Microscopic structure of the semiconductor surface in the external electric field
In this paper a theoretical model for the free semiconductor surface is proposed. The principled capability of the correct calculation of the electrostatic potential of the real semiconductors surface is demonstrated on the example of Silicon surface. The potential relief V(r̅,F) of Si(100) surface...
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| Datum: | 2001 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Chuiko Institute of Surface Chemistry National Academy of Sciences of Ukraine
2001
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| Online Zugang: | https://surfacezbir.com.ua/index.php/surface/article/view/58 |
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Surface| _version_ | 1869291145127788544 |
|---|---|
| author | Il'chenko, L. G. Il'chenko, V. V. Goraychuk, T. V. Rangelow, I. W. |
| author_facet | Il'chenko, L. G. Il'chenko, V. V. Goraychuk, T. V. Rangelow, I. W. |
| author_institution_txt_mv | [
{
"author": "L. G. Il'chenko",
"institution": "Інститут хімії поверхні НАН України"
},
{
"author": "V. V. Il'chenko",
"institution": "Taras Shevchenko University"
},
{
"author": "T. V. Goraychuk",
"institution": "Інститут хімії поверхні НАН України"
},
{
"author": "I. W. Rangelow",
"institution": "University of Kassel"
}
] |
| author_sort | Il'chenko, L. G. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-11-27T09:42:39Z |
| description | In this paper a theoretical model for the free semiconductor surface is proposed. The principled capability of the correct calculation of the electrostatic potential of the real semiconductors surface is demonstrated on the example of Silicon surface. The potential relief V(r̅,F) of Si(100) surface are investigated theoretically using methods of nonlocal electrostatics. It is shown, that taking into account the microscopic structure of the free semiconductor surface can lead to the local change of the potential barrier height along the surface. V(r̅,F) (and its amplitude δφ(r̅)) is determined by the microscopic structure of the real surface and the bulk (macroscopic) parameters of the semiconductor. |
| first_indexed | 2025-09-24T17:44:39Z |
| format | Article |
| fulltext |
NIIСRosсoPIсSTRUСTURЕoFТItЕSЕNIIСONDUСTOR
SURFAСЕIГ{Т}IЕЕхTЕRNALЕLЕСTRICFIЕLD
L.G. Il,сhеnkol, v.v.Il,сhеnko2, T.V. Gorayсhukl, аnd I"W. Rangelow3
t Instittttе оf Suфсе Сhеmis|ry, Nаtioпаl Аcаdеmу of Sсiепсes ,
Gеn, Nаumoу,"'i ii,?уi",-03161, uкл'ltllr,, е-mаil', vаi@mаil.univ'kiеv.ttа
2Rаdiophуsicаl Dept', Tа,а, Shiu,:h,nko Llпi,,ersiry'V?'l?|,:,::h;::. u1, Kуiv, 0l033' UKRАINЕ
' t
^,
ii,,}" J i,: с h tt o l сl g i с а l P h1,si с s, I М А, LI п i v е r s ф- of Kаs s е l,.iii,,'i,n-pt,,t
Si'аussе iо' зl t зz Kаssеl, GЕRMАNry
^o..r.,.n,, papel a theorеtiсal modеl foг thе frее^ sеmiсonduсtoт .::.fu."
is pгoposеd' Thе
prinсiplеd сapability "i Б сorleсt сalсulation of thе еlесtrostatiс pоtеntial of the геal
sеmiсonduсtors suгIaсr
j, а..onu,u,еd on thе .-.йpr. "г
Siliсon surfaсe Thе potеntial геliеf
VV'F) oГSi(100) surfaсе aгe in.,,estigatеа tь.o..ii.uttу using mеthods of nonloсal еlесtrostatiоs, lt
isshown,thattakingintoaссountthеmiсrosсopiоstruсtuгеofthefrееsеmiсonduсtoгsuгfaсeсan
lеad to thе loсal сhangе "гli.
p".Ъ",ьl baпiеr ь"igйi urong thе suгfaсе' V (i , F) (and its amplitudе
6фе))isdеtеrminеdbуthеmiсrosсopicstгuоtur.oftь.rеalsurfaсеandthеbulk(maсrosоopic)
parametегs оf тhе sеmiсonduсtoг
1. Introduсtiоn гo.lесtгoniсs requirеs thе dеr,еlopmеnt of bеttеr
,n.o,.".,l}i,i:".ж'}#.T;l];i'Ti''}"Щ -1}:;$i::l1Ц:'::'''J:.t,i.i:,:*JуilЁ:';::
propeгtiеs dеpеnd on.r'.'Ё'ЁЪl"p*i.' oi'ь. л.jJ.'i,sion.utьoа.s, thеir gеomеtriс shapеs and
ihе statе of thеir suгfaсеs, Foг thе thеoгеtical сalсulation of thе сurгеnt-voltagе сharacteгistiсs and
optimization of thе fiеld еmitter paramеtегs it is nесеssary to know a prеоisе ihapе of thе potеntial
baгriег in the pгеsеnсе;ffi;;;;i.;i;;;,i. field Л ' Rесentlу sеmiоonduсtoг matеrials (siliсon'
diamond, diamond.lit<е--сaьЬ",.i,.i.* .on,iа.,.i io ь. р,on.'i'ing for vaсuum miсгoеleоtroniсs
dеviсes [l-3]. n . ^..l^^1^^+.^.i. рmiqqiоn from thе rеal sеmiсonduсtor
Тhеthеorеtiсalсompгеhеnsionofan^autoеleсtгoniсеmissionfr-omthеrеalsеmiсonduсtс
surfacеs is onе of thе ;#;;;.;';ьiй, oгuu."й,.ii.,Ъ.r."',oniсs [4]' As against the emission
сhaгaсtегistiсs "t
..,uЁ, *ii.ь J- '".п
.*pruin.а bу available thеorеtiсal modеls, thе emtsston
сharaсteristiсs of thе non.mеta! сathodеs j" .;
;;;6.; of сasеs havе not adеquatе thеoгеtiсal
il;;;;yT,l:llii*:}#]т'тl*ff l*'.'."J#,Jn"':1l#:,.'T''':l:'":.}!l{l:
;T;;::ffiТъiil..Lx'';''}i:""d;;;i'тф::{:*::}::."l.",7""':;;::'-xr'Ё:':''?;lж"
сonditions' whiоh сan.й"ng" thе statе of thе frее sейiсonduоtог surfaсе- (foг еxamplе, in thе геsult
of thе rесonstгi-rсtion oiiь.Ъ,гu..) Foг thе *"..r'lь. p'.sеnсе of thе fiхеd сhaгgеd suгfaое statеs
(СSS) on u fi"" s...,fu"e if",;;;;;i.,1h. du"gli;;,;;;;; й'to thе formation of a sсrееning layer
of thе fтeе еlесtгons ,;,h.,;;;;; ,.gion ts,o]
,j."i'.йo*n,
that in thе сase of thе sеmiсonduсtors
thе fiхеd CSS on th. f;;;;;;.i;;;;. 'й.
ь,.м"".of .й. ,рu.. сharse rеsion (SCR) in its bulk
with thе сonсеntration of thе frее сarriers t.r..*o",Ъ, ioЬ,i *ьi.ь"'е..еisеntlattу difГеrеnt from its
bulk сonсеntration [7,8]' SuгГaсе рrop:гtl^еs
-oi
,"*i.onduсtoтs inсluding thе еmission and
adsorption .ьu.u.t.,i,ti.".,u..".on,]а.l.bly influеnсеd bу сhangе in thе СSS.
186
ТoR
:lоw3
'I
|3 UKRАINЕ
:эosеd. Thе
эi thе real
:еntial Irliеf
::iostatiсs. It
suгГaсe сan
:s amplitudе
:.]сгosсop1о)
|:.: of bettеr
r:: emission
: shaреs and
:::;stiсs and
:-..е рotеntial
- - - /-:t:^^-
, : ) \ьl lr!vr r'
:::.есtroniсs
- :оnduсtor
l. з еmission
:-: еmission
Е ::еoгеtiсal
f -,еtals and
].. еmission
е : :paгation
. :зе rеsult
п....:е statеs
eе.-,ng laуег
в: - - nduсtors
t - its bulk
Е. -. iгom its
г .эn and
In this papег thе distгibution of the total potеntial rf 'F) in thе extегnal eleсtгiс fiеld Ffгom thе eхaсt solution of thе nonloсal Poisson equation foг thе sеmiсonduсtor.vaсuum system isdеtеrminеd. It is shown that thе сoпeсt aссount of thе sсrееning propегties of thе sеmiсonduсtогpгovidеs the сontinuitу (finitеness) ofthе potеntiaI I/(7,b-)
" il;;;;i;;"duсtor-vасuum inteгfaсеand thе сommon (vaсuum). levеl of thе сounting out of thе еnеrяy [9-1l.l.Тhe сontinuity (finiteness) of thе poteniiы rlr*,гi in"'i.l'#i*мuсtoг suгfaсе allows usto еnter сoггесtlу the latегal distгibution ofthe fiхеd СSS o,(y,z) along thе suгfaсe. In thе givеnwoгk the dеnsity of thе fiхed charge o,(1l,z) on the sеmiсonduсto. iu.faсe сonneсts with thеmiсгosсopiс (atomiс) stп]сtuге of thе semiсonduсtor suгfaсе, whiсh is dеtегminеd by eхpeгimеntalinvеstigations oг by miсrosсopiо (quantum-сhemistry) ."r.urutiЬn, Ьгiй" ,p..lлс sеmiсonduсtoгsurfaсе. The intгoduсing of thе distribution of fiхed сss
",1y,,;
in й -oo.r form, whiсh is usеoin thе miсгosсoрiс сalсulations [8,l2-14]' has allowеd us to link thе maсгosсopiс сharaсtеristiсs ofthе sеmiсonduоtor with thе miсrosсoрii stгuсturе of the suгfaсе in framеworks of the proposеdtheоry In this papеr the potеntial гetiеf l,1r,л; oin-Si(l00)
'ur.г*.
ui.,nu.,tigutеd thеorеtiсallуustng mеthods of nonloсаl еleсtrostatiсs. It is shown, that thе miсrosсopiс struсtuгr of thе frееsеmiсonduсtoг suгfaсе сan lеad.to thе loсal сhange of hеight "i. p"..".Ыbaпiег along thе suгfaсе.Thе total potential L,(f,F) (and its osсillati"ng paг1 6феD is dеtеrmined not only by thеmiсгosсopiс stгuсturе of thе гeal surfaсe (fiхed СSS) but also thе maсrosсoprо propепiеs (bulkpaгamеtеrs) of sеmi сonduсtoгs,
z. Fundаmеntals of thе theоretiсаl mеthod
In this sесtion wе сonsidег the problеm of a'point chargе е intегaсtion with thе suгfaсе oГasеmi.infinite semiсonduсtoг in an ехtеina| еleсtгiс лЪtа д
'"Ёй
lй"*"unt thе sсreеning effeсtsin its bulk and thе сiensity of fiхеd сhargеd surfaсе statеs (CSS)-o, Ql,z) onthе fгее sеmiсonduсtoг
surIасе
An еxaсt solution of this pгoЬlem
еIесtrostatiсs [9-l l] Тhe Gгееn.s funсtion
desсribing thе sсгееnеd Сoulomb intеraоtion
dеteгminеd by the Poisson еquation [9]
maу be obtained in thе fгamewoгk of non*loсal
of a longitudinal sеlf-сonsistеnt fiеld D(q;х,х'1
bеtwеen the сhaгgеs at the points х and х, is
(! ')(iт- { ),
о1q,х,х,)_ате'tdt,П(q;х,х,)D(q;х,,х)=6(х-х,), (i)
whеrе d(;) is thе dеlta-funсtion; П(r7:r,х,) is thе polaгization opегator of thе inhomogenеous
systеm, o = |l,,l,} is thе two-dimеnsional сomponent of thе wavе vесtor and &, is the сomDonеnt
of thе wavе vесtor whiсh is noгmal to thе inteгfaсе:
Тhе approхimation (2) сoпеsponds to thе speсular геflесtion oГthе longitudinal polarisаtion
from thе intегfaсе (x=0), d(х) is thе stеp-funсtion, 7 = ] is usеd foi tье sеmiсonduсtor
x < 0, whilе j =2 for thе vaсuum rеsion х > 0,
(2)
wavеs
rеgion
r87
Thеsolutionofthеhоm.o*.l.:1:..lo,,sonеquation(1)forthеFouriеrсoеffrсiеnts
о tq'']Ji#i"*'r,i*inthеfoilоwingtoгm '}' (з)
J ..
T,;. ',);)0D'(q.,o,х,)
+ а,(q,х)0(-х)Ф,G,О,х,;
+ b,',-,({',,,,)J
ю'(а,х,|)\ is thе dеrivative in thе сasе of a,(Е1-+ t fo'
whеre thе funсtion 0D,(я'o'r,) = ---Т-\=o
Е-+-andЭD,(а',,o,х,)=,,9ЧЧ-o,,,,.Е,+e,whileE->..Thеfunсtionsа,(Ч,х)
arе thе soiutio"::,;:*?fi:xil:i;i:t,:}Ёi1$"
(1) in thе сasе whеn thе polarization opеrator
Ъiq.''',lhastheform(z)."";;;, =liдffi7,,
(4)
whеrе а,(k1'{,:j]ll"::;":1,,:l;':н':';i'i:il"'l,т;:жl"1]ll"J",Ti,,iъYi#),;':,:l
vaсuum rеgion. Thе tu
;." til *nn thе zегo boundarу .::::'Т;,
(q; x - x,) + a, ({; х + х,)], (5)
ь,(а'х'х,) -- 1|а
whеrе5,,Ь-:.ff :"".:"jjJ,!l**ж:l;iffi r.:,"il"::1хl'..ffiJ,l#"t:*;iii""fl:'jffi
vaсuum int.,fiс.^.,.,=юJ}:.:'i'.:ъ.;t'.inj;i;;l fi еld F thе b
Ё1':.i..Ё;;:;o'
u, lnс Ьut,."^-,
n ',. -
D'-'(q;..х,) = 0 \ (6)
ЭD, (q''О, х, 1 - Ь, -,{n.,o'', ) : : :::, ":;:' ll,** and F(q) is thе
whеrе o,(q) is thе Fouriеr ."'*",:il:];T..3'ii.;т}1,'--Т;i;j';;;;;"" thе sign of thе
i"'n., .9*n9i.;|,!f thе еxtетnal .l.."]:.:."
in thе foilowing form
(7)ехtеrnal еlесш:ii::
Ь,{q.,',) сan bе writt
D,(Ч,х,х) = oiG,,х,х) + AD,({;l,*.^"."'
иl(x) oг thе potential'
wьerе D|(с;х'х) dеtеrminеs unambiguously thе polaп,1'"-1^.^":[Т*jJ]. *}l |,"J...',.o
,io**;"*.",ч,i"i,;.#r*,:'*::::Б:.:thеbulk''":;';"Urо9J*--- (s]poi*iuj."ti..*.
{(х)= -,\,t
аа\,о:,rq,х'хl+ /z)
Тhr seсond tеrm in Еq (7) -l.:^1.jl,]T,;-";;*J::#Т.1ТH,:::-''..l
(1) with thе
(e
ьounсu.у сonditions (3) ' whiсh o""T?';l
=,.i,i -
^1!1:l sеmiсonduсtor suгГacе and als.
ЬD,(q,х) rs сaused bу сharging сondition of thе maсrosсopiс snaт
u.o.ni, on thе extеrnal Гleld F l
188
;:t.:сiеnts
(3)
i ->l for
щг. 'i (q;х)
El:. :эеrator
^V
c, F ) = -
" I. ̂ r ̂ ** eхp|i (q,у + q, z)].
^D(q,,
r, D .._4. a qz.n)
For thе sеmiconduсtoг.vaсuum systеm thе Grееn funсtions D0,(q'х'х) havе thе
[l0'll]
пa|^'u -,-еqа,(q;'x|) €r r r,.l
Di Q, х, х 1 =
| * qo(q.'o) - 1Lа(сt'0)
+ а(q'2|х|)j'
D| (q ; х, х) = ;|же*p(*zq') - r], r > 0. (12)
Thе Grееn funсtiоns ЬD,{q,х) in thе сasе of thе fiеld еmission fгom sеmiconduсtoгs arе expгessеd
as follows
| ц Io ^( tI\- F(с)l' а( q'|х|l
ЬD,(q,х)=#, х<0, (l3)
1- qа(q;O)
(10)
following form
х<0, (ll)
(14)
(4)
Ш,* .-t=l ln
j '. Poisson
(б)
;) is thе
:r of thе
(8)
with thе
Lеt us сonsider thе intеraсtion of a point сhaгge e with thе surfaсе of thе semi-infinitе
semiсonduсtoг taking into aссount thе sсreеning еffесts induсеd both bу frеe сaгriегs (eleсtrons or
holes) and bу bound еlеоtrons of ion islands. We deteгminе thе dielесtгiс funсtion of thе
sеmiconduсtoг in thе гegion х S 0 in thе following foгm [9]
(5)
:.ductor-
:::irostatiс. :.avе thе
,i, с-| K- i: 12 2с(k)=1+ 1;z ,'---Ё' k.=ki+q
l+'" ,:,(с-l)
A
(ts)
(7)
: jotеntial,
- so-сallеd
whеrе e is the diеlесtгiс сonstant of a сrуstal lattiсе in a homogеneous fiеld (whеn t + 0), ,t-' is
thе еffесtive sсгeеning lеngth Ьy bound eleсtгоns еqual in thе оrdеr oГ magnitude to thе ion (atom)
., . 4zе2n
radius, к, = # in thе Dеbye.Huсkеl apprохimation (DHA) in a сasе of non-degеnегatе
elеctroniс gas, k o is thе Boltzmann сonstant, п is the сonсеntгation of fгее еlесtгons (oг holеs) in
thе bulk of sеmiсonduсtors (in this woгk wе сonsidеr the n - tУpe sеmiсonduсtoг) and
к, =6в,nleЕo in the Тhomas.Fегmi approхimation (TFA) in a сasе of dеgеnегatе еleсtгoniс gas,
t" is Fеrmi еneгgy of frеe еlесtrons in thе sеmiоonduсtoI. Thе fiгst two teгms in Еq. (15)
сoпespond to thе intегPolation Inkson modеl [15]. As was shown in Ref' [9]' suсh a сombination of
the Inkson modеl with DHA (or ТFА), lеading to thе as1,mptote e1Е) - t *
gp
when ,t >> 2 ,
pгovides thе сontinuitу of thе full еlесtrostatiс рotеntral V(r ,r) (l 1) at the ,u,J." foг х = 0.
By substituting of Еq. (l5) intо Еc (4) wе obtain uрon intеgrating oveг *.
| -\'lp, r
а,(q;х)=#el, o:roiPPI +'+ '-t
hеre
а\ _1хB z .\-l
э эh"\ е '-! ^э э эh.||_q. _K. т) p- |n:_а.
-K.-)|'o6)
t ,-l
(e)
: and also
в: =)|xo+ А2)+ 2,],]t+
1n
к(l +
^'?)'?
Bу substituting Еq, (16) into (1.]l]''1l,To thеn into Еq (s) we oЬtain thе rea1 spaсe
distribution of thе polaгizu,ion .o*pon.ш и;t')"(;;:;J;; po,.niiut of imagе forсеs in loсal
еlесtrostatiсs)fromthе.o*'onvaсuumlеvеlin,asеmiоonduсtor-vaсuumsуstеminthеintеgratеd^
form. Wе want to *.,.., ,n.. ,;i,l-n .onn..t.аЪ"rу *nь thе diffеrеnсе in thе bulk propегtiеs ot
thе сontaсting mеdra and it аoеs not vary с.pйing on thе o, and ехtегnal fiеld F. Whеn
tx\+-- thе funсtion ,,.n'',', =-}а'Qс1,o) -o *: ,-::'::^:::::-.."H.":;l:'::
сontinuitу on thе surfaсе for х = o and at |х\
_r -- it dеГrnes thе rlесtront<
ofsemiсonduсtoг'Undеrthесоnditionl'io(--)=-Е",whеrеЕ"isthеbottomofсonduсtionband
";;;;;;;".J::i'#;:H::.ilJl.":.rТjH"i bу the fiхеd сhargеs on a frее surfaсе of thе
- - + o, = coпst( v is thе numbег of tуpes of thе surfaсе сhargеs, whiсh dеfinе thе
sеmiсonduсto' o' = *
."'o*,;';::,11Н*ll"1{;i!!iffi ir"i.s.дl'}".:у.R--.:],;:"",T"fl l#*::':l
:НJi:j J:;,:"::"I:ЖШ;:. 2 lт)2 o,6 (q,) 6 (q,) and F (q) -_ (2 т), F6(q, )6(q, ) )
in thе following foгm
' . .' ^l l -* - F\. n.| iсonduсtor rеgion); 1l')-
ш l' (i x [ л]' = -,
!| ̂
n
!:i?. .i l ь ;i ] :;:'
" L:} iff ;::ЖТ-,"-'"" l'.-]ЬV,(х, F) = -е(47тo s * ,.]
1.'а pеnеtration еffect as
of
ry.,,.'J*'.li,."lу'Н::'*S":?Т:Т:i;ж;;;J.t.,.in.а
bу the sсrееning propeгtiеs
,,i.t,..'."*ljil
'*"
aссount.a "1i::o,::l,^:.,truсtuге
of thе sеmiсonduсtor suгfaсе assuming,jhat
i;i.fl l11,J,I#:1T}::ff .'.;;'t'-:ffi ,'''жн*#:;jH*tt]r..:t
*l.i' *#'я:*lr."',;жT'.'#'*;**H":H*",i."...*r*:сhargеdеnsitу1.,;.:^?:::j;:"-i.,--" \/ ^,\l
:: : ж l
%
::;'il : "t iБцr.fi r*,^)^..-, "
-
.,::
From Еqs 1,1.1,.f ,n. сomplеtе oo'.."ll.' |,'(i,F) of thе sуstеm'
u..oun,Еqs (15)-(16)and(19)rnth:Л:o,]JBT'f;,,t,,г).n^ш",,t..) (20)
ТhеmodulatеdpaгtArl,,(i)сanЬ.:]:'].::?I',o,,i'o),(',),('o),(rь)unoЕq.(19)with,taking
,*\:"ffi ,:::.,5ilх:,+*l.iьlн,;*'ft lh*н*i;fr.::*ni,'[1Ъi:'ll",ii::;
osсillation paп Aw,(i)oГthе fultoo..*..,[?r;; i:ъ;'ilеd bу thе bulk pгopепiеs ot :
and subsidеs ,n.o ,i. sеmiсonduсtor and into thе vacuum геgton'
3. Rеsu
:
Iесhnс. .
niсгоs:
R.еаl]r..
,,]с lULdl
\t -
- -Г
a
0
i90
) rеal spaсе
эеs in loсal
е intеgгatеd
)гopeгtirs of
l Л Whеn
' ir) is the
gу in a bulk
.сtion band
-зсе of thе
:; Jеfinе thе
a potеntial
]1ogenеous
'L)6(q,))
:,. (17)
(18)
.:nIlon paгt
г: pегtiеs of
*,--.L^.ц l lst Lll4L
е :асh typе
s ::s ) with
в:Гthе l-
- of thе
I '_ rcnnnin
(1e)
f. -q into
(20)
:aking
:.' our
:Г thе
: '.iсon
3. Rеsults and сonсlusions
Siliсon is onе of most suitablе matеrial foг fabriсating fiеld emittеr aггays in batсh
teсhnology. In the pгеsent work is сonsidегеd thе л - type Siliсon. Wе take into aссount a
miсгosсopic structureof thе fiхеd сhaгgе dеnsity o"(у'z) along Si(10O) suгfaсе assuming' that it is
formеd by an oгdеred lattiсе (foг thе simpliсitу we assumе a squarе lattiсe) of thе suгfaсe atoms'
Rеаlly thе Siliсon surfaсе is faг fгom idеal and thе CSS is foгmеd by defесts Thе presеnсе of
сhaгgеd dеfесts (CD) on a suгfaсе of thе sеmiсonduсtor сan гeduсe nЬt only to the сhangе of a
maсrosсopiс potеntial barriег for the eleсtrons (aсtually to сhangе ofthrеshold voltagе)' but also to
the loсal downtuгn (growth) of height оf a potеntial baпiег. Aссording to thе propЬed modеl wе
obtained that taking into aссount thе miсгosсopiс struсtuге of the free sеmiсonduсtor suгfaсe allows
us to detегmine the loсal еmission (adsoгption) сеntrеs.
Wе usе thе following paramеtеrs of Si Ii6]: dieleсtгiс constant is e= I l.9, еffeсtive masses
aге m L = 0'98 (tгansvеrse) and ml = О.19 (paгallеI); еlеоtron affrnity in thе bulk is
x=-Ес=4О5е|,,tеmpеratuгеis Z=300.K; bulkdеnsityofthеfгeееlесtгonsis л=1glsсra_].
-400 -300 -200 -100 0 2s 50 75 100
x (А)
Fig. 1. Thе distгibution of thе potеntial barier V,(х,F) in 0rе ехtегпаl
As was shown bеfoге,
the maсгosсopiс dеnsity of the
fiхеd сhargе o, on the surГaсе
detегmines thе Spaсе Chaгge
Rеgion (SСR) in thе
semiconduсtor. Sinсе thе Siliсon
surfaсe сan еxhibit donoг oг
aссеptor сhaгасtег [8,12-14], thе
formation of the potential barrieг
V(х'F) in thе eхtеrnal еlесtгiс
fiеlrl F=з.1o6V,/ foг' -' '" /cm
diffегеnt maсrosсopiс dеnsitiеs
of сharge on thе surfaсе
,. ^ /o, = -3'4.|О', /,,z (сuгvе l),
o" = 0 (сuгvе 2) and
,^ ^ /o, = З'4 '10'. /,.z (сuгvе 3) is
shown in Fig. 1
The distribution of thе
elесtпс Гrеld ,Г = 3.106V/,
^,
diffеrеnt maсrosсopiс dеnsitiеs of potеntial V,(x,F) in Fig. 1,
сhargе oп iltе surfaсе o, = -3.4.\О,, /,., (сuп'е l). o" = 0 (сuп,е 2) :.1';h; 'ff .i!.ъ
.Ёъ]'Н;
,. ^ / аllя,д 1\ 1-Ьа i."ь li.. ;. rьa г^_: thе aссount (15), dеmonstratеsaлd o, = 3 4 . 10 - /,,l Gurve 3)' Thе dаsh liтrе is the Fermi епеrgу and ;й ;; foгmation of the SСR in
thе dot line is t}е polеntiа-l of imаgе forсеs. thе subsuгfaсe rеgion of Silicon'
Notе, that thе SСR' whiсh is
сonnесtеd with thе rеdistribution of thе fтее сaггiегs in thе sеmiсonduсtor' еnsurеs thе
quasiеlесtronеutгality сondition in the vaсuum region for х.-) со.
As сan sее from Fig. 1, thе сoггect сonsidегation of thе spatial dispегsion еffеоts in thе
sеmiсonduсtoг allows us to obtain not only сontinuous сoursе of thе imagе foгces potеntial
l9l
цoiх1цtrеdotсurvеsinFig1)inthеSiliсon-vaсuumsystеm,butalsothе.сommon(vaсuum)lеvеl
ofthе сounting oГthе рot.i.iut еneгgy [9-1 rl ть. .onii"uous сoursе of thе image forсеs potеntial
},,.(x)(and also thе г.,rr poi.nilы т,,(i,t,л at thе sharp sеmiсonduсtoг. vaсuum inteгfаcе allows us
thе corrеct соnsidеration of miогosсopiс struсture оf thе Siliоon surfaсе.
Let,s takе ,n.o йoljn, thе miсrosсopi. ;;;;;; ;i thе оhaтge densitу o(y,z) оn thе
surfaсe' Lеt.s assumе,nui oiу',l is formеd by an oгderеd lattiсе (for the simplicity wr assumе a
squarеlattiсе)ofthеsuтfaсеS.atomswithtwo-dimеnsionalсonсentгationр"=6,8.|0'.сп-,,whiсh
is сoпеspоnded t" Si('0;;,'nu.., *n.,. o=(ш.)_' is thе sizе o:.'ou.ul"^'*.iсе. Bесausе thе СSS
on thе frее Siliсon suгfaсе ехhitrit donoг o, u...j,o, сharaсtег i*]^*: ".1"
intгoduсe thе еffесtivе
сharge on thе surfaсе.,;; ;: ;; . paгameter, гo,."*u.pt. е; =o.oz. In thе сasе of onе tyре of thе
СSS on si(10o), *t'"n u= i in вq1tяl,,ь. po,."iiuiiе|iet V(f ,F1is calсulated. Thе amplitudе
6фf)ofthеosсillationpaгtofthеtotalpotеntialV(f,F)isdеtегminеdbуeiandthеbulk
paтamеtеIs of s"m,сond,-iо tor п,T'с and for u,.o ou.un]oers is 6/(0,y,z)=О.a|6еV ' Fог thе
гесonstгLlсtеdsi(loo).u.Г...,whentь.'i.,o,...'rеof"tьеsurfaсеisdetеrminеdbythe
suрегlattiсе(7х7)(withthеsizеofthеsquaгelattiсеisа'х21,l;,*.shouldеntеrtwotypеsofthе
СSS(y=2inЕq(19)),foгехamplervithеffесtivесhu,g.onthеdеfесtsеi=О5(inthisсasеthе
total valuе ol the dеnsitу of chaгgе ts o. = -6з84 |О,'f,,.), Rеsults of thе diгeсt сalсulation
6фf ) aтeshown bу solid сurvе in Fig, 2
-- 0 io zo .o. 3o
у (A)
оf dоwnturn (gгowth) of
.a
Fig. 2. Lаtега1 drstгibutioп of thе оsсillаtio" o: _ч,',:] :l:ъ:;] ::,"у*:i".".n.G,",.*}/",3lo.lrlЕ'. !. Lal!.* --_ ^ /., _ ,)\ г^r p. = 0 02 . valuе ot tne IIlaU| UJUvPl\
nolеntial v.(v,F) along Si(l0Оl surlaсе \y - 4,, . 'l baгrieг И(i,0) (20)
РU(lllllg^ ..;.'-r fl /da(|).tlп'е} in potentlа
еi=0,5atх=0(sоlidсuп,е),х=lA(dotсuп,е)алdх=2A(dаshсLrп,е)tn ;;;;;. of arеas of loсal
thЪ u".uu. rеgion for F = 0 аo*ntu- (growth) of height of
a p otеnti al b ar ri е г al o n g
1 :y.li.:^ : :
j}: :.,T' ff:."i:lТ,:; ;:ff , [*l.H:",H'жT:ili"':
:"ж:::'3*Т::..:Т3'?jli:ff;Jfi;ъ,;;;;;';а
*oа.t showеd that the loсal downtuгn
02
Тhe osсillation paп Aф(i) of
the full рotential baпieг
V (| F\ is dесrеasing in thе
vaсuum rеgion (thе dot сuгvе
for х= tl and thе dash сuгvе
foг х= z)inrig.z1.
As wе сan sее fiom
Еis 2 thе prеsеnсе of the
iuЪе,luttiс. of suреrfiсial
uto*', whiсh arisеs Гоr
е*a*р1е in rеsult of
."сonЪtruсtion of a surfaсе . tn
a сasе Sl(i00)-(7,7), when
е| * еi , rеsults in еssеntial
.йung. potеntial rеliеf of a
surfa-сe and oсcurrencе of aтеas
01
^nh
Х-
-0.1
40
192
L.]^-] levеl
:s : ]tеntial
S : .CWS US
: on thе
Е ]lsuml a
;r : rvhiсh
Lъj ::.е сsS
[е:..aЭсtive
!' . cгthе
Е ] -:litudе
в: .-е bulk
r' .oг thе
Е: ] ]v thе
t..:iofthе
т -]sе thе
Е '. :jlation
(gгowth) of a potential baгriеr сan dеtегminе thе emission (adsoгption) сеntгеs not only in the plaсе
ofan aпangеmеnt ofthе dеfесt.
Thе сhargеd dеfесts (СD) on a suгfaсе of thе sеmiсonduсtor (adsorbеd atoms oг impuгities
iпsidе thе sеmiсonduсtoг) with two-dimеnsional сonсеntration N, сan геduсе not onlу to thе
сhangе ofthе maсгosсopic рotеntial barгiеr foг thе сhargеd paгtiсlеs (еlесtrons oг ions), but also to a
local modifiсatiоn of thе potеntial barгiеr hеight along thе surfaсe and foгmation of the new
adsoгption (еmission) сentrrs' So thе introduсing into thе struсtuге of thе rесonstruсtеd suгfaсе
ii_Sl(100), whiсh is pгеsеntеd in Fig 2, thе сhargеd impuгitiеs with an еffесtivе сharge e, =-l
and two-dimеnsional сonсеntration N.. whiсh forms an inсommеnsuгablе squaгe lattiсе with thе
lattiсе оonstanI аз= 461.7 l, геsults in a modifiсation of a maсrosсopiс (mean) density of сhargе on
a suгfaсе oз =155'7.|О,3 еf сm2 and signifiсant modifiсаtion o|a potеntial rеlief of thе suгfaсе. Thе
lateгal distribution of the osсillation part 6ф(. of thе full potеntial (2O) on thе гесonstruсtеd
ll_Si(l0O) _(7х1) suгГacе x=0 (solid сuwе) and its сhanging into the vaсuum foг х= z) вot
0
сuгvе) and ioг x= 5l (dash сuгve) aге shown in Fig 3.
From Fig. 3 we сan sеe that thе
introduсing of thе doping
impuritiеs in a planе of a
suгfаcе essеntially сhangеs
(augments) amplitudе 6ф(7)
'so thе сhargеd paпiсle in
vaсuum ..fеels'' the plaсеs of
the grеatest downtuгn or
gгowth of a potеntial baпiеr
(minima oг maxima of thе
potеntial dеpеnding on thе sign
of an intеraсting chaгged
paпiсles) on the spaсing
inteгvals considеrably
c jю
y (i) l00
eхсееding thе diгесt quantum-
сhеmiсal inteгaction.
The diгесt сalсulation
of thе 3D distгibution of 6фf)
on thе rесonstruсted
l' _ Sl(1 00) - (7 х 7) suгfaсе
( х = 0 ) in thе сasе of the thгее
typеs of thе CSS and CD
(и=3 and еi=0.0z' еi=as
and e, = -1) foг thе two.
dimеnsional сonсеntгaIlon
N з = 4.69 .\О,2 сrn-2 is shown
in Fig' 4 (сoпesponds to solid
сuгvе in Fig 3).
t'
Ei
ts'.
tr.
-- (r-) of
эaпier
in thе
: сuгVе
.' сuryе
:: from
э| thе
- егficial
:: foг
..;е . in. whеn
. s sеntial
.: oГ a
. :'i arеas
'of a
,
- lsсopiс
(20)
.: loсal
-3ight of
. -.е of its
: .Jntuгn
Ф ll
яc
Х
д .^l
Fig. 3. The latегal distribution of the osсillation гвrt. 6ф$,у,О) alоng
Si(t00) surfaсе in thе \,асuum геgion at х=0(solid сuп'е), х=l taot
сuпе)aлd x=5l(oаst'сun.е)for el =O0z'еi=о5 and e, =_1
19з
vасulrm
Lеt's note speсially,
that foг thе сhargеd paгtiсlеs,
whiсh aге in thе vaсuum on
spaсing intеrvals х -) .o,
tlrе suгГaсе of thе
sеmiсonduсtoг is
quasinеutral at the ехpеnse
of геdistгibution of frее
сaгrieгs (fоr a sеmiсonduсtor
ofa n - tуpе - еlесtгons) -
foгmation of thе SСR.
Fig. 5 shows thе
diгесt сalсulations aссording
to Еq (20) thе сhangings of
a full рotеntial barгteг
|/,(i ,F) of thе
л - Si(1 00) - (1 х 7) suгfaсе
(lvith thrее typеs of suгfaсe
сhaгges r, = 3 and with thе
рaгamеtегs, whiсh arе
dеtеrminеd for Figs' 3' 4) in
thе ехtегnal еleсtriс fiеld
F --3.1О6Vlсm (sее in
Fig. 1) at thе moving fтom
thе suгГaсе into vaсuum at
0
х =О,I,-.',6А (thе bottom.
up сuгvеs),
In this papеr wе
demonstгatе thе prinсiplеd
сapabilitу foг thе сolтeсt
сalсulation of thе rеal
suгfaсе of sеmiсonduсtors
on thе basis of the Grееn,s
funсtions method [9- 1 1]
whiсh takеs into aссount thе
spatial dispегsion еffесts in
thе sеmiсonduсtoг- Thе
ргoposed method of
SШс (.7хD
vU"1 = 1,12
Fig. a. 3D drstгibution ot 6фQ,у,О) on the Sr(100) suгfасе ( х = 0 ) for thе
tfuееt1pеof thеCSSaлdсhатgеddеfесts (r,=3) аt ei =0'02' е,=0,5'
e] = - l aлd N. = .1 69l.10': слl-r '
0 50 y (Ё) 100 150
iq
l0
(,
O
>.
Хv сБ
.1
Fig.5.Thесhалgеofthеpotеntiа] re|ietV(х,у,О,Л) of Si(1O0)surfaсеrlith thеoгеtiсal сalсulation of a
struсtuте prеsеntеd in Fig.4 алd solid linе in Fig, 3 ln thе vасuum rеgion at рotеntial reliеf of thе гeal
х = 0' 1'2,З,4;5,61 1f,o,,'thеbottоm)forЛ= з ю,V/сm' ll.,i,Т"n?l*j:r;:ъ*:H;
еlесtriс fields has allowеd us within the framеrvoгk of onе modеl сoпесtlу to unify thе maсrosсopiс
propeгtiеs of the sеmrсonduсtoг with the miсгosсopiс stгuсtuге of thе rеal spесific surfaсе' Wе want
to notе. that in thе framеwork oГ the proрosеd йodеl wе сan takе into aссount thе miсrosсopiс
1l
l2
l
lз. :
в
It (
i
(
l5, Е
16. J
j
194
.aIe spесiallу,
:gеd paгtiсlеs'
]е vaсuum on
' 3ls х -) .o,
of thе
is
: thе еxpensе
:'^ n of frее
s. r1iсonduсtoг
. е]еclrons, -
.: SСR,
Siows thе
::.s aссoгding
r .]angings oг
::.:, зi baггiег
thе
- . 7) suгfaсе
:.. of suгfaсе
.. J with thе
. зiсh arе
':rs3,4)in
;:;iгiс fiеld
- (sее in
-. ,:.^ г.^*
' lllB rl vrlr
r: ']сuum aI
' -: bottom-
struсtuге of the suгfaсе using thе striсt quantum-сhеmiсal сalсulations of thе spесifiс sеmiсonduсtorsuгfaсеs (not onlу in thе foгm (lя), whiсh is usеd in tьi' "йia.й;;"^
.,
Тhe obtainеd сalсulations havе shown that the dist'ib;ti;;;iiie potеntiat I/ jf 'F) (and in aсonsidегable ехtеnt thе amplitudе of its osсillating paгt 6ф0) is dеtегminеd by maсгosсopiс(volumetгic) pгopеrtiеs of sеmiсonduсtoгs (the lеvel of bulk doping r, thе diеlесtгiс сonstant 6, thelattiсе сonstant ofa sеmiсonduсtor 2_l) and also thе ехtегnal сonditions (the tеmpегature 7' and thepгеsеnсe ofthe еxtеrnal еleсtгiс fiеlds Л.)
Rеferenсеs
t. Physiсal pгopегties of thin-solid field еmission с.atь9o99 with molybdenum / C.A.Spindt,I.Brodiе, L Humphrey and Е,R.WestеrЬeтgl/J Appl Phys' - ls1Ё.'-v.47,N 12..P.5248-526з
2' Dеrivation of the imagе intегaсtion-foг non.pla-naг pointеd еmittег geomеtгies: appliсation tofiеld еmission I-V сhaгaсtегistiсs i Jun нe, Ё н сuttrг, ш.м. мi*ййкy, T'Е Fеuсhtwang,T Е' Sullivan, I!{oon Chung /i Suгf Sсi, - 199l - У 246' - P з4s-зъ;з Fiеld еmission сathodе arrayrvith sеlf.alignеd gatе еlесtгodе fabгiсated by siliсonmiсгomaсhining / W.Baгth, T Dеbsky, F- shi,-P. Hudeс, r. к"'ti.,]w. Rangelow, S. Biehl,T Iwегt, P' Gгabiес, K Studzinska, s' Мituгa, I I. Bеkh, A.в. Lushkin, L.G. Il,сhenko,V V Il'сhеnko and G. Нaind| /lJ'Vaс. Sсi. Tесhnol. в - zooo. -V. 18, N 6. - P. з544-з548'+. Мodinos A Fiеld, Thегmioniс, and SесondaгyЕlесtгon Еmission sp..t.o,.opy.- Plеnum,Nеw Yoг\ 1984 -p 328
s Lang N.D. and Williams A R Thеoгу of vaсuum сhemisoгption on simplе mеtals // Phys' Rеv.B - 1978 .v 18,N2 .Р 616-6з6
с. Lang N.D. Thе dеnsitу - funсtional formalism and thе еlесtroniс struсturе of metal suгfaсеs //Sol, St. Fhys' - 197з -v 28 . P 225-Зoo
l SzеS.М.Physiсsof SеmiсonductoгDеviсеs'-JWilеy&Sons,NеwYork, 198l -320.8. Мonсh W. Sеmiсonduсtor Suгfасеs and Interfaс.' spнng."v..r"gЬolin HeidеIbеrg, l995.- p442
q. Il'сhеnko L'G.' Pashitskii Е A, and Romanov Yu A. Сhaгgе intегaсtion in layеred systеmswith spatial dispегsion /i SuгГ Sсi'- 1982 . v. 12i.. - P. з7'-зg5,
t0. Il'сhenko L G., Kгщсhеnko Yu'V. Ех1егnal fiеld penеtгation еffeсt oп сuгrеnt-fiеld
сhaгaсtеristiсs of mеtal emittersii J'Vaс'Sоi'Tесhnol B - l995' - v. 13, N 2.- P. 566-570.tl. Еlесtгostatiс еneгgy and sсreеnеd сhaгgе intеraсtion nеaг thе surfaсoif mеtal with diffeгеntFегmi suгfaсе shapе/ A.М, Gaboviсh, L.G Il'сhеnko, Е,A' Pashitskii and Yu.A. Romanov //Suгf, Sсi, - 19s0. .У 94. -P 1,79-2Оз
tz Sсanning Тunnеling Мj:l9':9рy and Spесtгosсopy: thеory, tесhniquеs and appliсations /Еditor Dawn A' Bonnell // - Nеrv York, 1993 - p 436
13. Sсanning Tunneling Мiсrosсopу I: Gеnегal Pгinсiples and Appliсations to Clеan andAdsoгbatе-Covегеd Suгfaсеs / Еds H -J, Gunthегoit, к tViеsйdangеr // Spгingег-Vеrlag
BегIin, 1992-p245'
t+. Sergеi N. Мagonov, Ir,Iуung-Hrvan Whangbo, Surfaсе Analysis with STМ and А!М:
Ехpeгimеntal and Thеo.г-еtiсal Aspесts of imagе Analysis йinь"i.. Nеw York; Basеl;
Cambгidgе; Tokio: VCH, 1996,
l5. Bennеt М., Inkson J С Ехсhangе and сorrеlation potеntial in siliсon // J.Phуs. С. -|9'77..v 10,N5-P.981_999.
l6 Jеnsеn K L' Impгoved Fowlег-Nогdhеim еquation fоr fiеId еmission fгom sеmiсonduсtoгs //J'Vaс. Sсi Тесhnol. B. - l995. . V lз, N 2' - P. 516-521.
E
tr]:
l
::
Е-
rЕ.
E.'
!-
!.'
: ]реr wе
эгinсiplеd-. сorтесt
:hе геal
'..nduсtors
-: Gгееn's
: [9-11]
. ':оunt thе
:tЪсts in.: Thе
-.1 of
.-эn of a
.:hе rеal
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| id | oai:ojs.pkp.sfu.ca:article-58 |
| institution | Surface |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-09-24T17:44:39Z |
| publishDate | 2001 |
| publisher | Chuiko Institute of Surface Chemistry National Academy of Sciences of Ukraine |
| record_format | ojs |
| resource_txt_mv | surfacezbircomua/b8/b1ec74c338bb07095931f83e455730b8.pdf |
| spelling | oai:ojs.pkp.sfu.ca:article-582018-11-27T09:42:39Z Microscopic structure of the semiconductor surface in the external electric field Microscopic structure of the semiconductor surface in the external electric field Microscopic structure of the semiconductor surface in the external electric field Il'chenko, L. G. Il'chenko, V. V. Goraychuk, T. V. Rangelow, I. W. In this paper a theoretical model for the free semiconductor surface is proposed. The principled capability of the correct calculation of the electrostatic potential of the real semiconductors surface is demonstrated on the example of Silicon surface. The potential relief V(r̅,F) of Si(100) surface are investigated theoretically using methods of nonlocal electrostatics. It is shown, that taking into account the microscopic structure of the free semiconductor surface can lead to the local change of the potential barrier height along the surface. V(r̅,F) (and its amplitude δφ(r̅)) is determined by the microscopic structure of the real surface and the bulk (macroscopic) parameters of the semiconductor. In this paper a theoretical model for the free semiconductor surface is proposed. The principled capability of the correct calculation of the electrostatic potential of the real semiconductors surface is demonstrated on the example of Silicon surface. The potential relief V(r̅,F) of Si(100) surface are investigated theoretically using methods of nonlocal electrostatics. It is shown, that taking into account the microscopic structure of the free semiconductor surface can lead to the local change of the potential barrier height along the surface. V(r̅,F) (and its amplitude δφ(r̅)) is determined by the microscopic structure of the real surface and the bulk (macroscopic) parameters of the semiconductor. In this paper a theoretical model for the free semiconductor surface is proposed. The principled capability of the correct calculation of the electrostatic potential of the real semiconductors surface is demonstrated on the example of Silicon surface. The potential relief V(r̅,F) of Si(100) surface are investigated theoretically using methods of nonlocal electrostatics. It is shown, that taking into account the microscopic structure of the free semiconductor surface can lead to the local change of the potential barrier height along the surface. V(r̅,F) (and its amplitude δφ(r̅)) is determined by the microscopic structure of the real surface and the bulk (macroscopic) parameters of the semiconductor. Chuiko Institute of Surface Chemistry National Academy of Sciences of Ukraine 2001-06-10 Article Article application/pdf https://surfacezbir.com.ua/index.php/surface/article/view/58 Surface; No. 4-6 (2001): Chemistry, Physics and Technology of Surface; 186-195 Поверхность; № 4-6 (2001): Химия, физика и технология поверхности; 186-195 Поверхня; № 4-6 (2001): Хімія, фізика та технологія поверхні; 186-195 3154-8091 3154-8083 en https://surfacezbir.com.ua/index.php/surface/article/view/58/57 Авторське право (c) 2001 L.G. Il’chenko, V.V.Il’chenko, T.V. Goraychuk, I.W. Rangelow |
| spellingShingle | Il'chenko, L. G. Il'chenko, V. V. Goraychuk, T. V. Rangelow, I. W. Microscopic structure of the semiconductor surface in the external electric field |
| title | Microscopic structure of the semiconductor surface in the external electric field |
| title_alt | Microscopic structure of the semiconductor surface in the external electric field Microscopic structure of the semiconductor surface in the external electric field |
| title_full | Microscopic structure of the semiconductor surface in the external electric field |
| title_fullStr | Microscopic structure of the semiconductor surface in the external electric field |
| title_full_unstemmed | Microscopic structure of the semiconductor surface in the external electric field |
| title_short | Microscopic structure of the semiconductor surface in the external electric field |
| title_sort | microscopic structure of the semiconductor surface in the external electric field |
| url | https://surfacezbir.com.ua/index.php/surface/article/view/58 |
| work_keys_str_mv | AT ilchenkolg microscopicstructureofthesemiconductorsurfaceintheexternalelectricfield AT ilchenkovv microscopicstructureofthesemiconductorsurfaceintheexternalelectricfield AT goraychuktv microscopicstructureofthesemiconductorsurfaceintheexternalelectricfield AT rangelowiw microscopicstructureofthesemiconductorsurfaceintheexternalelectricfield |