Rvu ds Enrgis Rnouvlabls Vol. 12 N 1 (2009) 125 135 Characrizaion of smi-insulaing GaAs:Cr by mans of DC-CPM chniqu. ibrmacin 1* and A. Mrazga 2 1 Laboraoir ds Maériaux Smi-conducurs Méalliqus, Univrsié Mohammd Khidr, B.P. 145, 07000 Biskra, Algéri 2 Dparmn of Physics, Faculy of Scinc, King Khald Univrsiy, P.O. Box 9004, Abha, Saudi Arabia (rçu l 15 Décmbr 2008 accpé l 21 Mars 2009) Absrac - In h prsn papr, consan phoocurrn mhod, CPM is usd o drmin h dfcs disribuion from h opical absorpion spcra of smi-insulaing Cr-dopd GaAs. By using h drivaiv mhod, w hav xracd h disribuion of h dnsiy of sas DOS clos o valnc band dg E v from h masurd opical absorpion spcrum. W hav also dvlopd a compur cod program -CPM which hav bn usd o compu h oal absorpion spcrum and hir componns using a modl dnsiy of sas infrrd from wo complmnary chniqus: consan phoocurrn mhod, CPM and ransin phoocurrn PC. I is found ha by combinaion of h wo masurmn chniqus CPM and PC, and h wo absorpion spcra componns α n and α p, w ar abl o hav a full rconsrucion of h dnsiy of sas disribuion blow and abov h Frmi lvl for such marials. Résumé - Dans c présn ravail, on a dérminé la disribuion énrgéiqu ds défaus du GaAs:Cr n uilisan son spcr d absorpion opiqu msuré par la chniqu du phoo couran consan, CPM. Ainsi par dérivaion du spcr d absorpion opiqu msuré, on a pu dérminr la dnsié d éas élcroniqu DOS près d la band d valnc E v. On a aussi dévloppé un programm pour modélisr la chniqu -CPM n régim coninu. Un modèl d dnsié d éas a éé proposé n s basan sur dux chniqus complémnairs, la chniqu CPM la chniqu du phoo-couran ransioir PC, pour calculr l cofficin d absorpion opiqu oal, ainsi qu ls dux cofficins d absorpion opiqu α n α p,dus aux élcrons aux rous rspcivmn. On a rouvé qu par la combinaison ds dux chniqus CPM PC d un coé, ls dux spcrs d absorpion α n α p, d un aur coé, on aboui à dérminr la disribuion énrgéiqu d la dnsié d éa élcroniqu sur ou l gap audssous au-dssus d nivau d Frmi pour c yp d maériaux. Kywords: Consan phoocurrn mhod, ransin phoocurrn, Opical absorpion spcrum, Gallium arsnid, Dfc sas. 1. INRODUCION Gallium arsnid GaAs marial is widly usd in h smiconducor indusry du o is widr dirc band gap nrgy E g and highr lcron mobiliy μ n ( E g = 1.42 V and μ n = 8500 cm 2 V -1 s -1 ) compard o crysallin silicon ( E g = 1.12V and μ n = 1350 cm 2 V -1 s -1 ). hs propris mak his marial vry usful for infrard ligh miing and lasr diods manufacuring. * awfik_ibr@yahoo.fr 125
126. ibrmacin al. GaAs can b dopd wih Chromium (Cr) in ordr o obain a smi-insulaing gallium arsnid (SI-GaAs:Cr) subsra as silicon dioxid. Chromium bhavs as an accpor wih an impuriy lvl clos o h cnr of h nrgy gap [1-3]. Dfc lvls in smiconducor band gaps drmin h lcrical and opical propris dvics. hs propris ar drmind by h rlaiv posiion of h lvl and h capur cross scion of h carrirs. h dfc lvls can capur minoriy, majoriy carrirs or boh carrirs for h dp sas and hy ac, in his cas, as rcombinaion cnrs. Usually, capur and rlas of majoriy and minoriy carrirs a dfc lvls phnomna in smiconducors marials is characrisd by dp lvl ransin spcroscopy, DLS [4] and minoriy carrir ransin spcroscopy, MCS [5]. For smi-insulaing (SI) crysals lik GaAs and amorphous marials lik a-si:h ohr chniqus should b usd such as CPM [6-8], PC [9] and modulad phooconduciviy MPC [10, 11]. h purpos of his prsn work is o invsiga h shallow and dp dfc lvls disribuion in smi-insulaing GaAs:Cr by consan phoocurrn mhod by combinaion of masurmn and simulaion rsuls. 2. HEORY AND SIMULAIONS Phoocurrn chniqus dc opically inducd ransiions bwn localisd (dfc) lvls in h band-gap and xndd lvls in h bands, which gnras fr carrirs. his should allow on o drmin, by appropria spcroscopy mhods, h dnsiy and nrgy posiion of h dfc sas wihin h forbiddn opical gap. h CPM was firs inroducd by Vanck al. [12, 13] wih h basic ida o adjus h phoon flux φ ( h ν ) in such a mannr ha h phoocurrn rmains consan for all incidn phoon nrgis hν Undr hs condiions, on nsurs ha h occupaion of h lcronic sas, h concnraion of h phoo-gnrad carrirs and h produc ( µ τ ) rmain consan for all usd wavlnghs λ. hs ar h condiions of validiy of h CPM mhod. If h phoocurrn is consan during h masurmns, h invrs numbr of h incidn phoons is proporional o h absorpion cofficin α ( h ν ). α 1 h (1) φ ( ν ). φ( h ν ) = C α ( h ν ) ( h ν ) Figur 1 illusras h hrmal and opical carrir ransiions for h CPM for a uniform sub-gap illuminaion. Whil singl lvl rprsnaion appars in h illusraion, h DOS is nrgy-disribud. A room mpraur, phooconducion is carrid ou by fr carrirs, and so h only ransiions akn ino accoun ar hos bwn localisd sas in h gap and xndd sas in h bands. In addiion, bcaus of hir small probabiliis, band-o-band ransiions ar ignord. h hrmal ransiion ras hav h following significanc: () - ( E ) n (p) / CB( VB) : Ras of rapping (mission) of lcron (hol) ino (from) a lvl E a h conducion band ail (valnc band ail).
Characrizaion of Smi-Insulaing GaAs:Cr by Mans of DC-CPM chniqu 127 a- hrmal ransiions b- Opical ransiions Fig. 1: Carrir ransiions involvd in h CPM simulaion o: Hol, ----- : Hol ransiions : Elcron, : Elcron ransiions h rapping ra is a funcion of fr n ( p ) and rappd n ( p ) carrir dnsiis following h rlaion whr ( E ) [ D ( E ) n ( p )] n (p) ( E ) = Cn (p) n ( p ) (2) D is h oal DOS a lvl E and C n (p) is h capur cofficin of h rapping sa. Similarly, h mission ra is a funcion of rappd n ( p ) carrir dnsiis following h rlaion:
128 n (p) ( E ). ibrmacin al. ( E E / ( k )) = Cn (p) DCB( VB) n ( p ).xp CB( VB) B (3) whr D CB(VB) is h ffciv DOS a h conducion (valnc) mobiliy dg E CB( VB) ( k B is Bolzmann consan and h mpraur). h opical gnraion ras G hav h following significanc: - G n (p) / VB( CB) ( E ): Ras of lcron (hol) gnraion from a lvl E a h valnc band ail (conducion band ail). h opical gnraion ra is funcion of h fr and rappd carrir dnsiis following h quaion: ( D n ( p) ) n ( D)( E ) K Gn (p) ( E, h ν ) = φ CB( VB) h (4) ν whr φ is h incidn phoon flux and K = 4.34 10 38 cm 5 V 2 is a consan proporional o h momnum marix lmn. For h sady-sa rgim, w hav o solv h following quaions: Nuraliy quaion Ec Ec n + n ( E ) p n ( E ) Dop = 0 (5) E E v Whr Dop is ionisd dopan charg dnsiy. v Coninuiy quaion for fr chargs d n ( ) = d 0 n and p ( + ) + n / CB d p ( ) = d n / CB G n / VB.d E + 0 n / VB n / VB G n / CB.d E = ( + ) + p / CB p / VB G p / CB.d E + p / CB p / VB G p / CB.d E =.d E 0.d E 0 (6) (7) Ra quaion for rappd carrirs d n ( E, ) d = 0 n and p
Characrizaion of Smi-Insulaing GaAs:Cr by Mans of DC-CPM chniqu 129 n / CB n / CB + p / CB p / CB + G p / CB G n / CB = 0 (8) d p ( E, ) d = 0 p / VB p / VB + n / VB n / VB + G n / VB G p / CB = 0 (9) o solv h -CPM quaions (5) o (9), w divid h nrgy gap ino N closly spacd nrgy lvls E i, including h band dgs E V = E1 and E C = EN. In modling coplanar sampls, i is a common pracic o assum uniform lcric fild, prfc ohmic conacs, and o nglc any ranspor drivn by fr-carrir diffusion. Undr hs assumpions, h coninuiy quaion for hols is auomaically saisfid whn h coninuiy quaion for lcrons and h charg nuraliy condiion ar fulfilld. W hav dvlopd a compur cod o solv h sysm of quaions (5) o (9) using appropria numrical chniqus. All h hrmal and opical ransiion ras ( E ) and G ( E, h ν ) can b dducd from quaions (2), (3) and (4) as follow: [ D(E) n (p ) ] n(p) (E) = Cn(p) n(ppc) (10) ( E E / ( k )) n(p) (E) = Cn(p) DCB(VB) n (p ) xp CB(VB) B (11) ( D n ( p ) ) n ( D ) ( E ) K G n (p) ( E, h ν ) = φ CB( VB) h (12) ν As rquird by h CPM xprimn, h phoon nrgy h ν is varid and h phoon flux magniud φ is adjusd o kp h magniud of h phooconduciviy q (µ n n + µ p p ), consan ovr h whol h ν rang. h singl ransiion absorpion cofficin is hn dducd from quaion (12) as: ( E, h ν ) Gn (p) i K α ( ) n (p) E i, h ν = = DCB(VB) n ( Ei ) [ D ( Ei )] h φ (13) ν and h oal absorpion cofficin as: α n (p) ( ν ) = α ( Ei, h ν ) h n (p) (14) i h DOS disribuion is calculad from h absorpion cofficin, afr Pirz a al. [15], using h drivaiv: g ( E ) ( h ν α n (p) ( h ν )) d ( h ν ) d 1 = (15) K g ( ) h ν = E E C
130. ibrmacin al. 3. EXPERIMENAL DEAILS h GaAs:Cr 1713 sampl was prpard a Ruđr Bošković Insiu Division of Marials Physics, Zagrb, Croaia. h 1713 sampl was par of a smi-insulaing GaAs chromium dopd wafr (GaAs:Cr) of 400 µm hicknss. I was cu from h ingos grown in h <100> dircion by h liquid ncapsulad Czochralski (L) mhod undr B 2 O 3 ncapsulaion. h chromium concnraion was 1.5 x 10 16 cm -3. Arrays of coplanar ohmic lcrods wr dposid on h polishd surfac of h wafrs wih a gap of 0.8 mm bwn lcrods. Singl chips of 4 x 9 mm 2 in ara wr cu from h wafrs and mound in h sampl holdrs of cryosas. h schmaic of h CPM xprimn which hav bn usd in his work is shown in figur 2. A xnon lamp was usd as a ligh sourc. h monochromaor had a graing of 600 groovs/mm wih a filr whl wr usd for scanning wavlngh. h - CPM currn was masurd by a picoammr insad of a lock-in amplifir bu h ligh innsiy was moniord by h sam lock-in mhod as in h cas of ac-cpm. In h CPM, absorpion cofficins, α ( h ν ), wr obaind as h invrs of h incidn phoon numbr, 1/ φ ph, undr a consan phoocurrn, I ph, by using convnional CPM assumpions. Absolu CPM spcra wr obaind by monioring h ransmid phoon flux following h procdurs dscribd by Vanck al. [12, 13]. Daa wr hn calibrad by rfrnc o opical ransmission masurmns, hrough h us of h Rir-Wisr formula [14]. h DOS was obaind by diffrniaion of h absorpion curv mhod dscribd by Pirz al. [15]. Fig. 2: DC-CPM s up 1. W-halogn lamp; 2.Opical choppr; 3. Monochromaor; 4. Filrs whl 5. Bam splir; 6. Cryosa+ Sampl; 7. Dcors; 8. Lock-in amplifir 9. Picoammr; 10.Sampl powr supply; 11. Lamp powr supply
Characrizaion of Smi-Insulaing GaAs:Cr by Mans of DC-CPM chniqu 131 4. RESULS AND DISCUSSION Figur 3-a show h masurd Cr dopd GaAs CPM spcrum. A rapid dcras in h absorpion cofficin is obsrvd a abou 1.4V which is h band dg for his marial. Figur 3-b show h dnsiy of sas disribuion of occupid sas clos o valnc band dg drivd from figur 3-a using h drivaiv mhod of Pirz al. [15]. (a) (b) Fig. 3: -CPM spcrum (a) and h corrsponding dnsiy of sas disribuion (b) for SI GaAs:Cr # 1713 sampl
132. ibrmacin al. A dnsiy of sas disribuion modl for h smi-insulaing Cr-dopd GaAs is inroducd and shown in figur 4. h inroducd dnsiy of sas consiss of wo pars: (i) h lowr par clos o conducion band dg is drivd from ransin phoocurrn masurmn PC, [2], high rsoluion phoo inducd ransin spcroscopy HRPIS and modulad phoocurrn masurmns MPC [3], (ii) whil h uppr par nar h valnc band dg is drivd from CPM masurmn as shown in figur 3-(b). Fig. 4: Smi-insulaing Cr-dopd GaAs dnsiy of sas disribuion modl usd for CPM numrical modlling h mos imporan paramrs usd for his dnsiy of sas disribuion ar summarizd in abl 1. abl 1: Dnsiy of sas paramrs usd in opical absorpion spcrum modlling of SI GaAs:Cr Elcron mobiliy Hol mobiliy Dnsiy of sas a h mobiliy dg Dnsiy of sas a h mobiliy dg Mobiliy Gap E c E v μ n = 4400 cm 2 V -1 s -1 μ p = 100 cm 2 V -1 s -1 N c = 4.7 x 10 17 cm -3 N v = 7 x 10 18 cm -3 E g = 1.42 V mpraur = 300 K * Frmi lvl posiion E F 0.75 V *E F is calculad from h charg nuraliy condiion
Characrizaion of Smi-Insulaing GaAs:Cr by Mans of DC-CPM chniqu 133 Using h SI GaAs:Cr DOS modl, w hav compud by our CPM program cod h oal absorpion cofficin α o and hir componns α n and α p, corrsponding o opical ransiions associad wih fr lcron and fr hol craion rspcivly. hs absorpion spcra ar usd o infr h dnsiy of sas ovr h nrgy gap nar band dg and clos o mid-gap. Figur 5 and 6 show h obaind rsuls. As w can s h acual DOS is wll fid ovr a larg rgion of h band gap of h smi-insulaing Cr-dopd GaAs. Fig. 5: Simulad -CPM spcra for Cr dopd GaAs using h DOS of figur 4: ( ) oal absorpion spcrum α o (hν) ( ) Simulad -CPM lcron absorpion spcrum ( ) Simulad -CPM hol absorpion spcrum α n (hν) α p (hν). Fig. 6: Rconsrucd dnsiy of sas from absorpion spcra of figur 5
134. ibrmacin al. 5. CONCLUSION In conclusion, h masurmn rsuls hav shown ha h absolu CPM chniqu is applicabl o non-silicon marials such as Gallium Arsnid and o any phooconduciv marials. Whil, and on h ohr hand, h simulaion rsuls hav allowd us h drminaion of h disribuion of dfcs blow and abov h Frmi lvl from α n ( h ν ) and α p ( h ν ) absorpion cofficins. I is also found ha by combinaion of h wo wll known masurmn mhods CPM and PC, and h wo xprimnally inaccssibl opical absorpion cofficins componns α n ( h ν ) and α p ( h ν ), w ar abl o hav a full rconsrucion of h occupid and unoccupid dnsiy of sas disribuion for such marials. ACKNOWLEDGMENS h auhors ar hankful o C. Main and S. Rynolds for provision of basic CPM modlling cod and for fruiful discussions during a rsarch visi o h Univrsiy of Dund (UK). h auhors ar graful o h Algrian Minisry of Highr Educaion and Rsarch for suppor. REFERENCES [1] U.V. Dsnica, B.G. Provic, M. Skowronski and M.C. Crlla, On Quaniaiv Mapping of EL2 Concnraion in Smi-Insulaing GaAs Wafrs, Journal d Physiqu III, Franc 1, pp. 1481-1487, 1991. [2] H. Blgacm, A. Mrazga and C. Longaud, Drminaion of Dfc Lvl Paramrs in Smi-Insulaing Gaas:Cr from ransin Phoocurrn Exprimn, Smiconducor Scinc and chnology, Vol. 20, N 1, pp. 56-61, 2005. [3] C. Longaud, J.P. Klidr, P. Kaminski, R. Kozlowski, M. Pawlowski and J. Cwirko, Invsigaion of Dfc Lvls in Smi-Insulaing Marials by Modulad and ransin Phoocurrn: Comparison of Mhods, Smiconducor Scinc and chnology, Vol. 14, N 9, pp.747 756, 1999. [4] C. Koco and C.A. Sol, Backgaing in GaAs MESFE s, IEEE ransacions on Elcron Dvics, Vol. Ed-29, N 7, pp. 1059 1064, 1982. [5] J.A. Davidson and J.H. Evans, Dcion Saisics of Dp Lvls in Minoriy Carrir ransin Spcroscopy, Journal of Applid Physic, Vol. 81, N 1, pp. 251 259, 1997. [6] F. Sibk, H. Sibig, A. Abo-Arais and H. Wagnr, Chargd and Nural Dfc Sas in A- Si:H Drmind from Improvd Analysis of h Consan Phoocurrn Mhod, Solar Enrgy Marials and Solar Clls, Vol. 41-42, pp. 529-536, 1996. [7] A. Mlr, N. Wyrsch, M. Goz and A. Shah, Dp Dfc Drminaion by h Consan Phoocurrn Mhod (CPM) in Annald or Ligh Soakd Amorphous Hydrognad Silicon (a-si:h), Solar Enrgy Marials and Solar Clls, Vol. 34, N 1-4, pp. 533 539, 1994. [8] C. Main, S. Rynolds, I. Zrinscak and A. Mrazga, Comparison of AC and DC Consan Phoocurrn Mhods for Drminaion of Dfc Dnsiis, Journal of Non Crysallin Solids, Vol. 338-340, pp. 228-231, 2004.
Characrizaion of Smi-Insulaing GaAs:Cr by Mans of DC-CPM chniqu 135 [9] C. Main and D. Nshva, ransin Phoocurrn chniqus as a Mans of Characrising Amorphous Smiconducors, Journal Opolcronic and Advancd Marials, Vol. 3, N 3, pp. 653-664, 2001. [10] S. Rynolds, C. Main, D.P.Wbb and M.J. Ros, 2000. An Exprimnal Evaluaion of ransin and Modulad Phoocurrn Dnsiy of Sas Spcroscopis, Philosophical Magazin B, Vol. 80, N 4, pp. 547-559, 2000. [11] K. Haori, Y. Adachi, M. Anzai, H. Okamoo and Y. Hamakawa, Modulad Phooconduciviy Sudy of Chargd and Nural Dfcs in Undopd Amorphous Silicon, Journal Applid Physic, Vol. 76, N 5, pp. 2841 2850, 1994. [12] M. Vanck, J. Kocka, A. Poruba and A. Fjfar, 1995. Dirc Masurmn of h Dp Dfc Dnsiy in hin Amorphous Silicon Films wih h Absolu Consan Phoocurrn Mhod, Journal Applid Physic, Vol. 78, N 10, pp. 6203-6210, 1995. [13] A. Fjfar, A. Poruba, M. Vanck and J. Kocka, Prcis Masurmn of h Dp Dfcs and Surfac Sas in A-Si:H Films by Absolu CPM, Journal of Non-Crysallin Solids, Vol. 198-200, pp. 304-308, 1996. [14] D. Rir and K. Wisr, Supprssion of Inrfrnc Frings in Absorpion Masurmns on hin Films, Opics Communicaions, Vol. 57, N 5, pp. 336-338, 1986. [15] K. Pirz, B. Hilgnbrg, H. Mll and G. Wisr, Journal of Non-Crysallin Solids, Vol. 97-98, pp. 63-66, 1987.