Optical properties of ferromagnetic semiconductors with laser induced surface gratings
This article introduces the basic physical concepts of laser radiation influences on physical properties of ferromagnetic semiconductors (FMSC). A system of transport equations is derived to describe the electron-magnon system in a FMSC illuminated with several coherent light beams (CLB) along with...
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| Datum: | 2001 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Chuiko Institute of Surface Chemistry National Academy of Sciences of Ukraine
2001
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Surface| _version_ | 1869291144710455296 |
|---|---|
| author | Semchuk, O. Yu. Grechko, L. G. Willander, M. Karlsteen, M. |
| author_facet | Semchuk, O. Yu. Grechko, L. G. Willander, M. Karlsteen, M. |
| author_institution_txt_mv | [
{
"author": "O. Yu. Semchuk",
"institution": "Інститут хімії поверхні НАН України"
},
{
"author": "L. G. Grechko",
"institution": "Інститут хімії поверхні НАН України"
},
{
"author": "M. Willander",
"institution": "Chalmers University of Technology and Göteborg University"
},
{
"author": "M. Karlsteen",
"institution": "Chalmers University of Technology and Göteborg University"
}
] |
| author_sort | Semchuk, O. Yu. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-11-27T09:42:39Z |
| description | This article introduces the basic physical concepts of laser radiation influences on physical properties of ferromagnetic semiconductors (FMSC). A system of transport equations is derived to describe the electron-magnon system in a FMSC illuminated with several coherent light beams (CLB) along with a static heating electric field. It is shown that interference of CLB in FMSC has the effect that several parameters of nonequilibrium electrons and magnons exhibit superlattice behavior. The depth of modulation of the parameters describing superlattices is estimated. Propagation and diffraction of an additional electromagnetic wave in a FMSC with a gratings induced by CLB is considered. The light reflection coefficient and the refractive index of FMSC with laser induced gratings are calculated. |
| first_indexed | 2025-09-24T17:44:39Z |
| format | Article |
| fulltext |
OPТIсAL PROPЕRTIЕS oF FЕRROMAGNЕTIС
sЕMIсoNDUсToRs wITн LASЕR INDUCЕD SURFACЕ
GRATINGS
o.Yu. Sеmсhukl, L.G. Grесhkol, ]vI. Willаnder2 аnd М. Karlstееn2
1Institutе of Suфcе Сhеmistry' Nаtionаl Аcаdеmу of Scienсеs,
]7 Gеnerаl Nаumov Strееt' 030]61' Kуiv' UKRAINЕ, е-mаil'.usеr@uфhеmJrееttеt.kiеу.uа
'Dеpаr|mеnt of Phуsiсs, Сhаlmеrs Utttl,'еrsilу of Тесhпolog,, аnd Gёtеborg {Jniversitу,
S-1 1 29б, Gёtеborg, SWЕDЕN, е-mаil.. mhl(@fu.сhаlmеrs.sе
Abstraсt
This aгtiсlе introduсеs thе basiс physiсal сonсepts оf laseг radiation influеnсеs оn physiсal
propегties of fепomagnеtiс sеmiсonduсtoгs (FМSС). A sуstem oГtransport equations is dеrivеd to
dеsсribе thе еlесtron.magnon sуstеm in a FМSС illuminatеd with sеvеral сohеrеnt light bеams
(CLB) along with a statiс hеating еleсtгiс fiеld' It is shown that intегfеrеnсе of CLB in FМSC has
thе еffесt that sevеral paгamеtегs of nonеquilibrium еlесtrons and magnons ехhibit superlattiсe
behavioг. Тhe dеpth of modulation of thе paramеtегs dеsсribing supегlattiсеs is еstimated,
Propagation and diffгaсtion oГ an additional еlесtromagnеtic wal'e in a FМSC with a gгatings
induсеd by СLB is сonsidегеd, The light rеflесtion сoе{T.iсiеnt and thе rеfraсtivе indех of FМSС
with laser induсеd gratings arе сalсulatеd,
1. lntroduсtion
Fеrromagnetiс sеmiсonduсtoгs is a nеw сlass of matегials having both semiсonduсtor and
fегromagnetiс propеrtiеs and bеing thе uniquе matеrials with nеw qualitativе fеaturеs of phуsiсal
propепiБs for the last fеw yеars aге intеnsivеlу studiеd. In сonnесtion with the last aсhiеvеmеnts in
synthеsis of nеw ''high-tеmpeгatuге.. fеггomagnеtiс semiсonduсtors on a basis on LaМno, and
dilutеd fеrromagnеtiс semiсonduсtoгs ц,ith thе Cuгie tеmpeгaturе of thе order of 300K' thеsе
systems are of grеat intеrеst [1]. Тhе pгesеnсе of a strong s.d-еxсhangе intеraсtion bеtweеn
еieсtroniс and mignеtiс subsуstеms FМSC еnablеs onе to obsеrvе a lot of uniquе еffесts in this
systеms: mеtal . Ъiеlесtгiс phasе tгansition, giant magnеtorеsistansе, shift of edgе of optiоal
aЬsorption, anomaly of еlесtгiсal propегties near thе Cuгiе temperaturе, photoinduсеd magnеtiс
еffeсtЪ еtс [2,3]' on thе basis of FМSС and multi.layегs (thin.film planar stгuсtuгеs) mеtal /FМSC
сontaining FМSC: Еuo, ЕuS, СdСr2Sе., HgСг2Sеo, LaМno, , еtс. thе solid-state souгоеs of
polarizеd еlесtrons [4], spin transistoгs [5], fепomagnet-sеmiсonduсtoг-dеviсеs with tunablе tunnel
сharaсtеristiс [6] arЪ at'.lay havе beеn dеvеloped. on the basis of suсh FМSC and FМSC multi.
Iaуеrs a new dirесtion in miсгoeleсtrоniсs - ..miсromagnеtoе1есtгoniсs'' alгeady emегgеd.
All mеntionеd abovе еffeсts rеpresеnt a rеsult of intегaсtion of equilibrium еlесtroniс and
magnеtiс sub.sуstеms. Тhе prеsеnсе of a strong elесtromagnеtic wavе еssеntiallу сhangеs
сhйaсter of quasipaгtiсlеs intеraсtion ln sеmiсonduсtoгs It produсе in a lot of thе various
nonlinеaг and nonеquilibrum phеnomеna in dеtail dеsсribеd in thе litеrature[1-9l The presenсе of
a strong еlесtromagnеtiс wavе among otheг things mеans that in quasipaгtiсlеs systеm of thе
sеmiсoiduсtoгs thеiе are nеW сharaсtегistiс sizеs: amplitudе of сonduсtion еlесtrons (whеrе and
fгom now on wеll for сегtainty, wе will spеak about сonduсtion еlесtгons, but it сonсегns holes as
well) osсillations in a field of an еleсtгomagnеtiс wavе A and frеquenсy of an еlесtromagnеtiс
wavе o [1O] If <о Ьесomеs сomparablе with one of сhaгaсtеristiс fгеquеnсiеs of thе
t96
tС
lFAсЕ
я rIstееn2
: |:е i. kiеу.uсI
,::
' еrsiф,
:.: cn physiсal
г-. :s dегivеd to
зг: ,lght bеams
l ' FМSC has
r.: ' superlattiсe
l . эstimatеd.
l .. a 8гatings
г::l^ of FМSC
ш :Jсtor and
l: Г physiсal
E l '3l]l€ПtS lП
-,:.1nO, and
' ]K, thеsе
.. bеtween
,:ls in this
:i oрtiсal
. l-ragnеtiс
-. :l ,ЕМSC
.rrсеs of
.е tunnеl
.I multi-
.зiс and
r langes
: .''Э.lloLtS
:::nсr of
_ cf thе
::е and
- rles as
J tn"
sеmiсonduсtor: quasipaпiсlеs геlaхation timеs, fгее run timеs of quasipaпiсlеs еtc. it is possiblе to
eхpесt oссurтеnсе on nеw еffeсts. Foг ехamplе, quasipartiсlеs intеraсtion in sеmiсonduсtoгs
еssеntially dеpends on thе гatio bеtrvееn quantum energy Of an еlесtromagnеtiс wavе €r =ho and
avегаgeeleсtronenergy с..If |ta <Е,thеelесtromagnеtiсwavеwill bеwеakanditsaсtionrvill bе
rеduсеd only to oссuттеnсе of the small amеndmеnts to the phеnomena аlrеady ехisting and without
it. If ho > Е ' thе еlесtromagnetiс wavе will be strong and its oссurгеnсе bу all means will rеsult in
both еssеntial updating of existing phenomеna and in oссuпеnсе of nеw onе in this сasе it is
impossiblе to usе сlassiсal Boatsman kinetiс equation for thе dеsоription quasipaгtiсles kinеtiсs. On
thе othеr hand, if thе amplitudе оf еlесtromagnеtiс wavе is сonsiderеd is not sma1l, so thе
influenсе of an еlесtromagnеtiс lvavе on сharaсteг of quasipartiсles tntеraсtton сannot be
сonsidеrеd within thе framewoгk of thе pегturbation thеory and foг thе dеsсription оf thе
quasipaпiсles kinеtiоs in thеsе сonditions it is nесеssary to havе thе new kinetiс equatiоns . thе
quantum kinеtiс еquations' It rvas obtainеd by a numbеr of аuthoгs foг vaгious оasеs. foг thе
dеscriрtion of еleсtron-phonon intегaсtion without thе aссount [10], and in viеw, of spatiаl
dеpеndеnсe of an еlесtгomagnеtiс wavе field [ 1l'12], for еlесtгon-magnon inteгaсtion withоut thе
aссount [8] and in viеw of spatial dеpеndеnсе of an еlесtгоmаgnеtiс wavе fiеld [ 1 1 , 12]
on thе othег hand, thе situation whеn sеvеral СLB гatheг than a singlе Ьеam induсe оn a
semiсonduсtors is of a spесial intегеst' Having a high dеgгеe оf monoсhromаtiсity a CLB undег
сeгtain сonditions сan сгеatе in medium a intегfеrеnсе piсturе of intеnsity modulation in spaсе
undеr thе pегiodic law' Тhis major ргopегty of СLB, distinguishing them fгom a usual single
еlесtromagnеtiс wavе, is now widеly used in sсiеnсе and еnginеering and has рraсtiсal usе оf
vaгious nonlinеar oрtiсal еffесts [13]' Foг ехamplе, in a fiеld of intеnsivе CLB thе optiсal
рroprгtiеs (е.g. rеfгaсtivе indех, сoеfТlсiеnt of absоrption, еtс,) of mattег bесomе spatial1y
modulated. Howevеr the mоst intегеsting Гrom the sciеntifiс and praсtiсal points of viеw is thЬ
ability of СLB to induсе iп mеdtum, and, in paгtiсular, in sеmiсonduсtors, sрatial . peгiodiс
struсtures - gгatings of vaгious typеs and natuге. Thе first tуpе oГ lasег induсеd gгatings arе
pегmanеnt gratings' Thеsе gratings aге сгеatеd by СLB геgisteгеd by usual methods, using silvег-
halide photogгaphiс еmulsions' photoсhromiс, thеrmoplastic and othег matегiаls and used for
pеrmanеnt hologram rесoгding (seе foг ехamplе [1a) Thе seсond tуpе oflаsег induсеd gratings arе
dynamiс oг transient gratings Тhеse gгatings disappеar aftеr thе induсing light sourсе (CLB)
switсhing off Thеsе gтatings havе bееn produсеd in a large numbеr of solids, liquids and gasеs,
arld arе dеteсtеd by diffraсtion oГa probing bеam or bу selГ-diffгaсtion ofthe light wavеs induсing
the gгating' Thе foгmation of tгаnsiеnt gratings is thе basis of rеal+imе hologгaрhy, phase
соnjugation, and foг-wavе miхing Il4]
Тhе spесial plaсе among lasег induсеd gгatings is oссupiеd by surfaсе gratings on
nonеquilibrium frеe elесtгons аnd anothег quasipaгtiсlеs' This gгatings foг thе first timе was
сonsiderеd for thе usual (non-fеггomagnetiс) sеmiconduсtors in Ref. Il1,12]' and foг thе
fегromagnеtiс sеmiсonduсtoгs in Rеf, [15.16]' flог thе сasе whеn the frеquеnсy of CLB satisfуing
thе inеqualitу Е <<ha <<с, ('с, is thе band gap), It foilou's that thе CLB whiсh do not
еxсhаngе thе total numbеr ofеleсtrons in semrсonduсtor оan lеad to a геdistгibution ofthеiг dеnsity'
IntсгГегеnсе еffeсts, pгoduсing bу CLB, lеad to nеw fеaturеs ofthе interaсtion ofa high.frеquenсу
field with fгее сarriеrs , рhonons and magnons Foгmallу, thе situations with a singlе
еlесtгomagnеtiс wavе and sеvеral CLB's diffеr fгom еaсh that sinсе thе pгobability of sсattering of
a сoгег from phonons, magnons and impuгitiеs in a sample illuminatеd with singlе an
еlесtгomagnеtiс wavе and in a samplе illuminatеd with sеvегal СLB, by sрatially modulation of
sevеral сLB thе probability of quasipaпiсlеs intегaсtion and also bесausе thе transpoгt еquation for
еlесtrons сontains a spatially modulatеd foгсе oГthе high-Ггеquеnсy prеssuге of thе fiеld of CLB's
aсting on fтее сaгriегs. Spatial modulation ofthе соllision intеgrals and thе forсе duе tо thс high-
{iequеnсy prеssuге on еlесtrons оausеd by intегГегеnсе еffесts сan gеneгatе nеw type of nonlinеariy
t97
.statiоanddуnamiсgratingsinthеsystеmofnonеquilibrium^frеееlесtronsinnormal(non-
fеrгomagnetiс) sеmiсonduсtoй and freе j1есtrons unJ*uJnon' in fепomagnеtic semiсonduсtors. In
thе diffеr from the non-magnetiс semiсonduсto'' ;;;йъ. Jеvotе for thЪ wеaklу оoupling with
magnons and phonons and-intensitу еlесtron.magnon ini.o.tion сan bе hеating not only еleсtrons
buйagnons too [15'16]. ihus, in FМSC w9 may ;'.;. thе nеw typе of gгatin8s - the grating on
nonеquilibгium magnols *a .Ь"pri"e with it, aj.thе magnon tеmperaturе сoupling aссoгdlng to tnе
Bloсh law magnet1zallon,'ь. йi"i"Г nonequiliЬгium magnetization'
Thе givеn aгtiоlе is dеvoted to rеsеarсh
"f
i"f];;;;; сi.в on optiсal propeгties of FМSС. The
сonsidеration ь.gin, *iti,iuау or inлu.n"е C.LB on сhaгaсte' of сonduсtion еlесtron movemеnt ln
thе FMSC. We wеrе th;;.;;;,;;" саlсulatеd th. ;;;. funсtion and quasi-еnегgу of сonduсtion
еlесtrons inthе fiеld.rёiв'.rt is shown, tьut oniь".onduсtion еlесtгons in the fiеlds of CLB aсts
thе Гorсе whiсh coггеspйJ'.ou prеssuгe ехeгtеd bv CLB оn thе еlесtron gas.
FМSС with
'aseг
induсеd gratings u,. of g..ui,ini.,.u in physiсs of dvnamiсal hologгams as
the nеw rеgistration mеdia, and.may havе.unу^int.i.,ting appiiiations at ihе various bгanсhes of
semiсonduсtor tесhnoiogу, nonlinеar optiс, radioih;;;;#;i::l":1l.ffjiJ*ni'ТJТt*fi;
;;x.,1;ч
.}fr
ж ж:*ж : :,:' 1Т T;li : HJ ТiJ: "''i.lffi il":' ж.i'ж'
.
;р;i ;.j
-
.;а Ьa g ;.еt i с
;;;;;;'ыйsс *i*йl.*, indu.еd grating sееms rathеr intегesting.
2.Wavеfunсtionandquаsi-enеrryofсonduсtionеlесtronsinF]!!SCinthеfiеtdofСLB
Let us сonsider thе motion of еlесtгons in FN1SС in an infinitе сonduсtion-band in thе field of
CLB. Thе CLB vесtor potential is given as | ; - \ (1)
А(r't1=I,l, сos\ol -k,r -Q,l
Herеthefrеquеnсу(,satisfiеsthесondition0)т>>1(risthе.еlесtronmeanfrеetimе)inthе
approхimatiоn oг i,ot'ofr.'.гг..ii,. ^mаss
Fьt.S-c aге a speсial tуpе of sеmiсonduоtors whiсh
oropегtiеs dереnd on ,ii.ini.,u..ion of еlесtгon..*i.ь
't.'.
quanta оГ magnetiс subsystеm . magnons.
tJsuallу a modеl а.,.,iьi"giБ"й,u.tion ofthе сonduсtion еlесtrcns with thе loсalizеd spins thе
so-сallеd s-d "*сt'ungi".!мr
r,."'.J-ill' тьi, йoс.t'.uiа.ntlу, сan dеsсribе the rеal physiсal
situation for йdе-ba;а.,йi"onJu".o,,
-in
a suffrсiеntlу adеquatе. waу. The effесt of the s.d
ехсhangе intеraсtlon ыii..""o'.tion "t..t,Ь]-.,,'.rin-,inu,.'
ih. d"g.n.'ution of spin and thе
сonduсtion band splitsint" .*"!lrЁ""o, h*i";ъifг";;;;;;;; oп.n'uйn' [з] So' thе speсtгum of
еlесtrons is givеn by \ (2)
€ pi,I ='i+;
^" :'^
whеrеA-/Sisthеsubbandsshift,1istьеs.dехсhangeеnегgу,.Sisthеmеanvaiuеofthе
loсalizеd spin' In thе isotгopiс еffeсtivе *u,, uip.,o*"ii1;;j;' й; ,i"njt.-"l..t'on operator is wтittеn
as
й =lГ Ь-9АF'l| _}а '
(3)
'- е 2m|' с .l /.
*n.l.n.";];,*"':;';::lъl1'}
еleсtrоn in FМSC in a high-frеquеnсу fietd of CLB is dеsсribеd
the Sсhrodingег еquation
(4)
198
rormal (non-
)пduсtoгs. In
,upliпg with
niу еlесtrons
hе gгating on
огding to thе
ЕМSC. Thе
:ovеmеnt in
: сonduсtion
i ..|CLB aсts
: ] logгаms as
s :гanсhеs of
:.so tool foг
:. Ьу highly
l-.: magnеtiс
:i СLB
: ''..е fiеld of
(1)
-е) in thе
:- ':s whiсh
. ]]agnons.
: - -<pins the
:: рhysiсal
: the s-d
(2)
-э of thе
; wтittеn
(з)
. . lсribеd
',vhеге e and m are сhaгgе and еffесtir,е mass of elесtron. с is thе veloсitу of light, and p = *iу1у
thе сanoniсal momentum opегatoгof thе еlесtгon' Тhе solution of Е g. (4) is
v,1'- (/, r)= z., .-o{, + ; l,\'|г,
_ 9 лtт ',,l.l, - +}"
}
*n.,. 2. = [1.l, ,t = [:.l arе thе eigеnfunсtions of thе spin oрегator o-t0, ( r,
By assuming that thе fiеld of CLB is adiabatiсallу inсiuded at tg = -х), rvе obtain frоm (4)
( \ ( oу,,,),(,.,.-,,,,,
.l
,j,:\'.j;il, *\.,i,')!.nt,
YР^ (г,1) = 2l't.-p]itлг]i i ',,,,-,|.т:?V,| ^ -:+t,lfi.. .),'Е " .', '\mсhoэ
)
,|вn,,-п'
1
( / . э \)| 1! n. \ р] Гt- l l I
ехp]- т| - = ] + --:_-. Т-.4,.4, t'оs[[t ,
_ k, F + q i - Ф , |+ пha |t |.,Lrl\2m 2 4mс-l -l -l
rvhегe "l(х) is thе Bеssеl funсtion,
(бi
ls
Ii r
i
..i, !
(8)
у '-- -/
- v - \ lt- - \ 'l
=Ztt,д \p,а poslit< k F -Р-'_ Ф, } .,.;,
t, \( T пs .\'in|k '| - tp ' l't:'
= аrсrti'''У r,д'Сos|k'7 +o'lt
'ra' t ! "')
I
I-Qi Q,'-Qr!
Fгom (6) it follows that thе timе dеpеny'еnсе o{ еlесtгоn 1."aVе funсtion in thе fiеid оi
еlесtгomagnetiс wavе has not оf thе tyре .*р(_ i';,,1l)' Тhегefсlrе, ц'е havе nо statiоnaгу state With
thе еnеrgу €Fl,+ А nеw quantum numbеr, the quasi.еnеТBУ Е;:L, dеsсгibing thе сonduсtion
сlесtгons inthеfiеldofanelесtromagnеtiс rvave[17] dеtегminеdfгопlthегelation:
Yрl,r (i,l * Гo ) = .-p{. _
л
Ь гt .1', lvu,.' (,-' r) Q)
,'"=* is a pегiod of thе СLB fiеld ) Bу соnrpaгing (7) and (5), wе obtain an ехprеssiоn for
quasi.enегgy ofсonduсtion еleсtгons in FN{SC undег thе ilе1d оfСLB '
Еiэt.{А,.n =* + *2А,i,с,",|p,
_i F l p, _ Q;'j+ nпa
From (8)'oneсansееthatthеquasi-еnеrgyiscеfinеdvrithinsizепЙtсо(n=0+1,+2,...').Тhevaluе
(4) (e)
сan bе сonsiderеd as thе mеan valuе оf quasi-еnеrg1' and thе r'aluеs, wltiсh aге ргоduсеd by thе
adсiitional nha can bе геgardеd as satеliitеs or.'photоn 'еpеаting..,
l9q
Intheоasеofthestandardparaboliсenеrgylawofеlесtronsandwhenthеamplitudеofеleсtriсal
fiеld of еlесtromagnеtiс wave Ё do.* not deреndof сoordinatе i Go=Ёnsiпat) wе find fтom
(s) and (9)
- p2 , Ь- +
е, Е:-
+ nha . (l0)
Е i,i'll,,n = Е p = 7;'' - i,',
Тhus,inthisсasеquasl.enrrgyisсonnесtеdonlуwiththеelесtromagnеtiсwavеwhiсhproduсesa
shiftof ЬE=е2Е3l\amсo,).Thеvaluе AД issmallandсanbеneglectedin(12). Butinthеfiеld
ofCLB'whitthespaсеdеpеndеnсеofvесtor-potеntialСLB,weсannotnegleсtthistегm'Inthis
сasе thе valuе o2 |l. - \. ( l l .
ЬE:=ЬЕa,iti =fu,,А,А,,сo,|$' _i,'Y *Ql -Ql (ll)
and,obviouslу,thequasi.enеrgy,willbесomeafunсtionsofсoordinatе/.ThevaluеAt,,-,hasa
simplе phуsiсal mеаning Lеt,s. сonsid-еr^T'""^.^T..n. of a сonduсtion еleсtrоn in thе FМSС in a fiеld
ofCLB.Foтstmpttсrтуshallbегestriсtеdсonsiderationofеlесtronmovеmеntinsub-zonеwith
o =t , In thе non.rеlativЬti. upp,o*i.ation, thе еquation оf motion of сonduсtion eleсtrons ls
d,v .i/;1).. Lt" ЙG',\ (12)
,-d7 = еL\r 'L '1- 7 аt
,. Y '.л
wtreге Ё(r,l) ano н(r,l) ше еlесtгiс and-magnеtic fiеlds of СLB, rеspeсtivеlу,
lfthе fгеquеn"у oг.ь.'jlв Ь suffrсiеntlу high' thе solution of еquation (13) сan bе wтrttеn as a
sum of slowly varying (in tеrms oГ tье os.ittu,r"" Ъ.л"а of thе сLв) function /o(l) and an
osсillation funсtion r'(l) 1frequеn cу (,)) Assuming tttat ilQ) is muсh smallег than the distanсe l
ovеr whiсh thе amplitude of thе СLB сhangеs noй',, l.,l .. . and neglесting teгms oГ thе oгdег
of|{zr!and]ioll|,byavеragingеquation(l2)ovегthеpегiodofCLB,weobtainanеquatiоnгor
it(l)'
s2; (,\ o2 t/- - L .^ 1 (13)
,# =
_
f,*,o,
н,А,'Сos|\k,-k, Гo
_ Q., - a i l
This is mеan that on ,ьJ.onаu"tion."t..,.on in thе field "'.::
thе-following force асts
e.Lу 7 А''сo'1|i,-k,,to-Ql_Ql' l' \.",
f =_grаdЬЕ:4,a, =_;;iL^J1LJ..""L|:. l J,v ,' '.'.
n,
whiсhis сoпespondingtothepressuг:*:l:;ьy
сr-вonthееleсtтons'asIl5'i6] Тhеехprеsston
for this forсе has ьееi obtainЬd .']l.:^!]:,iJi T1; ;' ;-'*.n:.,Il,1:l. #"ixll,x1Т'lн;
transpoгt еquations and quantum.mесhaniс^opегators for the сonst,
;е of
equations fo,.t".,,oi,,.u,i"*le;""' rn tь" п.ij oГCLB Тhis mеthod doеs not rеqulrе usa*
**.lun"tion. I'th;;.;.;iй:-ч:^1::жжi,жтЧ'xT'j:"}1l.i.1".,,:#:'.,':*.
It is possible to spесifу somе such.T:::::.,,
with diffеrеnt сtrarges or еffесtivе masses. In this
i fh. ',y"'J:ff?#:':}ж''JtН';fiТ?;il,
^, '
;;;;';й;. сhangе of distanсе bеtweеn
, llн:';''lli'"H'*.illHТ..iЩ*oliс, i.e' еlесtron еffесtivе mass havе diffеrеnt values tn
.'fi .".Yil'Jj"1#}::..1HHЩ,.'ч'^"l'i:Y"'^.'*:уff
:ffj?ii"tr1.o;hassomе
appliсations' гo, .l"u',iд.];;й; ьеlp oi the obtainеd wavе funсtion (9) onе сan studу thе
probabilit
statе p'o
in the fiе
еquations
method a
onеself t}
interactio
3. Тhе сl
Cr
symmеtгi
bulk of tt
whosе vс
ехpressiol
tr(; ,
tr2С,'
Rесеived
СLB thе i
jе aрproх
spaсlng I
''.''avеlеngl
:he bulk
.рproхimi;/
.]':еге
е]:
.2nt
: Е;-
200
оi еlесtriсal
lе find from
(10)
i pгoduсеs a
.: in thе field
:егm. In this
(l i)
rt--- - has a
,lSС in a fiеld
;-l-zonе with
.;::..ns is
(12)
:: .'\ rittеn as a
. ;ir) аnd an
..: jrstanсе |
т. :l thе oгdеr
г .-quation foг
(1з)
( 14)
i _ : еxprеsston
Е ] '. Оf quantum
: -. :um kinetiс
L -: - --.Гe usagе ol
*' ..,е first timе.
nЕ. _.sses. In this
Г : '.rсе bеtwееn
,E :: -itt values tn
]е has somе
.n studу thе
z - 12
W =[
еLo I Sin,k-,
\Zma )
pгobabilitiеs оf elесtгon transitions from thе statе desсгibеd by the сanoniсal momentum poto the
state p,o' eхposеd to a wеak potеntial И at thе timе /
(ls)
in the fiеld of СLB, This faсt offегs a possibility foг anothеr waу of сonstruсting quantum kinеtiс
еquations foг intегaсtion of quasi-partiсles in thе fiеld of CLB' In оompaгison with thе standard
method a quantum tгanspoгt еquation foг thе quantum-mесhaniс oрeгators [19-20], it allows onе
onеsеlf thе еffeсt of ехtегnal СLB fiеlds that aсts on thе еlеmеntary рroсessеs of quasi.paпiсles
interaсtions to be analyzеd' Тhеrе arе alгеady similar mеthods suggеsted, for ехamplе, in [8].
3. Thе сonduсtion еlесtгons mесheniсаl trajесtoгу in the fiеld of CLB
Considег thе instanсе whеrе thе outеr suгfaсе z:0 of FМSC is еxposed to two
symmеtriсally oгientеd CLB that сonverge in the
bulk of thе sеmiсonduсtor at a small angle 23 and
whose veсtor-potential is givеn bу the fotlowing
ехprеssion (Fig.. l )
А(r,t) =,а,Сo'(cх - k -,х _ k,z _,p1) r
А2Сo,(at _ k-.х - k.z * Qt)' Z1t|оу
(16)
Rесеivеd as a rеsult of an intегfеrеnсе thеsе tr,vo
CLB thе intеrfегenсе piсtuге with good рrесision сan
be appгoхimatеd by a standing lasеr wavе with thе
spaсing peгiod Z = 2c l2Siп9 (Аo is thе CLB
wavеlength in thе semiсonduсtor bulk) [i8]. Thus, in
thе bulk of sеmiсonduсtor, СLB may bе
approхimatеd by thе laseг standing wavе
Е = Eosin(k,')Sin(r:lt), (17)
. = a)- Ф-whеre Еo = Аt -: Аz aуeragе еlесtгiс fieldсc
intеnsity of a standing lasег wave (CLB). Now
wе shаIl analуzе the сharaсtеr of еlесtron motion
in the bulk of FМSС in a fiеld of CLB moге
dеtails. With this aim, we shall rе-wгitе (13) as ч
d2v,r(t\
= _\,|/У
o
dt'
t{igh frеquеnсy potential Исoпеsponding to thе o
interfегеnсe piсturе in the bulk of FМSC is
еqual to 0.
уr po - p, o, = *lir' . v'r,
",
(rl,r/lvr. k)'l
(18)
Fig.l. Intегfеrеnсe piсtuгe from two CLB when
thеу illuminatеd thе fгont surfaсe z:0 of FМSC
Samplе (L = ц l2sin 9 is thе period oi
interfегеnсе oiсture)
k
Fig. 2. Thе struсture of dimеnsionless high-
frequеnсy potеntial |Y l||g as a funсtion of
dimensionless сoordinate }z.
In a Fig. 2 the struсtuге of dimеnsio"':'.njчo
frequenсy Potential |ц lI4/o| щ = [ #. l li,
\ \tm(D ') )
shown.l:
Тhеrеfoге, thе high.fгеquеnсу potential W maу bе сonsidегing as a pеriodiс potеntial wеll for thе
сonduсtivity еlесtгons ';;;
jong tь. ОZ aх\s in thе inside of sеmiсonduсtor bulk.
Тhat a сonduсtion еlесtron, whiсh moving with veloсitу vo (vo : F;т;мis thе initial vеloсitу
ofсonduсtionеlесtroniпthepointz=0),alon.ganoZaxisсouldbеloсatedininsidеofapotеntial
*Ъri, "й"J
bу СLB, thе fulfrllment of a сondition is nесessarу
еVo lm <W (l9)
whiсh togеthег with a сondition l,'l .. r imposеs thе following rеstгiсtion on amplitudе of an
еlесtriс fiеld of CLB, сгеating
P9lеntr-al
wыt
.2 т t ^ r?0)
2o'! m|,'olе<Е0<<ma,Llе \Lwl
Тhus, if at сentегs of a potеntial wеll Е6 =0, thе сonduсtion еlесtгons with еnеrgу еqual eИo, is
lосatеdinsidеapotеntialwel.l,onwhiсhthеboundaгусonditions(20)arеехесutеd.
Now wе shall сonsider "
тn"".*.* oг u .onаu.iion .lесt.on inside of the potеntial *:ll,,:-:?:.
dеtails. Substituting tril.u"а irв) into (l2) and (13) wе obtain thе following equatlons tor
dеtеrminingzandх l - \. /.1\
2+ol|z=0, ,=_|J1'lаlo,)sinох' (2tl
where a" = g[,o l J\mc is thе elесtгon osсillation Гrеquеnсу inside of a onе-dimеnsional potеntial
wеll,pгoduсеdbуCLBThеfiгstofthееquationsundегnumbеr(21)isthе|rеeelеоtгonharmontс
osоillation еquation. Its solution
z = СtСosa,t +С,Sitla,t, Q2)
whiсh satisfies the initial сonditions Сt = 0, Сz = \,o l a" has thе foгm
z = (vo l a,)Sino,t. Qз)
Мakingusеof(2l),writеdоwnnowthееquations,whiсhdesсгibеthесonduсtionеlесtron
mесhaniсal tгajесtory as :
;=(,ot'}sin',,, ,=-(,u tr,l|1sin(a,,)'::Ч). Q4)
InaFig'3theсonduсtionеlесtronmесhaniсaltrajесtoгiеsinafiеldofCLBisshown.
х
0в
о
о
0
о
.o
.0
'ol
a
Fig.3. Thе сonduсtion еlесtrons mесhaniсal trajесtoгiеs in a fiеld of
meanings of paгamеtеrs.-^- . t', =|О,@zZmaxlc =t'z > О', Ь.сlэ lоl, =
СLB foг thе following
|1,сo,z^u*lc=|,z>0.
202
' wеll Гor the
riтial veloсity
of a potential
( 1e)
piitudе of an
(20)
:.:ual eИo ' is
''iеll in morе
Чuations for
(21)
::аl potеntial
:: r harmoniс
(22)
(2з)
: :r еlесtron
(24)
Depending on a гatio bеtv;ееn fгеquеnсу oГ a Сi-B Гte|d аl and a frequеnсу of osсillatton ofсonduсtion еleсtгons insidе a рotеntial rvеll а-l. thе сonduсtion еlесtгons mесhaniсal tгajeсtoгiеs
will be various' From thе Fig 3a, fог ехamрlе, ц,hgn jL
= ]O fоi]ows, that thе сonduсtion elесtгon
mесhaniсal trajeсtory insidе of a роtеntial well wiIl bе madе, It mеans that thе еleсtron altematеivbеing геflесted fгom wal1s of a potеntial wеll rviil makе inside otоscitiations with frеquеnс, ,.
.;;
a сasе when З_=|1 , fтom a Fig, Зb follows, that thе сonduсtion elесtron meсhaniсal tгajесtory
will bе opеn' It mеans, that har,ing madе some osсillations in insidе of a potеntia] wеll thе elесtrоnсan bе abandon and furtheг morе Ьnlу undеr thе aсtrvitу of a fiеld of CLB'Тhus, thе eleсtron in thе field oг ёI-в takеs paгt ,]-"ri."."".ry"in two motions' Namеlу, it
osсillates with thе fтequenсу со and amplitu a, а = !!э, in thе fiе]d of CLB and pегforms foгсеdпt(D -
osсillation at thе frеquеnсу .i).- << o of insidе оn onе-dimеnsional rvеil, produсеd along oZ rжisbу СLB
4. Sуstеm ofkinеtiс equations for eleсtrons аnd mаgnonsLеt us сonsideг а widе.gap donоr typе гйsс *i]ь mеan сaгriеr dеnsrty l,0 ln thе spin.wavеtеmpегaturе rangе piaсеd in an ехtегnal сonstant еlесtriс fletа Fo|iОz.Its from surfaсe is subjесtеd
to sеveгal CLBs, whosе fгеquеnсiеs satisfу thе inеqualitу в <<|l,''<<€g (sg is thе еnегgy-gap
width) Е]есtгons aгe сonsidегed to bе non-genегate, and thеir eneгgy in the СLB fiеldср <<JS G = F*еА(r-,l)u сis thе еiесtгon еlесtгomagnеtjс momеntum) Тhis inеqualitу makеs il
pоssiblе to сonfinе ouг сonsidеrаtion to a subzonе with o =i, so that the spin indех o mаy bеomittеd, In thе sесondаry quantization гергеsentation, thе HamiItonian of thе system of еlесtronsand magnons, whiсh arе subjесtеd to aсtion of thе ехtегnaleleсtгiс fiеld Fo
^"o '"
;,;";';;fгequеnсy CLB field aге intегасt ,'r'ith рhonоns, has the followins form:
I
н = 2|-l- pl, aJ:- lrzl ,^' ( a . )l--iiL пс, , z,n,
oi -,,ool'-d t.o )fi-яzа е +
Q5)
Е-С,q,oin l-,h; b4., - Й
"
* Й,, - Й., - Й,p,
'
-: . t1\wnere Аiand А'i, aге Furiег сomрonеnts of thе СLB veсtor potеntia| 7(|) and д,(r,,),
rеspесtivеly, С,n, is thе еlесtгon-magnоn intегaсtion matгiх еlеment taking into aссount both two.
magnon pгoсesses in thе fiгst-oгdег appгoximаtiоn of peгtuгbation thеory and onе-magnon
pгoсessеs in thе sесond apргoхimation |2], o;(аu) and ь;(ьu) arе сгеation and аnnihilation
opегatoгs forelесtгons and magnons rvith quasi-momеntum of land f , rеspeсtivеlу, H" and Н,
arе thе Hamiltonians for fгeе еlесtгons and magnons, геspeоtively ' fr.- descibеs proсеssеs oГ
intегaсtion bеtwееn magnons [18], and Й ", i, the Нamiltonian of thе magnon-phonon interaсtion
[1e]
In thе gеneгal сasе, thе kinеtiс еquations ior е1eсtrons and magnons are quantum еquatlons,and wе shаll dеrivе thеm on thе basii of quantum analoguеs of"thе miсгosсopiс distгibution
funсtion for еlесtгons / and magnons ff in Wignег гepгеsеntаtiоn. Thеm, from the еquations of
lwlng
_->0.
20З
motion foг / and ly' oреrators
distribution funсtions of elесtrons
with thе Hamiltonian (25), a set of еquations foг ordinary
Аr,F,t) and magnons м(r,d'l) is obtained in thе usual waу
'',,'u,.,.,,, lеt us сonsidег a set ofkinеtiс еquations for thе amplitudеs subjесtеd to frеquеncу
uu"'ugin'-(o t а), /olf ,F) anа /i
(0)(i
' 4). тьis sеt has thе following foгm It5,16]:
iцу-[,7^_! ^ L|z;,,i,'.o,(Е, -i,'| -o,_,, li +=,r,'fttol,"tol1
i сr ]-.
U
4mс1 e| |; J 1 J) Ur
Q6)
+ * = I ."v*o,'рtor }+ 1.. {,,.o), м(o' }* 1'' tN
(o)
}
oq or
WhеndеrivinBQ6)'itissupposеdthatbothе.nеrgyandmomentumofthееlесtгonsгеlaхon
magnons, and thе аi,р.,йnii* for еlесtrons and magnons aгe isotropiс and paraboliс'
Thеintеgralofelесtron.magnonсollisions/",,,maуbewrittеninthеfollowingformIl5'16]:
l =Ц , l:(,, u,,].,""
I,{,::lr
Ptt.l1r,a,{r-лi|]t,'u]l_}"
- еп h яfi., ;| ,,r* ]l.
л оо l 1r..)(., F)vt.)1;' 4,{r + мtol(;' 4)) J Q7)
6(P - E - F' - E'bG r - € P,
* Ф4 - a u,
* t,ha)
lпtеgгals of magnon-еlесtгon 1,,", magnon-phooon I.,, and magnon-magnon /,,n сollisions in
еxpliсit fоrm сan bе found , for ехamplе, in [15'16]
As follows fгom thе aпaiysis of thе sеt еquatrons-(26)' thе high.frщuеncу fiеld of CLB aсts on thе
FМSС еlесtron.'ugnon?y,;; i;l*" ways. гiгstiy, ihе еlеоtrons ехpегiеnсе an additional prеssurе
сausеd by thе CLB' Sесondly, I
"^
aod 1,, bесoпrе periodiс funсtions of i .It is this pеriodiс
vaгiation ofthе сLв prеssuге, alongsidе with thе pеriodiс dеpеndenсе of I ". and I." on /, that
сausеdthеfoгmationofsupегlattiоes.lasеrinduсеdgratingsinFМSCForthefiгsttimе,theу
wеrе disсussеd in [15,16], whеrе it was shown that thе systеm on non-еquilibrium еlесtrons and
magnons of a FМSС **p'. in а СLB fiеld foгmеd g,uting' of сшriег dеnsity пo, elесtгiс fiеld
intеnsitу,Е,еlесtronГ"andmagnon7)tеmpегaturеs,etс.InthесasеofinсidеnсеonthеЕМSC
surГaсe,ofonly,*o*uu.,symmеtriс{lуoгiеntеdbрams(16)thisвгa1n1sсojdb;rеPгеsеntеdas',.=-,,(|
" с, Ьos 2k,, z it,i't" 2k,, z\. F = Л. (1 + g, cos2k,. z + E,с sin 2k'. z I
т" =т!)(t.+Qo +Qtcos2k,-z+4,сsin 2k,,,\
,
(28)
I,, = г,!.)(1 + |Jo + Р l cos2k'. z + p,c sin Zk,.z }
неrе, rjo) and If) arе еlесtron and magnon tеmperaturеs in thе absenсе of thе CLB fiеld, Тhе
ехpгеssionsforamplitudеs€,'€,'rll,Р,|nthеgеnеralсasеhavеvеryawkwardfoгmsandarеglvеn
in [15] Thе сommоn сharaсtегistiс рropегty af с,,E', 1,'д, amplitudеs is that all of thеm tеnd to
zетo, when thе ехtегnal еlесtriс fiеld stгеngth inсrеasеs.
5. Еlесtromаgnеtiс wavеs diffraсtion on thе lаsеr induсеd grаting
of elесtrоn сonсепtration in FМSC
Now lеt
",
*"iи?.lь. ЪЪ.'й"'i'у оf thе propаgation of еlесtro.'uc"",:.:^1::'.:l':Y'.
with thе еlесtron сonсеЬtration grating, producеd Ь сr-Ъ Lеt a weak еlесtromagnеtiс wavе' with
thе polarization that ;#;;;"; СLЪ,.whiсh prоЪuсtion- a grating, рroрagatе in sеmiconduсtor
alons thе oХ.axis, W;;;;;"'; foг simpliсitу.that thе amplitudе of thе wеak eleсtromagnetlс wavе
;;;;"";;";;i. "oo'аinut.
i and is givеn by thе ехprеssion
.:' . ё.ё
:
:;lutic: _
ii tlh the bс
Тhus, us:ne
|r r (хJ
Sinсе in ouг
'.vith /-0 anr
еquations:
'*hiсh havе a
204
|г ordinary
usual way
) frеquеnсy
-l
Ь
(26)
:.s геlax on
r \!,. ')'
(2't)
:.: :isions ln
3 ::ts on thе
Е..:, рrеssuге
:.. -. pеriodiс
- :r i, that
s .т'е , thеу
::-::ons and
, : .::гic fiеld
,г ..е FМSC
р:..rtеd as
(28)
: :iid, lnе
] ]:e glvеn
* i-. tеnd to
Е = Е(х)е*p[(s'x + s.z - Ql)} (2e)
Wе сonsidегing геsonanсе сasе whеп S, =kt, and the frеquenоy of weak wavе Г) is сonsidеrably
higheг than the frequеnсy ofеlесtron сollisions
Whеn еlеctгomagnеtiс wavе pгoрagate in thе еleсtron gas in semiсonduсtoгs it produсed thеpeгturbation ofеlесtron vеloоity Дй, (and' thеrеfoге, рroducе thе additionаl еleсtriс сuггеnt) whiсh
may bе dеtегmined from thе linеarization thе motion еquation foг thе inсidеnt wavе (29)
ОЬi"
=, Ё
and сan be writtеn as
at m
^n"
= !:- E
Олt
Тhus, сuггent dеnsity i, induсеd bу wavе (29), now can be prеsentеd as:
i = еttЬi^ =,
е2 n(z) -
= i,, noГ
l * n,(,)]r. {)лt - -{lп|.,
no 1"
Substitution (32) into Маxwеll еquations foг thе wavе (29), wе obtainеd
o,Ё"э#=-Ч+ (33)с- с|. с. сI
aлd supposing that thе gгating of еlесtгon сonсеntгation, produсing by CLB already ехisting
n(z)= n"11 + {,Сos2k,,z + 6,siпzt,-,) and weakly elесtгomagnеtiс *u.,,. (29) only pгoduсing
small pегtuгbation of this grating, wе obtain
v.Е+}(о' _')Е=o'(€. еxp(2.ik,,z)+E"*p(-zit,,,))E' Q4)
| 1 4mtnе2 €nсo2.
where ai =-----!i--, ar =Чl. 6, =€, -i€z Fuгthег, using well-known pгoсeduгe the. €om 2с,
solution of equation (34) wе may be look in thе form
(30)
(31)
Е =Z E,(х)expft (s,х + k,z) + 2tk,,z),
with thе bоundary сonditions
l
с(o)= д-o ' дIlA = o
Thus' using thе еquation (34), wе maу bе гесеivеd thе nеxt сoupling bеtwееn funсtions
L, '|х |
+-zi,'9-4l(l+1)k?,El =o,(€'Ё' *Ф,u) (з7)dх, ' dх
Sinсе in our сase 16 .. 1i , the most signifiсant tеrms in thе abovе еxpansion of Е, (x) arе thosе
with /:0 and'i=-1' Мoгеovег, thе small value of the paramеtег |4| lеaаs to the following sеt of
*=-'*t,-,' +=-,#t,,еquatlons
(32)
(3 s)
(36)
Ir / \хJ ano
(3 8)
whiсh havе a simplе solution satisfying the boundaгy сonditions (33):
Еo = ЕФ,Сo,fчщ'l Е, -' = -iB- gto) 5in. (2}. ) С
205
Thеsolutions(39)dеfinestwowavеs,whiсharisеasеresultofdiffraсtionofaninсidentwavе(29)
on gгating of еlесtron """'j;,:
г,JJ'r"" Б1,.."ь"'li.irigii ьЫ', *ьi"ь turns out to bе a pегiodiс
;ff.i;;;f ;-cooгdinatе' тьe ietativе intеnsity of this wavеs
.,,'f "il6i'l
I lд.l' "'' |2k' ) rцol=_--'
I o lДo'. 6,,.[ #l , l-
[2/,, )
Thus,wесansеthattakеplaсеthеpегiodiсalеnergуtransfегfгomonеwavestoanotnеI'
dеpеndеnсе with сoordrnat" ,' o. thе pеriod oг,ьi, *uй propoпional i6i-. anа dеpеndеnсе with
лo,thatсonstantеlесtгiсfieldmaуbеproduоеthеvariationсharaсteтofdiffгaсtion,and,аtthе
fiхеd thiоknеss of the sеmiсonductor samplеs d ('<d) , maу bе сrossing from thе Bragg-
diffraсtion to anothеr tуpеs of diffraсtton,
6. Еlесtromagnеtiс wavе sсattеring in FМsс with lаsеr induсеd gгatings
l
Now lеt сonsidеr']*euк еlесtroйa^gnеtt;;;.';; йe polarization that diffеrs from thе
CLB failing from on tьЁ,.*i.""а"сtoт suгficе,:o r'' еlесtriс frеld сan bе writing as
Ь = it-'z)еxp(- iси) (41)
we now сan bе writtеn foгthe amPlrt:.-. * *;":.".::Т"."::,::y' nalogy еquations (34)'
n uY,-,n"equation (43) rve maу bе using pегturbation thеory
":' ":::,] :::
Bгagg resonan.. ,.*,on *n.n ,, :u,.,.! !.
(^t+0 thе paramеtегs whiсh desсribе thе
dеviationfromthеBгaggresonanсе)thisthеoryisnonсorтесtandwemaуbeusingthedуnamiсally
thеoryofеlес,,o.nugn..i.wavеdiffraсtionono.noJ"struсtuгes[20].Givеnthеfunсtion
Y asthе
sum
,n/.\_+ {я..*ot|itt+1).t., + 6!z\+e ,ехp{-i[(zl+r)t., -а]z}} (44)
whеre 6_+0 thе,'.ll;.,;;.'еr wh1сь,wr^r] bе dеtеrminе. Just as takе plaсе thе inеquality
(с,,lk|')...1inthe*"'t^olgivеupоnlуtheteгmswith/=O,i'е.usingtwowaveappгoxtmatlon:
9(z) = вo ехp{l(&', + 6)z}+ i. е*p{- i(lс,,'- a)z\. (45)
SuЬstituting(45)rnto(43),wеdеtегminеth.p.,u*"t.,6andthеamplitudеsrеlativityЛ"Гalling
Using thе designation
Ё('' z)=9(z)еxp(is'х)
(42)
8n and rеflесtion Сo wavеs
;\" o =9n= ?,1 =_Щ{:D (46)
Notе that thе sign д i,l!,ь" .^o"..lJ"'чu)::iТT:. Ё пnit..oгtье solution (45) at z -+ со and thе
-"il:Т
*Jlr::;:r*i..тн;;ъ't}l1i::}':1x}1J,HJ';;;"
.lесшomagnetiс wavе on thе
surfaсе z:0 in sеmrс*d;;;;;,.;й a p",iodi.ai ;;;s of еlесtгon сonсentгation, pгоduсеd bу
206
-.: lvave (29)
е a pегiodiс
(40)
: ] anothеr,
::':еnсе with
: з:1d, at thе
' :.:е Bragg-
Е3\
]::. from thе
(41)
(42)
шi- :.s (34):
CLB, Wе dеtеrmine the еleсtriс field of thе wеakly inсident wave in vaсuum (aссoгding with thегеfleсtion wavе fields) as :
E,(r,t)=Е(o){ехp[i(ll,'r +u,z)]+to eхp[(и'r-и,z)]}eхp{-tо} g7)
whегe a, = ",(r1
tu,,\
": =(+), *
tj -("., _1Ь",,
S. = k,. + Д,o, Ьk --> 0
\ - .i ao
Continuitу of the funсtions (43) and (47) and thеir dеrivаtivеs at the point z=0 togеther with thе
ехpгеssion (46) епables us to dеtегminе the сonstants lo and Bo and refleсtion сoеffiсiеnt iдo|.Foг ехample' thе obtainеd геfleсtion сoeffiсiеnt to bе еqual too
,Rol'= /^o\
(i'. *u,), -(k,. -tt,)'tД'l, - @; -,'i\n' * к;) tao,,
Fгom (48) follow the Bгagg геsonanсe геgion whеn |л,|' = 1 the wеaklу wavе rеflесtion сoеffiсiеnt
lлol, =1 and takе plaсe thе full гeflесtion, Somеwhat involvеd сalсulation givеs thе following
еxpression foг thе rеflесtion сoеffiсiеnt neaгly the Bragg rеsonanсe геgion:
From (49) whеnсе it follows that at suсh At r-vith inсгеasing fiеld d thе rеflесtion сoeffiсient will
сontinuouslу pass fгom some initial valuе (if initial value smallеr lл. li. i to its limiting valuе,
lлoIi. сoпеsponding to thе геflесtiоn сoеfТlсiеnt of thе homogеnеous (non illuminatеd bv CLB)
sеmiсonduсtor matегia] :
/ | ,, \,- ,r | |
lR.lu. = lii) (so)
Note, that thе dеpеndеnсiеs {,,{, and 6 of лo allow, сhanging d at the fiхed A.&, сhangе
|лo|,aom 1 to its limiting valuе ]R.|- ' Intегеsting, that thе depеndеnсe its fгom Лo dеtегmine not
onlу thе value of A,t and its sign too' IГthе sign of Ьk and {' is еqual thеn |лo|, havе minimum at
*_а' k',,+u| €,, -€:-_т u'- a (5I)
Тhis faсt сonfirm thе numeriсal сalсulations, prеsеntеd on Fig 4 and Fig.5 , wherе one сan sее thе
геsults of thе numеriсаl сalсulations thе depеndеnсies of thе rеflЪсtion сoеffiсiеnt on thе
paгamеtегs Ьk aod Fo '
Fгom the analysis of fic4 onе сan sеe that
пo-7О|9сm-|, o)=5.l0l5s_l, Z=05.10-2r-/, Fo=2,|o3V lсm thе
dесrеasе up to thе minimum equal to 2.547 ,ю-1 at Ьk = _o.2 Г211.
(4e)
(43)
:'еaгly the
.:гibе the
:.amiсally
P as thе
, (44)
:.еquality
-ratlon:
(4s)
.:, Гalling
(4б)
- and the
-=onthе
-;cеd by
in thе Еuo at
reflection оoеffiсiеnt
207
.з i l: t'
дк
Fig.4. Thе dеpеndenсe of thе ]Лo1, oГthe
paramеteгs A} ' Foг the valuе A,t intгoduсе thе
maгks' 0 - 0 2,5- (.0 50), 10 - (-0 22). 15 _ (-
0.2з 8)
Fig.5. Тhе dеpеndеnсе |Лo|' of thе d
(KViсm) Curvеs 1 - tlk = 0.3 ,2 - Д,t = 0 1' 3.
At=-01
i*
f
.а
on Fig. 5 one сan sее the геsults of thе numегiсal сalсulations еleсtгic field deрendenсe on |,Ro |, in
fегromagnеtiсsеmiсonduсtorЕuo forthеdiffеrеntvaluеsofthе tsk=О3, 0.1' -0'l.
Fгom thе analуsis of Fig'5 onе сan sее (сuгve 3) as thе Ьk =_О'l' |Лo|.rеally slowly inсreasing
with inсrеasinc of Лo fгom ]лo|' = 0,3 and set to |л,!|- -О'4О26 ' As thе A* > o' whеn thе initial
valuе of the rеfleсtion сoeffrсiеnt Iл.li.. ,lлoi|- onе сan seе only slowly inсrеasing iRoi, {сurues t
and 2).
iьu,,, *. havе сaпiеd out a study of the optiсal phеnomеna in the FМSС with a pеriodiсal
struсtures - gratlngs on nonеquilibiium quasipaпiсlеs produсing by сohеrеnt light beams. Rеsults
of this study allow thе following сonсlusions:
1, As a result of the еlесtтomainеtiс wavеs diffгaсtion on thе pегiodiсal grating of еlеоtron dеnsitу
in sеmiсonduсtoгs, appеars two waves pгopagatе along oХ-aхis and takе plaсе thе pегiodiс
еnегgytransfегfгomonеwavеtoanotheг,depеndеnсеоncoordinatе'
2' Тherеfleсtion сoefГrсiеnt |Ro|' undеr сonditions ofBragg rеsonanсe depеnds indirесtlу on thе
strеngth of heating fiеld' on thе angle of impingе wavеs and on thе paramеtеrs oг
sеmiоonduсtoгs. Varying those and thе valuе of Лo ' onе сan dесгеasе thе rеfleсtion сoеffiсiеnt
|лo|', iе. makе sеmiсonduсtoг..antiгеflесtivе''' as wеll as to inсrеasе it up to the valuе lеading
to almost.total rеflесtion of thе еlесtromagnеtiс wavе from outеr suгГaсе of sеmiсonduсtoгs.
3, Тhе light rеflесtion сoеfftсiеnt !лol. at thе Bгagg геsonanсe aгеa dеpеndеnсе at thе сonstant
hеating еlесtгiс field tq-. . Whеn this field inсrеasing up' the геflесtion сoеffiсiеnt is slowly
inсreasing too, as thе A/r=-0,1 rеfleсtion сoеfftсiеnt in FМSC Еuo rеally inсгеasing with
208
l
-li
I
i
I
i
l
ъ
=
,.
inсгеasing f from |Дo|, *о 3 and sеt to |л.|j. =О'4026' as the Д* > O, when the initial valuе
of rеfleсtion сoеffiсiеnt
|Лn ll' ' tл. li- , onе сan seе only slowlу inсгеaslng
|лo l
,
7. Conсlusiоn and outlook
In this геport some nеw гesults obtainеd гесеntlу in.the thеory of kinеtiо and optiсal phеnomenain FМSC on strong eхtегnal сonstant еlесtгiс fiе]d and high.fйе;;| fiеlс of сohеrеnt light beams(CLB) have beеn surveуеd. Thе appгoaсь ь"'.а
"".ь..Т."."Ё;;;;;' of thе system of quantumkinеtiс еquations for intегaсti^on.qu.'ip.п;.t.s
'in
the ;.;;;-;;;;al fiеlds, whiсh, as bееndemonstгatеd, maу bе su-с:.щl using.fo. iйе се.sс.iption
"u;io";;l;nomеna,s in FМSС underhigh-fгequеnсу field of СLB' Thеrе i, ;"' *."y.g . Ь.li.".lь.iйJi.u"lop'.nt of thе thеory ofnonlinеaг and nonеquilibrium phеnom.nu inЁмsс under intеnse iiЬЪыа, is intегеsting not onlyfrom thе point of view, of сonsideгing й possible nе* mесhaшsms of thе сrеatinя thе
ffi:H:fjЦъ.ж.l
and nonlinеar рh;o;;n;. but also to iь.-|.uoi.al apрliсation oг-th.sе
Ь.9y..n"y .lJ;;;l;,:.:;'i::l,,,J.:;J'*il:,d;l!,l'...u,'n* nе* .iui..iut, ."j а.'i... й' йlgь-
FМSC aсquiгеs nеw
ч:oр.Ii:'. in a high-fг1q.u.n:y ClP fiеld fn paгtiсulaг, thе еffесt of high-fгеquеnсу CLB fiеld on jh.. сollisions b;il.;; quasipaгtiсles in гМЪс Dесomе lmpoгtant at thеquanta еneгgy of СLB fie|d |tсо moгe of thе al
take plaсе tti" .гг..йi-:.i.1:.;;;jй;;,"#,i-.Т::ll;., *fiI,'3;,T#;.""i3жi.:.il:,.l;as the intегГегеnсe еffbсts apреar thе spatial modulation of thе с;Llision intеgrals and high.fгеquenсу prеssuге on еlеоtrons тьu', ii ьrrows fгom thе foгеgoing that thе СLB produсe rnFМSС a statiс and dynamiс pеriodiсal siruсtuгеs - gratln8s (supегlattiсes).
. Pгesеnсе оf this gгatings es.sentiallу сhanging-thе -physiЬar
p.-opй,., of FМSC. Gгating ofеlесtron сonсеntration еssеntiall1, ехсhangе ihе optiсai i.op.n;.,.м semiсonduсtoгs. on thisgrating may bе takе plaсе thе diffгaсtion oТtь. *.uщ.r".t.iйujn.й *uu., whiсh pгopagatе atthе еntеr of thе sеmiсonduсtoг' As thе rеsult oitь;. аiгг,*tio" up;;;;i;ъ wаvеs, and takе plасе thерeriodiс еneгgу transfeт from one wavе to йtь.. As thе p"i"J
"ilш, wavеs dеpеndеnсе oГсonstant eleсtгiс fiеlds it maу be pгoduсе thе variatiоn oг tье iiггiaсtion сh....t.., and at thе nехtfiхеd thiсkness of thе sеmiсonduсior samplе, may ьeсrossing f.o' th. в.agg difТraсtion to anotheгtypеs ofdiflгaсtion. Thе сoеffiсient ofеlЁctiomagnеtiс wаvе геfleсtion foг thе outeг suгfaсе of thеsеmiсonduсtors undег thе сonditions^of Bгagg геsonanсe dеpеnds indirесtly on thе stгеngth ofheating fiеld, high-fтеquеnсy fiеId оf СLB' ;; the. angle ii.t;pъ;;';nd on the paгametегs oГsеmlсonduсtors. Varying thosе and the vaiuе of elесtiiс леrа !t.е.щtь , onе сan dесгеase thегеflесtion сoеfТ.iсiеnt' i.е. make sеmiсonduсto. ..unti..л..ii;;'".;.;;ii.;s
to inсrease it up to thе
;i.:*т;::loalmost
total rеflесtion of the wеakly еlесt.omagrteti. *a'е from thе outеr suгfaсе
Ciгсumsсribеd in this paper, thе methods of theoгеtiсal invеstigation of еlесtгiсal and optiсalpropегties of FМSC with spatiallу - pегiodiс nanostruсtuгеs - laseг induсеd gratings onnonеquilibгium еleсtrons and.magnons сaпy rathег geneгal сharaсtег and are not гendеrеd .on.,.t.]Thеrеforе thеy сan be aрplied foistudy of iwidе сliss of tlrе;;;;,;й;"mеna in FMSC, сausеdby influenсе stгong еlесtгiсal' magnеtiс and intensivе high.frеquеnсy CLB fiеlds' Thе fuпherdеvеIopment of ехаminations in this diгесtion now lеaves Ъn u n.* iJvet. somе moге years agoinvеstigations in thе field of physiсs of FМSC сaгriеd, in main, onty sсi"ntiл" interest' Fог Сuriеtеmpегаturе of thе majority from them did not eхсeеd lOoli and the pгoblem on their widеintгoduсtion in praсtiсе did not stand' Now thе situation *u,
"u,Jiiui.Jьangес. With oссurrеnсesomе yеars ago of new ,.high-tеmpеraturе.'
fепomagnetiс sеmiсonduсtoгs on a basis on LaМnoзand diluted magnеtiс sеmiсonduсtors (Ga, Мn)N and (Zn, Мn)o, and etс., whiсh havе Сuriеtemperatuгe above at room tеmpегatuгe (T"> зoOK) [1] intегеst.oo Ьug".'i. and, in partiсular, toFМSС haгdlу has inсrеasеd. Norv ц,е stand on thе vегge of a .,magnеtoeleсtгonrсs',
геvolution. in
.; =o I 'l-
l^ ll'
:< rn 1..(ol rn
.
..:nсrеaslng
:е. thе initial
l .
(сuгvеs 1
: оегiodiсal
:i::.s Rеsults
х'::n dеnsitу
. -. ^-";^ni^
ir:::1у on thе
L.1]]еtеrs oг
г:эеffiсiеnt
'. -е lеading
ш: -::ors.
[ .-: сonstant
r' s slowly
в:..rng with
209
whiсh thеsе nеw phenomеna will bе ехploitеd in deviсеs сombining magnеtlsm with traditional
еleсtгoniс elеmеnts' Тhе.ехploration of spin рolaгization of сarгiеrs Ьpгеsents not only dеpaгtuгеfor the fiеld of magnеtism and magnеtiс matеrials but also a nеw diгeсtion for thе field ofеlесtгoniсs - spin-dеpеndеnое еIесtгoniсs' Now alгеady proposеd a numbег of nеw solid-statе
dеviсes, using еleсtгon spin, foг ехample: spin-polaгizat;on iight.еm;tting diodе, spin tгansistor,
ma8nеtoгеsistivе гandоm-aссеss mеmory сhips, magnеtiс field sеnsors. etс,
All abovе-stated аIlows to appгovе, that thе fuпhеr dеvеlopmеnt of invеstigation of influenсe oflaseг radiation on phуsiсal propегties of fеrromagnеtiс sеmiсonduсtoгs now Б..o,n., u..y u.iuur,
both with onlу sсiеntifiс, and with pгaсtiсal oГpoints of viеw.
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-
in Rеsistivеly in Magnеtorеsistivе La-Ca.Мn.o Films /Jin S.,
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| id | oai:ojs.pkp.sfu.ca:article-59 |
| 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/b7/3cc9ebdd552385348080278e7e0accb7.pdf |
| spelling | oai:ojs.pkp.sfu.ca:article-592018-11-27T09:42:39Z Optical properties of ferromagnetic semiconductors with laser induced surface gratings Optical properties of ferromagnetic semiconductors with laser induced surface gratings Optical properties of ferromagnetic semiconductors with laser induced surface gratings Semchuk, O. Yu. Grechko, L. G. Willander, M. Karlsteen, M. This article introduces the basic physical concepts of laser radiation influences on physical properties of ferromagnetic semiconductors (FMSC). A system of transport equations is derived to describe the electron-magnon system in a FMSC illuminated with several coherent light beams (CLB) along with a static heating electric field. It is shown that interference of CLB in FMSC has the effect that several parameters of nonequilibrium electrons and magnons exhibit superlattice behavior. The depth of modulation of the parameters describing superlattices is estimated. Propagation and diffraction of an additional electromagnetic wave in a FMSC with a gratings induced by CLB is considered. The light reflection coefficient and the refractive index of FMSC with laser induced gratings are calculated. This article introduces the basic physical concepts of laser radiation influences on physical properties of ferromagnetic semiconductors (FMSC). A system of transport equations is derived to describe the electron-magnon system in a FMSC illuminated with several coherent light beams (CLB) along with a static heating electric field. It is shown that interference of CLB in FMSC has the effect that several parameters of nonequilibrium electrons and magnons exhibit superlattice behavior. The depth of modulation of the parameters describing superlattices is estimated. Propagation and diffraction of an additional electromagnetic wave in a FMSC with a gratings induced by CLB is considered. The light reflection coefficient and the refractive index of FMSC with laser induced gratings are calculated. This article introduces the basic physical concepts of laser radiation influences on physical properties of ferromagnetic semiconductors (FMSC). A system of transport equations is derived to describe the electron-magnon system in a FMSC illuminated with several coherent light beams (CLB) along with a static heating electric field. It is shown that interference of CLB in FMSC has the effect that several parameters of nonequilibrium electrons and magnons exhibit superlattice behavior. The depth of modulation of the parameters describing superlattices is estimated. Propagation and diffraction of an additional electromagnetic wave in a FMSC with a gratings induced by CLB is considered. The light reflection coefficient and the refractive index of FMSC with laser induced gratings are calculated. 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/59 Surface; No. 4-6 (2001): Chemistry, Physics and Technology of Surface; 196-211 Поверхность; № 4-6 (2001): Химия, физика и технология поверхности; 196-211 Поверхня; № 4-6 (2001): Хімія, фізика та технологія поверхні; 196-211 3154-8091 3154-8083 en https://surfacezbir.com.ua/index.php/surface/article/view/59/58 Авторське право (c) 2001 O.Yu. Semchuk, L.G. Grechko, M. Willander, M. Karlsteen |
| spellingShingle | Semchuk, O. Yu. Grechko, L. G. Willander, M. Karlsteen, M. Optical properties of ferromagnetic semiconductors with laser induced surface gratings |
| title | Optical properties of ferromagnetic semiconductors with laser induced surface gratings |
| title_alt | Optical properties of ferromagnetic semiconductors with laser induced surface gratings Optical properties of ferromagnetic semiconductors with laser induced surface gratings |
| title_full | Optical properties of ferromagnetic semiconductors with laser induced surface gratings |
| title_fullStr | Optical properties of ferromagnetic semiconductors with laser induced surface gratings |
| title_full_unstemmed | Optical properties of ferromagnetic semiconductors with laser induced surface gratings |
| title_short | Optical properties of ferromagnetic semiconductors with laser induced surface gratings |
| title_sort | optical properties of ferromagnetic semiconductors with laser induced surface gratings |
| url | https://surfacezbir.com.ua/index.php/surface/article/view/59 |
| work_keys_str_mv | AT semchukoyu opticalpropertiesofferromagneticsemiconductorswithlaserinducedsurfacegratings AT grechkolg opticalpropertiesofferromagneticsemiconductorswithlaserinducedsurfacegratings AT willanderm opticalpropertiesofferromagneticsemiconductorswithlaserinducedsurfacegratings AT karlsteenm opticalpropertiesofferromagneticsemiconductorswithlaserinducedsurfacegratings |