,nrln,s,rraa.r.liri)lu.)pi,iJ[+trp!qrt]iralsrp,iu)iit,lrr)r{}i,r:)lr{siu]-,.1r)
ot'J-+lrOr1pF-+oUoTd'UJrI'lrUlozTlr{.sZlrclElcFtlaarorr.rrr€O-po;1l+r.pr:trsor)?psrprc.irI)r{ls1lolF?tL{?cl)ulnisu)r>rrrcoJ-uuqt}rru.nlru.o'll)rr-uto,rlrrtJ+utnut;p1trri"Jt-,it1talllroc,(un,cle.ulr,ldro3iono1.sqro:rl'uraozrorpln'JuJua0rr)Inru-r1.lrriBlor'io-JtlrlSrzlrlrzutl'drflrp.rtrr\rc0[rru,Ji)-rg)l]:lszio{R,itpl]arlrBdu{iluiiJ}reBlrg,iaicy.rpurr,rlr1Jodol1pll,rri{srtr:i,rir1,{ro?r}o2{c5,c8t.rti1a.]lyzi):i
ra.rtp,rEqruoq o+so i):|r3.nlc .rolitio;,tz,rds u ;r,rauifrlo up Rpo+ixr|Bnol) \.

i_r_ii--:''(onrOogiraOi.ould'f,ar.,r)(ru(cor(11la9an)5su(a.r1e.ulra11ormtd)iarrpiopua+ndlr Tneaepulld_rE]JyJn!rzpJru?-doD,anp'aa,pIlOirF,ir,pulrBrzu(oouorlplga3l4,lS€lrlroptlyltq)su.,o,tq(lS:ocnIrqoSuu.oipIll)oJsozfcar.;$l,fr,ip,1or\3su1-Ed-)r-nrfllt1.lrjoI1"i-rl.-.rrrl,fr?i,.rils"ltlg,n-o._5uuD1ilurli1r.iAlo){irprnocorliIipOiriiplIpr*l"rs.rp,t:,.,nrr.;rrJ-rrrlinr11i.cJuy)i]
rr;II I-ur (tt?ipE*1ldindlnEdrnd(1)pu1u.r"rrra"lorrEp?oaIciin.Bnr't(r-sOsrA,zrrf'r1lrfcn?)15o3aFur'les[nrl{ulda1cintn;€a;1otrl-+5{lrauurqp+uJodslrlr3pncrnrlcrFa'o.(pIilioruo]zr;I+lruaru:s.a)lursrc-Jirlrlfnn.;clil-ic.i-rr(u.rrnrrz?l{ltrodull'.}Bmrp;8-ot.arlr.rurnxc,p,;11.rVuclpuiu,nlzrJpl'pujdO,,,F.,,r)rpa-nJr,ouJriud1rlr.-luJr,or',ilr1rsls3rra*go1prn-.r"'r,.rrrto4us"n)cp:lq\}uiitrtJuonlrnuili"oi.r,".1upiisll,.orr8u1?.r.*,<i4i1i,l1i,,,ru1..ir,,1,i1_1o,+..Ja,o.Ffprp,rrli

d.e efect cle cimp gi r.iteza cle recomtrinare la supra{a!d,. Pe suprafele cruate
se fac milsur'5,ioii asupra lumcorduilfuiciacr1eeaiecEoirnecltusci etafnicleieinpleriob_ceui apnrtiinceaepxlitcearnreea.
Efectul de cimp const5 in pe supra-
ri unui cimp norrnal pe, suprafa!5,. Se cunoaDte cd, armi,tur[,
f,a,cl$appoaacti"tivfii" adusir, salcin[ in exces c1ac5 se foloseqte P{opa ca o
i a iroui condensaiol pe cale se aplicd, o tensiune electricir' Cealalti al'md,-
tu1d, este o plac[ me?alicil iar inire arn['turi se gi,se;te un clielectric. Sar-
cina care apare in rnetal se localizeazl pe suprata{a lui iar pe semiconductor
I sarcina se tlistribuie intre
nivelele de su.prafa],5, ;i stratul tle iing[ $upla-
fa!i. Sarcina in acest strat se poate determina cunoscind caracteri'uticile
cchp1iirnveoeavbroesimleiu. omtMebn5ialfs,l,seiuucnrsleiniepdmaepicclionocinanvtdteeluuleccpltteeoivrdcuitoelauntisd.eueaApncrspaaerfotaaob{slietis,iei scpdaooernca-itantreidbl,du,uenisctpgerIrueaml dic"neqoaontrsdvaeuatbucriitlraiuei-liridaiplieteaancsteetarsaru--
teia cu- sarcina c1e*ting5, suprafa![. ]li,sur5,torile se fac pe probe suficient
de suiri,iri pentru ca r;aria!1a rezi,stenlei sil constil,uie o parte importantS,
clin rezisteila totald,. Avind in vedere relaliile (3.11) qi (3.12), conceu:r'at'i-
ile purtirtorilor exces din stlat sint tlate c1e

l,r : ,,ro[*i.,'o - -1)/ t'l"r" : 3J&' i' tll rl9. (cttr-r).
Jo
2l;1' -t,, l'(9*.'..)

i3.25)

-J-p! : r',"n"(J*(o,'-i'Q - l)clr: n 2t:k'='r"iJ' ," -:}.':('9-i, 1 r1',. Ictn-z):

t')

iar conductivitatea stratului cle iingX suprrafa![ este (3.26)
o : {} y,oLn { lVpNPe

Dependenia lui o t1e inflllimea barierei, tJr, re11f!i, din depenrlenf,a de in-il-
liniea bari'erei a lui Az qi Ap, ecualla (3.25).-llisurintl. o sc_poate giisi clin
:icvc-.riaearnilploaoaCa'*laUticiorii,eettaauiltn(ixer3c,at.1r2ienSc6c.o)U2lnufq1cseiliscis(,3tendp.s2gtSaie5ectn)usoXesnrizoDuiiuittlntauneeditenseatApaaiae.ialntccupu1inqeltni-acaciaptlarQ-tei5etee,,Q,asdpi,une,idsnp_eesrpaseloadftmar,brcai!iel5iciltre,,uoremn_lcr.dco]ds.ul,neal"'ci_drmltcqi.onciie_rngnin!sfec,l$0aesrs"ttoeso"utelrptQurdprcaleoiun=-aifpdatqeefi?iilLtosrLt.tritl'e4iS8rei"9r:asit1:litrree--,

cle sup""rpd"fa"i!m5 e(nsatar1ci.ni imobilil care nu acluce contribulie la- o)',Din depen-

i'rcdqtcrliereirume,andrap-t.l3p"tmnba.trHsnilalauit,ctirilauod3m0iue0"1icaa",0ucrpdKe"oaru".onp"b,Rad"fa"epuiatrsacotmdeelieit'pa"ui.cgcis1idaeilteenretreacmigdoi-giac.ongilnlisdleuiuuiurpraaiciadn.cleriu3Catp-met.oiSradpuinnecldsacnsutr,etiiecepqnlteiigaruscc_nila,eetluprapatooirdpne_zfeez.iiitgpse,iiitnuanaecvt,rarmuenitirriavsa-so\ierm]uieonlnienute-llaor--dfi-rlue.e;v}nict'aeclreadlir;or:mii"ee.nqr2iiurn^-piit:-r1rrrrlte't,earaeo_1fraat0lpeuri1tJneaiati'

mic5, in cazul stratului de epuiza,re. Conductanla atinge raloarea maxim*
pentru S* care se determini anaiitic din conclilia

dG : -1t-,no{e!{m 1) + ltopo(e'9{* - 1) : 0: /9 .)7\

*

98

6I

bo 'c)uaJsoullll llilpr{oJ
esJarrlp ut u dll irp irn uI qsnpu!
paan JaD eulalrrs ap clirul'rj
uI 'I0iE,jiBJ'd,3n1.s{
gdnp utw g ap Eiuelcnpuol
-

PAAn JAD uozo pdnp utut 1 T
tl,
uoto pdnp utu 1
I1
anrlurJ{r+tcsr/drCossdu-gn'af-r-.?u{grc8rr'lgdl0:Klcrg"lts0tg+o:ouruarr+,firrnS{copttoltdtscwouDpr'cF/a+r\puqrgmJTEduo-srnRus+rrEnJrSurlro0l +Iocp:orJrn.erdard-nog.iJ{+eou;}o,uidl,JrcIru?sJJo} ts

(sa's) 'g ooe : t0 li
II
o+so E lntlnrgc op Ksnpur BrrrcJEr.,gieyu;rdns op J0ITJF+S uluarciu uL ,!
6'4znlcuoc ro+socql uoJrucrJr+snf tu1 ocnpuoa eleod BcrJaurnu oJtsnl€aa llclruri
lulcfuaoz.ratsroduTopclp11u1l togcd€eoyaecrd(qn1s1'ra:1p"eeIJcKn+,rsq.ouepd (a_ucsr0l: +rr0l) _I
'o"ruoldacce r* ri q1c aluzr,rupcl o
al
Jfurnrr a.ruru rlrun
-1
n.rluad ?l+/r? col oJu toJr3uuJcfl '?tsu€"rco a+n-o Inunlo.,\. .rcr yfu;e"rclns dp aIaI
-a-r.ru arl g1ulrluc o+so fsnpul lurcl€s trr3ta.rlur ac{tao;rdu gc eliapo,Lol) .),r trac .t1
'raqo.rcl r.?ofrfr:rrfcllp[oc cr+cts.rd gcr;pour uu nnrrr+uoJ crr?cala cluq.t rnun
ualrcrlclu Kc +€+F.rts n€ al€rro+tsut o+I€ I,! IS 'aO ecl olncpy a1oi1uar.radr11 u
'cr;r1ca1.r iodrp -I
un uc pg..roduroc oospg+c€luJ+aspuanlaclnnpcoo;lrodugr crlorlcanpprur.orcorculurol secrndutnnluu{u1 rtru. :crhd1na.pI id
dl+ op all (
er{cnpuoc
rJga-acodp{niualpJy;pouueq+;orpoTdc.,nr+mcosulpsiosup+.uorrn3rcqJ.lrrn+olnssulocuuo+ndorrBo+asJ"+caraI1ncnJ1zps1peoolt;'rrm[gcyglul+€]luanl;uIlurziolieopu+;FuarIdr€onxeclgr;;rru?oo'orgsus'J,gnpar;6si^utur'l1.opomqp; .5ur,,uor!rymapTab]ua€-cr1rnl1{+ocaurupsunlnr3dqc(al.dun.€r1r1c€ornaeu+.pirrcu+pn'lrutrpmra.uulaarortlnrrrrrrprjl.uotrraonosadt -

-ca1a arrlcad-sa.r'ri rogmlo8 ai' nrqrlrqoa ep epr{,u.r+uocuoc 1u1s0tr, tt f}t:Tr".i* 'F

qld -
v
0
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<t o

t

5
g\-'
'unlol ep Jolljplllrqour pundsa.roa cp
olulcund
cloclrrJ JEI pielr:ldns
.rolliFlIIrqout pundsiuoc aurid JI.lqrn:)
'pjcguldns
qiu;u.rdns BoIpopuIinuluBlrclunaploucol3a-p or1Irnl u1

'S't '3!J

(vid) dc 10-e cur crstc necesi-lr'sii sc:rlrlice o tensiunc rle 103\'pcntrlr,t, st)
oblintr o asemorlc?r, villoare a, cimlnilni. J)t'nsitzrteir de sttiri dc suprrrfalri

ptv'suittlctuitiliritaappilirrcottaab,trcrip'.dtc'I'sr5iun,l5rlau. flltLOtutirrlllc'c(m,u, ll?l)tr,,[atl,tsrr1ntf1rt'lsstcrnIplrlol'uiinlfte,iicfelasecosriuztt'aas,e1om,ovctariecraia(lviittai'l,oaaS'rcciortntirrdrtuoricctltttrir--,
citrrltrilui contirruu nu porte da, r'ezulta,1,e ilsupla. s1 utliului stirilor tle strpra,-
1ilt,1l"t, tliltot'itij ecltrtri'ilii r'ointrmlni tle erii,lr'e stirlile rlc srrll'u.fa{i. I',.'ntt'tt

sttpi:ttfr,{c lea,lt', in cazul cintl slratul rlt'st'p:llirlc rle alnritrua trretir,lit'ir esttt
tle cxerrtphi clilL rnicti., cinr1ir.1| ttraxiru (,are se 1r<tattr ttinge esttr 2 ' 1()rrVicrllr
I ,.sr Q,,1't:: l013crn-!. Pt'n1,r'u celc ilitri rnulte solirr,c :tct'lrsti"r. valorr't, rsle

ioitlte a,plotritr.ti"r tle valoart'rr cirnpul ni rle st.r'tipungt'r't'. in cirnlr r-irlittlril

grad.ul de ccLr-luilro so nricsolci[zi"l (,tr cleslerea fi'r,cvenlci pinii Ia, lircr'r-r,'tt{t-'

clc 10e+JI9T-Iz, a,poi ccrirnirlt'u riinrint' conslir,nlir pilrii ll 701EIz ;i iicste

a,cca,stli r-tlloarc a, frecr.c'ntci tru tnai eristii plrtctic I'clirn?u'('. J)e ircet'li pcrt-

tnr stucliul sulllafe(elor dc Si;i (it'se frilos:e;te tnetorla, r,irupului vir.r'itllril.
Accast,:i nretorlii ct-rnst[ irt rnirsui'alea, r-aritr,iiei rlifelrn]irrlt: a, r'ontlut'tit-i-

ti1.,ii ,superficii-r,lt' itt frrnc{ie tlc srr,r'r.lirrir rlift'r'entitl[ a1:lir'atir 1rt plicile cr )]t{.lolt-
sator ului.

-\e rlefittcstc tnollilitrrtclr, t'lt' t'ft,r.t tlt' r,itnlt

?,t.t = - tlJo'dQ, {ii.J9 i

,Jo : o --- r,.,, 1rnt1e on t'str, t,oltrluc1,ir-i1a,teir itr r'orrtlil.ii rlc irarttlir pltttit
(+-:0). Ilc,urr{ia (3.29) ttu tlii valoalca iuler-t-rra,tii il rrir-rbililat,ii tk'r,irt'et'e

nu. toa"iir, sarr:jttir, Q t'sl,e nrobilti; salcina Q"" rle pe sl,ilile tL' suprli'irtir st'
Tllcsul)ilne imobilti. Senrttul p1.rr.o;.7's- ltr'paotrai,tetiier,scitrii,rrsau, ptllta'ttfsiri,tlaillcta,srtkt'"tl:tt'itrii1tt1lt:
sit,u clt'tip p iar tlin vttloalea hLi
lrri

,srrlrr':rfllt,ti lingir nivelrd lferitti. Se poiite sclic

tl,l.; il0 ,i.it0)

lI'.r

trlr/.irl..) --- (rl(./"" rl'7.)

tt.tltlt, g.r.,i ;i {, se pot cleielt'trin* e-r1;crinrt-n1rrl. tl(lo) rl l. ;i tlQ. tl r. -s(:
pot; r,.a,lcula dupil relat,iilc (IJ.25), (li.26) li (ll.2l ) si sc po:ttc tr-ir,lrul rlQ.. ri0":
ratil tle r-aria{ie cu potenfitrltil cle sullnfalril a srrrcinii cirplat(' pe st'irrile
d-e -srprafa![. Sir eonsirlelirrr o
suplafal.[, crrrati. in cirznl cirrrl il.onrin[
st'iirikr rle supla{u,tii so uj-r1,itre tlin lelal.ia (:}.30)

!1(0rlq)-_ l_cl.\o r;j.;11)
d0. e7tr (1+"

I.)errtru o snprafalil' rte lip 1, ou oorl(letrlll.itr ulAl'c:ri eolulilor', d.ar rtu
degent'r'atl,, din membml dlt'1rt al ccnaliei (3.17) rirnrine trutnri ulii-rrtul
l,el'r'nen ;i atinrl in redcre c[ ] tlAirid y" | < tllpld {" , ccun{ia (lt.l}0) sL' r'e{luce

in,

-(#.-)q(9r,is\ :"?: | .).,): I
{10" =

i00