Acoustomagnetoelectric effect in a degenerate semiconductor with nonparabolic energy dispersion law.
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1 Acoustoatolctric ct i a drat sicoductor it oarabolic ry disrsio la. N. G. Msa Dartt o Matatics ad Statistics Uirsity o Ca Coast Gaa. Abstract: Surac D acoustoatolctric ct SAM ad bul D acoustoatolctric ct AM a b studid i a drat sicoductor it oarabolic ry disrsio la. rssios ar obtaid or t acoustoatolctric ilds i.. τ << ad stro >> SAM ad AM udr a τ atic ilds. It is so tat SAM ad AM dd o t oarabolicity aratr i a col ar. Uli AM ic cas si t atic ild is rrsd or t coditio π < θ < π. SAM tis oo occurs r θ satisis Kyords: Acoustoltric Acoustic oo Acoustoatolctric drat sicoductor Acoustotral lctctrocaical costat Doratio ottial.
2 Itroductio acoustic oos itract it coducti lctros it lads to t absortio or aliicatio o acoustic oos [] acoustolctric ct A[ 9] acoustoatolctric ct AM[-5] acoustotral ct [6] ad acoustococrtratio ct. Acoustoatolctric cts ic cosists o ratios o lctrical currt duri t roaatio o acoustic oos trou a coducti atrial lacd i lctrical ad atic ild ar did i a sall rio i t sctru o t oo ubrs. It ca tror b usd i dtrii ry ital ioratio about t atrial udr study.. coductiity du to diusio o cars lctrocaical costat doratio ottial ad ay otrs. T oo also as is alicatios i dic roductio. T AM as irst rdictd tortically by Gribr ad Krar [] ad obsrd ritally i bisut by Yaada []. Sic t so ors a do o it to udrstad t oo. sti ad Gulya [] studyi tis ct i a ooolar sicoductor oticd tat AM ct occurs aily bcaus o t iddc o t lctro rlaatio ti o t ry i.. τ ad tat τcost t ct aiss. I [] sti aai attributd t scattri cais or t aarac o AM to t ilasticity o t lctro scattri by otical oos at lo traturs. T ddc o t AM o t aisotroy o t cti ass ad rlaatio ti as also b rortd i [8]. It is itrsti to ot tat tr ar uit a ubr o rits to istiat t ct [9 - ]. I all ts ors t disrsio la as assud to b uadratic. T irst or r Ka s oararbolic disrsio la as usd ca b oud i []. I tis ar t ddc o t AM ild AM o t oarabolicity aratr T is ry dirt i a τ<< ad stro τ>> atic ild. I a ilds t AM dcrass o icras o ras i stro ild AM icrass it t icras o.
3 Rct or o tis ct by Kaao t al. [] oud out tat t ct is ry ssiti to t structur o t lctro sctru. As a rsult it ca ist at τcost. T ct as also b studid i t uatu ri by Galri ad Kaa [] ad Marulis ad Marulis [4]. Msa t al a studid t ct i sicoductor surlattic [5]. Tir rsult is siilar to tat obtaid by [4] or uatu acoustoatolctric ct. I tis ar sall cosidr AM i a drat sicoductor it oarabolic ry disrsio la. sall obtai t ral rssio o AM ad t aalysis o t rsult. T ar is oraizd as ollos: I sctio rst t calculatio ad ral solutio ad i Sctio discuss t rsults ad dra so coclusios. CALCULATION sall us Ka s odl or ostadard ry disrsio la ic is i as 8 >> i.. i << obtai t stadard arabolic ry disrsio r 4 Cyclotro rsoac rit sos tat t cti ass o lctro at t botto o t.. coductio bad i ISb is sral tis sallr ta t r lctro ass
4 4 c i ca b lctd ad so bcos 4 4 ad bcos 5 ro s 4 ad 5 or ostadard ry disrsio la i t aroiatio >> is ritt i trs o lctro otu as 6 r is i as 7 r is t bad a ad is t cti ass.
5 or surac acoustoatolctric ct sall cosidr t coiuratio r t acoustic oo atic ild ad t asurd cosidr t situatio r o a lctro ad t sol t itic uatio SAM li o t sa la. sall urtr l >> is t acoustic aubr ad l is t a r at [ ] r π {[ ] δ τ ρ s 8 δ } r is distributio uctio ρ is t dsity o t sal s is t locity o soud is t costat o t doratio ottial τ is t ddc o rlaatio ti o lctro o ry ad c is t lctric car is t atic ild is t ass o lctro as i i 7 ad c is t sd o lit i acuu. is t ry o t lctro as i i 6. It is iortat to ot tat t uits bi usd ar suc tat ad r Plac s costat diidd by π ad is Boltza s costat. To sol 8 ultily it by currt dsity R t olloi rssio. R τ [ R ] Λ X δ ad su it or. obtai or t artial 9 5
6 6 r R δ Λ δ { s X δ ρ π } δ δ I t liar aroiatio o ad ad cosidri as a uilibriu distributio uctio trasor t suatio ito itrals ad t itrat or t srical coordiat to obtai t olloi rssios or Λ ad X. s ρ Λ ϑ Γ X s 4
7 7 r 5 ad ϑ - st uctio ad t coicit o absortio o soud i tis cas bcos πρ s Γ 6 No soli 8 it t l o ad 4 ad cosidri t currt dsity j as d R j 7 obtai { } { } ] [ ] [ j s Γ 8 r >> << > < l u c τ τ ad
8 8 r π > < ad >> << ; ; τ τ u Cosidri a lar coiuratio r t acoustic oo is dirctd alo X ais ad t atic ild lyi i t XY la. T surac acoustoatic ild SAM ill b aralld to t Y ais. Assui tat t sal is o i.. j soli [8] ill i SAM as ollos: si SAM θ 4 r is t acoustolctric ild.
9 Discussio T colity o as aalysis uit diicult. Tror sall cosidr scial cass o it. τ <<. t atic ild is a i.. T rssio or SAM i rducs to SAM < uτ < uτ si θ { < uτ ><< τ >> ><< τ >< uτ >> < uτ > << τ > > ><< τ >> } < u > τ >>. t atic ild is stro i.. SAM << >> << τ >> < u > < uτ > si θ ro ad it ollos tat i a a atic ild SAM is roortioal to ils i a stro atic ild it is iddt o. or ad t ry disrsio turs to arabolic ry disrsio la ad trasors to t rsult obtaid i [4]. urtr or drat sicoductor r τ is i as τ τ 4 T 9
10 Isrti 4 ito ad ad soli atr cubrso aiulatio obtaid or a ild τ<<. si µ θ c SAM { } r T y y τ µ ; ; ; ; T T d ν ν υ 6 6 is a ri s ralizd Itral alus o it ca b oud i [5] or stro atic ild. si θ SAM 7. ν ν
11 To coar t surac acoustoatolctric ct D it bul acoustoatolctric ct D sol 8 usi t olloi coiuratio OY OX OZ AM obtai or t a atic ild <<. µ o c AM 4 8 ad or t stro ild >> τ µ o c AM 4 µ ν 9 obsrd tat uli AM r ca o si occurs t atic ild is rrsd or SAM ca o si occurs r it satisis t coditio π θ π < <. ially or τcostat 8 ad 9 bco > < > >> < ><< < u u u c AM µ
12 τ or >> ad µ AM c < u > << >> < u >< > << >> < u > < u > ad r irst obtaid i []. I coclusio a studid acoustoatolctric ct i t drat oarabolic sicoductor or bot D ad D cass. sod tat oarabolicity aratr i a ry col ar. Uli t atic ild is rrsd or π θ π coditio < <. SAM ad dds o t SAM AM AM ic cas si tis oa occurs r θ satisis t
13 Rrcs. G. M. Sl Q. A. Nuy G. I. Tsura ad S. Y. Msa Pysica Status Solidi b S. Y. Msa.K.A. Alloty ad S.K. Adjo J. Pys.: Cods. Mattr R.. Partr Pys. R. B J.M. Silto D.R. Mac V.I. Talyasii M. Galri Yu M.Y. Soids M. Pr D.A. Ritci J. Pys.: Cods. Mattr L 5 5. J.M. Silto V.I. Talyasii M. Pr D.A. Ritci J... rost C.J. ord C.G. Sit G.A.C. Jos J. Pys.: Cods. Mattr L 5 6..A. Maaø Y. Galri Pys.: R. B S. Y. Msa.K.A. Alloty ad S.K. Adjo J. Pys.: Cods. Mattr S. Y. Msa.K.A. Alloty ad N.G. Msa J. Pys.: Cods. Mattr S. Y. Msa.K.A. Alloty ad N.G. Msa. Arobotu G. Nrua Surlattic ad Microstructur A.A. Gribr ad N.I. Krar So. Pys. Dolady 965 Vol.9 No T. Yaada J. Pys. Soc. Jaa M. sti ad Yu. V. Gulya So. Pys. Solid Stat 967 Vol. 9 No 88. M.I. Kaao S.T. Mύlyut ad I.M. Suslo So. Pys. J..T.P A.D. Marulis ad V.A. Marulis J. Pys. Cods. Mattr S. Y. Msa.K.A. Alloty ad S.K. Adjo J. Pys.: Cods. Mattr S. Y. Msa ad G.K. Kaa J. Pys.: Cods. Mattr V. L. Malic ad.m. sti iz. T. Polurood A.A. Lii Iz. Vyss. Ucb. Zad. iz M. Koai ad S. Taaa J. Pys. Soc. J Yu. V. Gulya V.V. Prolo ad S.S. Tursuo iz. Trd. Tla V.V. Prolo ad A.V. Grs iz. T. Polurood V.A. Ldo Russia Pysics Joural 98 Vol No 4. Yu.M. Galri ad V.D. Kaa iz Trd Tla M. sti So. Pys. Solid Stat B.M. Acro Kitic ooa i sicoductor. Lirad; Scic. 97 P
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