PHYSICAL REVIEW 8 VOLUME 52, NUMBER 15 15 OCTOBER 1995-I

Photoluminescence of tetrahedrally coordinated a-Si& „C„:H

Leandro R. Tessler* and Ionel SolomonLaboratoire de Physique de la Matiere Condensee, Ecole Polytechnique, 91128Palaiseau CEDEX, I'rance

(Received 12 December 1994; revised manuscript received 11 April 1995)

We have measured photoluminescence spectra of a series of hydrogenated amorphous silicon-carbonalloys a-Si l C„:H (0 & x & 0.4) prepared by plasma-enhanced chemical-vapor deposition fromSiHQCH& mixtures. The power delivered to the plasma during the depositions was below the thresholdof primary decomposition of CH4 ("low power regime"). Carbon in the samples is mostly in the form of-CH3 groups, keeping its sp hybridization from the gas in the solid. These samples are tetrahedrallycoordinated in the sense that they do not have sp carbon. They have higher gap and are more strainedthan ordinary "high-power" alloys with corresponding carbon contents. The results indicate that forlow carbon concentrations (including pure a-Si:H) the photoluminescence spectra are determined bystatic disorder only, electron-phonon efFects being negligible. The effective disorder for radiative recom-bination is higher than the disorder probed by optical absorption. For higher carbon contents, highroom-temperature luminescence efficiences (of the order of that of a-Si:H) with very small temperaturedependence are found. This is interpreted as due to the enhancement of a fast excitonlike recombinationprocess.

I. INTRODUCTION

Amorphous hydrogenated silicon-carbon alloys (a-Si, „C:H) have been extensively studied in the past fewyears. ' Alloying a-Si:H with carbon widens its gap andshifts the photoluminescence (PL) and electrolumines-cence spectra to higher energies. Presently, the main ap-plication of a-Si& C:H is the p-type window layer inamorphous-silicon —based solar cells of improvedeKciency, which takes advantage of the gap widening.Visible light-emitting devices with a-Si, C:H activelayers operating at room temperature have already beenobtained. Like a-Si:H, Q-Si, „C:H can be deposited byplasma-enhanced chemical-vapor deposition (PECVD) inlarge areas making electroluminescent Hat panel displaysan important potential application. The realization ofthis application depends on the comprehension and con-trol of the PL mechanism in the material.

Pure a-Si:H of electronic quality (low density of statesat the Fermi level) presents a featureless, slightly asym-metric, very intense -0.2-eV-wide PL band centered at—1.3—1.4 eV at low temperatures. The mechanismdetermining the PL band shape is still controversial.The Stokes-shift Inodel, proposed by Street, attributesthe PL band features to a strong electron-phonon cou-pling. The static disorder or zero-phonon model,developed by Dunstan and Boulitrop, assigns the PLband shape to the distribution of carriers in both bandtails that result from the disorder. Both mechanisms canin principle coexist and add to determine the PL band.Searle and Jackson noted that the PL band width varia-tion upon alloying could be used to elucidate the deter-minant process. They studied a-SiN:H alloys withdifferent nitrogen contents and concluded that the staticdisorder model alone provides the best description of thePL over a wide composition range, including pure a-Si:H.

Being an element of the column IV of the periodictable, carbon could in principle incorporate substitution-ally in the amorphous silicon network. However, thepeculiar chemistry of carbon makes such incorporationvery unlikely with the usual sample preparation process.At the temperature and pressure conditions used for sam-ple preparation the sp hybridization has a slightly lowercon6gurational energy than the sp hybridization. This isthe opposite of silicon or germanium, for which the sphybrid is much more stable than the sp . Carbon atomstend to form a mixture of diamondlike 0. bonds andgraphitelike ~-bonded clusters in a-Si& C:H if the sys-tem is allowed to reach its lower-energy con6guration.However, saturated sp carbon hybrids as in CH4 arevery stable, due to high amount of energy necessary tobreak a C-H bond. Samples of a-Si& „C:Hprepared byPECVD from SiHQCHz gas mixtures can have as pre-cursors either saturated carbon (the low-power regime )or unsaturated carbon (the high-power regime). Thesepreparation conditions will be characterized in Sec. II A.

Several authors reported PL studies of a-Si& C:Hprepared under diverse high-power conditions. Suss-mann and Ogden studied PECVD samples preparedfrom SiH~/CzH2 gas mixtures. They observed a singlePL peak that widens and shifts to higher energies as thecarbon content increases, and concluded that the zerophonon contribution to the PL is very important, and at-tributed the reduced temperature quenching in carbon-rich samples to a stronger Coulomb interaction betweencarriers. Siebert et aI. ' prepared samples fromSiHQCH4 mixtures, and reported a very strong decreasein the radiative lifetime ~, for high carbon contents.These authors pointed out the conelation between PLpeak position and width and the Urbach parameter.Liedtke et al. ' proposed that for high carbon contentthe fast radiative recombination takes place in sp-

0163-1829/95/52(15)/10962(10)/$06. 00 10 962 1995 The American Physical Society

PHOTOLUMINESCENCE OF TETRAHEDRALLY COORDINATED. . . 10 963

bonded clusters. More recently, the St. Petersburggroup' ' reported the coexistence of fast and slow radia-tive processes for samples with low carbon content, withonly the fast component remaining in samples with highcarbon contents and high luminescence efticiencies.

In the present paper we report a PL study in low-power a-Si, C„:H, an alloy that is structurally closerto a-Si:H than a-SiN:H or conventional high-powera-Sii C:H, even though carbon is not substitutional inthe sense of replacing silicon atoms at random. In low-power a-Si] C:H carbon is incorporated onto the net-work primarily as methyl groups. We explored a widerange of energy gaps and Urbach parameters. Forx &0.2 in fact virtually all carbon is in the form ofmethyl: the hydrogen concentration ' ' CH varies as 3x,the density of states (DOS) at the Fermi level' changesvery little with x and the "average gap" changes as theoptical gap. ' Van Swaaij et a/. ' have shown that as xincreases above x =0. 1 the average number of hydrogenatoms bound to C decreases. They attributed this to sur-face reactions of the methyl groups. In our films, thesereactions become important only for x &0.2, probablybecause of lower atomic bombardment during growth(see the last paragraph of Sec. II A). For x)0.2 theslope of CH is smaller than 3x, ' the DOS at the Fermilevel increases very abruptly (faster than the density ofparamagnetic centers' ), and the slope of the "averagegap" variation becomes higher. This indicates that forx & 0.2 there is a change in the bonding of carbon. Thereare indirect indications of the formation of C-Si and C-Cbonds. '

As far as the PL results are concerned, there are clear-ly two different recombination mechanisms, each dom-inating in a different carbon concentration range. Forthe low carbon content range (x (0.2) we confirmed themain conclusion of Searle and Jackson, that only staticdisorder determines the PL band in the alloys and in purea-Si:H as well. In contrast to a-SiN:H, for low-powera-Si, „C:H the static disorder model correctly predictsnot only the dependence of the luminescence bandwidthon the disorder but also the shape of the low-energybranch of the PL band. We also show that the charac-teristic energy of the exponential density of states avail-able for recombination is higher than the Urbach param-eter related to subband gap light absorption.

For higher x the PL intensity is narrower than expect-ed from the static disorder model and depends very weak-ly on the temperature between 77 and 300 K. For x =0.4the PL efficiency is only a factor 2 below that of pure a-Si:H at 77 K, although the density of states at midgap ismuch higher. This is interpreted as an indication that theradiative process becomes much faster as x increases.The factors leading to this e6'ect are discussed.

II. EXPERIMENT

A. Samyle yreyaration

The preparation of a-Si, C:H by PECVD is muchmore complicated than the preparation of pure a-Si:H.The simplest precursor gas mixture that can be used con-

sists of SiH4 and CH4. That the dissociation energies ofthese two gases is not equal causes very different deposi-tion conditions depending on the power delivered to theplasma in the reactor chamber. If the power delivered ishigh enough, both SiH4 and CH4 are decomposed pri-marily and the sample formation is dominated by the sur-face processes in the growing film. This is the high-power (HP) regime, in which most of the samples studiedin the literature are prepared. If, however, the powerdelivered to the plasma is between the threshold of pri-mary decomposition of SiH4 and that of CH4 all the car-bon incorporated in the film results from secondarydecomposition of CH4 by the debris resulting from theprimary decomposition of SiH4. This characterizes thelow-power (LP) regime, in which methyl radicals (CH3)are the only form of reactive carbon in the plasma duringdeposition. Since the carbon atoms remain saturatedthrough the whole deposition process, sp hybridizationis maintained in the growing solid. In the low-power re-gime the incorporation of a carbon atom to the film in-volves a chemical reaction with at least one silicon radi-cal, and this limits the carbon content of LP Q Sii C:Hto x &0.5. Indeed, the deposition rate tends to zero asthe gas (low ratio g = [CH4]/[CH„]+ [SiH4] ) tends tounity. ' ' As long as there is enough SiH4 to produceCH4 decomposition, the carbon content depends veryweakly on reactor parameters such as gas partial pres-sures and Bow rates, substrate temperature, etc.

High-power a-Sii C:H samples normally contain amixture of sp and sp carbon hybrids. The sp hybrid ofcarbon has a lower configuration energy than the sp hy-brid in the deposition conditions, so unsaturated carbonobtained from the primary decomposition of CH4 mayform ~ bonds with a neighboring carbon in the solid.The presence of m states affects in many aspects the elec-tronic properties of the material. In contrast, the low-power deposition technique yields a-Si, C:H with vir-tually no sp carbon hybrids ' up to x -0.2. Wepresent evidence below that even above x -0.2 most ofthe carbon consists of sp hybrids.

The samples studied were prepared by low-powerPECVD decomposition of SiH4/CH4 mixtures, with g be-tween 0 and 0.995. In all depositions, the following pa-rameters were kept constant: total pressure -40 mTorr,power density -0.06 W cm, total gas Row -4 1 hBoth glass (for the optical measurements) and roughenedglass (for PL measurements) substrates were kept at250 C during the deposition. Under these optimized con-ditions the deposition rate for pure a-Si:H was -0.8 pmh ', and did not depend on g up to g -0.85, but startedto decrease considerably above this value of g. Differentcarbon contents in the films were obtained by varying g.All samples are approximately 1 pm thick. The carboncontent in the films was calculated fitting chemical reac-tion rate equations to the results of direct chemicalanalysis of 5 samples and the extreme x (g =0)=0.Analytical chemistry methods require large amounts ofmaterial, being impractical for x & 0.3 due to the reduceddeposition rate. In the absence of a direct measurement,the carbon concentration is estimated from the extrapola-

10 964 LEANDRO R. TESSLER AND IQNEL SOLOMON 52

tion of the 6t for lower concentrations. We are aware ofthe uncertainty of this procedure, since this concentra-tion range corresponds to a plasma regime where the re-actions are modified by the lack of chemically active radi-cals ("starving regime"). Nevertheless, the value of x isexpected to continue growing with g and not to exceed0.5.

B. Measurements

Optical transmission spectra for 0.01(ad &5 weremeasured by a conventional double beam spectrophotom-eter. The thickness d, the refractive index no, and the ab-sorption coefficient a(hv) for each sample were calculat-ed from these data.

Photoluminescence was measured at room temperatureand at 77 K with the samples placed in a liquid-nitrogencryostat. Excitation was provided by one of the un-focused lines of a Kr+ laser. The excitation energies foreach sample (between 1.6 and 3.5 eV) were as close aspossible to EO4, the value of hv for which o.=10"cmThe luminescence signal was Altered, dispersed by a 25-cm monochromator and detected by two-color (Si andthermoelectrically cooled InGaAs) photodiodes usingstandard in-phase techniques at 16 Hz. The spectral sen-sitivity of the whole system was calibrated by a tungstenhalogen lamp.

All spectra were taken at laser intensities below 10'photons cm sec '. We verified that in the measure-ment conditions the PL intensity depends linearly on theexcitation intensity. All the discussion of PL results sup-poses germinate recombination.

s -s 1 —2x Xs -c 2x Xc-c 0 (3)

Low-power alloys present a special case of chemical or-der, in the sense that x ~0.5 and each carbon atom isbonded to one silicon. Then the bond concentrations are

This value is closer to the true mobility gap than theTauc gap. Nevertheless, a Tauc plot for our pure a-Si;Hsample yields a Tauc gap of 1.7 eV.

The exponential slope of the subgap absorption tail(the Urbach parameter E„) was obtained from opticaltransmission down to a=500 cm ' and by photothermaldeffection spectroscopy (PDS). The results from bothtechniques are in good agreement for E„above 0.150 eV.The values of the gas concentration ratio g, the carboncontent x, the thickness d, the gap Eo4, the Urbach pa-rameter E„,and the infrared refraction index no for eachsample are listed in Table I.

In a recent paper, Robertson discussed the results ofthe virtual crystal approximation for a-Si& C:H.Neglecting the effects of topological disorder, in a purelya-bonded alloy (absence of sp hybrids), any band energyE, is given by the linear combination

E.=Es &s,-s +Es c&s -c+Ec&c-c

here Esl Eslc and Ec are the energies of the resPectiveband in crystalline silicon, SiC, and diamond, and Xs; s, ,Xs;c, and Ncc are the concentration of the respectivetypes of bonds in the alloy. For a random-bonding alloy,

Xs -s =(1 x) Xs -c 2x(1 x) Xc-c=x (2)

and for a perfectly chemically ordered alloy with x ~ 0.5:

III. RESULTS AND DISCUSSIQN

A. optical absorption

For the a-Si, C:H system, the commonly used Taucextrapolation is not a reliable procedure to characterizethe optical gap. In order to have reliable values for theoptical gaps, the (ahv)'/ vs hv curve should be linearover at least one decade, a condition that is not verified ingeneral for carbonated material in the range of u mea-sured. ' Instead we characterize our samples by E~.

s-s 1 x Ns-c x Xc-c 0

The gap is- computed by the difference between theband edges, that are Si-like in this concentration range.The inclusion of hydrogen has the effect of widening thegap. The case of SiHCH bonding was calculated byRobertson. For low-power samples the correct form toobtain the effect of hydrogenation is to considerSiHSiCH3. However, Eq. (3) can be viewed as a valid ap-proximation, since the smaller gap increase predicted byEq. (4) is compensated by the stronger gap widening

TABLE I. Carbon ratio x = [C]/([C]+ [Si]), thickness d, optical gap Eo~, Urbach parameter E„andfar-infrared refractive index no as a function of the gas flow ratio g = [CH4]/([CH4]+ [SiH4]).

0.000.500.600.800.870.920.950.9750.980.99

0.000.070.100.190.240.290.330.370.380.40

0.931.141.080.921.060.940.850.950.961.29

EO4 {eV)

1.932.012.222.522.662.713.293.443.563.36

E„(ev)0.0600.0700.0910.1610.1800.2150.2650.2950.3620.350

no

3.323.022.722.182.071.891.841.801.781.76

PHOTOLUMINESCENCE OF TETRAHEDRALLY COORDINATED. . . 10 965

This work

Kuhman et al. [18]Herremans et al. [25]van Swaaij et al. [14]

~ Sussman et al. [9)Baker et al. [24]

4.0

+ Mui et al. [23]Boulitrop et al. [21]Sotiropoulos et al. [22]Petrich et al. [26]Siebert et al. [10]

effect of CH3 respective to CH.Figure 1 represents the gap EO4 versus carbon content

obtained by different laboratories ' ' ' ' ' as well asthe results from Robertson's calculation. Only samplesprepared in the low-power regime' ' ' present the pre-dicted values and linear dependence of the gap on theconcentration over an extended range. We follow Rober-ston and attribute the smaller gap systematically ob-served in HP samples to the presence of importantamounts of sp carbon hybrids. Note that our samplewith the highest carbon content (x =0.40) has EO4 lowerthan the one with x =0.38. In fact for this sample theexponential absorption tail extends well above E04. Theabsorption at E04 is still dominated by the disorder, andin this case E04 is not the good parameter to define theoptical gap. It should always be remembered that theconcept of a gap becomes ill defined when E„ increases.

The formation of graphitic bonds relaxes the networkby reducing the average atomic coordination and also be-cause the m bonds have one topological degree of freedommore than the u bonds. As a consequence, the potentialAuctuations near the band edges are reduced and there-fore a steeper Urbach tail is formed. In contrast, low-power samples are severely strained. A plot of the Ur-bach parameters E„as a function of carbon content (Fig.2) displays this feature: the low-power samples have sys-tematically higher E„ than high-power samples withsimilar carbon content.

Another special characteristic of the samples studied isthat they are prepared in a reactor with an extremely

0 5 I ~ sI g s ~ ~ ~

I~ ~ ~

I1 ~ ~

0.4

0.3

0.2 00 0

o

0 0 ~ ~ 'I I ~ ~

0

I I ~ I ~ I i ~ ~ I ~ ~ ~

0.0 0.2 0.4 0.6 0.8 1.0

asymmetric electrode configuration (highly anodic depo-sition), in order to minimize atomic bombardment in thegrowing film. This guarantees that the methyl groups areleft undisturbed after they are incorporated onto the film.This minimizes the formation of sp carbon hybrids afterdeposition. Atomic bombardment during low-powergrowth may also promote network relaxation by assistingbonding between carbons already bonded to one siliconand a second silicon or a carbon neighbor. This is possi-bly why low-power samples prepared by different groupsmay present gaps lower than that predicted by Eq. (3)when the carbon concentration increases.

8. Photoluminescence

The normalized PL spectra at 77 K for all samples arerepresented in Fig. 3. All these spectra were taken withthe excitation energy above and very close to E04, in or-

FIG. 2. Measured. Urbach parameters E„as a function of thecarbon content from different laboratories. The symbols are thesame as in Fig. 1.

3.5—

3.0—CLCU

2.5(0

K 2.0 Jlg~~xLI

~ z-states

X

1 5 a s s I a ) I I s s ) I s s s I s

0.0 0.2 0.4 0.6 0.8 1.0

1.0

0.8

(D

c4 0.4

0.2—

FICx. 1. Optical gap E~ as a function of the carbon contentfrom different laboratories. The brackets indicate the corre-sponding reference numbers The full line represents the resultof the tight-binding calculation by Robertson (Ref. 20). The re-gion between the dotted lines in the right corresponds to m

states.

Ozo.o I

0.8 1.2 2.0E {eV)

2.4 2.8 3.2

FICx. 3. Some typical normalized PL spectra. The carboncontents x are, from left to right, 0, 0.10, 0.19, 0.24, 0.37, 0.40.

10 966 LEANDRO R. TESSLER AND IONEL SOLOMON 52

10"

=. 10'

& 10-

n. 10o

10

0o ~I==I

0000

U

o 77K300 K

where ~ is the dielectric constant of the medium, E isthe energy of the emitted photon, e is the electron charge,c is the speed of light, and (i lx lf & is the dipole-matrixelement between the initial and final states. For perfectlyoverlapping localized wave functions the dipole-matrixelement can be approximated by

(2Rq )l&ilxlf &I'-

(R, )

gLj10~&ls I I s i s i I gags I ~ i ~ & I i s i s

0.0 0. 1 0.2 0.3 0.4 0.5

FIG. 4. Integrated PL intensities corrected for the generationrates at 77 and 300 K. Although systematic errors limit thecomparison between different samples to an estimated incerti-tude of 30/o, the ratio between low- and room-temperature datafor each sample is much better.

where R& is the hole localization length. For purea-Si:H, PL decay data are well fitted supposing~0„—10 sec, corresponding to R, —1. 1 nm andR& -0.3 nm.

Since at low temperatures the carriers are frozen in thetail states with very low mobility, the nonradiativerecombination process is also tunneling limited. Thenthe non-radiative lifetime ~„, is also determined by theless localized carrier:

der to prevent the PL band narrowing reported forsubgap excitation. '

The integrated PL intensities corrected for the genera-tion rates at 77 K and at room temperature are represent-ed in Fig. 4.

In order to discuss our data, let us review the presentmodels for photoluminescence in a-Si:H. As pointed outin the Introduction, there is still not universal agreementconcerning the process that determines the photo-luminescence band width and position.

1. I.oav-temperature photoluminescence

In a-Si:H the photoluminescence efficiency g is veryhigh at low temperatures (q-0. 3). The PL process isthe result of the competition between radiative and non-radiative recombination channels. Radiative recombina-tion occurs by transition between an electron and a hole,each in a localized state in the band tails. The nonradia-tive process is primarily associated with a defect lyingnear midgap (like the Shockley-Read process) as is thecase of, for example, a dangling bond. Indeed, the PL in-tensity decreases very strongly when the dangling bonddensity increases.

For low excitation rates the radiative recombination isgerminate. The radiative recombination rate ~„of anelectron and a hole in the band tails is determined by theoverlap of the wave functions:

r„=ro„exp(2R /R, ),where ~o„ is the lifetime for completely overlapping elec-tron and hole wave functions, R is the carrier separation,and R, is the localization length of the electron, assumedto be the less localized carrier. Carrier separation arisesfrom the di6'usion of carriers in the extended states dur-ing thermalization.

The lifetime ~0, is derived from Fermi's golden rule:

r„,=ro„,exp(2r /R, ),where the "attempt-to-escape" frequency ~0„,

' =vo—= 10 ' sec corresponds to a typical photon frequencyand r is the distance between the electron and the nonra-diative center.

A critical distance R, can be defined such that for acarrier whose distance to a nonradiative recombinationcenter is smaller than R, the probability of nonradiativerecombination is higher than the probability of radiativerecombination. From (5) and (8) it follows that

R,R, = 1n(voto„) .

For a-Si:H, with its relatively narrow PL band (whencompared with the alloys), R, can be considered constantwithin the whole band tails. A good fit to experimentaldata is obtained for R, —12 nm.

The origin of the photoluminescence bandwidth hasbeen attributed alternatively to an electron-phonon —in-duced lattice relaxation process (Stokes shift) or as a nat-ural consequence of the existence of band tails due tostatic disorder. The next sections describe briefly themain predictions of each. To date, there is still nouniversal agreement about which of them is the most im-portant.

a. The Stokes shift model. In -the simplest form of theStokes-shift process, the photoluminescence peak EL isshifted due to the relaxation of the lattice configurationalenergy in the excited state (Stokes shift) by an amountEs. Thus EL =E~ —Es where E„ is the peak in the ab-sorption band. In an amorphous semiconductor there isa continuum of possible excited states and the absorptionband grows monotonically instead of presenting a peak.Consequently Ez is not a mell-defined energy, Since thePL bandwidth depends on the excitation energy belowE04 but not above it, ' we shall estimate E~ to be equalto Eo4. For excitation above Ez, photogenerated carriersrapidly lose energy (thermalize) by phonon emissionwhile jumping between states. This thermalization pro-cess may also continue within the localized tail states,since E„may in fact be different from the mobility edge.

PHOTOLUMINESCENCE OF TETRAHEDRALLY COORDINATED. . . 10 967

Due to the thermalization process EI may be shifted bythe energy E,h lost by the carriers before recombination.This thermalization term should be included for the cal-culation of El .

EL. E04 Es Eth- (10)

P;(s) =No;exp( —e/E; )

Xexp[ —u, (c, )NO;E;exp( e/E; —)], (12)

where i indicates the band (valence or conduction), No; isthe density of states of the band i at the mobility edge, c,

is the energy of the state measured from the mobilityedge, v, is the volume of a sphere of radius R„and E&;are the characteristic energies of the exponential densitiesof states. Considering u, independent of s, Eq. (12) corre-sponds to a slightly asymmetric Gaussian-like shape witha maximum at c, ,„:

The photoluminescence bandwidth in case of relaxa-tion via a single phonon energy AEI' ~" is given by

GAEL "=2[in(2)E, E ]'

where Eo=hvo is a typical phonon energy. The typicalphonon frequency vo is the same as used in Eq. (8).

b. The static disorder model. In the static disordermodel, the photoluminescence band shape is a result ofthe steady-state carrier distribution within the assumedexponential band tail density of states available for radia-tive recombination. After having thermalized rapidly tothe band edges, photogenerated carriers start a muchslower thermalization within the band tails up to ~„, cor-responding to transitions among states over distances upto R, . Radiative recombination then takes place betweenstates that are the lowest within spheres of radius R, ineach band. For each exponential band tail, the density P,.of such states is

(GAEL ) =41n(2)(E04 EL —E,h)E—O+(HEI"") (16)

In Fig. 5 we represent (HEI ) against E04 EL, so the—

hole localized states distributions, and absorption refIectsthe superposition of such states, E; ~E&;. This will bediscussed in more detail in Sec. III 8 1 c.

Searle and Jackson noted that, because of thedifference of characteristic energies, the valence band taildistribution of minima Pz(e) is much wider than the cor-responding conduction band tail distribution Pc(e), andis by itself a good approximation for the photolumines-cence spectrum. For any a-Si& C:H alloy with x &0.5the band edges remain siliconlike, with the valenceband tail p-like and the conduction band tail s-like. Sincethe symmetry of p-like states is much more sensitive todisorder than that of s-like states, we expect small varia-tions in E c related with carbon alloying, with most ofthe disorder effects affecting E z. Thus we shall alsomake the assumption that the valence band tail dom-inates the PL band shape, which corresponds to approxi-mate the narrow Pc(e) by a delta function.

e. The a Si:H -like samples (x &0.3): Photoluminescence bandwidth and band shape. In principle, both theelectron-phonon process and static disorder contribute tothe photoluminescence bandwidth. The two photo-luminescence bands are Gaussian-like near the peak, sothat the widths add as

(&E ) =(&E'~")'+(&Es™)'

In the Stokes-shift model (GAEL ") scales with E,while in the static disorder model EEL" scales with E„.Following Searle and Jackson, we tested the predictionsof expressions (6) and (9). If the Stakes-shift process isdominant,

e,„=Eq; ln( u, No; Eg )

and a width hc. ; independent of v, :

(13)

1.2 0

Ac,. =—2.45E&,- . (14) 1.0

The PL spectrum is obtained by the convolution of thedensity of minima described by Eq. (12) for each bandtail. This convolution has to be calculated numerically.The characteristic energies E&, reAect the densities ofstates available for radiative recombination. The ex-ponential slopes of the band tails E, have been measuredfor a-Si:H. The slope of the valence band E & is 2 to 3times higher than that of the conduction band ' E~&.The parameter E & is identified with the Urbach parame-ter E„obtained from absorption measurements. It istempting to associate E&,. =E,. =E„, and this has beendone in previous papers. ' ' However, absorption bylocalized-to-localized transitions [the inverse of the pro-cess described by Eq. (S)] is much less probable than ab-sorption by localized-to-extended transitions due to thewave-function overlap factor. Nevertheless, since theluminescence comes from the convolution of electron and

0.8W

0.6

0.4

0

0.2 00

0 ~ ~ ~

0.5~ I ~ ~ ~ ~ I ~ I ~ ~ I I ~ ~ ~ I ~ ~ ~ ~ I ~ I ~ I I ~ ~

0.6 0.7 0.8 0.9 1.0 1.1 1.2

E04 EL {eV)

FIG. 5. The squared experimental PL spectrum width vs thePL peak separation from the gap EO4 —EI. According to theStokes-shift model, all the data should lie in a single straight11ne.

10 968 LEANDRO R. TESSLER AND IONEL SOLOMON

Figure 6 represents AEI against E„. The straight-linefit is better than in Fig. 5, but the samples with thehighest E„(and highest values of x) are below the linearbest fit. These samples will be treated in detail in Sec. III8 a b, and we will not consider them for the moment.The zero intercept is —0.040+0.056 eV, confirming theconclusions of Searle and Jackson that the electron-phonon contribution for the PL width is negligible. Inthe worst case, assuming E h-60 meV, it indicates thatfor a-Si:H E& =0.010+0.019 eV. This value is compara-ble to the ones obtained by Searle and Jackson (0.02 eV)and by Schmidt de Magalhaes et al. (0.036 eV), butmuch smaller than the 0.5 eV obtained by Street who at-tributed the PL bandwidth to the electron-phonon in-teraction only. The validity of the extrapolation of alloydata to pure a-Si:H has been questioned in the case ofa-SiN:H. The present results, however, were obtained

1.2

1.0

00

0.8

0.6

04

0.2

00 s s

0.0 0.1 0.2 0.3 0.4

E (ev)

FIG. 6. The PL spectrum width as a function of the Urbachparameter E„. The prediction of the static disorder model ofDunstan et al. (Ref. 6) is a straight line with slope 2.45. Theslope of the best fit is 3.85 instead, and we attribute thedifference to the fact that in a-Si& C:H the effective energyparameter of the exponential band tail density of states forluminescence is not quite the Urbach parameter. 1n the sampleswith x & 0.25 a different radiative recombination mechanism be-comes predominant (see text).

zero intercept yields (AEr"") 4—ln(2)E, hEO. The typi-cal phonon energy Eo is obtained from the slope. The ex-perimental points present some scattering. Forcing astraight-line fit, we obtain E0=0.569+0.170 eV. Thisvalue is roughly ten times the energy of a typical phononin a-Si:H, which is about 60 meV. Furthermore, even ifthe disorder term is negligible, the value obtained for E,his -0.53 eV, which corresponds to twice the PL band-width. These results are not physically acceptable and in-dicate that the electron-phonon interaction is not themain reason for the PL bandwidth.

If static disorder is dominant, Eq. (15) can be writtenas

(hE ) =(2.456,E ) +(b,E'~")

in low-power a-Si 1 C:H, which has an electronic struc-ture ' very similar to that of a-Si:H for low x (up to 0.2),carbon being tetrahedrally coordinated. We claim thatfor our samples the extrapolation to x =0 is justified, andour data provide definitive support for the static disordermodel.

The slope of the straight line fit of fig. 6 is 3.85+0.30,higher than the 2.45 predicted by Eq. (14). Searle andJackson found 4.4+0.2 for their a-SiN:H. More re-cently a value of 3.3 can be directly obtained from the re-sults of Magalhaes et al. for low carbon concentrationHP a-Si, C:H prepared under hydrogen dilution. Pal-sule et al. 3 found 1.8 for a-Si& „C,:H prepared by rfsputtering. However, the photoluminescence peaks ofthe latter authors do not follow the variation of the gap,suggesting that their sputtered samples may be inhomo-geneous. Searle and Jackson concluded that althoughthe underlying assumptions of the static disorder modelare correct, the detailed description of the luminescenceprocess as described above is wrong, and suggested thatthe disagreement between theory and experiment comesfrom an oversimplified treatment of the statistics. In par-ticular, they questioned the correctness of considering thecritical volume v, well defined and constant. We investi-gated the effects of letting v, vary in Eq. (12), by expand-ing the function near its maximum. Our conclusion isthat up to second order in e/Ez (which corresponds toapproximating the distribution by a Gaussian) the effectof the variation of U, over the maximum position is pro-portional to In(Bv, /Be), and its effect over the width isnegligible. The only way to increase the 2.45 coeScient ofEq. (14) is to suppose critical volumes that increase withc, a rather unphysical situation.

The variation of critical volume within the bands is notthe cause for the lack of agreement between theory andexperiment. However, although the Urbach parameterincreases with the disorder, there is no reason to haveperfect equality between E ~ and E&~. As said before,each characteristic energy is related to a different pro-cess, the former to absorption and the latter to absorp-tion followed by diffusion, so it is natural to expect themto be proportional rather than equal. To the first order,we can define p=E&/E . The effect of disorder can bedescribed in terms of parallel and antiparallel potentialfluctuations. The former rejects the medium- and long-range variations due to, for instance, average compositionfIuctuation that exist in any nonstoichiometric alloy. Thelatter is associated with atomic scale potential fluctua-tions, as a distorted bond or the precise site of a carbonatom. Absorption is sensitive only to the antiparallel po-tential fluctuations, while after the thermalization processthe carriers can access states that are related to bothparallel and antipara11el fluctuations. This will be ex-pressed as a higher effective density of states for recom-bination than for absorption, resulting in E&z & E z. Thecoefficient P is thus an estimation of the medium-rangedisorder, and its value is always greater than unity. Sincethe medium-range disorder is expected to be sensitive tosample preparation parameters, it is not surprising thatdifferent laboratories render different values of p. Our

52 PHOTOLUMINESCENCE OF TETRAHEDRALLY COORDINATED. . . 10 969

0.25

0.20

0.15

0.10

0.05

0.000.0 0.2 0.3

0

0.4

a-Si:H.The PL peak position in the static disorder model is

essentially the prediction of Eq. (13) for U, constant, shift-ed 0.1 —0.2 eV due to the convolution with Pz(e'). Figure8 shows that indeed there is a weak correlation betweenEO4 —EI and E„. However, the average value of U, de-creases exponentially with the carbon content x, follow-ing the variation of the density of states at the Fermi lev-el' for x)0.06. The product NoE„ is not expected todepend strongly on x. The combined effect is that thevariation of the logarithmic term compensates the varia-tion of E„and consequently Eo~ —EL depends very weak-ly on E„.

2. Luminescence e+ciency and temperature dependenceE (ev)

FIG. 7. The low-energy exponential slope of the PL spec-trum as a function of the Urbach parameter E„. The straight-line fit corresponds to the prediction of the static disorder mod-el.

data corresponding to very disordered samples yields thehighest p among the a-Si, „C:H, but for a-SiN„:H it iseven higher. Since P is close to unity and E„ is easilymeasurable, equating E& and E„ is convenient for model-ing purposes.

Equation (12) predicts the low-energy side of the pho-toluminescene band to be exponential with characteristicenergy EI& equal to E&. Figure 7 shows El& vs E„.ForE„smaller than 0.25 eV El+ follows E„. This is in con-trast with a-SiN:H for which EI~ has no relation withE„. Again this indicates that for low carbon concentra-tion low-power a-Si1 C:H is more closely akin to pure

vpr„=exp[ED(T)/kT] . (18)

Supposing that the limiting process is the thermal ac-tivation of carriers in the wider band tail, the lumines-cence efficiency g is given by the fraction of carriersdeeper than ED:

g( T) =gpexp[ ED( T)/E ]

a. The model for good quality a Si:H -For .pure a-Si:H,the temperature dependence of the photoluminescenceabove 50 K is closely related to the temperature depen-dence of the carrier mobility. The nonradiative lifetime7 —10 ' sec is so much shorter than the radiative life-time ~„—10 sec that it can be assumed that any carriertrapped in the band tails that is thermally activated to themobility edge has enough mobility to eventually reach anonradiative recombination center. Thermal activationto the mobility edge is the most probable event for car-riers at states shallower than a demarcation level ED(T)such that

kT=gpexp — ln( vpr„) (19)

1.2

1.0

0.9

0.8I

0.7

0.6 0 0

0.5

04 I s

0.0 0.2

E (ev)

0.3 04

FIG. 8. The PL peak separation from the gap EO4 —EL vs theUrbach parameter E„.The data do not correspond to a straightline intercepting the origin as predicted by Dunstan et aI. (Ref.6). We attribute this to the decrease of the critical radius R, asx increases (see text).

Since ln(vpr„) varies very weakly with the temperature,an activated behavior is expected. This simple picture ig-nores the possibility of carriers hopping directly to thenonradiative recombination centers, since it is negligiblein good quality a-Si:H in this temperature range. In thealloys, however, with their increased density of states inthe gap, g( T) shall be reduced due to this process.

b. Alloys with high carbon concentration (x )0.3):Highphotoluminescence e~ciency at room temperature. Thelow-temperature luminescence efficiency decreases withcarbon alloying, up to approximately x =0.2, as shown inFig. 4. In this carbon concentration range the effect ofcarbon incorporation in the luminescence efficiency isquite clear. Alloying increases both E„and the density ofsilicon dangling bonds that act as fast nonradiativerecombination centers. The temperature quenching be-tween 77 and 300 K is reduced mainly due to the increaseof E„,as described by Eq. (19).

As the carbon content increases above x =0.2, howev-er, the photoluminescence efficiency starts to increase andthe temperature quenching decreases, although the densi-

10 970 LEANDRO R. TESSLER AND IONEL SOLOMON

ty of silicon dangling bonds starts to increase moreabruptly with the carbon content.

The decrease of the temperature dependence of theluminescence efficiency and increase of its absolute valueindicate that not only the radiative recombination rate ~,decreases' ' ' for these alloys, but also the radiativerecombination rate for completely overlapping wavefunctions 'To„. Indeed, values of 7o„as low as —10sec have been reported ' for different forms ofa-Si& C:H with low to moderate carbon content. %'emould like to note, however, that in our wide-gap high-E„samples the concept of a mobility gap is very illdefined, and that EO4 that we are using to characterizethe gap may correspond to transitions among band tailstates. For instance, in the sample with x =0.4 the ex-ponential dependence of a(h v) continues well above EO4.

In these alloys with high E„, the density of band tailstates is very high, the wave functions are very localized,so that nearest-neighbor hopping is the predominanttransition within a band. Nonradiative recombinationwould be expected to occur if the carrier could reach adeep state. The only possibility to explain the highluminescence efIiciencies is to assume that, just like ingood quality a-Si:H at low temperatures, in these samplesthe carriers recombine radiatively before they can reachthe nonradiative centers. We still do not have a completeunderstanding of the factors leading to the shortening ofthe radiative lifetimes. One possibility is the onset of astrong Coulomb interaction, leading to a fast excitonlikerecombination process analogous to molecular lumines-cence. Since the electron and the hole are separated by adistance of the order of the interatomic distance, theCoulomb energy can be of the order of hundreds of meV,preventing them from separating and accelerating therecombination process. Thus the photoluminescencebandwidth is reduced in relation to the noninteractingcase because the carriers recombine before completelyprobing their neighborhood. This explains why Eq. (15)is not valid for the samples with high carbon content, forwhich the PL bandwidth is almost independent of x.Indeed, recombination kinetics characteristic of anexcitonic process has been observed in high-powera-Si& C~:H of high luminescence eKciency. '

IV. CONCLUSIONS

We presented PL data in a set of low-powera-Si, C:H with 0 &x &0.45. This material has negligi-ble amounts of sp carbon hybrids, and consequentlyhigher gaps and higher disorder than conventional high-power a-Si& C:H. For low carbon concentrations allthe carbon is in the form of methyl, while for higher car-bon concentrations carbon starts to have multiple bonds

to the network. Under excitation intensities that corre-spond to germinate recombination, we found twndifFerent luminescence regimes, more or less coincidentwith the two regimes of carbon binding:

(a) For low carbon concentrations (x &0.25, E04 (2.7eV, E„(0.2 eV), as the carbon content increases thelow-temperature PL eKciency is reduced, the PL peakshifts to higher energies and the PL bandwidth increases.The PL band is determined by static disorder, i.e., by thedistribution of band tail states for which the probabilityof radiative recombination is higher than the probabilityof further thermalization in the band. Throughout thewhole range of carbon concentrations (including x =0,pure a-Si:H) the electron-phonon interaction contributionto the PL bandwidth is negligible when compared to thewidth induced by disorder. This extends earlier con-clusions by Searle and Jackson who studied thea-SiN:H system. Since the low-power a-Si& C„:H sys-tern at low carbon concentration has its electronic struc-ture very similar to a-Si:H we claim that the presentstudy provides- definite support for the static disordermodel even for a-Si:H. The value obtained for the Stokesshift is E& =0.010+0.019 eV. The simplified state disor-der theory of Dunstan and Boulitrop correctly predictsthe linear dependence of the PL bandwidth and the 1ow-energy tail of the luminescence spectrum on the Urbachparameter. The detailed dependence of the luminescencebandwidth on the Urbach parameter indicates that forthe radiative recombination process the effective disorderis higher than for the optical absorption process, which isreasonable when we consider the different electronic pro-cesses involved.

(b) For higher carbon contents (0.25 (x (0.4,2. 8 eV (Eo& (3.5 eV, E„)0.2 eV), the PL eKciency in-creases while the temperature quenching is reduced. Forx =0.4 the integrated PL efIiciency is only a factor 2below that of pure a-Si:H at 77 K and does not presenttemperature quenching. The PL bandwidth almost doesdepend on x for excitation at 3.5 eV. This indicates thatthe radiative process is very fast in these samples, possi-bly due to the electron and hole being strongly correlatedby the Coulomb interaction. The bandwidth is reducedin relation to the noninteracting case as the diffusion pro-cess is interrupted by recombination.

ACKNOWLEDGMENTS

The authors are indebted to Dr. Georges Lampel andto Dr. John Robertson for a critical reading of themanuscript. One of us (L.R.T.) acknowledges supportfrom the European Union/CNPq under the "Marie Cu-rie" Research Initiative.

Qn leave from Instituto de Flsica Crleb Wataghin, Universi-dade Estadual de Campinas, 13081-970 Campinas, SP, Brazil;Electronic address: tessler@ifi. unicamp. br

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