The Electrical Characteristics Model of GaN/InGaN/GaN Heterostructure in InGaN-based LED

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1 ppld Physcs Rsrch Vol. 4, o. ; Th Elctrcl Chrctrstcs Modl of G/InG/G Htrostructur n InG-bsd LED ud Mulynt, Ll Hsnh & Khrurrjl 3 Dprtnt of Elctrcl Engnrng Educton, Fculty of Tchnology nd Voctonl Educton, Indons Unvrsty of Educton UPI, Jl. Dr. Stbudh o 7, ndung 435, Indons Dprtnt of Physcs Educton, Fculty of Mthtcs nd turl Scncs Educton, Indons Unvrsty of Educton UPI, Jl. Dr. Stbudh o 9, ndung 435, Indons 3 Physcs of Elctronc Mtrls Rsrch Dvson, Fculty of Mthtcs nd turl Scncs, ndung Insttut of Tchnology, Jl. Gnsh, ndung 43, Indons Corrspondnc: ud Mulynt, Dprtnt of Elctrcl Engnrng Educton, Fculty of Tchnology nd Voctonl Educton, Indons Unvrsty of Educton UPI, Jl. Dr. Stbudh o 7, ndung 435, Indons. E-l: b_ulynt@yhoo.co Rcvd: Fbrury 3, ccptd: Fbrury 7, Onln Publshd: My, do:.5539/pr.v4np98 URL: bstrct Th clculton odl of tunnlng currnt through G/InG/G htrostructur n InG-bsd LED usng th trnsfr trx thod ployd to vrfy th rsult of clculton of tunnlng currnt plntd nlytclly. Th nlytcl thod ppld through solvng thortclly th Schrödngr quton, whrs, th trnsfr trx thod dvdd th soluton r nto lss s of sgnt coprd to th obsrvd potntl wdth s, whr th potntl nrgy of ch sgnt ws ssud constnt. Vrfcton ployd to th thcnss of dplton rgon nd bs voltg vrtons. Th obtnd rsult hs shown tht th nlytcl rsult of clculton slr wth th clculton rsult usng trnsfr trx thod. Th clculton odl ws thn xtndd to clcult th tunnlng currnt for dffrnt tprtur. Kywords: tunnlng currnt, G/InG structur, InG bsd LED, TMM. Introducton t prsnt, crolctronc dvcs hv bttr dvlopd wth thr or ng prfornc. Th ncrs of th dvc prfornc hs bn trggrd by th sllr s dvc. Effort n nng th s of th dvc nd ncrsng th prfornc of th dvc wll surly on dy rch ts stgnncy, spclly whn th dvc cnnot b nd ny longr, whrs th rqurnt to ncrs ts prfornc should thn b fulflld. To solv such probl, nowdys, th scop of th rsrch trl s n coponnt dvc hs bn drctd to th srchng of th nw trl tht ts chrctrstcs r coptbl to th dvc through sultng th trl-bsd dvs chrctrstcs, so th chrctrstcs of th dvc cn b prdctd bforhnd wthout frst fbrctng th dvc. It wll, of cours, b or ffcnt nd ffctv to b drctd to th ffort of fndng nd srchng nw trl. Snc 999, InG-bsd LED s hv gnd grt ttnton nd provd th prssv rsults du to thr hghst xtrnl quntu ffcncs of 8% nd % t low currnts of.6 nd., rspctvly Mu t l, 999. lthough InG-bsd LEDs r lrdy corclly vlbl for vsbl lght sson such s n dsply nd utootv lghtng pplctons, furthr provnt of th lght output powr nd th xtrnl quntu ffcncy r rqurd Chu t l.,. To fnd out th ffcncy of LEDs, t would rqur th study of lctrcl chrctrstcs n dvnc. Th lctrcl chrctrstcs of LEDs cn b obtnd by xnng th p-n juncton of htrostructur. In ths study, th brupt p-n juncton s usd by ssung tht ll dopnts r fully ond. rrrs of n brupt p-n htrojuncton r grtr thn tht of th grdd juncton du to th forton of lctron brrr t th brupt juncton. Furthror, lctrcl chrctrstcs of th LEDs r conductd to dtrn th lg currnt tht occurs t hgh njcton currnt dnsty Polyov t l., 4; Schubrt t l., 6. Study of th thory of lctrcl proprts of G/InG/G htrostructur n InG bsd-led thortclly cn b prford usng crrr trnsport odl such s dffuson-drft trnsport, nrgy trnsport, 98

2 ppld Physcs Rsrch Vol. 4, o. ; hydrodync, nd quntu trnsport odls. Howvr, th ost coon odl usd s dffuson-drft trnsport odl Pjcnovc t l., 989. Wth th shrnng of th dvcs s, th lctron trnsport du to dffuson nd drft bcos sllr thn tht of th quntu trnsport, thrfor th dffuson-drft trnsport cn b gnord n th clcultons nd n othr word, only quntu trnsport ncludd n th clculton. Quntu trnsport n th htrojuncton structur cn b dtrnd by solvng Schrödngr quton. Thr r two nds of thods cn b usd to solv th Schrödngr quton, thos r nlytcl L, 993 nd s-nurcl thods Mo, 7. nd t hs bn provd tht th trnsfr trx thod TMM s or ccurt thn th convntonl fnt dffrnc thods bdoldr t l., 4. To xn th nlytcl forul obtnd, n ths ppr th tunnlng currnt through G/InG/G htrostructur n InG-bsd LED ws lso clcultd usng TMM.. Thortcl Modl. Tunnlng Currnt Clculton Usng nlytcl Mthods Th Schrödngr quton tht should b solvd to obtn th bhvor of lctron n th nsotropc htrostructur s Hsnh, 8: H r E r. H s Hltonn nly: H p p U, nd r ffctv ss of th lctron prpndculr nd prlll to th ntrfc, rspctvly, p s ontu vctor nd Ur s potntl nrgy. Fgur shows th potntl profl n -drcton. Th lctrons co fro rgon I towrd potntl brrr n rgon II whr th ffctv ss of lctron only dpnd on th -drcton. Th wv functon n Eq. s Hsnh, t l., 8: r xp xp x x y y 3 Th wv functon n Eq. 3 stsfs th followng on-dnsonl Schrödngr quton: whr: 4 p p U E E G E 5 r G s th nrgy of ncdnt lctron n -drcton, nd r r th wv vctor nd th trnsvrs coordnt, r rspctvly, of th lctron n th pln prlll to th ntrfc, G s ffctv ss of lctron prpndculr to th ntrfc n th G rgon. Th longtudnl nrgy of lctron n th InG rgon thn cn b wrttn s: InG r E E 6 InG InG ffctv ss of lctron prlll to th ntrfc n th InG rgon. Whl th totl nrgy of tunnlng lctron hs to b constnt, thrfor: InG s r r E E 7 G InG In th G nd InG rgons, Schrödngr quton long th tunnlng drcton cn b wrttn s: G U E 8 G InG U E 9 InG 99

3 ppld Physcs Rsrch Vol. 4, o. ; Fgur. Enrgy-bnd dgr of InG / G brupt p-n juncton Fro Eq. 3, 4 nd 5, t cn b obtnd: r G G U E InG G InG. Clculton of Tunnlng Currnt Usng Trnsfr Mtrx Mthod TMM Th trnssson coffcnt cn b clcultd usng trnsfr trx thod TMM. Th TMM s vry coon s-nurcl thod n Physsc nd Mthtcs to solv th probl whn th totl syst cn b dvdd nto subsysts tht ntrct only wth nghborng subsysts. In ths cs, th TMM s usd to solv th Schrödngr quton whn th soluton rgon of potntl nrgy s dvdd nto sgnts. Th wdth of ch sgnt uch sllr thn tht of th ctul potntl, whl th potntl nrgy n ch sgnt s ssud to b constnt s shown n Fgur. If th nubr of sgnts ncrs, th pproxton potntl wll rch th ctul potntl. Th Schrödngr quton of ch sgnt could b solvd through pplyng th xponntl functon, tht thn rrngd n st of trcs tht contn th boundry condtons t ch sgnt ntrfc. Th trnssson coffcnt s thn clcultd fro th st of trcs. Th clculton s don for th brupt p-n htrojuncton, whr ts rsstnc s grtr thn tht of th grdd juncton du to th xstnc of lctron brrr ford by brupt juncton, s shown n Fgur. Th sold ln shows th ctul potntl profl whl th dottd ln rprsnts th pproxton potntl usd to solv th Schrödngr quton usng th TMM. Fgur. Th G/InG potntl profl dvdd nto sgnts tht ppld n th clculton of th coffcnt trnssson usng trnsfr trx thod TMM Th wv functon of lctron rgrdlss to th t of ch r tht bco th soluton of Schrödngr quton of th pproxton potntl s ny s sgnts cn b wrttn s: ψ ψ j xx y y xx y y,. < < d,.b

4 ppld Physcs Rsrch Vol. 4, o. ; y x y x 3 3 ψ d < < d,.c whr,,,, nd r constnts, wth =,..., -. To splfy th clculton, th constnt vlu of s tn s, nd s ro, bcus t s ssud tht thr s no rflcton n th ntrfc of sgnt. Th wv nubr for th rgon < <d, s sttd s follows:, whrs th wv nubr, for th dcrs of potntl brrr, on d < < d, s,,, d V C. 3 Th boundry condtons nd contnuty t ch sgnt of th ntrfc hv to b ppld. If thr s nubr of sgnt, thn th nubr of ntrfc ponts r - ts, hnc th nubr of boundry condtons r - ts. Th rsult of pplcton of boundry condton t th pont of s:, 4 whr nd. Th rsult of pplcton of boundry condton t th pont of to - s:, 5 whr nd. nd th rsult of pplcton of boundry condton t th pont of - s:, 6 whr nd. Fro Eq. 6-4, t cn b obtnd th followng quton:, 7 nd lctron trnssson coffcnt, t cn b clcultd fro

5 ppld Physcs Rsrch Vol. 4, o. ; Whl th lctron trnsttnc T cn b obtnd fro: t. 8 T t t, 9 Whr t s th conjugt of trnssson coffcnt, t. Tunnlng currnt cn b clcultd usng quton blow Khrurrjl t l., 6: q o, J T E 3 f L E f R E de xy de whr TE s th lctron trnsttnc s functon of longtudnl nrgy E nd E xy s th trnsvrsl nrgy. Th functons of Fr dstrbuton on th lft nd th rght contcts, r: nd f E L xp[ E E / T] FL f E, R xp[ E E / T] whch dnot th probblty of lctron nrgy, E s occupd. E FL nd E FR ch rspctvly s lft nd rght sd fry nrgy. 3. Rsults nd Dscusson Th clculton of trnstnc nd tunnlng currnt trough brupt p-n htrojuncton of G/InG n InG-bsd LED hs bn prford. Th dscontnuty bnd btwn G nd InG rgons s round. V, tht bcus of th potntl brrr hght. Th vlu of lctron ffctv ss n InG s hghr thn tht of n G, nd bs voltg of V s gvn to th p-n juncton. Th tunnlng currnt of lctrons through brupt p-n htrojuncton of InG/G wth brrr thcnss of n nd 5 n, nd bs voltg V vrd fro to V rsultd by nlytcl nd s-nurcl thod usng TMM clcultons r shown n Fgur 3 nd 4, rspctvly. Th rsult of tunnlng currnt clcultd usng th trnsttnc obtnd by nlytcl thod quls to tht of s-nurcl thod usng TMM. Furthror, Fgur 5 shows tht th tunnlng currnt of lctron tnds to dcrs by th ncrs n th potntl brrr thcnss. Ths s cusd by th ncrsd n ffctv potntl n Eq. tht would cus th dcrs n trnsttnc nd tunnlng currnt of lctron. For ths cs, th clculton rsult of tunnlng currnt usng nlytcl trnsttnc quls to tht of tht ts trnsttnc ws clcultd usng TMM. FR Fgur 3. Th tunnlng currnt through brupt p-n htrojuncton of InG/G wth th brrr thcnss of n, nd bs voltg vrd fro untl V, rsultd fro nlytcl nd TMM clculton

6 ppld Physcs Rsrch Vol. 4, o. ; Fgur 4. Th tunnlng currnt through brupt p-n htrojuncton of InG/G wth th brrr thcnss of 5 n, nd bs voltg vrd fro untl V, rsultd fro nlytcl nd TMM clculton Fgur 5. Th tunnlng currnt of brupt p-n htrojuncton of InG/G t vrd brrr thcnsss of, 5 nd 5 n nd bs voltg of to5 V rsultd fro nlytcl clculton. Th forulton of tunnlng currnt s thn ppld to clcult th tunnlng currnt n dffrnt tprturs s shown n Fgur 6. Ths clculton s lso ppld n th brupt p-n htrojuncton wth vrd tprturs of 5 K, 3 K nd 5 K for V vrd fro to V, nd th dplton thcnss of n. Fro ths study, th rsult shows tht th tunnlng currnt tnds to dcrs by th ncrs n tprtur. Fgur 6. Th tunnlng currnt of brupt p-n htrojuncton of InG/G wth vrd tprturs of 5 K, 3 K nd 5 K for dplton thcnss of 5 n nd vrd bs voltg fro to V 3

7 ppld Physcs Rsrch Vol. 4, o. ; 4. Concluson Ths rsrch ployd th clculton of tunnlng currnt through G/InG/G htrostructur n InG-bsd LED by nsrtng th quntu ffct. Tunnlng currnt rsultd fro th clculton of nlytc trnsttnc quls to tht of clcultd fro th trnsttnc usng th trnsfr trx thod. Th rsults of th clculton show tht th ncrs n dplton thcnss cuss th dcrs n th tunnlng currnt whl th ncrs n voltg bs cuss th ncrs n th tunnlng currnt. Th obtnd odl ws thn ppld to clcult th tunnlng currnt n dffrnt tprtur, whr th ncrs n tprtur cuss th dcrs n th tunnlng currnt. Rfrncs bdoldr, T. M., Hssn, H. H., Fry, W., & Or, O.. 4. Soluton of Schrödngr n Doubl-Gt MOSFETs usng Trnsfr Mtrx Mthod. Elctroncs Lttrs, 4,. Chu, Y. C., Jn,. L., Sng, J. L., Sng, H. H., T, Y. P., K, J. W., K, Y. C., & Song, J. P.. Iprovnt of Lght Output Powr of InG/G Lght-ttng Dod by Ltrl Eptxl Ovrgrowth Usng Pyrdl-shpd SO, Optcs Exprss, 8,. 46. Hsnh, L., bdullh, M., Surno, Wnt, T., & Khrurrjl. 8. Modl of Tunnlng Currnt n n nsotropc S/S-xGx/S Htrostructur wth notr-thc rrr Includng th Effct of Prlll-Prpndculr Kntc Enrgy Couplng. Scond. Sc. Tchnol., 3, Khrurrjl, My, S., & Hros, M 999. Elctron Fld Esson fro Slcon Subsurfc sd on Gnrld ry Functon pproch. S J. Vc. Sc. Tchnol.., 7, L, Elctron Tunnlng T through Htrostructur Potntl rrr, Supprlttcs nd Mcrostructurs, 4, Mo, L. 7. Th Effcts of th Injcton-Chnnl Vlocty on th Gt Lg Currnt of noscl MOSFETs. IEEE Elctron Dvc Lttrs, 8, 6. Mu, T., Yd, M., & ur, S. 999: Chrctrstcs of InG-bsd UV/lu/Grn/br/Rd Lght-Ettng Dods. Jpn. J. ppl. Phys, 38, Prt, o Pjcnovc,., Ky, L. E., Tng, T. W., & von, D. H urcl Sulton nd Coprson of S JTs nd S -x G x HTs. IEEE Trns. Elctron Dvcs, Polyov,. Y., Srnov,.., Govorov,. V., K, J., Rn, F., Thlr, G. T., Frr, R. M., Gl,. P., brnthy, C.R., Prton, S. J., uynov, I.., Rudo, G.Y., Chn, W. M., Pn, C. C., Chn, G. T., Chyl, J I., & Zvd, J. M. 4. Elctrcl nd Lunscnt Proprts nd th Spctr of Dp Cntrs n GMn/InG Lght-Ettng Dods, Journl of Elctronc Mtrl, 33, 4. Schubrt, E. F. 6. Lght Ettng Dods. Cbrdg Unvrsty Prss, p