Transport properties of evaporated versus sputtered amorphous germanium films

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Transport properties of evaporated versus sputtered amorphous germanium films

M.-L. Theye, A. Gheorghiu, T. Rappeneau, A. Lewis

To cite this version:

M.-L. Theye, A. Gheorghiu, T. Rappeneau, A. Lewis. Transport properties of evaporated ver- sus sputtered amorphous germanium films. Journal de Physique, 1980, 41 (10), pp.1173-1181.

�10.1051/jphys:0198000410100117300�. �jpa-00208944�

Transport properties

of evaporated ^versus sputtered amorphous germanium ^films

M.-L. Theye, ^A. Gheorghiu, ^T. Rappeneau

Laboratoire d’Optique des Solides (*), Université Pierre-et-Marie-Curie, 4, place ^{Jussieu, 75230} Paris Cedex 05, France

and A. Lewis (**)

Division of Applied Sciences, ^Harvard University, Cambridge, Mass., U.S.A.

(Reçu ^{le 28}

1980, accepté ^{le 29 mai} 1980)

Résumé. 2014 La conductibilité électrique ^{en courant continu et le} pouvoir thermoélectrique de couches minces de Ge amorphe préparées par évaporation ^sous vide dans différentes conditions ont été mesurés avec soin dans un

large domaine de température (50-600 K). Les résultats sont comparés ^{en détail à ceux} obtenus dans des expé-

riences identiques ^sur des couches minces de Ge amorphe préparées par pulvérisation. Les similarités entre les

propriétés ^de transport ^{de ces deux} types d’échantillons sont mises en évidence et discutées dans le cadre des théories existantes. On suggère que les différences ^sont liées à l’inhomogénéité ^{de structure} des couches minces

amorphes.

Abstract.

The electrical d.c. conductivity ^{and the} thermoelectric power of evaporated amorphous ^{Ge films} prepared under various conditions were thoroughly ^{measured over a wide} temperature range (50-600 K). ^The

results are compared ^{in detail to those} of similar measurements on sputtered amorphous Ge films. The similarities between the transport properties ^{of the two} types ^of samples ^are emphasized ^and discussed. The discrepancies ^are tentatively attributed to the non-homogeneity of the different amorphous ^films.

Classification

Physics ^Abstracts

72 . 80N

1. Introduction.

One of the most challenging problems ^{in the} field of elemental tetrahedrally

coordinated amorphous semiconductors is the inter-

pretation of the electronic properties attributed to states distributed throughout ^the pseudo-gap. ^A

successful theory ^{for these} properties should take into account the nature and the energy distribution of these states, which ^are intimately ^{related to the}

details of the sample structure. Although topological

and quantitative ^{disorder, which are well desctibed} by

continuous random network models [1, 2], may be

responsible ^{for some} tailing of the band edges, ^states

in the pseudo-gap ^are mostly introduced by ^structural

defects associated with the occurrence of unsatisfied

or dangling ^{bonds, and} by impurities. Although significant progress ^was obtained recently ^{in the} understanding ^{of defect states} [3, 4, 5], ^the proposed

densities of states are still partly conjectural. ^More-

over, most theoretical models assume that the amor-

(*) Equipe ^{de recherche associée}

^{C.N.R.S. no 462.}

(**) ^{Présent address : Texas} Instrument, Dallas, Texas, U.S.A.

phous material is homogeneous ^{on a} semi-macro-

scopic scale, ^even when it contains structural defects, while more and more evidence for the _presence of

large-scale heterogeneities ^{can be} gained from various

experiments.

The observation of pronounced low-angle ^scatter- ing in electron diffraction patterns ^{of thin} (100 A) vapour-deposited a-Si films on NaCI substrates was

very early interpreted ^as indicative of the presence of regions ^of appreciable density deficiency, ^viewed

as voids or pores [6]. ^{Defect states were then asso-}

ciated with dangling ^{bonds at} the internal surface of such voids. The existence of low-density regions

was confirmed by small-angle X-ray scattering experi-

ments on thick evaporated [7] ^and sputtered [8] ^a-Ge

films. Significant differences between the data relative to electrodeposited, evaporated ^and sputtered samples [8] suggested ^{that the} shape, size and distri- bution of voids strongly depend ^on the method of

preparation. ^{On the other hand, direct} observation of thin (100 À) evaporated a-Ge films on KCI substrates by high-resolution ^electron microscopy

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198000410100117300

1174

revealed the _presence of a network of oriented slit-

or crack-like voids surrounding islands of about 100 A in diameter [9] ; similar results were obtained

on thin sputtered ^{a-Ge films on} NaCl substrates [10].

However, ^the formation of an array of such large

voids seems to be favoured by particular ^substrates

with high ^ad-atom mobility [11]. ^More recently, systematic investigations by high-resolution ^electron microscopy ^and small-angle electron diffraction _per- formed on a variety ^of amorphous samples ^have

demonstrated that most of them present ^{a characte-} ristic quasi-periodic density fluctuation described

as a rod-like or supernetwork ^structure [12]. ^The

films are continuous and do not contain macro-

scopic ^{voids, but} they would consist in rods of high- density ^material separated by channels of lower

density material where small voids are expected ^to

be concentrated. The rod size usually depends ^on

substrate temperature during deposition but is little affected by annealing, which rather produces ^a

densification of the channels. Similar structures were observed in thin (250 A) ^{as well as thicker}

(up ^{to 4 000} A) a-Ge films prepared by evaporation ;

for sputtered films their existence seems to depend

on deposition conditions. Glow-discharge ^{a-Si films}

were the only samples ^under consideration which

systematically ^{did not} show such density ^fluctua-

tions.

All these results, ^{even if} they ^{lead to different}

models for the heterogeneities, strongly suggest ^that

most amorphous ^{Ge and Si} samples ^{are best} repre- sented by non-homogeneous structures. More homo- geneous high-density ^{films can} only ^{be obtained}

under special deposition conditions, especially ^at high ^substrate temperatures. ^The sample ^non-homo- geneity should influence the electronic properties appreciably. Although ^{the need for} heterogeneous ^theo-

retical models for the transport properties ^has already

been emphasized [13, 14], homogeneous ^models

continue to be applied ^to a-Ge and a-Si films because

samples of different origins appear ^to behave approxi- mately according ^{to the same} laws. The anisotropy expected ^{from a rod-like structure could not be} proved by ^d.c. conductivity measurements either in

evaporated ^{or in} sputtered ^films, except ^{in thin}

ones [15, 16]. However, ^the existence of voids has been invoked to analyse ^the optical properties ^of evaporated a-Ge films deposited ^at different substrate temperatures [17].

In order to obtain more information on the rela- tions between electronic properties ^and sample ^struc-

ture and to check the validity ^of existing theories, it seemed interesting ^to compare in detail ^{over a}

large temperature range the transport properties

of amorphous ^{Ge films} prepared by ^vacuum evapo- ration and by sputtering ^{in Ar} atmosphere ^{in various}

conditions. The structure of both types ^of samples

was investigated very carefully, although by ^difi’e-

rent methods, ^and compared ^{in order to detect}

possible differences. The optical properties ^of evapo- rated [18] ^and sputtered [19] ^films prepared ^{in the}

same conditions as the ones considered here were

found to be very similar, ^{even in the} region ^{of the} absorption edge, ^{and to show the same trends as}

a function of deposition conditions or annealing.

However, optical absorption ^{related to localized}

states at the band edges and in the _gap is not very sensitive to the energy distribution of these states for matrix element reasons ; moreover, it cannot be determined _very accurately ^{on thin} films. The compa- rison of both d.c. conductivity ^and thermoelectric power ^{over a} large temperature range is expected

to bring ^more information on defect states and

non-homogeneity effects. The transport properties

of the sputtered films have already ^{been discussed}

in detail [20]. ^We describe here the results of similar measurements on evaporated films and ^we try ^to analyse all the data within the same theoretical models.

2. Experimental conditions.

The same substrates

(Corning ^{7059 float} glass) ^were used for both _evapo- rated and sputtered films. The evaporated ^{films were} prepared by ^thermal evaporation ^{from a} tungsten crucible in an oil-pumped ^vacuum system ^{with base} pressure 5 ^x 10 - g torr and _pressure during deposition

better than 5 x 10-’ torr. The crucible to substrate distance was 30 cm in order to avoid shadowing

effects and the deposition ^{rate was rather} high :

30 to 150 A/s. ^{The film thickness was limited to}

about _{0.5 pm} in order to prevent ^the formation of

pinholes ^{and cracks} usually ^{observed in thicker}

films due to excessive intemal strains. The substrate temperature during deposition Ts ^was varied between

room temperature ^{and 250} °C; ^{some films were} annealed in situ at TA

^{350 OC for an hour at a}

pressure of 1 to 5 x 10-’ torr. The sputtered ^films

were prepared by ^r.f. sputtering ^{in 5 mtorr} of pure Ar, the base _pressure being ^{4 x 10-’ torr. The} deposi-

tion rate was about 3 Â/s, and the film thickness

was between 10 and 30 _gm. The films were deposited

on substrates at room temperature; ^{some were} annealed inside the measurement cryostat ^at TA

250°C under 1 x 10-’ torr. Further details

on preparation conditions have been given ^else-

where [20]. All films under investigation ^were entirely amorphous, ^{as verified} by ^{electron or} X-ray ^diffrac-

tion.

After deposition ^{of 1 000 A} thick nichrome elec- trodes, four-probe ^d.c. conductivity (u) ^measure-

ments and thermoelectric _power (S) measurements

were performed ^{on the} evaporated ^{films in} exactly

the same way ^as for the sputtered ^films [20]. ^These

films being ^thinner by ^{about a} factor of 50 and having,

as we shall _see, higher resistivities, ^{the low} tempe-

rature measurements were limited to 50 K for conduc-

tivity ^{and 70 K for} thermopower (instead ^{of 25 and}

40 K respectively ^{for the} sputtered films). ^The accuracy

was very good ; ⁱⁿ particular, ^{the random error}

on the thermopower ^{is estimated to less than 1} %,

with a systematic uncertainty ^{of 5} % ^{due to} sample positioning, ^etc.

Because of the différent thickness of the evaporated

and sputtered ^{films, their} structures were not investi-

gated by ^{the same} methods. The structure of the

evaporated ^{films was studied} by ^electron microscopy

and electron diffraction, using ^thinner (200 ^{to 400} Á) samples prepared simultaneously and detached from their glass substrate with collodion [21]. Large

crack-like voids were never observed in these films.

The characteristic rod-like or supernetwork ^structure

could hardly ^{be detected even for films} deposited

at room temperature. ^It appeared ^more clearly ^at places where the glass substrate had been either

damaged ^or contaminated, ^{as well as in films} deposited simultaneously ^on microgrids covered with amor-

phous ^carbon layers [22]. These results again empha-

size the importance of nucleation _processes at the earliest stages ^{of film} growth ^for determining ^the

final structure. The film density could be estimated from the index of refraction for X-rays deduced, together with the film thickness, ^from X-ray ^inter-

ferences in reflection at grazing ^incidence [23]. ^The

films presented negligible density variations with

preparation conditions and _very little density ^deficit (of the order of 1 %) ^with respect ^to crystalline ^Ge.

Investigations ^{of the} crystallization processes sug-

gested however that the details of the structure, i.e. the local atomic configurations and their distri- bution throughout ^the network, varied with deposi-

tion conditions [24]. ^The sputtered ^{films were} very

thoroughly ^studied by X-ray diffraction [25]. ^No large ^{voids were} found in these films ; ^the intensity

of low-angle scattering ^{related to} voids between 7 and 250 Á in size was very low. The density ^deficit

of a few % ^measured by weighing unsupported ^films

was attributed to the _presence of small voids, ^assumed

to be spherical ^and uniformly distributed, ^whose size was estimated to be about 6 Á. Increasing ^the deposition temperature produced ^a densification related to the elimination of these voids ; ^{this was} accompanied by ^an increase of near neighbour coordination, ^{with a} consequent reduction in the number of dangling ^bonds.

3. Comparative analysis ^of transport properties.

For both evaporated ^and sputtered ^{films, the curves}

of log (1 ^versus reciprocal temperature liT display

a continuous change ^of slope throughout the investi-

gated temperature range. The ^more rapid ^increase

in slope ^{above room} temperature suggests ^{that at} least two mechanisms contribute to d.c. conduction.

We shall discuss separately ^{the low} temperature

range, where hopping ^{between localized states in}

the pseudo-gap ^is expected, ^{and the} high-tempe-

rature range, where conduction occurs a few tenths of an eV away from the Fermi level.

3.1 LOW-TEMPERATURE DATA.

The d.c. conduc-

tivity ^{data for three} typical evaporated films whose

preparation conditions are given ^{in table 1 are} plotted

as a function of T-1/4 in figure 1 ; the data for a

sputtered ^film deposited ^{at room} temperature ^and non-annealed [20] ^are also shown for comparison.

Table I.

Deposition parameters of ^the amorphous germanium films : ^H evaporated; ^SP sputtered.

Fig. ^1.

^d.c. conductivity

function of (temperature) -1/4

over

the whole measurement range for evaporated ^films H2 (0), H4 (E) ^and HS (+) ^{and for} sputtered ^{film SP} (0), ^the preparation

conditions of which

given ^{in table I.}

The behaviour expected for variable _range hopping

in the vicinity of the Fermi level [26] :

neglecting any temperature dependence of the pre-

exponential ^{factor Qa,} is observed in all cases at the lowest temperatures, up ^to about 110 K for the sputter- ed film SP and the non-annealed evaporated ^films H2 ^and H4, ^and up ^to about 130 K for the annealed

evaporated ^film H5. Similar results have already

been reported ^{for a} variety ^of amorphous ^{Ge films} prepared in different conditions, ^{the estimated} range of validity ^and accuracy of the T - 1/4 law varying

with the authors [10, 27-29]. ^The To values deduced from the data of figure ^{1 are} identical within experi-

mental uncertainties for the three evaporated ^films

and equal ^{to 1.7 x 108 K.} Very close values are

obtained over the same temperature range for the

1176

as-deposited sputtered films : 1.5-1.8 ^x 108 K ; ^these values are slightly increased after annealing :

2.0 ^x 108 K. Contrarily ^{to the} slope ^{of the} T-14 lines, the absolute values of the conductivity depend very

strongly ^on preparation conditions. They ^are higher ^for

the sputtered ^films than for the evaporated ^{ones in}

similar deposition conditions (films ^{SP and} H2);

for each method of preparation, they decrease with

increasing ^substrate temperature during deposition (films H2 ^and H4) ^and even more with annealing (films H2 ^and Hs). Therefore structural differences

only affect the absolute values of the conductivity

and not its variation with temperature. ^{This is a} very

general result ; To values of the order of 108 K are

typical ^of amorphous ^Ge films whose conductivities

at low temperature may differ by ^{several ordérs of} magnitude. ^Even hydrogen incorporation, ^which

can change ^the conductivity ^of sputtered ^films drastically, modifies the To ^values very little [30].

Only ^ion bombardment, which introduces extrinsic

disorder, has been found to have an appreciable

effect on the slope of the variation with temperature of the conductivity [31]. ^{Such a} vertical shift of the

experimental ^{T - 1/4} lines is difficult to explain ^{in the}

framework of the variable _range hopping theory,

since the two quantities ^of interest, To ^and Qo, ^are both related to the same parameters, ⁱⁿ particular

the density ^{of states at the} Fermi level N(EF). Besides, the experimental ^values of o-o, for example ^{6 x 109}

to 2.8 ^x 108 Q-1 cm -1 ¹ for the evaporated ^films

of figure ^{1, are much too} high compared ^{to the}

values predicted by ^the theory. ^These points ^have

been raised _very often, and various limitations of the theory ^{have been} pointed ^out [32].

If a T- 1/4 law represents ^{the low} temperature behaviour of the conductivity correctly, ^the nearly

constant slope ^found experimentally ^{must indicate}

that the density ^of states at EF ^{or at} least the ratio

a3/N(EF), ^{where a} is the localization parameter of the electronic wavefunctions [33], ^varies little with

sample history ; ^{this does not} preclude ^more important

modifications of the distribution of localized states elsewhere in the pseudo-gap. ^The pre-exponential

factor is difficult to estimate theoretically, ^because

it requires ^a good knowledge ^{of the} electron-phonon coupling ^{in an} amorphous ^material [34]; ^this may account for part ^{of the} discrepancy ^between experi-

ment and theory. Moreover, ^{what is more} essential for our purpose, it will reflect the percolation aspects of d.c. conduction and will depend ^{on the choice}

of paths for the current, which is directly ^{related to}

the problem ^of heterogeneities ^{in the} amorphous

network. This could explain why the structural differences due to different preparation ^conditions

affect essentially the absolute values of the conducti-

vity. ^{It must be} pointed ^{out that a different} approach

has been proposed recently : ^the general ^{trends of}

the conductivity ^{data as} outlined above can be

reproduced quite satisfactorily by ^a percolation

treatment, if différent ad hoc density ^{of states models}

are used ; ^{in this case neither} To ^nor ao ^are connected with the density ^{of states at} EF [35].

It has often been emphasized ^{that the variable}

range hopping theory is in fact strictly ^{valid at} tempe-

ratures lower than the ones where the characteristic behaviour is usually verified. The fit of our experi-

mental data to a T-1/4 law _up to temperatures ^as

high ^{as 110 or 130 K} may then be fortuitous. Above 110 K, ^{the data} points ^deviate downwards, i.e. the

conductivity ^{values are} smaller than expected ^from

this law. Similar results ^were already reported ^for evaporated films, above 140 K. They ^{were inter-} preted within the variable range hopping theory

as due to the presence of ^a peak ^{in the} density ^of

states at the Fermi level [36]; ^the temperature ^at which the deviation occurs would then be related to the width of that peak. ^{But such a behaviour can also}

be viewed as a proof that ^{a 7" law does} not account

properly for the data. We therefore tried to find an

empirical law which could reproduce ^{our data over}

a larger temperature range. The data on the sputtered

films were shown [20] ^{to follow a T- 3/8 law from}

25 K to room temperature. ^{The same law also} applies

to the as-deposited evaporated ^{film H2, as shown} by

Fig. ^2.

^d.c. conductivity

function of T-’l’ over the whole measurement range for the

evaporated ^films H 2 (0), H4 (0) and H5 (+) ^and sputtered ^film (0)

ⁱⁿ figure ^1.

figure ^2, but the data relative to evaporated ^films

are in general ^best represented by :

0-

a’.exp[- (TO’IT) 1/2] , ^{as shown on} figure ^3.

These results tend to demonstrate that it is extremely difficult to détermine the exact law for the variation of conductivity ^with temperature. ^{Moreover, the} empirical ^{laws which can be found can} just ^{be a} phenomenological description ^{of a more} compli-

cated behaviour. Nevertheless, ^{one can} try ^{to relate}

Fig. ^3.

^d.c. conductivity

function of T-li2

the whole measurement range for the

evaporated ^films H2 (0), H4 (D) and H_î (+)

ⁱⁿ figure ^1.

the temperature dependence ^{of the} conductivity ^at

intermediate temperatures ^{to the} shape of the distri- bution of localized states in the pseudo-gap, ^as sug-

gested by percolation ^treatment [37] ; ^{a T-1/2 law}

would be consistent with a density ^{of states} increasing

as (E-EF)2 away from EF, ^{which is not} unreasonable.

It is worth noting ^{that for films} H2 ^and H4 in figure ^3,

the experimental points ^deviate upwards ^{from the} T- 1/2 lines below 70 K ; ^this might indicate the temperature range where a T- 1/4 law really applies.

Only ^states very close to EF ^should participate ^{in the}

conduction at sufficiently ^low temperature. ^{On the} high temperature side, ^the experimental points ^also

deviate upwards, above about 150 K for H2 and ^about

250 K for H4 and H,5. ^{The new} conduction processes

setting ^{in at these} temperatures ^{will be} analysed ⁱⁿ

the next section.

More information on transport mechanisms can

be gained from the simultaneous study ^{of other} transport properties. Figure ⁴ presents the thermo- power data relative to the same films as in figure 1,

Fig. 4. Therinopow c; ^.S’

^fllnc1ton ot’teiii tire ^{T oBcr thc} whole measurement range for the

evaporated ^films H2 (0), H4 (0) ^and HS (+) ^and sputtered ^{film SP} (0)

ⁱⁿ figure ^1.

plotted ^{as a function of} temperature ^{between 70} and 300-500 K. We concentrate here on the low temperature range, where S has small, negative ^values

of the order of - 90 to - 60 pV/K. Similar results

were already reported ^{for a} variety ^of amorphous

Ge films [38-40]. ^The present measurements extend to lower temperatures ^{and their} accuracy allows us

to determine the behaviour of S with temperature

more precisely. ^{For the} as-deposited sputtered ^films

like film SP in figure 4, S ^is remarkably ^constant

from 70 to 300 K, ^{its value} varying only slightly

with deposition conditions [20]. ^{For the} evaporated films, S ^{shows the same} tendency ^{to become tem-} perature independent ^{at the lowest} temperatures, but over a more limited temperature range. S ^starts increasing ^towards positive ^{values at} about 150 K for H2, ^{200 K for} H4 ^and Hs, ^{more or less} steadily depending ^{on the} sample. ^The evaporated ^films

present ^{in fact the same behaviour as} the annealed

sputtered ^films [20]. ^{The constant} low-temperature ^S

values are very close for both types ^of films ; ^their magnitude ^decreases only slightly ^with increasing

substrate temperature during deposition ^{or with} annealing. ^{As mentioned} earlier, ^{it was} unfortunately

not possible ^to extend the measurements ^on evapo- rated films below 70 K ; ^{therefore we do not know} whether their thermopower ^also displays ^the sharp

increase in magnitude ^{observed for} as-deposited sputtered ^films.

This temperature range may correspond ^{to the} regime of variable _range hopping for the conduc-

tivity. ^Various expressions ^{for the} thermopower

have been derived within this theoretical model [41- 43] ; ^for example, according ^to Zvyagin [42] :

where 9 0.35. Small S values ^are predicted, ^the sign of which will depend ^{on the} asymmetry ^{of the} density ^{of states in the} vicinity of EF ; S

⁰ is obtained for symmetric N(E). ^{The different} treatments disagree

in the estimation of the temperature dependence,

which is expected ^to be small but to exist. None of them can therefore explain ^the fairly ^{constant S}

values which were measured for both sputtered ^and evaporated ^{films over} large temperature ranges.

Moreover, ^{if one tries to} correlate the behaviour of both d.c. conductivity ^and thermopower ^{for these}

films within the variable _range hopping assumption,

no special ^{feature in the} thermopower ^{data can be}

observed at the temperature (110-130 K) ^{where the} conductivity data deviate from the characteristic T - 1/4 law; ^{if the} interpretation ^{for this deviation}

mentioned above is correct, ^one would expect ^the cut-off in the density ^{of states related to the finite}

width of the assumed peak ^at EF, ^to affect also the

thermopower behaviour. This discrepancy ^{could be}

an argument ⁱⁿ favour of preferring ^{other laws}

1178

than a T - 1/4 law for the temperature dependence

of the conductivity at not too low temperatures.

It _may be noticed that the temperatures ^{at which S} deviates from its low temperature ^constant values, which depend ^{on the film, are related to} whose where

Q seems to deviate from our empirical ^{T-12 law.}

This obviously ^{indicates the onset of a new conduc-}

tion mechanism, which is felt ^more sensitively by ^the thermopower.

For the sputtered films, ^the temperature indepen-

dence of S between 70 and 300 K, ^{as well as} its increase in magnitude ^{below 70 K, have been} explained by assuming conduction by ^nearest neighbour hopping

in a partially filled band at the Fermi level with _very small width, of the order of 0.01 eV [20]. This assump- tion _may be unrealistic, ^{and the} conductivity ^beha-

viour difficult to reconcile with narrow band trans-

port. On the other hand, ^{it must be} emphasized

that the thermopower ^of practically ^all investigated amorphous ^{Ge films} presents ^{the same behaviour}

at low temperatures, ^i.e. nearly ^constant, small, negative ^{values of the same order of} magnitude,

even if it differs markedly ^at high temperatures, being ^for example ^either positive ^or negative depending

on sample history. ^This striking similarity ^{is difficult}

to understand, ^{unless a common constant} additional

term which obscures the particular temperature

dependence ^of S, ^{must be} taken into account ; it could be, ^as recently suggested, ^a spin entropy

term [44].

3.2 HIGH-TEMPERATURE DATA.

Since both types of samples begin ^to crystallize ^at about 380-400 oC

depending ^on preparation conditions, ^{it was} possible

to anneal them and investigate ^their transport pro-

perties up ^to quite high temperatures. Figure ⁵

shows the conductivity data between 190 and 620 K

plotted ^{as a} function of reciprocal temperature ^for the same evaporated ^{films as in} figure ^{1. The contri-}

bution of conduction through ^{localized states in}

the pseudo-gap ^which predominates ^{at low} tempe-

ratures is still ^so high ^{that an activated behaviour}

can only be observed for the annealed film Hs ^at

the highest temperatures, ^between approximately

520 and 620 K. Any activation energy which can

be deduced from the slope ^{of the raw data curves at}

intermediate temperatures will then be meaning- less ; ^{even the value} corresponding ^to H 5 ^{which can}

be determined above 500 K will have large uncertainty.

Analysis ^{of the} high temperature mechanisms requires

that we subtract the contribution of the low tempe-

rature processes. ^{We can} estimate the latter by extrapolating ^{the T - 1/2} behaviour, ^{which was found}

to reproduce ^{our data} satisfactorily ^{over a wide tem-} perature range. For films H.5 ^and H4, ^{we then obtain}

an activated behaviour above room temperature :

(1

Q 1 exp[ - E(11/kT], with activation energies equal

to E(11

=

0.50 and 0.47 eV respectively (Fig. 6).

The pre-exponential ^{factor (11} is in both cases of

the order of 10’il-’cm-’ (2.8 and 1.6 x 103fl-ICM-1

Fig. ^5.

^d.c. conductivity

function of reciprocal tempe-

rature 1 /T ^{in the} high temperature range for the

evaporated

films H2 (8), H4 (0) ^and H.5 (+)

ⁱⁿ figure ^1.

Fig. ^6.

Difference between the d.c. conductivity

^{and the} quantity Qextr obtained by extrapolation of the low temperature T -1/2 behaviour,

function of reciprocal temperature ^{for the}

same evaporated ^films H2 (0), H4 (0) ^and Hs (+)

ⁱⁿ figure ^1.

respectively), which could indicate [45] ^{that conduc-}

tion is due to carriers excited into extended states

beyond ^the mobility edges. The values of E,,, ^correlate

well with the values of Eo/2, ^where Eo ^{is the} optical

gap determined by extrapolation ^of hv.(82) 1/2 ^versus

hv (82 being ^the imaginary part ^{of the} complex ^dielec-

tric constant) ; ^we indeed found Eo

1.0 and 0.97 eV for HS ^and H4 respectively. ^{This means} that in both

cases the Fermi level is approximately ^{located at}

mid-gap. These results are in agreement ^{with those}

obtained for the sputtered films annealed at 250 OC,

for which a similar analysis gives ^an activated beha- viour with an activation _energy of about 0.44 eV and a pre-exponential factor of the order of 103 S-1 cm-1. One can also see in figure ^{6 that,}

when the temperature approaches ^{350 K and} below, there is a decrease in slope, ^{and a} different activated behaviour is observed between 350 and 200 K, with an activation _energy E., --- 0.31 eV for both

Hs ^and H4. ^The corresponding values of the _pre-

exponential ^factor Q2 ^are smaller than before by

about two orders of magnitude. A similar behaviour is obtained for the as-deposited ^film H2 ^between

150 and 300 K after subtraction of the low-tempe-

rature contribution, ^{with an} activation _energy

E«, ^{0.21 eV and a} pre-exponential ^factor

U2 10 Q-l cm-’ . At these temperatures, ^conduc- tion is then more likely ^{to occur} by carriers excited into localized states at the band edges, ^{which means}

lower density ^{of states} and lower mobility ^than

before. If the ^same mechanism works for H 5, H4

and for H2, ^the difference of about 0.1 eV between the corresponding activation energies may indicate

a reduction of band tailing ^when increasing ^substrate temperature during deposition ^{or when} annealing.

It must however be emphasized ^{that such an} analysis

is valid only ^{if the} low-temperature contribution has been estimated correctly. ^{The results} concerning

the highest temperature process will be little affected, but those relative ^to intermediate temperatures ^can be modified appreciably if another variation law, different from the empirical ^{T-l/2 one chosen here,}

is preferred.

It has already ^been pointed ^out that the thermo- power of the evaporated films deviates from its

low-temperature ^{constant values at} about 150 K for H2, ^{200 K for} H4 ^and HS (Fig. 4). ^These tempe-

ratures are close to the ones where the conductivity

data deviate from the low- temperature ^{T-l/2 law}

and where we have assumed that conduction at the band edges ^is setting in. Above room temperature, S becomes positive, which indicates that the hole contribution predominates. ^No pure activated beha- viour is observed over the investigated temperature range. These results are in complete agreement ^with those already ^{obtained on} evaporated films pre-

pared ^{in the same} conditions and extending up ^to 650 K [39]. ^{In that} work, ^both conductivity ^{and ther-}

mopower data ^were carefully analysed ^{in terms of}

three contributions with different weights : ^{a low-} temperature ^{one, with S constant and Q} following

a T-l/4 law, ^{and two} high-temperature ^activated

ones, for electrons and holes ; ^a difference of 0.12 eV between the activation energies ^{of S and a had to be}

used. This treatment led to very close values for the activation energies for electrons and holes, increasing by about the same amount upon annealing. ^The

conclusion that the Fermi level stays approximately

at mid-gap, slightly shifted towards the valence band,

agrees with our conclusions. For the annealed

sputtered films, ^the thermopower ^{becomes also} posi-

tive above room temperature [20], which confirms their great similarity ^{to the} evaporated films studied here. It is worth noting ^that hydrogen incorporation produces ^a sign reversal of the thermopower ^of sputtered ^films at high temperatures, and that conduc- tion is then essentially ^{due to electrons} [30]. ^{The Fermi}

level has therefore moved ^across the pseudo-gap

towards the conduction band. The same result was

obtained when bombarding evaporated films with active impurities ^{like oxygen} [39]. Thermopower

is then particularly ^{sensitive to the} shape ^{of the}

distribution of localized states in the pseudo-gap

and to the location of the Fermi level.

4. Conclusions.

We have investigated ^{and com-} pared ⁱⁿ detail the transport properties ^{of amor-} phous ^{Ge films} prepared by ^two different methods :

vacuum evaporation ^and sputtering, ^{in order to}

better understand how the sample ^{structure can}

influence thèse properties. Unfortunately, ^{the film}

structure could not be studied by ^{the same methods}

for both types of films, therefore the information cannot be compared directly. ^{It can} however be

argued ^{that the} density deficit is slightly larger ^for

the sputtered films than for the evaporated ^{films in}

the present ^case, perhaps because of the presence of _argon atoms, and that microscopic ^{voids are} probably the main structural defects in both types of samples. ^The problem ^of semi-macroscopic ^hetero- geneities ^{like the} quasi-periodic density fluctuations inferred from electron microscopy observations on

various amorphous samples ^{is more difficult to} solve, ^{since we have no} information on the sputtered films ; ^{for the} evaporated ^{films, our results are in} agreement with those obtained by Barna et al. [12]

on their samples, ^{and we} follow their conclusions.

We expect ^however that the essential structural diffe-

rences between the two types of films studied here

concem the distribution and size of such hetero-

geneities, since the latter are determined by ^{the film}

formation mechanisms, ^{which in tum} depend ^{on the} deposition ^mode [45].

The d.c. conductivity ^and thermopower ^{of both} sputtered ^and evaporated films show a strong ^simi-

larity. ^{At low} temperatures, ^o follows the same laws

versus temperature, ^{i.e. a} T- 1/4 law from 25 or

50 K up ^to about 110 K in agreement with variable range hopping theory, ^{or an} empirical ^{T-3/8 or} T- 1/2 law over a larger temperature range. In all

representations, ^the slopes ^are very close, ^and nearly independent ^of deposition conditions and annealing.

This suggests ^{that the} density ^{of states at} EF ^{is little}

sensitive to the details of the amorphous ^network

or is related to peculiar defects which exist indepen- dently ^of deposition conditions ^or annealing. ^Another possibility ^{is of course that the} slope is insensitive to the density ^{of states at} Ef, ^{which means that} existing

theories do not describe the low-temperature transport

process properly. S ^{has a constant} value which is

1180

difficult to explain by ^{variable range} hopping theory only. ^At higher temperatures, ^{a new conduction} process ^sets in, ^{which can be seen on} both J and S

at about 150 K-200 K depending ^on deposition ^condi-

tions and annealing ; band-like conduction can be assumed above 350 K, with activation energies ^for

the conductivity which correlate well with half the

optical gap. The S behaviour indicates that hole contribution predominates ^at high temperatures.

Some indication of conduction at the band edges

at intermediate temperatures ^has been found for the

evaporated ^films. Therefore, ^{for both} sputtered ^and evaporated films, ^not only ^the optical gaps (and pro-

bably ^the mobility gaps) ^{are the same,} but also the Fermi level is located at about mid-gap, slightly ^below,

and its position ^{does not} change while the _{gap is}

opening up by increasing ^substrate temperature

during deposition ^or annealing. ^The density ^{of states}

in the pseudo-gap ^must then be reduced rather

symmetrically ^{and in} approximately ^{the same} way.

This similarity in the conduction mechanisms suggests that the network in these sputtered ^and evaporated

films has similar characteristics and contains the same

type ^of structural defects, although in variable _pro-

portion, ^{and that the structure} is modified in the

same way by changing ^the deposition conditions or

by annealing. ^The particular density fluctuations and distribution of defects throughout the network is not important ^{for the} conduction mechanisms.

In striking contradiction with the similarity ^{of the} temperature dependence ^of both d.c. conductivity

and thermopower, ^we have however seen that the absolute values of 6 may present huge differences from sample ^to sample ^{at low} temperatures, ^while the values of S are about the same. This sensitivity

of the (1 values ^to sample ^structure is difficult to

understand within existing ^theories only ^{in terms of}

the proportion ^{of defect} centres at which hopping

occurs. The influence of the material non-homoge- neity ^must certainly also be taken into account.

The differences between sputtered ^and evaporated

films _may indicate more effective heterogeneities

in the former. The reduction of a by increasing

substrate temperature during deposition may be related to the change ^{in the} characteristic distances of the supernetwork, ^{the even} larger ^{reduction by} annealing ^to the densification of the channels leading

to a more homogeneous ^structure.

Acknowledgments. ^{- We wish to} thank Professor W. Paul for his interest in this work and critical

reading ^{of the} manuscript.

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