Peculiarities of THz-electromagnetic wave transmission through the GaN films under conditions of cyclotron and optical phonon transit-time resonances

Transcription

1 Semconducor Physcs Quanum Elecroncs & Opoelecroncs 013. V. 16 N 1. P PACS 7.0.Dp H; Peculares of TH-elecromagnec wave ransmsson hrough he GaN flms under condons of cycloron and opcal phonon rans-me resonances V.V. Koroyeyev V. Lashkaryov Insue of Semconducor Physcs NAS of Ukrane Deparmen of Theorecal Physcs 41 prospec Nauky 0308 Kyv Ukrane; e-mal: koroeev@ukr.ne Absrac. The heory of TH radaon ransmsson hrough he flm of compensaed GaN of cubc modfcaon under acon of elecrc and magnec felds has been developed. In he TH frequency range specra of he dynamc mobly ensor have been obaned for appled seady-sae elecrc felds of several kv/cm and magnec felds of several T. The specra of ransmsson reflecon and loss coeffcens have been analyed for he Vog confguraon used for he appled felds. I has been shown ha he ransmed wave becomes ellpcally polared and he specra of polaraon characerscs such as ellpcy and roaon angle of he large as of polaraon ellpse were nvesgaed under condons of cycloron resonance and opcal phonon rans-me one. I has been found ha n ceran frequency bands polaraon characerscs have he feaures vald for boh resonances. The new opcal mehod based on he analyss of ellpcy and roaon angle specra s offered for deermnaon of he low-feld mobly. Keywords: cycloron resonance opcal phonon rans-me resonance. Manuscrp receved ; revsed verson receved ; acceped for publcaon ; publshed onlne Inroducon In recen years nrde maerals n parcular GaN bulk samples and heerosrucures have araced much aenon due o perspecves of hgh-power and hghfrequency applcaons. In spe numerous epermenal and heorecal works devoed o ranspor properes of nrdes sudes of cycloron resonance (CR) n hese maerals receved much less aenon. Under appled hgh magnec feld H he phenomenon of CR manfess self n srong absorpon of elecromagnec waves wh he frequences close o he cycloron one c eh / m c where m s he elecron effecve mass e and c are he elemenary charge and lgh velocy respecvely. CR s one of powerful ools o characere he basc maeral parameers. In parcular s used for deermnang he effecve mass m scaerng me 013 V. Lashkaryov Insue of Semconducor Physcs Naonal Academy of Scences of Ukrane 18 and consequenly mobly. To observe wellresolved CR lnes requres he condon c 1. The CR epermens daed by 90s were conduced bascally for AlGaN/GaN quanum heerosrucuures [1-3] whle only one work was repored for GaN flm [4]. In hese works he epermens were carred ou a helum emperaures and even lower and he values of elecron mobly of he nvesgaed samples were of a few housands cm /(Vs). Typcally well-pronounced CR absorpon was observed for he far-nfrared radaon a H 13T n ref.[1] up o 40 T n ref.[3]. Weaklypronounced CR resonance was repored n refs.[4 5] for he eraher (TH) radaon a moderae magnec felds of several T. The recen progress n he growh echnque for hgh-qualy nrde heerosrucures wh he elecron mobly hgher han several ens of housands cm /(Vs) allowed o deec and sudy CR for he mcrowave

2 Semconducor Physcs Quanum Elecroncs & Opoelecroncs 013. V. 16 N 1. P radaon a he magnec felds less han 1 T [6 7]. Very ofen n he cases of mperfec samples he nerpreaon of he ransmsson specra under CR condons and deermnaon of he elecron mobly are dffcul due o he large broadenng of he CR absorpon lnes. Here we wll show ha for hese cases he analyss of polaraon characerscs of he ransmed wave can be more nformave han hose of ransmsson specra. Furhermore we wll consder he peculares of he elecromagnec wave ransmed hrough he GaN flm subjeced o acon of boh magnec felds and suffcenly srong seady-sae (dc) elecrc felds. I s necessary o menon anoher resonance-lke effec ha can be me when sudyng he hgh-feld elecrcal properes of nrdes. I s he effec of opcal phonon rans-me resonance (OPTTR) whch s assocaed wh formaon of a srongly ansoropc elecron dsrbuon funcon elongaed along he appled dc elecrc feld. Ths dsrbuon funcon s he resul of he cyclc quasballsc moon of elecrons n momenum space nerruped by he fas emsson of opcal phonons. Under OPTTR condons frequency dsperson of dynamc (ac) conducvy has specfc oscllang behavor wh frequency nervals where he real par of conducvy becomes negave. For he GaN bulk-lke samples [8 9] and nrde quanum heerosrucures [10 11] OPTTR was predced n he range of he appled dc elecrc felds of 1-10 kv/cm and a wde frequency range of abou 0.3 TH. In spe of sgnfcan heorecal progress n descrpon of OPTTR resonance he epermenal effors amed a measurng he ransmsson specra [1] have no ye provded relable evdences of OPTTR. However he specfc behavor of he polaraon characerscs of ransmed wave can clearly ndcae he esence of OPTTR.. Formalsm In hs secon we presen he heory of neracon of elecromagnec waves wh a flm of crysal of cubc modfcaon wh hckness d. We mply ha d s much greaer han de Brogle wavelengh of elecrons and consequenly elecron ranspor n he flm can be consdered as hree-dmensonal. Oher dmensons of he flm are assumed o be much greaer han boh d and wavelengh of he ncden radaon. All he calculaons wll be provded assumng he parabolc dsperson law of elecrons and he Vog confguraon of he appled felds (see Fg. 1). As shown n Fg. 1 he plane wave s ncden upon he normal o plane of he flm. The wavevecor k of hs wave s perpendcular o he appled seady-sae felds E and H whch are collnear and dreced along as. The elecrc vecor n E of he ncden wave les n he plane y = 0 and subends he angle wh as. Fg. 1. Vog confguraon. a) Transmsson reflecon and loss coeffcens In he hree consdered regons: on nsde and under he flm he vecor wave equaon 4 j E ro (ro E ) (1) c c for he Vog confguraon can be wren n he form of scalar equaons as follows: d E dy E c 4I c E c E c y 0 0 y d y d where I sands for magnary un; nde ; denoes dagonal componens of he ac conducvy ensor; scalar quany s he background delecrc permvy. The ac conducvy ensor s assocaed wh he ac mobly ensor by he followng relaonshp j en j () wh n denong he elecron concenraon. Generally speakng n he presence of boh srong dc elecrc and magnec felds he dynamc or ac mobly beng he characersc of he response of elecron sysem o a small-sgnal ac perurbaon becomes he 3 3 ensor ha for he assumed geomery of appled felds s wren as 0 y y yy (3) 013 V. Lashkaryov Insue of Semconducor Physcs Naonal Academy of Scences of Ukrane 19

3 Semconducor Physcs Quanum Elecroncs & Opoelecroncs 013. V. 16 N 1. P In he case of he parabolc dsperson law he dynamc mobly ensor conans only fve non-ero componens and only hree of hem y and are lnearly ndependen. Oher componens are epressed as yy and y y. Noe ha a H 0 non-dagonal componens are equal o ero. Beng based on he parabolc dsperson law he componen does no depend on H and depends on he ampludes of he elecrc feld E and nensy of he elecron scaerng processes. The sysem () has he followng soluons: A ep( Ik0 B ep( Ik0 y 0 E C ep( I D ep( I 0 y d (4) E ep( Ik0 y d where k 0 / c and k 0 1 4Ien / are he wave numbers n vacuum and n he flm respecvely. Usng he connuy condons for he E elecrc feld and s dervave de / dy on boh nerfaces of he flm y = 0 and y = d we can epress ampludes of he -componens for he ransmed wave E B and refleced wave amplude of he ncden wave n he erm of he n E. Afer some ransformaons we oban ha E A ep( Ik0d) and A r (as can be seen n Fg. 1 B n A E {sn( )cos( )} ) where k0 cos( ) sn( ) d I d (5) k0 k r I sn( d). (6) 0 k0 Fnally he specra of ransmsson reflecon and loss coeffcens are gven by he followng formulas: T R r sn ( ) sn ( ) r cos ( ); cos ( ); 1 L 1 T R. As follows from Eqs. (7) a 0 (he ncden wave polared along as) he specra of ransmsson reflecon and loss coeffcens wll be defned only by he componen and a 90 (he ncden wave polared along as) he specra of hese coeffcens wll be defned only by. I s useful o noe ha a 0 90 he Vog confguraon allows o sudy boh CR and OPTTR smulaneously snce CR manfess self n he componen and OPTTR manfess self n he componen. (7) b) Polaraon characerscs of he ransmed wave To clarfy he physcal properes of he ransmed wave s convenen o rewre he componens of s elecrc feld n he real form: n E ( ) E sn( ) cos( ) (8) n E ( ) E cos( ) cos( ) (9) where arg( ). In he presence of dc magnec feld H or srong dc elecrc feld E he dagonal componens are dfferen herefore and consequenly. As a resul he ransmed wave a he ncden angles 0 90 becomes ellpcally polared. In he plane durng one perod of oscllaon he elecrc vecor wll crcumscrbe some polaraon ellpse. Ths ellpse can be characered by ellpcy and roaon angle of he large as relavely o he nal angle. These quanes can be epressed as follows: (10) 1 1 p (1 p )(1 1 ) arcan. (11) pcos( ) In he laer equaons p an() / psn( )/(1 p ) and. The essenal smplfcaon of he epressons (10) and (11) can be obaned n he lm of a hn flm when d 1. To he frs order of quany d smallness he parameers of he polaraon ellpse ake he form convenen for analyss: sn() den Im[ ] Im[ ] c (1) sn() den Re[ ] Re[ ]. c (13) As we can see he specra of and are deermned by he dfferences of magnary and real pars of he and componens of he dynamc mobly ensor respecvely. The mamal values of and are realed a he ncden angle 45. Also s useful o noe ha here are wo characersc frequences 1 and when 0 and 0. They correspond o he nersecons of he magnary Im[ ( 1 )] Im[ ( 1)] and real Re[ ( )] Re[ ( )] pars of he dagonal componens of he dynamc mobly ensor. The poson of hese wo frequences does no depend on he nal ncden angle. As wll be shown below deermnaon of hese characersc frequences could provde values of he scaerng me. 013 V. Lashkaryov Insue of Semconducor Physcs Naonal Academy of Scences of Ukrane 0

4 Semconducor Physcs Quanum Elecroncs & Opoelecroncs 013. V. 16 N 1. P Resuls and dscussons We apply he heory developed n he secon o he flm of compensaed GaN of cubc modfcaon wh he followng parameers: concenraon of oned mpury N cm 3 elecron concenraon 3 n cm amben emperaure 30 K. The hgh-feld and hghfrequency properes of compensaed bulk-lke GaN have been analyed n deal n ref.[13] and was shown ha a hese parameers OPTTR s mos pronounced whn he range of he appled elecrc felds o 8 kv/cm. The low-feld mobly was found o reach he values around 5000 cm /(Vs) (correspondng scaerng me 0.57 ps ). Noe ha he smlar mobly values were measured epermenally n he free-sandng GaN flms [14]. Also s assumed he case of classcal appled magnec felds. The classcal reamen of he magnec feld s sasfed when c where s he average elecron energy. In he equlbrum condons for eample a 30 K he esmaons gve ha he laer nequaly s accomplshed a H 4.5T whch corresponds o c 4TH. In he hghly nonequlbrum condons when he eernal dc elecrc feld s appled wh he ampludes of several kv/cm he average energy can reach essenally greaer values of abou 300 K. Then he range of he classcal magnec felds eends up o appromaely 45 T. Below hese hree dfferen cases wll be eamned separaely: he case of only CR ( E 0 H 0 ) he case of only OPTTR ( E 0 H 0 ) and he case of he smulaneous coesence of boh CR and OPTTR ( E 0 H 0 ). a) The case of cycloron resonance ( E 0 H 0 ) When eernal dc elecrc feld s absen he response of elecron sysem o ac perurbaon s descrbed n he frames of he smple Drude-Loren model: 1 I (14) (1 I ) ( ) c 1 (15) 1 where me has a sense of he momenum relaaon me and relaes o he low-feld mobly as followng: e/ m. Fg. a llusraes he frequency dependences of he componens calculaed a H 4.5T and. As a resul a he magnec feld c. 7 he real par Re[ ] has a weak and que a broadened peak correspondng o CR. I s clearly refleced n he specra of ransmsson and loss coeffcens (curves and 3 n he panels (b) and (d)) and o a lesser degree n he specrum of reflecon coeffcens (he same curves n he panel (c)). A he 013 V. Lashkaryov Insue of Semconducor Physcs Naonal Academy of Scences of Ukrane 1 parameers assumed above for he GaN flm he mamal elecromagnec wave absorpon occurs a polaraon 90 and a he frequency / c / = 0.64 TH. The elecromagnec wave dsspaes around 11% of s energy. A he same me for oher polaraon 0 he elecromagnec wave dsspaes around 3.5% of s energy. The ransmsson coeffcen whch s drecly measured quany s weakly changed from 79 o 71% wh varaon of from 0 o 90. The accurae measuremens of hs small varaon of ransmsson coeffcens n TH frequency range can ceranly face wh serous epermenal dffcules. In prncple s general properes of hn samples wh respec o wavelengh of ncden radaon and low elecron concenraon. As seen from Fgs b and c elecron gas wh he 3 concenraon n cm weakly modfes frequency dsperson of he T and R coeffcens (dash-doed 3 lnes) of he deal delecrc flm wh n 0cm. Ths fac can be llusraed by he esmaons of he dmensonless parameers d and d : so a / 0.65TH 600 I 50cm / V s and 810 I 1840 cm / V s whch gves d I 0.07 and d I a d 10μm. For comparson k 0 d Thus he ransmsson and reflecon coeffcens of TH radaon are manly condoned by delecrc properes and geomery of he GaN flm and are less affeced by he elecron subsysem. However as follows from formulas (1) and (13) he polaraon characerscs and are manly condoned by he elecron subsysem. The specra of hese quanes are shown n Fgs 3b and 3c. I should be noed a once ha he specra of boh and calculaed usng he eac formulas (10) and (11) (sold lnes) are close o he resuls obaned n he lm of hn flm accordng o he formulas (1) and (13) (dashdoed lnes). Ths s n he agreemen wh he esmaons of he parameers. One can see ha he specrum of ellpcy has hghly non-monoonc behavor. There are wo asymmerc shoulders separaed by he uned pon (hs pon s fed a every angle ) where 0. The frequency correspondng o hs pon s close o he characersc frequency 1 (rgh vercal lne). The ero value of ellpcy means ha he ransmed wave s lnear polared and here s no phase shf beween oscllaons of he - and - componens of he elecrc feld vecor. The amplude of he lef shoulder of s much hgher han ha of he rgh shoulder. I corresponds o larger dfference Im[ ( )] Im[ ( )] a 1 han a 1. The specrum of he roaon angle also has he uned pon ha separaes he regon of posve and negave values. The frequency correspondng o hs pon s d

5 Semconducor Physcs Quanum Elecroncs & Opoelecroncs 013. V. 16 N 1. P close o he characersc frequency (lef vercal lne). A frequences ( Re[ ( )] Re[ ( )] ) he elecromagnec wave ransmng hrough he sample has sronger encon of he -componen of he elecrc feld vecor han - componen. As a resul he roaon angle s posve. A frequences ( Re[ ( )] Re[ ( )] ) and vsa versa as a resul he roaon angle s negave. In he hgh-frequency range where c 1 he elecron response becomes weaker and elecromagnec wave ransmng hrough he samples remans praccally lnear polared. For he parameers of he GaN flm under consderaon he mamal values of ellpcy are of he order of several percens and he roaon angle s appromaely several degrees. These values can be easly deermned epermenally wh hgh accuracy [15]. Fg. 3. Panel (a) s he same as n Fg.. Panels (b) and (c) are he specra of ellpcy and roaon angle respecvely. Sold lnes are obaned accordng o he eac formulas (10) and (11) dash-doed lnes are obaned accordng o he appromae formulas (1) and (13). Vercal lnes denoe he poson of characersc frequency 1 / and /. The angle = 45 oher parameers are he same as n Fg.. Fg.. Panel (a) specra of (curves 1 and 1 a are he real and magnary pars respecvel and (curves and a ) calculaed a H = 4.5 T ( c / = 0.64 TH). Panels (b) (c) (d) specra of ransmsson reflecon and loss coeffcens respecvely. Curves 1 3 are obaned a = respecvely. Dash-doed lnes are he resuls for pure delecrc flm n = 0 cm 3. Vercal hn lne denoes he poson of cycloron frequency c /. The hckness d = 10 m. The delecrc permvy = 8.9. To fnale he dscusson of CR should be menoned he possbly o deermne he relaaon me by usng he measuremens of he polaraon characerscs nheren o he ransmed wave. If he elecron response obeys he Drude-Loren model (Eqs. (14) and (15)) hen he characersc frequences 1 and are eplcly defned as follows: 1 c 3/ and 1/3 ( c 1/ ). Epermenally deermnng he frequences whch correspond o 0 or 0 (for he suffcenly hn flms hey praccally concde wh 1 and ) he relaaon me can be easly eraced usng he laer formulas. b) The case of OPTT resonance ( E 0 H 0 ) Under condon of he srong appled elecrc feld he elecron response canno be descrbed by he means of 013 V. Lashkaryov Insue of Semconducor Physcs Naonal Academy of Scences of Ukrane

6 Semconducor Physcs Quanum Elecroncs & Opoelecroncs 013. V. 16 N 1. P he smple Drude-Loren model and frequency dependences of mobly have o be found as based on he numercal soluons of Bolman ranspor equaon by usng he Mone-Carlo echnque. Analyng he peculares of TH-lgh ransmsson he specra of dynamc mobly wll be used from ref. [13]. The specra of and under OPTTR are presened n Fg. 4a. As s clear seen from Fg. 4a he elecron sysem has que a dfferen response o ac perurbaon dreced along and perpendcular o he dc elecrc feld. Ths ansoropy of elecron response s he resul of formaon of srongly ansoropc dsrbuon funcon of elecrons n he range of he suffcenly srong appled dc elecrc feld. The componen reveals oscllang behavor wh he frequency nerval of TH where negave dynamc mobly (NDM) akes place. The mamum of NDM s realed near 0.65 TH wh he ampludes around 5cm / V s. A he same me he componen does no reveal any vsble feaures of OPTTR and remans Drude-lke. In he frequency nerval of OPTTR he values of componen are by an order of magnude smaller han hose n he case of CR. Therefore he sgns of OPTTR n he ransmsson and reflecon specra (Fgs 4b and 4c) are less pronounced han n he case of CR. In he frequency range of NDM he loss coeffcens a polaraon 0 (curve 1 n Fg. 4d) become negave whch ndcaes amplfcaon of TH radaon. The nensy of ransmed wave s ncreased by 1% a he frequency / ~ 0.64TH. Noe he amplfcaon effec arsng a OPTTR s sensve o he drecon of polaraon of he ncden wave. For eample a 30 he loss coeffcen becomes posve and nsead of amplfcaon absorpon of TH radaon akes place. A he same frequency bu a polaraon 90 he loss coeffcen s equal o.5%. The feaures of OPTTR n he specra of T R L coeffcens appear o be more sgnfcan a a hgher elecron concenraon. However as shown n ref.[16] he effec of OPTTR s hghly sensve o he values of elecron concenraon and can be srongly suppressed n he dense elecron gas due o elecron-elecron scaerng. In spe of formdable obsacles n denfyng OPTTR resonance n he ransmsson specra measuremens clear denfcaon of OPTTR can be obaned by measurng he polaraon characerscs of he ransmed wave. As seen from Fgs 5b and 5c boh specra of ellpcy and roaon angle have oscllang behavor n he frequency range of OPTTR whch reflecs oscllang behavor of he componen. However n conras o he prevous case of CR he esence of uned pons correspondng o he frequences when 0 or 0 s no oponal. For eample for he case under consderaon he ellpcy specrum has no hese pons (noe he magnary pars of and do no nersec) however he roaon angle specrum has hree hese pons. Generally speakng he esence of oscllaon n he and specra s more represenave for OPTTR han he esence of he uned pons. Also n conras o CR n he low-frequency range Re[ ] Re[ ] and he roaon angle s negave. The ampludes of oscllaon n he frequency range of OPTTR are abou 1 whch can be also resolved epermenally. Fg. 4. Resuls are presened for E = 3 kv/cm. All he curves have he same sense as n Fg V. Lashkaryov Insue of Semconducor Physcs Naonal Academy of Scences of Ukrane 3 c) The case of he coesence of CR and OPTTR ( E 0 H 0 ) The specra of he and componens of he dynamc mobly ensor obaned usng he Mone-Carlo echnque are presened n Fg. 6a for he case of parallel confguraon of he appled dc elecrc and magnec

7 Semconducor Physcs Quanum Elecroncs & Opoelecroncs 013. V. 16 N 1. P ncrease of he ransmsson coeffcen and amplfcaon of he ransmed wave (loss coeffcen becomes negave and has he values 0.3% down o 0.1%). The specra of ransmsson and loss coeffcens a he large angles of ncdence (curves 5 and ) nsead of sgns of OPTTR clearly demonsrae he sgns of CR. Around he CR frequency / 0.97 TH here s a vsble decrease of he ransmsson coeffcen and absorpon of he ransmed wave (loss coeffcen becomes posve wh he values close o 4 %). I s noeworhy ha he absolue values of amplfcaon and absorpon are hree mes less han he values obaned prevously n subsecons (a) and (b). Ths s because he flm hckness was chosen here hree mes less. A he angle 45 (curves 4) amplfcaon s absen bu he T and L coeffcens ehb he sgns nheren o boh OPTTR and CR. Fg. 5. Resuls are presened for E = 3 kv/cm. All he curves have he same sense as n Fg. 3. felds. In hs confguraon was esablshed ha he magnec feld does no change he elecron response o ac perurbaon dreced along aes and he componen remans he same as a H 0. Ths resul s he consequence of he parabolc dsperson law of elecrons a whch elecron dynamcs n magnec feld along as and n he perpendcular drecons are uncoupled. A he same me he componen reveals specfc behavor nheren o CR. The shape of he specrum of componen can be well-descrbed by he Drude-Loren formula (14) nroducng he same effecve scaerng me. Under condon of OPTTR hs me corresponds o he average me of flgh beween wo sequenal processes of he opcal phonon emsson. Thus here s a possbly o sudy boh effecs smulaneously analyng ransmsson of TH radaon a dfferen polaraon angles. As seen from Fgs 6b and 6d a he small ncden angles 0 0 (curves 1 and 3) he specra of ransmsson and loss coeffcens clearly demonsrae he sgn of OPTTR: around he OPTTR frequency / 0.65TH here are a vsble Fg. 6. Resuls are presened for E = 3 kv/cm and H = 6.8 T. Vercal lnes denoe he poson of he OPTTR frequency R / = 0.64 TH and he CR frequency c / = 0.97 TH. The curves are obaned a = Oher curves have he same sense as n Fg.. The hckness of he flm d = 3 m. 013 V. Lashkaryov Insue of Semconducor Physcs Naonal Academy of Scences of Ukrane 4

8 Semconducor Physcs Quanum Elecroncs & Opoelecroncs 013. V. 16 N 1. P o deermne he elecron relaaon me and consequenly he low-feld mobly. Acknowledgemen Ths work has been carred ou n he framework of he Comple Program of he Fundamenal Researches of NAS of Ukrane Fundamenal problems of nanosrucured sysems maerals and nanoechnology ( ) and parally suppored by The Sae Fund for Fundamenal Researches (projec Ф40./057). References Fg. 7. Curves 3 4 and 5 n panels (b) and (c) are obaned a = The dash-doed curve presens he appromaon of hn flm and s calculaed a = 45. Oher parameers are he same as n Fg. 6. The same smulaneous manfesaon of hese effecs s observed n he frequency dependences of polaraon characerscs and (Fgs 7b and 7c). There are uned pons correspondng o he frequences 0 and 0 ypcal for CR and here s nconspcuous frequency modulaon boh and ypcal for OPTTR. 4. Conclusons In summary he measuremens of he polaraon characerscs of ransmed wave hrough he sample are no less mporan han he measuremens of he ransmsson specra. In he cases of hn flms such polaraon characerscs of radaon as ellpcy and roaon angle are manly deermned by he hghfrequency conducvy of he elecron subsysem. The wdely dscussed n leraure effecs of opcal phonon rans-me resonance and cycloron resonance can be epermenally denfed by he dsncve feaures of he specra of ellpcy as well as hose of he roaon angle. In he case of cycloron resonance he nvesgaons of polaraon characerscs can enable 1. W. Knap H. Alause J.M. Blue J. Camassel J. Young M. Asf Khan Q. Chen S. Huan M. Shur The cycloron resonance effecve mass of wo-dmensonal elecrons confned a he GaN/AlGaN nerface // Sold Sae Communs. 99(3) p (1996).. Xaoguang Wu and F.M. Peeers Cycloronresonance mass of wo-dmensonal elecrons n GaN AlGa1 N heerosrucures // Phys. Rev. B 55(3) p (1997). 3. W. Knap S. Conreras H. Alause C. Skerbsewsk J. Camassel e al. Cycloron resonance and quanum Hall effec sudes of he wo-dmensonal elecron gas confned a he GaN/AlGaN nerface // Appl. Phys. Le. 70 p (1997). 4. M. Drechsler D.M. Hofmann B.K. Meyer T. Dechprohm H. Amano and I. Akasak Deermnaon of he conducon band elecron effecve mass n heagonal GaN // Jpn. J. Appl. Phys. 34 p. L1178-L1179 (1995). 5. Z.-F. L W. Lu S.C. Shen S. Holland C.M. Hu e al. Cycloron resonance and magneoranspor measuremens n AlGa1 N GaN heerosrucures for = // Appl. Phys. Le. 80(3) p (00). 6. S. Syed M.J. Manfra Y.J. Wang R.J. Molnar and H.L. Sormer Elecron scaerng n AlGaN/GaN srucures // Appl. Phys. Le. 84(9) p (004). 7. A. Wolos W. Jansch K. Dybko and Z. Wlamowsk C. Skerbsewsk Plasmoncycloron resonance n wo-dmensonal elecron gas confned a he GaN AlGa1 N nerface // Phys. Rev. B (007). 8. E. Sarkov P. Shkorov V. Grunsks L. Reggan L. Varan J.C. Vassere and Jan H. Zhao Mone Carlo smulaon of he generaon of eraher radaon n GaN // J. Appl. Phys. 89() p (001); E.A. Barry K.W. Km and V.A. Kochelap Group-III nrdes ho elecron effecs n moderae elecrc felds // Phys. Saus Sold (B) 8() p (001). 013 V. Lashkaryov Insue of Semconducor Physcs Naonal Academy of Scences of Ukrane 5

9 Semconducor Physcs Quanum Elecroncs & Opoelecroncs 013. V. 16 N 1. P G.I. Syngayvska and V.V. Koroyeyev Mone Carlo smulaon of ho elecron effecs n compensaed GaN semconducor a moderae elecrc felds // Semconducor Physcs Quanum Elecroncs & Opoelecroncs 10(4) p (007). 10. V.V. Koroyeyev V.A. Kochelap K.W. Km and D.L. Woolard Sreamng dsrbuon of wodmensonal elecrons n III-N heerosrucures for elecrcally pumped eraher generaon // Appl. Phys. Le. 8 p (003); K.W. Km V.V. Koroyeyev V.A. Kochelap A.A. Klmov and D.L. Woolard Tunable eraher-frequency resonances and negave dynamc conducvy of wo-dmensonal elecrons n group-iii nrdes // J. Appl. Phys. 96 p (004). 11. E. Sarkov P. Shkorov V. Grunsks L. Varan C. Palermo J.-F. Mllhaler and L. Regan Frequency lms of eraher radaon generaed by opcal-phonon rans-me resonance n quanum wells and heerolayers // Phys. Rev. B (007); Teraher generaon n nrdes due o ransme resonance asssed by opcal phonon emsson // J. Phys: Condens. Maer 0(38) (008). 1. T. Lauren R. Sharma J. Torres P. Nouvel S. Bln L. Varan Y. Corder M. Chmelowska S. Cheno J.-P. Faure B. Beaumon P. Shkorov E. Sarkov V. Grunsks V.V. Koroyeyev and V.A. Kochelap Volage-conrolled sub-eraher radaon ransmsson hrough GaN quanum well srucure // Appl. Phys. Le (011). 13. G.I. Syngayvska V.V. Koroyeyev Elecrcal and hgh-frequency properes of compensaed GaN under elecron sreamng condons// Ukranan Journal of Physcs 58 (1) p (013). 14. D.C. Look and J.R. Selove Predced mamum mobly n bulk GaN // Appl. Phys. Le. 79(8) p (001). 15. L. Ren C.L. Pn T. Arkawa K. Takeya I. Kawayama M. Tonouch R.H. Hauge and J. Kono Broadband eraher polarers wh deal performance based on algned carbon nanoube sacks // Nano Le. 1 p (01). 16. J.T. Lu J.C. Cao and S.L. Feng Ho-elecron dynamcs and eraher generaon n GaN quanum wells n he sreamng ranspor regme // Phys. Rev. B (006). 013 V. Lashkaryov Insue of Semconducor Physcs Naonal Academy of Scences of Ukrane 6