Effective Density of States Map of Undoped µc-si:h Films: a Combined Experimental and Numerical Simulation Approach

Transcription

1 Effective Desity of States Ma of Udoed µc-si:h ilms: a Combied Exerimetal ad umerical Simulatio Aroach Sajay K. Ram * ad Satyedra Kumar! Deartmet of Physics, Idia Istitute of Techology Kaur, Kaur-2816, Idia The hototrasort roerties of lasma deosited highly crystallie udoed hydrogeated microcrystallie silico (µc-si:h) films were studied by measurig the steady state hotocoductivity (SSPC) as a fuctio of temerature ad light itesity. The films ossessig differet thickesses ad microstructures had bee well characterized by various microstructural robes. µc-si:h films ossessig dissimilar microstructural attributes were foud to exhibit differet hototrasort behaviors. We have emloyed umerical modelig of SSPC to corroborate ad further elucidate the exerimetal results. Our study idicates that the differet hototrasort behaviors are liked to differet features of the roosed desity of states mas of the material which are differet for µc-si:h films havig differet tyes of microstructure. PACS umbers: 73.5.Pz, h, r, k, 73.5.Gr, 72.2.Jv, 81.4.Gh I. ITRODUIO Plasma deosited hydrogeated microcrystallie silico (µc-si:h) has immese otetial i large area electroic alicatios, as it offers the ossibilities of high carrier mobilities 1 ad better stability agaist light ad curret iduced degradatio as comared with amorhous silico (a-si:h). 2,3,4,5,6,7 These features, alog with a ease of large area rocessig caabilities 2,8,9,1 eve at low temeratures 11 make it a attractive cadidate for use i solar cells 12 ad thi film trasistors. 13 Microcrystallie silico material is heterogeeous i ature cosistig of crystallie ad amorhous hases with resece of desity deficit regios. 14,15 The microstructure of µc-si:h is ot uique due to the rocessig history, therefore, a comariso betwee various electroic trasort models is futile, ad there is still a log way to go i exlaiig the trasort roerties i the light of film microstructure. The resece of sigificat disorder i terms of variatios i size ad shae of crystallites (grais) 16 ad ature of disordered hase (itergrai ad iter-columar boudaries) 17 comlicates a comrehesive descritio of the otoelectroic roerties i this material. 18,19,2,21 It is evidet that smaller grai size imarts roerties similar to those of a-si:h, while large grai sizes cofers roerties closer to crystallie silico. 18 Thus resetly, little is kow about the recombiatio mechaisms ad the ature / distributio of the desity of ga states (DOS), ad due to the above metioed comlexities, it is ureasoable to search for a uique effective DOS rofile that would satisfy whole rage of µc-si:h materials ad exlai all the itricacies ivolved * Corresodig author. address: skram@iitk.ac.i; sajayk.ram@gmail.com! satye@iitk.ac.i i its trasort mechaisms. 22,23 urther, it eeds to be emhasized that by aalyzig a few samles of µc-si:h roduced uder a arrow deositio regime, oe caot costruct a DOS rofile alicable to the whole class of µc-si:h materials. Istead, it would be more scietific to costruct DOS rofiles based o film microstructure that would be alicable to a wider rage of samles havig some commo uique microstructural features. 24,25,26 The effects of the desity ad ature of ga states i semicoductors ad isulators are extesively studied usig hotocoductivity ad its recombiatio kietics. 27,28 Trasiet hotocoductivity (TPC) 29,3 ad drift mobility measuremet techiques 31,32,33,34 have bee used to robe exoetial coductio bad ad valece bad tail (CBT ad VBT resectively) states i µc-si:h films. I additio, subga absortio sectroscoy techiques such as costat hotocurret method (CPM), 33,35,36,37,38 dual beam hotocoductivity (P), 39 ad hotothermal deflectio sectroscoy (PDS) 37,38,4 are used to characterize the VBT states. Electro si resoace (ESR) has also bee used to robe the midga states i µc-si:h. 41 Some attemts have bee made to deciher artial DOS distributios i the viciity of CB edge usig these robes. 5,42,43,44,45 I cotrast to the above methods that study oly a secific ortio of the DOS i the ga, steady state hotocoductivity (SSPC) is a efficiet ad easy techique to examie the ga states over a wider rage i the badga, ad is sesitive to both desity ad ature of all the defect states actig as recombiatio ceters betwee the quasi ermi levels i the bad ga. SSPC allows a comrehesive study of the hototrasort roerties of the electroic system of the corresodig material. The observed effects with this method ca be the cosequeces of several differet hototrasort rocesses occurrig i the system. Therefore, it is difficult to attribute the observed behavior to a articular effect. Certai fea-

2 tures of SSPC i a-si:h ca be uderstood usig the famous Rose model, 27 but this model is ot always alicable i µc-si:h films. 25 umerical modelig has bee extesively used to elicit iformatio about the recombiatio kietics ad exlai the exerimetal hotocoductivity results i a-si:h 46,47,48,49,5,51 ad has added greatly to our kowledge of the ature ad desity of ga states i a-si:h. I cotrast, umerical modelig has bee less emloyed to uderstad the SSPC i heterogeeous µc-si:h. 22,24,25 However, efforts have bee made to umerically model the trasiet hotocoductivity (TPC), 29 time-of-flight (TO) measuremet 52,53 ad modulated hotocoductivity (MPC) rocesses 43 i µc-si:h system. As discussed above, the hotoelectroic roerties of µc-si:h are still iadequately uderstood due to a lack of kowledge about the DOS mas of µc-si:h. I 24, Balberg et al. 22 roosed the DOS of a sigle-hase µc-si:h material usig a comrehesive study ivolvig SSPC exerimets ad umerical modelig that emhasized the dissimilarity of µc-si:h with both olycrystallie ad amorhous silico. I this aer, we reort the fidigs of our study of hototrasort roerties of microstructurally differet µc-si:h films emloyig both exerimetal methods ad umerical modelig of SSPC, ad roose the effective DOS mas of these materials. or this urose, we have first structurally characterized the µc-si:h films usig a variety of tools to elucidate a comrehesive icture of film microstructure ad morhology. The dark electrical trasort roerties of these films, correlative with the microstructural fidigs led us to classify the material broadly ito three tyes, havig distict microstructural ad morhological attributes, with a articular dark electrical trasort behavior eculiar to each class. The results of the structural ad dark coductivity studies have bee reorted elsewhere, 54,55,56 but the fidigs have bee summarized i III.A, as they lay the foudatio for the correlatio betwee the structural asects ad hototrasort roerties. The hototrasort roerties of these wellcharacterized films were the studied usig SSPC ad CPM techiques, the fidigs of the latter are ot reorted i this aer. The SSPC data was aalyzed qualitatively, with a view to correlate the observed hototrasort roerties of each tye of µc-si:h material to its microstructural fidigs. However, elucidatio of some other imortat hototrasort roerties such as recombiatio traffic, the role of differet ga states i recombiatio rocess, ad the comlete DOS distributio i these microstructurally differet µc-si:h films require a umerical modelig study of the hototrasort roerties. I order to exlore these asects that would shed light o the hototrasort roerties of µc-si:h ad also substatiate the exerimetally elucidated facts, we coducted a umerical modelig study of these three tyes of µc-si:h. This aer is orgaized as follows. I Sec. II, the theory of hotocoductivity is reseted. The Sec. III describes the SSPC exerimetal details, results ad qualitative aalysis. umerical modelig study is described i Sec. IV, icludig the backgroud, basic formalism, simulatio rocedure, ad data aalysis. ially, the overall fidigs of the qualitative ad quatitative aalyses are summed u i Sec. V. II. THEORY Photocoductivity ca be described to cosist of three mechaisms: irst, absortio of hotos ad geeratio of free electro-hole airs; secod, trasort of mobile carriers; ad third, recombiatio of excess free electros ad holes through recombiatio ceters. 27,28 Photocoductivity uder steady state illumiatio is give by: h [ μ ( ) + ( )] σ e μ, (1) where μ ad μ are free-electro ad hole mobilities resectively; ad rereset the steady state cocetratio of hotoexcited electros ad holes, whereas ad are their corresodig cocetratios i the dark at a give temerature T. Sice udoed µc-si:h shows - tye behavior ad μ > μ, electros are take to be the majority carriers. I geeral, hotocoductivity exhibits a o-iteger ower law deedece o carrier geeratio rate G L over several orders of magitude give by: γ σ h G, (2) L The geeratio rate G L is determied by the exteral arameters ad iteral material arameters as: G ( 1 R )[ ] α. d e φ (3) d L 1 where φ is the flux of hotos i cm -2 s -1, R is the reflectio coefficiet at hν E, α is the absortio coefficiet of the material at eergy hν E, ad d is the film thickess. The hotocoductivity light itesity exoet, γ rovides iformatio about the recombiatio mechaisms i a semicoductor material. γ.5 reresets bimolecular recombiatio kietics, where electros i the CB directly recombie with the holes i the VB. γ 1 reresets moomolecular recombiatio, that is, electros i the CB recombie with holes i the VB, through the recombiatio ceters i the ga. or γ value lyig betwee.5 ad 1, Rose 27 described a model i which the desity of traed electros t, aroximated by t ( ) Ef T ( T ) g( E) de, (4) tracks the desity of ositively charged recombiatio ceters P r to maitai charge eutrality. Rose showed that if the discrete states are distributed exoetially i the 2

3 ktc viciity of bad edges i the form of e ΔE, the hotocurret ad light itesity curve should have the ower γ as: kt c γ, (5) ( kt + ktc ) here ΔE is measured from the bottom of the CB ad kt c is the characteristic eergy of CBT greater tha or equal to the eergy corresodig to the measuremet temerature T. I that case, most of the traed electros reside withi kt of the steady state ermi level E f. The model as give by Eq. (4) is also alicable to the cases where DOS rofile g(e) does ot decay i a urely exoetial maer. The values for γ the corresod to certai ositios of E f, ad a aroximatig exoetial fuctio with a local bad tail arameter kt (E f ) i its viciity, givig g(e f ). The quasi ermi level ca be determied from the hotocoductivity i the same rage as was used to evaluate γ. The exressio is give by: ( φ, T ) ( ) d T σ h [ Ec Ef ( φ, T )] [ Ec Ef ( T )] kt l σ The above exressio ca be re-writte i the way as below: σ Ec Ef kt l (6) σ h ( T ) III. EXPERIMET: STEADY STATE PHOTOCODUIVITY III.A. Exerimetal details We reared a series of highly crystallized udoed µc-si:h films havig varyig degree of crystalliity by deositig o Corig 1737 substrates at a substrate temerature of 2 o C i a arallel-late glow discharge lasma deositio system oeratig at a stadard rf frequecy of MHz usig high urity Si 4, Ar ad H 2 as feed gases. 54,57 or the structural ivestigatios, we emloyed variety of structural robes like i-situ sectroscoic ellisometry (SE), Rama scatterig (RS, from film ad substrate side), X-ray diffractio (XRD) ad atomic force microscoy (AM). These wellcharacterized films were studied for the electro trasort behavior usig dark coductivity ad hotocoductivity as fuctios of several discerig arameters such as temerature, wavelegth ad itesity of robig light. 24,25 The effect of light itesity variatio o the steady state hotocoductivity was robed usig abovebadga light (He-e laser, λ m) i the temerature rage of 2K 324K. Photo flux φ was varied from 1 11 to 1 17 hotos/cm 2 -sec usig eutral desity filters givig rise to geeratio rates of G L cm -3 s -1. Peetratio deth of this light is 5 m. May of the µc-si:h films used i this study have bee characterized by the time resolved microwave coductivity (TRMC) measuremets. 58 TRMC is kow to measure the mobility of carriers withi the grais. 58 III.B. idigs of structural ad dark electrical trasort studies High crystalliity of all the samles was cofirmed by RS ad SE measuremets. SE data shows a crystallie volume fractio >9% from the iitial stages of growth, with the rest beig desity deficit havig o amorhous hase, ad a reduced icubatio layer thickess. RS results show a shar eak at cm -1, corresodig to TO (trasverse otical) mode i c-si, without ay amorhous hase that tyically accomaies the c-si eak i the RS rofiles of µc-si:h material. The detailed comositio of the films educed from SE data shows grais of two distict sizes, which is corroborated by the decovolutio of RS rofiles usig a crystallite size distributio of large grais (LG, 7-8 m) ad small grais (SG, 6-7 m). 54,55 The bimodal crystallite size distributio is further suorted by the XRD results showig large ad small sized grais with differet orietatios. 59,6 There is sigificat variatio i the ercetage volume fractio of SG ( cf ) ad LG ( cl ) with film growth. Preferetial orietatio i (4) ad (22) directios is achieved by otimizig the deositio coditios leadig to smooth to surfaces (surface roughess < 3 m). Smooth to surfaces with less defect desities are highly attractive roerties for device alicatios. 54,55 Based o the structural ivestigatios of the µc-si:h films at various stages of growth, we were able to segregate out the uique features of microstructure ad growth tye reset i the varieties of µc-si:h films from the colaar electrical trasort oit of view. All the µc-si:h samles were classified ito three tyes: tye-a, tye-b, ad tye-c, where we see the ifluece of the ature of ihomogeeities i µc-si:h o the temerature deedet dark coductivity [σ d (T)]. 56 Our fidigs idicate that sice deositio arameters have oly a idirect causal lik to the electrical roerties through their rimary effect o the microstructure of material, it is useful to cosider the fractioal comositio of costituet large crystallite grais ( cl ) as a simle yet hysically ratioal microstructural arameter that idicates the microstructural ad morhological coditio of the fully crystallized sigle hase µc-si:h films ad thus correlates accetably with the electrical trasort behavior. 55,56 To summarize this classificatio, the tye-a films have small grais, high desity of iter-grai boudary regios cotaiig disordered hase, ad low amout of coglomeratio. I this tye, cl <3%, σ ad E a are costat [ 1 3 (Ωcm) -1 ad.55 ev resectively]. The tye-b films cotai a fixed ratio of mixed grais i the bulk. Coglomeratio of grais results i a marked morhological variatio, ad a moderate amout of disordered hase i the coglomerate boudaries limits the 3

4 σ h Light itesity exoet (γ) σ d Φ (hotos/cm 2 sec) 1.2 x x x x / T (K -1 ) / T (K -1 ) 1. (b).8.6 electrical trasort. Here cl varies from 3% to 45%, there is a shar dro i σ [from 1 3 to.1 (Ωcm) -1 ] ad E a (from.55 to.2 ev). The tye-c µc-si:h material is fully crystallized ad crystallites are desely acked with sigificat fractio of large crystallites (>5%) ad referetial orietatio is see. Here σ shows a risig tred [from.5 to 1 (Ωcm) -1 ] ad the fall i E a is slowed dow (from.2 to.1 ev). 54,56 III.C. Results of SSPC studies Steady state hotocoductivity ad costat hotocurret method measuremets were carried out o wellaealed samles usig colaar geometry i differet σ h γ /T (K -1 ) (a) /T (K -1 ) IG. 1. (a) Temerature deedece of σ h (T) of samle #B22 (tye-a) for various light itesities (φ) are show by lie+symbol. The temerature deedece of σ d of the same samle is show by solid lie. The iset shows the zoomed view of σ h (T); (b) Temerature deedece of light itesity exoet γ (obtaied from light itesities deedece of σ h (φ) at differet temeratures) of the same samle. The iset shows the zoomed view of γ (T) from 325K dow to 5K. Here the lie is to guide the eye. exerimetal set-us. To robe the effect of microstructural ihomogeeity o the hototrasort roerties of udoed µc-si:h, we selected a few samles of each category of microstructure as described above. Though the studies were carried out o may samles, here we reort the hototrasort measuremet results of three samles: samle #B22, samle #B23 ad samle #6, which are reresetative of tye-a, tye-b ad tye-c µc-si:h materials resectively. The results of all the studied samles showed similar treds secific to the tye of material. The details of calculatio rocedure to determie E f ositio i the ga 2,22,61 of these samles alog with their electrical trasort arameters are metioed i the Table I. Tye-A µc-si:h The results of temerature deedet hotocoductivity for various light itesities, σ h (T,φ) for samle #B22 (tye-a) are show i ig. 1 (a). The temerature deedet dark coductivity of this samle is show by a solid lie i ig. 1(a). The σ d (T) shows a activated behavior over a large temerature rage ( K) with a activatio eergy E a.5 ev. The σ h (T) of this samle is essetially a icreasig fuctio of temerature for ay value of light itesity used i the rage metioed above. However, at higher temeratures, σ h is see to decrease with icreasig temerature, a effect kow as thermal quechig (TQ). This effect is clearly see i the iset of ig. 1(a) over a temerature rage of T K. The ower law behavior of the hotocurret of this samle with a chage i hoto flux was observed throughout the temerature rage of our study. The temerature deedece of light itesity exoet, γ (T) calculated at each measuremet temerature from the light itesity deedece of hotocoductivity, σ h (φ) of the same samle is show i ig. 1(b). The iset shows the zoomed view of γ (T). The variatio of γ is foud to be betwee.5 ad 1 i the whole temerature rage. Tye-B µc-si:h The σ h (T,φ) for the samle #B23 (tye-b) is show i ig. 2(a). The σ h (T,φ) behavior of #B23 is quite differet from that of the above case as σ h is foud to icrease mootoically with temerature without ay thermal quechig effect. The solid lie i this figure reresets the dark coductivity with a activatio eergy E a.34 ev. The γ (T) values obtaied for differet temeratures for this samle are lotted agaist recirocal of T ad deicted i ig. 2(b). The γ value of this samle is foud to vary from.5 to 1 ad it ever goes dow below the value.5 i the whole temerature rage. Tye-C µc-si:h ig. 3(a) shows the temerature deedece of σ h for the samle #6 (tye-c) at various light itesities. 4

5 σ h Light itesity exoet (γ) 1-5 (a) σ d / T (K -1 ) γ (b) Φ (hotos/cm 2 -sec) 1x1 17 5x1 16 1x1 16 1x /T (K -1 ) /T (K -1 ) IG. 2. (a) Temerature deedece of σ h (T) of samle #B23 (tye-b) for various light itesities are show by lie+symbol. The temerature deedece of σ d of the same samle is show by solid lie; (b) Temerature deedece of γ (T) of the same samle. The iset shows the zoomed view of γ (T) from 325K dow to 5K. Here the lie is to guide the eye. The temerature deedet dark coductivity of the same samle is also show by a solid lie i the figure. The σ d (T) shows a activated behavior over a large temerature rage ( K) with a activatio eergy E a.12 ev. The σ h (T) of this samle mootoically icreases with the icrease i temerature excludig the lowest temerature regio (<3K) where σ h is early ideedet of T. However, at higher temeratures, thermal quechig effect is observed i the σ h (T) behavior of this samle, similar to the kid of σ h (T) behavior see i samle #B22 (tye-a). This effect is clearly see for the temerature rage of T K i the iset of ig. 3(a). The maximum i σ h (T) deedece shifts with icreasig light itesity to higher temeratures where the dark curret also icreases, limitig the measuremets at σ h Light itesity exoet (γ) σ d Φ ( hotos/cm 2 -sec ) 1x1 17 2x1 16 2x1 15 1x1 14 (a) / T (K -1 ) / T (K -1 ) high temeratures. The γ values obtaied for differet temerature are lotted i ig. 3(b). While γ ever reaches 1 i the whole temerature rage, we observe a uusually low value of γ.13 at about 225 K. This aomalous behavior i hotocoductivity data o udoed µc-si:h has bee observed i all of our fully crystallized samles reresetig tye-c microstructure. It eeds to be metioed here that at higher light itesity (φ > hotos/cm 2 s), γ value further reduces to.5 for all the temeratures. III.D. Qualitative aalysis of exerimetal SSPC data It is iterestig to ote that the behavior of the hototrasort roerties of the samles belogig to the three tyes of µc-si:h material are differet. I brief, we ca summarize the major outcome of the observed hoto- σ h (b) / T (K -1 ) / T (K -1 ) γ IG. 3. (a) Temerature deedece of σ h (T) of samle #6 (tye-c) for various light itesities are show by lie+symbol. The temerature deedece of σ d of the same samle is show by solid lie. The iset shows the zoomed view of σ h (T); (b) Temerature deedece of γ (T) of the same samle. The iset shows the zoomed view of γ (T) from 325K dow to 5K. 5

6 Table I. Details of calculatio rocedure to deduce E f ositio i the ga. Tyes, Samle# (R, thickess) Tye-A #B22 (1/1, 17m) Tye-B #B23 (1/1, 59 m) Tye-C #6 (1/1, 92m) σ d 3x1-6 2x x1-4 E a (ev) σ μ (cm 2 /V-s) TRMC exerimet Reorted method of E f calculatio Method-1 E c -E f (ev) Method-2 E c -E f (ev) Method-1: Cosiderig the ga, ( E E ) 1.8 ev E g c v s Ec E f Ea kt l( σ σ ) ; where s σ is the stadard value of dark coductivity refactor σ 15 for µc-si:h system [Ref. 22 ] Method-2: Cosiderig the ga, ( E E ) 1.12 ev E g ; c v 8 E f Ei kt l( σ d σ i ) ; Stadard value of itrisic dark coductivity σ i 6 1 ad itrisic eergy E E.56 ev for µc-si:h system [Ref. 2]. i v trasort roerties i the three tyes of samles i the followig way: a) I tye-a material, light itesity exoet (γ) lies betwee.5 ad 1, ad temerature deedet hotocoductivity [σ h (T)] shows thermal quechig (TQ) effect. b) I tye-b material,.5 < γ < 1, with o TQ effect is observed. c) I tye-c material,.15 < γ < 1, with a TQ effect is observed. This subliear behavior of γ ad simultaeous resece of TQ effect is aomalous. Therefore, it is ow clear that o sigle hototrasort mechaism or model ca exlai the results of the samles of all the three sets. However, it is highly ossible that differet hototrasort behavior ad mechaisms are takig lace for differet microstructures ad thickesses i such a heterogeeous system. Some of the above metioed exerimetal fidigs of hototrasort roerties i µc-si:h films, thermal quechig of hotocoductivity ad subliear behavior of γ, are also observed i a-si:h. To draw ay valid arallel comariso betwee these two systems of materials, it would be helful first to recall the well established models to uderstad the hototrasort mechaism i a homogeeous system like a-si:h, which we are summarizig here. Photocoductio i a-si:h The TQ effect i temerature deedet hotocoductivity is observed i crystallie semicoductors 27 ad i a-si:h. 48,5,62 The heomeo of TQ i crystallie hotocoductors was exlaied by Rose usig a model of two levels of states, oe havig larger cature coeffi- ciets for the majority carriers tha the other level. The asymmetry i the cature coefficiets causes TQ to occur i σ h (T). 27 This theory is ot alicable i case of amorhous semicoductors havig cotiuous desity of ga states. I a-si:h these ga states cosist of VBT, CBT ad daglig bod () defects. Over the ast few decades, various models have bee roosed to exlai TQ i a-si:h, which rogressively imroved as the kowledge of defect mechaisms, esecially s, exaded. 47,49,63,64,65,66 I 1994, Tra 5 reorted his extesive work to exlai TQ i terms of the trasferece of recombiatio traffic from VBT to s. This work showed that TQ arises aturally from the asymmetry of bad tails ad the resece of states i the badga of a-si:h. Tra s simulatio results showed that TQ occurs eve whe all cature coefficiets are idetical, i cotrast to the Rose model where they are larger i oe of the two discrete levels. Usually TQ occurs for T > 1 K i a-si:h. Tra exouded o the well-kow exerimetal observatio that the oset of TQ i a-si:h shifts to higher temerature whe defect desities are less or -tye doig level is icreased. 67 Let us ow look at aother imortat feature of the hototrasort arameter, light itesity exoet γ. At low light excitatio, usaturatio of recombiatio ceters ca lead to suerliearity while subliear behavior ca be observed at high light itesity whe the saturatio of such ceters takes lace. The exlaatio of subliear hotocoductive behavior is rather more cotroversial, ad the model ublished iclude variatios o the classic Rose model, 27 bimolecular recombiatio, 68 the shift of ermi level E f towards bad edges, 69,7 ad the ifluece of surface defects ad surface bad bedig. 71,72 6

7 Aother exlaatio of the subliearity i σ h (φ) of doed a-si:h, as roosed by Mai et al., 51 is that if CBT is steeer tha VBT (i.e. kt c << kt v ) ad excess hotocarriers are comarable to thermal carriers i dark, the Rose model does ot hold; γ at low excitatio the becomes T/T v ad at high excitatio it chages to a costat value T c /T v. 51 Actually, with a icrease i light itesity, the traed hole quasi-ermi level moves toward the bad edge. To balace the resultig icrease i traed hole desity, the traed electro ermi level moves uward, but by a smaller shift i eergy, sice the CBT is steeer tha the valece bad tail. Thus, the rate of icrease of excess electros is much smaller tha the (liear) rate of icrease of excess holes with light itesity. These dee hole tras are comarable to the safe hole tras discussed by McMaho ad Cradall. 73 The safe hole tras have lower cature coefficiet for electros comared to a much higher rate coefficiet for electro cature to s. Recombiatio of holes traed i such states ivolves, first a emissio to the valece bad or shallow valece bad tail states, followed by cature by egatively charged state. 74 Photocoductio i µc-si:h Several tyes of hototrasort behaviors have bee observed i doed, udoed 22,41,44,75 or comesated µc-si:h films. 76 I some cases, TQ i the temerature deedet hotocoductivity measuremet has bee observed at 25K whereas mootoic behavior of hotocoductivity has also bee reorted. 22 Similarly, differet behaviors of temerature deedece of light itesity exoet γ have bee foud. 22,76 I additio, there are reorts of differet hototrasort mechaisms oeratig i differet temerature rages. 77 The costat behavior of σ h (T) ad γ 1 of µc-si:h films i low temerature regime have bee satisfactorily exlaied by eergy loss hoig of hotoexcited electros ad holes via localized bad tail states before o-gemiate recombiatio, similar to a-si:h case. However, o such agreemet is foud amog the reorts that have attemted to exlai the hotocoductivity mechaisms i the medium ad high temerature regime. III.D.1. Photocoductivity exoet: alicability of Rose model The iformatio about the distributio of ga states ear the bad edges of majority carrier is draw from the exoet γ. Accordig to Rose model, 27 whe the γ value lies betwee.5 ad 1, it is assumed that the discrete states are distributed exoetially i the ga. The model is also foud to be valid i a-si:h where the localized states are cotiuous i the ga ad it has bee successfully used to exlai several hototrasort mechaisms i the a-si:h material. 78 Sice amorhous or disordered hase reset i the boudary regios is oe of the costituets of the comlex microstructure of µc-si:h films, it is likely to ifluece the hototrasort behavior of these films as well. Bruggema 44 has alied Rose model successfully i µc-si:h films ad obtaied iformatio about the localized states i the viciity of CB edge ad their effective DOS rofile. Therefore, it is imortat to see if Rose model works for the varieties of highly crystallized µc-si:h material used i our study. To begi with, we try to aly the model to the results of the hototrasort studies of the tye-a material (samle #B22) show i ig. 1(a) ad (b). The bad-tail arameter kt c was calculated from the γ values at differet temeratures as show i ig. 1(b) by alyig the Eq. (5). The ig. 4(a) deicts the calculated kt c. The quasi ermi level was determied usig Eq. (6), from those hotocoductivity values that lie i the rage of a articular costat value of γ for ay articular T. The coditio, kt c > kt is maitaied i the whole temerature rage of our study. The temerature rage for which the data was evaluated i terms of the model i Eq. (5) tail arameter kt C (ev) desity of states (arb. uit) (a) quasi-ermi eergy E f (ev) 1 2 (b) DOS #B22 (tye-a) 125 K 15 K 175 K 2 K 225 K 25 K 275 K 29 K 3 K 31 K lie guide to eye E (ev) IG. 4. (a) Plots of bad-tail arameter kt c vs. quasi-ermi eergy E f of samle #B22 (tye-a), where kt c were calculated from the γ values at differet temeratures show i ig. 1(b); (b) Desity of states (DOS) distributio obtaied by fittig kt c vs (E c -E) data of art (a) to exoetial distributio of states. This sketch of DOS rofile i this samle is oly a aroximatio. 7

8 tail arameter kt C (ev) desity of states (arb. uit).7 (a) quasi-ermi eergy E f (ev) 1 2 (b) DOS #B23 (tye-b) lie guide to eye E (ev) IG. 5. (a) Plots of bad-tail arameter kt c vs. quasi-ermi eergy E f of samle #B23 (tye-b), where kt c were calculated from the γ values at differet temeratures show i ig. 2(b); (b) Desity of states (DOS) distributio obtaied by fittig kt c vs (E c -E) data of art (a) to exoetial distributio of states. This sketch of DOS rofile i this samle is oly a aroximatio. varies from 324 K dow to 128 K. Lower values of T were ot used i the calculatio as hoig coductio might be oeratig i that rage. 54 ially, based o the values of bad-tail arameter (at differet temeratures ad for differet eergetic ositios) obtaied from ig. 4(a), we could roughly calculate the desity of states below the CB edge for this tye-a material. The aroximated DOS rofile is show i ig. 4(b). Here, the umerical values have bee used oly to embellish the characteristic eergetic sloes with a visually areciable structure of the DOS rofile. It should be oted that this DOS rofile is oly a rough estimate, but it ca hel us visualize the shae of the localized bad tail distributio ear oe of the bad edges, i this case, the CB edge. The desity of localized tail states is foud to be exoetially distributed i the CB regio, though at deeer eergetic ositios the DOS decays very slowly. ow let us tur to the results of the hototrasort studies of the tye-b material (samle #B23) show i desity of states (arb. uit) DOS of tye-a μc-si:h DOS of tye-b μc-si:h #1 #2 #3 #4 # E (ev) IG. 6. Desity of states (DOS) distributio obtaied for SSPC measuremet of tyes-a ad B µc-si:h are lotted alog with DOS rofiles of µc-si:h suggested i literature obtaied with other exerimetal techiques (#1-5). This sketch of DOS rofile i this samle is oly a aroximatio. Here, #1 [Ref. 53; MPC-DOS colaar µc-si:h (I crs.5)], #2 [Ref. 5,79; MPC-DOS HW-CVD µc-si:h], #3 [Ref. 5,79; MPC-DOS SPC µc-si:h], #4 [Ref. 52; TO-DOS µc-si:h], #5 [Ref. 44; SSPC-DOS µc-si:h]. ig. 2(a) ad (b). The method of calculatio of bad-tail arameter kt c ad the quasi ermi level at differet temeratures was similar to the above case ad the lot of values obtaied is show i ig. 5(a). The coditio kt c > kt is maitaied i this case too. Here also low temerature regio is ot cosidered due to the ossibility of hoig coductio oeratig i that rage. The ig. 5(b) shows a rough sketch of the desity of states rofile below the CB edge for the tye-b µc-si:h material. I this case, DOS is foud to have slowly decayig states i the eergy iterval.2 to.3 ev, followed by a steeer tail. Similar to the DOS of tye-a, the desity of localized tail states at deeer eergetic ositio shows less stee tail. Therefore, we see that i samles of tye-a ad B, the behavior of γ is i agreemet with Rose model, suggestig the resece of a bad-tail state distributio i these two materials. or comariso we have lotted our exerimetally estimated DOS rofiles of both the tyes of µc-si:h alog with the DOS rofiles of µc-si:h suggested i the literature derived from other exerimetal techiques (#1-4) 5,52,53,79 i ig. 6. Though the obtaied DOS rofiles of our µc-si:h samles are just rough sketches, but they are ot uhysical ad are i excellet agreemet with the DOS obtaied by other grous. 5,53,79 The shae of our DOS rofile of tye-a material is quite similar to the SSPC-DOS estimated by Bruggema (#5). 44 However, the shae of DOS rofile of tye-b material ear the bad edge (from.2 to.3 ev) is similar to that of MPC-DOS obtaied for solid hase crystallized (SPC) µc-si:h (#3). 5,79 The reaso could be due to the highly crystallie ature of our tye-b material. The lower values of DOS of our µc-si:h at deeer 8

9 eergetic ositio i the ga ca be the result of the assivatio of grai boudaries by H 2, while the boudaries of SPC µc-si:h material are ot assivated, ad ca therefore give rise to high value of DOS at deeer eergies i the ga. However, i tye-c material, whe we tried to fit Rose model to its hototrasort results, viz., γ, we fid a very arrow width of CBT (kt c.1 ev). Here, kt c is foud to be less tha kt i the whole rage of temerature, which is ot a valid assumtio for Rose theory. Therefore, oe caot aly this model to the tye-c material. ow we shall discuss the results of each tye of material i cotext of its characteristic microstructural features, dark coductivity roerties ad hysically lausible DOS features that ca give rise to such hototrasort behavior. III.D.2. Phototrasort behavior of Tye-A µc-si:h (TQ ad.5<γ <1) It ca be recalled that tye-a µc-si:h films are crystallized with small grais. The smaller grai size results i a higher umber desity of boudary regios, the usaturated s are assumed to be located i these disordered boudary regios. Therefore, the material may ossess quite a sigificat umber of desities, though less tha what is reset i a-si:h. It is temtig to treat tye-a µc-si:h aalogous to a-si:h. However, there are certai strikig differeces i the hototrasort mechaisms i the two materials. I articular, thermal quechig of σ h (Τ) i a udoed a-si:h is usually accomaied by suerliear behavior of γ. 48,5,62 I cotrast, we see TQ accomaied by.5<γ <1 i case of tye-a µc-si:h. Moreover, TQ i a-si:h is see ear 1-15 K 5 whereas the oset of TQ i this case is ear 225 K. As we have see above, TQ effect i a-si:h ca occur because of the resece of s ad the asymmetry i the bad tail states. I fact, detailed simulatio of σ h by Tra idicated a icrease i the oset temerature of TQ by reducig the desity. 5 Regardig the asymmetry i the shae of both the bad tail states, we fid valuable iformatio about at least oe of the localized tail states as to its distributio i the viciity of CB edge by usig Rose model [ig. 4(a)]. The results of the deedece of sub ga absortio o varyig microstructure of µc-si:h films suggest that the width of VBT of tye-a material should be larger tha tye-b ad C materials. The VBT width of tye-a material is closer to that of a-si:h. Therefore, we ca coclude that the width of VBT is larger tha that of CBT, givig rise to asymmetry i bad tail states. ow the roblem remais to fid the cause of absece of suerliear behavior of γ, which usually accomaies TQ i a-si:h. The dark coductivity results of this samle 61 redict the ermi level ositio to be aroud E f (E c -.46) ev. If we assume the eergy ga of this disorder hase reset i the boudary (where the recombiatio rocess is takig lace) 1.8 ev similar to the value i a-si:h, the E f 1.34 ev above the VB edge (see Table I). I a-si:h it has bee observed that o shiftig E f towards CB edge either by doig or ay other meas, the γ value is foud to decrease. 69,7 I this case E f is also at a higher ositio tha foud i udoed a- Si:H. This might be the reaso why suerliear behavior was ot observed. However, we ca see a slight icrease of γ value ear the temerature regio of TQ oset. The rise i γ value at high temerature is due to the effect of thermally geerated carriers. III.D.3. Phototrasort behavior of Tye-C µc-si:h (TQ ad γ <.5) Observatio of γ <.5 alog with a thermal quechig is uusual. 24,25 Though it has bee observed i µc-si:h, 8 but the simultaeous occurrece of the two heomea has ot bee exlored. Here we eed to search for ossible reasos that ca satisfactorily exlai occurrece of TQ with γ <.5. Tye-C µc-si:h material cosists of tightly acked large crystallites with referred orietatio ad o trace of amorhous Si tissue. It is therefore difficult to lik the observed TQ to just the desity. ow, let us look at the role of asymmetry i bad tails i the causatio of TQ. or tye-c µc-si:h, we foud kt c < kt ( III.D.1). Therefore, a arrow width of CBT (kt c <.2 ev) ca be exected. Accordig to the defect ool model, -tye doig i a-si:h causes a large icrease i egatively charged s desity together with a decrease i ositively charged daglig bad states i the ga, which i tur shows a lower DOS ear the CB edge leadig to steeer CBT. 81,82,83 I tye-c µc-si:h, higher desity of available free carriers ad low value of defect desity ca also create a ossibility for steeer CBT. ow let us look ito the VBT regio. Accordig to reorts, it has bee foud usig costat hotocurret measuremet that Urbach eergy of the hole bad tail icreases with icreasig crystalliity. 37 This results i a higher umber of desity of states i the deeer side of VBT causig the overall width of VBT to be larger tha that of CBT. So it is evidet that the sloe of CBT must be steeer comared to VBT ad hece ca give arise to asymmetry i both the tail states, causig TQ to occur. Aother eculiarity observed is the subliear behavior of γ (<.5) i tye-c µc-si:h for most of the temerature regio excet at very low temerature where γ icreases above.5 [ig. 3(c)]. The subliear behavior of γ foud i doed a-si:h at higher excitatio of light has bee attributed to the shift of ermi level E f towards bad edges. 7 It has bee reorted that i µc-si:h the localized states are lower comared to a-si:h, thus makig it ossible for the E f to shift across the ga distributio, ad therefore, the hotocoductivity behavior ca be largely affected by the ositio of E f. 84 I our case, for this articular samle E f is foud to be very close to E c (E c -E f.34 ev) as calculated from dark coductivity E a 9

10 measuremet (see Table I). 61 This material is ot highly hotosesitive, ad excess hoto-carriers i it are comarable to thermal carriers i dark. Here, CBT is exected to be steeer tha VBT (i.e., T c << T v ), ad Rose model was ot foud to hold i this system (see III.D.1). 51 All these observatios are very remiiscet of the exerimetal data ad model simulatio of Mai et al. regardig subliear behavior i doed a-si:h. 51 Possibly the same exlaatio holds true for the observed subliear behavior of γ i tye-c material too, i which case the very low value of γ at higher illumiatio where γ acquires a costat value T c /T v is also well exlaied. ully crystallized tye-c µc-si:h should be comared with what is kow as hydrogeated oly-silico. If we look ito the DOS distributio of olycrystallie Si, 85 we fid that the VBT i such a material has two distict arts havig differet sloes; oe with a sharer sloe ear the edge ad aother with a less stee sloe at deeer eergy. A similar DOS distributio has also bee roosed by Vaderhaghe et al. 31 to exlai the hototrasort roerties i highly crystallized µc-si:h films havig grais joied together i the ercolatio regime. rom electroic trasort oit of view, a excellet ercolatio athway is exected i tye-c µc-si:h. Therefore, effective DOS i fully crystallized µc-si:h films of tye-c may exhibit two differet valece bad tails; a sharer, shallow tail origiatig from grai boudary defects, ad aother less stee, dee tail associated with the defects i the columar boudary regios. Cature cross sectio for the deeer VBT states is exected to be smaller tha the shallower states. 31 This deeer tail ca also work as safe hole tras. 51 These tra ceters are also reorted to be the reaso for the subliear behavior of γ, as has bee reviously described i the cotext of a-si:h. 22 This DOS rofile is comatible with the exlaatios of subliearity ad TQ as metioed above. A detailed umerical simulatio that is ecessary to suort the qualitative argumets roffered here is reseted i comig sectio. III.D.4. Phototrasort behavior of Tye-B µc-si:h (o TQ ad.5<γ <1) The hototrasort roerties observed i this case have tyically bee see i µc-si:h. Accordig to Balberg et al., semi-gaussia distributio of VBT alog with a arrow width is resosible for such observatios of hototrasort roerties i udoed microcrystallie silico. 22 urther, the absece of TQ emhasizes that both the tail states should be somewhat symmetric to each other. Regardig the shae of CBT i this tye of material, the characteristic width was deduced to be mev by alyig Rose model ( III.D.1), as was also observed i Ref. [44]. A rough sketch of the effective DOS rofile i the viciity of CB edge suggests that istead of a sigle exoetial bad tail of CBT, some hybrid form of DOS is aroximated [ig. 5(b)]. Let us ow cosider the ossible shaes of DOS ear VBT. The microstructural ivestigatios of this tye of material led us to evisage the films to be havig mixed grais (both small ad large) ad moderate disorder hase i the columar boudary regios. I the films of tye-b µc-si:h material, ercolatio aths are restricted. Accordig to Vaderhaghe et al., 31 the µc-si:h films havig uercolated colums ca also have two valece bad tail sloes cofiguratio like the films havig higher umber of ercolated colums. evertheless, the value of the desity of states of the deeer VBT will be lower i the film with uercolated grais tha i a film with ercolated colums. I other words, the steeer shallow tail states i uercolated colums luge deeer as they fall from the bad edge whe comared to the case of ercolated oes. After the iitial fall, it associates with a deeer tail state arisig from columar boudaries. To briefly recaitulate the exerimetal results reseted ad discussed so far, we have qualitatively exlaied all the hototrasort fidigs i the cotext of the differet microstructures of the three tyes of material ad their ossible DOS distributios, takig ito accout the various ossibilities for the origi of the differet hototrasort behavior ad the recombiatio mechaisms that ca exlai the fidigs comrehesively ad lausibly. The results of hototrasort studies of our µc-si:h films reseted i this sectio assert that i such a heterogeeous system, films of the same material havig differet microstructures ad thickesses ca have differet hototrasort behavior, differet uderlyig mechaisms ad differet effective DOS distributios. However, elucidatio of some other imortat hototrasort roerties such as recombiatio traffic, the role of differet ga states i recombiatio rocess, ad the comlete DOS distributios i these microstructurally differet µc-si:h films requires a umerical modelig study of the hototrasort roerties, which we have exlored i the followig sectio. IV. UMERICAL MODELIG O SSPC I µc-si:h SYSTEM A roer treatise o hototrasort behavior i µc-si:h is icomlete without a modelig study of hotocoductivity, that would brig to light may asects of the mechaisms ivolved. With this aim, we first costructed ossible effective DOS distributios of these samles of differet tyes by cosiderig the qualitative argumets ad aalysis for exerimetally observed hototrasort roerties for differet microstructures as described i the revious sectio, ad the carried out rigorous umerical simulatios with sesitivity aalysis usig Shockley-Read statistics i steady state coditios to determie the recombiatio rocess. 86 I this sectio, we first review the state-of-art modelig aroaches to uderstad the hototrasort roerties of a-si:h ad µc-si:h material i IV.A. I the ext 1

11 sectio IV.B, we have reseted the basic formalism of our simulatio model based o the recombiatio mechaisms i a-si:h material. To check the rogram flow ad correctess of our simulatio rocedure, we tested our simulatio code o a model of Tra (model B1; Ref. 5) ad used the arameters ad DOS rofiles as metioed i his work. Our results (ot show here) showed excellet reroducibility of the umerical values of carrier desities as obtaied by Tra. It may be oited out that ulike Tra, we have ot made ay assumtios ad aroximatios (e.g., emissio from ga states beig egligible at low temeratures) to simlify the calculatio rocedure. This validatio of our simulatio rocedure ad methodology led us to roceed to aly this methodology i umerical modelig of hototrasort mechaisms i our µc-si:h material. We alied the same rocedure with differet ad suitable DOS rofiles ad arameters as aroriate for the exerimetally observed hototrasort behaviors of the microstructurally differet µc-si:h films used i this work ( IV.C). Results of the umerical modelig are reseted ad aalyzed i IV.D. IV.A. Backgroud Shockley ad Read described the statistics of a sigle traig level i terms of four simle geeratiorecombiatio rocesses. 86 The aroach is extremely successful i describig o-equilibrium steady-state rocesses i crystallie semicoductors. Later o, the recombiatio statistics for a arbitrary distributio of ga states uder steady-state illumiatio coditio was itroduced by Rose 27 i a heomeological aroach. urther, Simmos ad Taylor exteded Shockley-Read statistics to more tha oe distict traig level ad showed that the robability of occuatio of a tra level at ay eergy is just the same as derived by Shockley- Read for a sigle tra level. 87,88 A arbitrary distributio of ga states ca also be cosidered as a esemble of sigle-level states ad should therefore obey the same statistics for discrete level states at the same eergy. However, it should be oted that this artitio fuctio is ideedet of the eergy distributio of the tras i the ga. The recombiatio statistics lay the foudatio for our uderstadig of various heomea ad lay a critical role i modelig the hoto-trasort behavior i disordered semicoductors. umerical simulatio studies of hototrasort roerties i amorhous silico were mostly carried out to uderstad the thermal quechig (TQ) behavior ad a variety of hotocoductivity exoet (γ) values. Hack et al. 7 cosidered four exoetial distributios i the ga states ad exlaied the deedece of γ o ermi level. Later, Vaillat ad Jousse exlaied this relatioshi by makig a recombiatio model for simulatio by icludig the statistics for correlated defects esecially the s, ad Shockley-Read ad Simmos-Taylor statistics for the exoetial bad tails. 46 They cosidered the recombiatio takes lace oly i s ad the exoetial bad tails behave as tra states. I 1988, Vaillat et al. 47 further added that recombiatio occurs at both s ad bad tails. Sice the various workers have adoted this basic formalism i simulatio models to uderstad a variety of hototrasort heomea. 89,9,91,92 I 1995, M.Q. Tra 5 reseted a comrehesive ad detailed recombiatio model to exlai the thermal quechig behavior of hotocoductivity rocess i a-si:h. The role of various arameters ivolved i model simulatio rocess ad their effect o various hototrasort roerties were thoroughly addressed. Based o this work, Balberg et al. 22 carried out similar umerical calculatios to exlai the exerimetally observed hototrasort roerties of µc-si:h. IV.B. Basic formalism of simulatio model IV.B.1. Geeral assumtio We cosider hoto eergy greater tha the bad ga ad suose that the hoto- geerated electros ad holes are excited above the mobility edges. Uder illumiatio, tail states ad s act as recombiatio ceters ad we assume that there are o other localized states i the ga active for recombiatio. We show a sketch of the ossible trasitios uder illumiatio i ig. 7. The details of each trasitio follow later i this sectio. I the rage of temeratures cosidered here, hotocoductio is carried out by free carriers. So, oly trasitios betwee a recombiatio ceter ad the bads are take ito accout. Because of their small robabilities, either the bad-to-bad trasitios ad recombiatio, or the trasitios betwee recombiatio ceters have bee cosidered. I additio, s are assumed to cature oly mobile free carriers ad because of similar reasos of small robabilities associated with s, the trasitio betwee two s is also ot cosidered here. IV.B.2. Pricile of calculatio Photocoductivity uder steady state illumiatio as described i Eq. (1), II, is give by: h { μ ( ) + ( )} σ e μ, where μ ad μ are the free-electro ad hole mobilities, resectively; ad rereset the steady state cocetratio of hotoexcited electros ad holes whereas ad are their corresodig cocetratios i the dark at a give temerature T ad ca be give as below: ( E E ) c f c ex ; kt ( E E ) f v v ex (7) kt If we assume the recombiatio of excess carriers 11

12 CBT R 15 R 1 R 2 R 3 R 4 R 9 R 1 U G L R 16 R 6 R 13 R 14 E V VBT R 11 R 12 R 7 R 8 R 5 VBT + - CBT IG. 7. Schematics of differet recombiatio rocesses takig lace withi the ga of a disordered material. takes lace i CBT, VBT ad i s, the the charge eutrality ad the recombiatio rate equatio ca be exressed as below: The Charge eutrality equatio: + Q + Q (, ) Q(, ) + Q(, ) (, ) Q (, ) + Q (, ) The Recombiatio Rate equatio: L (8) G U + U + U (9) I Eq. (8) Q (, ), Q (, ) ad Q (, ) are the carrier cocetratios i the CBT, VBT ad i resectively uder illumiatio. Their resective thermal equilibrium values are Q (, ), Q (, ) Q,. The et recombiatio rates through the ad ( ) CBT, VBT ad s are deoted by U, U ad U i Eq. (9). These are the rates of cature ito the localized states less the rates of thermal emissio from these states. Uder steady state illumiatio, the desities ad must simultaeously satisfy the above two coditios, amely that the total et charge i the samle is zero [Eq. (8)], ad the total recombiatio rate equals the geeratio rate G L [Eq. (9)]. The details of these equatios are give i the sectios that follow. IV.B.3. Emissio & cature rocess, artitio fuctios, ad rate equatios The flows of carriers through tail states ad levels ca be see i ig. 7. Here, the DOS icludes two exoetial tail states (CBT ad VBT) arisig from the disorder of the cotiuous radom etwork ad states situated aroud midga. There is cosiderable exerimet tal evidece that midga defects (daglig bods) i amorhous silico material are amhoteric, exhibitig three ossible charge states: A ositively charged door like state + with a eergy E, a eutral state ad a egatively charged accetor like state that lies at E + U, where U is the correlatio eergy. O the other had, tail states behave as either door or accetor like states. The carrier trasitios i states are rereseted i the followig maer: The trasitio of this tye has very small robabilities ad therefore has bee eglected. However, the allowed trasitios are betwee s ad VBT or CBT give by: + e +, + Uder Thermodyamic Equilibrium Coditios: e, I the dark, at thermal equilibrium, the ideedet equatios of coservatio characterize the system rereseted i ig. 7: d CBT VBT R1 R3 + R2 R4 + R9 R1 + R16 R15 (1-a) dt d CBT VBT R7 R5 + R8 R6 + R14 R13 + R12 R11 (1-b) dt + [ ] R + R R R d (1-c) dt 12