On the temperature dependence of the electrical and optical properties of Cu[sub 2]GeSe[sub 3]

JOURNAL OF APPLIED PHYSICS VOLUME 88, NUMBER 2 15 JULY 2000

On the temperature dependence of the electrical and optical propertiesof Cu 2GeSe3

G. Marcano,a) D. B. Bracho, C. Rincon, G. Sanchez Perez, and L. NievesCentro de Estudios de Semiconductores, Departmento de Fı´sica, Facultad de Ciencias, Universidad de LosAndes, Me´rida, Venezuela

~Received 19 January 2000; accepted for publication 11 April 2000!

The Hall effect and electrical resistivity measurements onp-type Cu2GeSe3 crystals were measuredin the temperature range from 80 to 300 K. The temperature variation of the hole concentrationpfrom about 200 to 300 K is explained as due to the thermal activation of a shallow acceptor levelwith an ionization energy of around 50 meV. At low temperatures the impurity band conductiondominates the electrical transport processes. From the analysis of thep vs T data, thedensity-of-states hole effective mass is estimated to be of the same magnitude as the free electronmass. The temperature variation of the hole mobility in the valence band is analyzed by taking intoaccount the scattering of charge carriers by ionized impurities and acoustic phonons. In the impurityband, the mobility is explained as due to thermally activated hopping transport. The opticalabsorption coefficient spectrum shows the presence of three absorption narrow bands below thefundamental gap. From the analysis of their temperature dependence, these bands are attributed asdue to free–to–bound transitions related to intrinsic defect acceptor states. Activation energies ofthese states are estimated to be around 0.12, 0.24, and 0.30 eV. Tentative assignment of the natureand origin of these defect states were also made. ©2000 American Institute of Physics.@S0021-8979~00!03014-0#

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I. INTRODUCTION

Highly efficient acousto-optic~AO! materials for appli-cations in the IR region are of considerable interest.1–5 Asuitable material for such AO applications must have a h‘‘figure of merit’’ M2 which is a measure of its inherendiffraction efficiency.1–4 This figure is given by the expression M25n6pe

2/rn3, wheren is the index of refraction,pe

the photoelastic coefficient,r the mass density, andn theacoustic velocity. This velocity can be related to the melttemperatureTM and the mean atomic weightM by Linde-mann’s formula,n2;TM /M . Sincepe does not vary verymuch between different materials as is about 0.15–0.3most usable solids, a good material for AO devices shothen have a low melting point and mass density and a hmean atomic weight and index of refraction.

The ternary semiconductor Cu2GeSe3 has several favor-able basic physical properties, listed in Table I, that mathis material a potential candidate for AO applications inIR region. Values of these properties for several usefulmaterials in the visible and IR regions are also listed in ttable for comparison.

Different crystal structure type for Cu2GeSe3 have beenreported for several authors.6 Earlier x-ray powder analysisby Palatniket al.7 and Rivet8 indicated that it crystallizes ina cubic and tetragonal chalcopyrite structures, respectivwhereas Parthe,9 on the basis of single-crystal analysifound Cu2GeSe3 to be orthorhombic with unit cell parameters a511.860, b53.960, andc55.455 Å. Recent x-raypowder diffraction studies on this compound10,11confirm the

a!Electronic mail: [email protected]

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results of Parthe. The unit cell parametersa, b, andc recentlyobtained11 were 11.878~8!, 3.941~3!, and 5.485~3! Å, respec-tively, in good agreement with those reported in Ref. 9.

The temperature variation of the energy gapEG ofCu2GeSe3 in the range from 10 to 300 K was measuredcently from optical absorption measurements.11 The band–to–band transition was found to be direct withEG around0.78 and 0.80 eV at 300 and 10 K, respectively. Howevmeasurements of the electrical conductivity and Hall coecient as a function of temperature in Cu2GeSe3 are veryscarce. From the analysis of the electrical data onp-typesamples, Endoet al.12 have found that in as-grown sampleat room temperature the hole concentration and the holebility are about 1019cm23 and 0.5 cm2/V s, respectively. Aconsiderable higher value of the mobility,m'10 cm2/V s,was obtained on samples annealed at high temperaturefew days. From the analysis of thep(T) data they also con-cluded that the observedp-type conductivity is due to shallow acceptor states with activation energies smaller than 0eV. Furthermore, from the Hall and Sebeeck data, the heffective mass was estimated to be as 0.94me , whereme isthe free electron mass. The band gap at 0 K they determfrom the temperature dependence of electrical resistidata, EG'0.25 eV, is considerably smaller than that otained from optical data.10,11 On the other hand, no detaileanalysis of the temperature dependence of the optical perties of this compound has been reported. For this reasothis article a combined study on the temperature dependeof the Hall effect, electrical resistivity, and optical absorptispectra near the fundamental absorption edge inp-typesamples of Cu2GeSe3 is presented. From the analysis of thdata, the density-of-states hole effective mass, dielectric c

© 2000 American Institute of Physics

AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp

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823J. Appl. Phys., Vol. 88, No. 2, 15 July 2000 Marcano et al.

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TABLE I. Several materials with useful acousto-optic properties in the visible or infrared regions.a Since insome cases values ofpe are not given in the data reported in Refs. 1–4, these were calculated from thedata reported by means of the expressionM 25n6pe

2/rn3. For Cu2GeSe3, M2 was calculated by means of thabove mentioned expression, usingpe'0.25.

Material

Wavelengthrange~mm!

r~g/cm3! n

n(106 cm/s) pe

M2

(10216 s3 g21)

SiO2 0.222.5 2.20 1.47 5.97 0.20 0.02TiO2 0.4526 5.4 2.58 8.03 0.15 0.03TeO2 0.3525.0 6.00 2.26 0.62 0.20 8Ge 1.8223 5.33 4 5.50 0.30 4.2GaAs 1211 5.34 3.1 5.3 0.30 1.0As2S3 0.621.3 3.2 2.61 2.6 0.28 4.3LiNbO3 0.424.5 4.64 2.20 6.57 0.23 0.05Pb2MoO4 0.4525.5 6.95 2.39 3.63 0.21 0.2PbMoO5 0.425 7.1 2.2 2.95 0.25 1.3a-HIO3 0.321.8 5.0 2.0 2.44 0.31 0.9a-HgS 0.62216 8.1 2.8 2.45 0.35 5.0Tl3AsS4 0.6212 6.2 2.83 2.15 0.34 9.7Cu2GeSe3 2.6215 5.6 3.2 4.0 ;0.25 ;2

aSee Refs. 1–4.

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stant, valence band deformation potential, concentrationimpurities, and activation energy of the defect levels westimated.

II. EXPERIMENTAL DETAILS

Samples used in the present study were prepared fthe melt by direct fusion of the constituent elements insealed and evacuated quartz tube as described elsewhe11

The chemical analysis of samples taken from the cenpart of the ingots, was performed by energy dispersive x-spectroscopy~EDX!. Although their compositions wereclose to the ideal value 2:1:3, slight deviations from thvalue were found. Thus, samples, which are denoted aS1

and S2 , used for the electrical and optical studies, resptively, have chemical compositions of Cu:Ge:Se28.4:15.0:56.6 and 28.8:15.6:55.6 atomic percentage, restively. That is, both samples have a deficiency of Cu wrespect to Ge~Cu/Ge'1.8– 1.9) and an excess of anion ovcations (Se/metal'1.25– 1.30).

As checked by a thermal probe, all the samples obtaifrom the ingots werep-type conductivity. The hole concentration p and Hall mobilitym in the temperature range from80 to 300 K were determined by combined Hall effect aconductivity measurements performed according to theder Pauw method.13 In-soldered contacts were made by etcing the sample’s surface with a low melting point solder flusing a low power iron solder. The contacts were ohmicthe range of interest with a resistance always lower thanof Cu2GeSe3. A magnetic field of 16 KG was employed ithe Hall measurements. The characteristic data werelected with an automated, high resolution, and high impance data-acquisition system.

For the measurements of the absorption coefficient sptra at various temperatures, the sample was placed in a2

cryostat operating in the range from 10 to 300 K. A fulautomated SPEX 1870 monochromator and a 170 W tu

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III. RESULTS AND DISCUSSION

A. Carrier concentration

The variation of hole concentration of the representatsampleS1 as a function of 103/T is shown in Fig. 1. It isobserved thatp first decreases with temperature up to abo180 K. At this temperaturep(T) goes through a minimumand it is then found to increase with decreasingT. The ap-pearance of such a minimum in the temperature variationthe carrier concentration is a characteristic sign of the pence of an acceptor impurity band.14,15 In the present casethis band is expected to be formed at temperatures beabout 180 K, because in this range of temperaturep de-creases with increasingT.

The variation ofp vs T in the high temperature region iprobably due to the thermal activation of a shallow acceplevel. In this case, the hole concentration in the valence bpv is given by the well known expression16

pv~pv1ND!/~NA2ND2pv!5~Nv /b!exp~2EA /KBT!,~1!

whereEA is the thermal impurity–to–valence band activtion energy,b the degeneracy factor of the acceptor groustate,NA the acceptor concentration,ND the compensatingdonor concentration, andNv52(2pmh* KBT/h2)3/2, the ef-fective density of states in the valence band.

On the other hand, the hole concentration in the impubandpi is obviously given by15

pi5p2pv . ~2!

Since in the present case the impurity band conducbecomes important below about 180 K, to estimateEA andmh* from the p(T) curve, it was assumed thatp'pv in therange of high temperatures. Hence, the variation ofp be-tween 180 and 300 K was analyzed by using Eq.~1!. By


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824 J. Appl. Phys., Vol. 88, No. 2, 15 July 2000 Marcano et al.

choosing the proper values ofNA and ND , a linear plot ofln$p(p1ND)/@(NA2ND2p)T3/2#% vs 103/T, as shown in Fig.2, was obtained above about 200 K. From the slope ofline, the activation acceptor energy is found to beEA5(5064) meV. The values ofNA and ND obtained from the fitwere 931021 and 131018cm23, respectively. Furthermorefrom the intercept at 103/T→0, with b52, which is thevalue for the degeneracy factor of the acceptor ground sin the case that the highest valence band is nondegener16

the hole effective mass is calculated to bemh* 5(0.9760.03)me . This value is in excellent agreement withmh*'0.94me estimated from the analysis of Hall and Seebecoefficients.12 On the other hand, if we assume that the heaand light hole bands in Cu2GeSe3 are degenerate, and therfore an acceptor should offer four states above this douvalence band~that is b54), a relatively higher valuemh* 5(1.5360.05)me , is obtained. Since in general, in tenary compoundsmh* is of the same order of magnitude a0.8– 1.0 me , this result apparently indicates that the highvalence band is nondegenerate in Cu2GeSe3.

With the values ofpv(T) in the temperature range from80 to 300 K calculated by means of Eq.~1! and the values ofNA , ND , andmh* given above, the variation ofpi with T wasobtained from Eq.~2!. This variation, together withpv(T), isalso plotted in Fig. 1. As expected, it is observed thatpvdominates at the high temperature region whereaspi does atlow temperatures. It can also be noted thatpv(T) andpi(T)

FIG. 1. The temperature variation of hole concentrationp ~s! of the repre-sentative sampleS1 in the range from 80 to 300 K. The temperature vartion of holes in the valence bandpv ~continuous line! and in the impuritybandpi ~broken line!, calculated from Eqs.~1! and~2!, respectively, are alsoshown.


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curves intersect each other at around 145 K. Below this teperaturepi predominates overpv . It is also found thatpv'6pi in the minimum of thep vs T curve, which occursaround 180 K.

B. Carrier mobility

If an acceptor impurity band is formed, holes in both tvalence and impurity bands contribute to the total mobiliIn such a case, the measured mobilitymp is no further equalto the hole mobility in the valence bandmv but it is related tomv and the mobility in the impurity bandm i by means of theexpression,14,15

mp5~pvmv21pim i

2!/~pvmv1pim i !. ~3!

As mentioned above, around 180 K it is found thatpv'6pi . Because is also expected thatpvmv5pim i at thistemperature,14,15 the parameterb5m i /mv is thus found to beb'6 at 180 K. Furthermore, sinceb depends much weaklyon temperature thanpi /pv , it can be assumed thatb is ap-proximately equal to 6 in all the temperature range.14,15

Under this assumption, Eq.~3! can be written as,

mp5@pv1pi~m i /mv!2#/~pvmv /mv21pim i /mv

2!

5@~pv1pib2!/~pv1pib!#mv , ~4!

and

mv5@~pv1pib!/~pv1pib2!#mp

'@~pv16pi !/~pv136pi !#mp . ~5!

FIG. 2. A plot of ln$p(p1ND)/@(NA2ND2p)T3/2#% vs 103/T of Cu2GeSe3sampleS1 in the range from 170 to 300 K. The straight line between 2and 300 K represents the fit of Eq.~1! to thep(T) data. From the slope ofthis line, the activation energy of the acceptor level is found to beEA

'50 meV. The resulting values ofNA and ND were 931021 cm23 and 131018 cm23, respectively. From the intercept at 103/T→0, the hole effec-tive mass is estimated to bemh* '0.97me .


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The mobility of holes in the valence band as a functiof temperaturemv(T) can be thus estimated from the expementalmp(T) curve by using Eq.~5!.

To estimate the strength of different scattering mecnisms in the valence band,mv can be calculated by usinMathiessen’s rule,

mv215m I

211mac211mop

211mN21, ~6!

wherem I , mac, mop, andmN represent the mobilities of thcharge carriers due to the scattering by ionized impuritacoustic-lattice modes, optic-lattice modes, and neutralpurities, respectively. However, according to the analymade in Ref. 11, it is not expected that optical modes apciable contribute to the scattering of carriers inp-typesamples. On the other hand, because the most active implevel detected from the electrical measurement is very slow (EA'0.05 eV), it is expected that neutral impuritieonly contribute to the hole mobility at very lowtemperatures17 (T,80 K). For these reasons, the last twscattering mechanisms in Eq.~6! were not taken into accounin the present analysis.

The usual formulas for the mobilities resulting from thdifferent scattering mechanisms are derived for a nondegerateds-like conduction band. Therefore, as pointed outLook and Manthuruthil,17 in the present case ofp-like va-lence bands one must consider~i! the overlap integral in thescattering matrix element, which is unity for a pures-likestate, and~ii ! interband scattering. Forp-like valence bandsthe overlap integrals have been shown to be close to 0.5the scattering by both lattice modes and ionized impuriscattering. Thus, for the analysis of themv vs T data ofp-Cu2GeSe3 we will need to multiply all the standard mobiity expressions by a factor of two in order to take into acount the effect of the overlap.17 On the other hand, based ithe results of the electrical properties indicating that theper valence band is nondegenerate, degenerate band eand interband scattering were neglected in the present ansis. The factor of 300 in denominator is also includedconvert to practical units~cm2/V s! when all the parameterare given in CGS units.

The acoustical-mode scattering mobility is given by17

mac5~2/300!~8p!1/2e\4rn2

3@3Eac2 ~mh* !5/2~KBT!3/2#21 cm2/V s, ~7!

where6 r55.6 g/cm3 is the density,n'43105 cm/s the lon-gitudinal velocity of sound, andEac the valence band deformation potential.

For p-type samples, the Hall mobility due to ionizeimpurity scattering is calculated according to the BrookHerring formula17

m I5~2/300!27/2e02~KBT!3/2

3@p3/2e3~mh* !1/2NI f ~x!#21 cm2/V s, ~8!

heree0 is the static dielectric constant,NI the ionized impu-rity concentration, and the functionf (x) is given by the re-lation ln(11x)2x/(11x), wherex56e0mh* (KBT)2/pe2h2p.


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To analyze the mobility in the impurity band, the themally activated hopping between localized states in sucband is considered.18,19 In this case the mobility is given bythe expression18

m i5~D/KBT!exp~2W/KBT!, ~9!

whereD is a constant andW the hopping activation energyThe experimental data ofmp and the calculatedmv and

m i as a function ofT are plotted in Fig. 3. It is observed thathese mobility values are nearly of the same magnitude tthose reported for as-grown Cu2GeSe3 samples in Ref. 12. Itcan also be noted that in the major part of the temperarange studiedmv increases with increasingT indicating thatthe holes are predominantly scattered by ionized impuritHowever, because is expected that at high temperatacoustic phonons should participate in the scattering procthe contribution ofmac to the total mobility was also considered in the analysis of themv(T) data. It is also observed tham i increases with temperature which is a characteristichavior of the hopping processes.

In order to fit Eq.~6! to the experimental data ofmv(T),it should be noted that in Eqs.~7! and ~8!, e0 and Eac areunknown, whereas from the analysis of thep(T) data,NI

'NA1ND is estimated to be 931021cm23. Hence, usingthe values ofr, n, mh* , andN1 given above, withe0 , andEac

as adjustable parameters, a good fit to the data, as showa continuous line in Fig. 3, is obtained withEac518.5 eV ande0514. A good fit of Eq.~9! to them i(T) data, also shownby a continuous line, was obtained with the adjustable

FIG. 3. Variation with temperature of the experimental hole mobilitymp

~d! and the calculated hole mobility in the valencemv(s) and impuritym i(h) bands of Cu2GeSe3 sampleS1 . The theoretical fit to themv(T) data,by using Eqs. ~6!–~8! with the fixed parametersr55.6 g/cm3, v543105 cm/s, mh* 50.97me , andN15931021 cm23, is shown by a continu-ous line. The parameters obtained from the fit wereEac'18.5 eV ande0

'14. The theoretical fit to themv(T) data, by using Eq.~9!, with the ad-justable parametersW'30 meV andD'0.7 eV, is also shown by a continuous line.


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rametersW'30 meV andD'0.7 eV cm2/V s. This value ofW is nearly of the same magnitude as the activation enefor hopping transport in Cu2SnSe3, W527 meV, estimatedfrom the analysis of the hole mobility data.19

C. Optical properties

The absorption coefficienta was obtained from the measured transmittance through a relation based in the LambBeers rule:a5(1/d)ln(I/Io)2ac , whered is the thickness ofthe sample,I andI o the intensity of light transmitted througthe sample and incident to it, respectively, andac is a termthat accounts for the losses at the sample’s surface.

Figure 4 shows the absorption coefficient spectraCu2GeSe3 sampleS2 in the energy range from about 0.50.8 eV at several temperatures between 10 and 300 K. SCu2GeSe3 is a direct gap semiconductor withEG'0.78 eV atroom temperature,10,11 the increase ina at around hn>0.77 eV observed in this figure can be associated withdirect band–to–band transition. In addition, residual absotion processes are observed in the low energy region athy1

;0.50, hy2;0.57, andhy3;0.67 eV. These can be attributed to the acceptor level–to–conduction band or valeband–to–donor level transitions. A free–to–bound transitis expected to occur at an energy given by20

hy~T!'EG2EI1KBT, ~10!

whereEI is the activation energy of the donor or accep

FIG. 4. Absorption coefficient spectraa(hn) of Cu2GeSe3 sampleS2 in theenergy range from 0.5 to 0.8 eV at several temperatures between 10300 K.


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defect state involved in the transition. Thus, the differenDE betweenEG and the energy of the peakhy as a functionof T should be a straight line given by

DE~T!5EG2hy 'EI2KBT. ~11!

Hence, the extrapolation ofDE to T50 gives the value ofEI

and the slope of the line should be nearly equal toKB . Thevariation ofDE with T for the peaks athy1 , hy2 , andhy3

was calculated from theEG(T) data given in Ref. 11. This isshown in Fig. 5. It is observed, in agreement with Eq.~11!,that in all the casesDE decreases linearly with increasingT.From the intercepts ofDE with T50, the values ofE11, E12

and E13 were found to be 0.306, 0.243, and 0.1260.004 eV, respectively. In all the cases the value of the lslope, 1.331024, 1.131024, and 1.160.331024 eV/K, re-spectively, is nearly of the same magnitude asKB which is8.631023 eV/K. The activation energies of these levels aconsiderable higher thanEA'50 meV obtained from electri-cal measurements. Hence, no transition related to this slow acceptor level was observed in the absorption spectperformed in this study. This is probably due to the fact ththe optical transition from ionized acceptors of this levelthe conduction band is difficult to observe because ofproximity to the fundamental edge.

D. Identification of the defect levels observed

Although a complete identification of the nature and ogin of the defect states observed in Cu2GeSe3 is not possible

nd

FIG. 5. Variation with temperature of the differenceDE betweenEG andthe energy of the peaks athn1(h), hn2(s), and hn3(n). The straightlines represent the fit of Eq.~11! to theDE(T) data. From the intercepts oDE with T50, the values ofE11 , E12 , and E13 were found to be 0.306,0.243, and 0.123~60.004! eV, respectively. In all the cases, the value of tslope, 1.331024, 1.131024, and 1.131024(60.331024) eV/K, respec-tively, is nearly of the same magnitude asKB which is around 0.931024 eV/K.


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at present, tentative assignments can be made. Thesbased on the analysis of the chemical composition ofsamples used in the study and in simple calculations ofactivation energies of the possible defect levels expectethis material. Since these samples were not intentiondoped, is probably that all the donor and/or acceptor levobserved are native and due to deviations in composifrom the ideal stoichiometry. According to the chemicanalysis performed by EDX, the samples are Ge rich,rich, and Cu poor. For this reason, based on analysis simto that was made for the I–III–VI2 chalcopyritecompounds,21 copper vacanciesVCu, antisite Ge on Cu sitesand selenium interstitials, Sei are expected to be the domnant defect species in the present samples. BecauseVCu is asingle acceptor21 in Cu2GeSe3 it should originate a shallowlevel whose activation energy can be estimated from thedrogenic model by using the expression,EA0

'13.6(mh* /mo)/e02. Under this approximation, with the va

ues of mh* /mo and e0 given above,EA0 was found to beequal to 70 meV which is slightly higher thanEA'50 meVobtained from the analysis of thep(T) data. This differenceis probably caused by screening effects due to high impuconcentrations. It is a well known fact22–24 that shallow-hydrogenlike impurity levels show a decrease in the actition energy with the increase of the impurity concentratioA large number of different effects have been suggested23,24

in order to explain theoretically the concentration depdence ofEA . In the case ofp-type materials these effectincluded,~i! rising of the valence band edge due to thetraction of conduction holes by ionized acceptors,~ii ! shift ofthe acceptor ground state energy due to free-hole scree~iii ! valence band tailing,~iv! acceptor-level broadening duto wave function overlap, and~v! level spreading due topotential fluctuations. Empirically, however, a simple depedence is generally found which is given by thexpression,22–25

EA~N!5EA02dN1/3, ~12!

whereEA0 , the activation energy in the dilute limit of acceptor concentrations, can be estimated from the hydrogemodel,25,26 andd is the screening parameter. For most of tternary compounds where the analysis of the concentradependence ofEA has been made, values ofd in the rangefrom 2.431028 to 2.931028 eV cm have been found.25–27

The exact meaning of the termN in Eq. ~12!, however, is notclear. Thus, in the case ofp-type samples, the majority impurity concentrationNA , the minority concentrationND , orthe net impurity concentrationNA2ND , have been used foseveral authors in the analysis of the concentration depdence ofEA .24 However, as has been suggested by Moneet al.24 the thermal activation energies of the majority of impurities depend mainly on the minority impurity concentrtions. Under this assumption, Eq.~12! can be written as

EA~ND!5EA02dND1/3. ~13!

Hence, withEA0'70 meV as obtained from the hydrogenic model,ND'131018cm23 estimated from the analysiof p(T) data, andd'2.531028 eV cm, the value ofEA cal-culated from Eq.~13! for the VCu acceptor state is 45 meV


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This is in excellent agreement withEA5(5064) meV ob-tained from the analysis of thep(T) data. It can be alsonoted that using a value ofND one order of magnitude highethan that obtained in the present samples, as is expectethe samples studied by Endoet al.,12 EA around 16 meV, invery good agreement with that estimated in Ref. 12, (EA

,20 meV), is obtained from Eq.~13!.The levels at about 0.12 and 0.24 eV probably cor

spond to the double acceptor Sei . The two activation ener-gies of such an acceptor state can be estimated by thepressionEA'13.6(mh* /mo)C/e0

2, where C is equal to 1.7and 4, for the energy of the first and second leverespectively.28,29Using these values ofC, we obtain for thesetwo levelsEA'0.119 and 0.269 eV. Both these values aregood agreement with those estimated from the present ocal measurements. A transition at about 0.25 eV, alsoserved by Endoet al.12 from the slope of the resistivity vsTcurve, has been identified by these authors as due toband–to–band transition. This, however, is in disagreemwith EG'0.78 eV obtained recently from optical data.10,11

Such a too low value ofEG is apparently due to the fact thaan incorrect assumption, concerning to the temperaturegion where the intrinsic conduction occurs, was made12 ininterpreting the temperature variation of the electrical dataCu2GeSe3. Therefore, it is then suggested that the featureabout 0.25 eV observed in Ref. 12 occurs in the regionextrinsic conduction and corresponds to the acceptor levto–valence band transition observed in the present opanalysis.

Finally, the most deeper level observed in the presstudy, E11'0.3 eV, cannot be probably predicted by thsimple model used in Refs. 28 and 29. This level probadoes not correspond to a donor state because the eleeffective mass in Cu2GeSe3, me* '0.02 mc ,10 is very smallas compared to the hole effective mass. Hence, no deepnor states are expected to be found in this material. Howeno definite conclusion about the origin and nature of tdeep level can be made at present.

IV. CONCLUSION

From the study of the temperature variation of the eltrical and optical properties ofp-type Cu2GeSe3 it is foundthat below about 180 K the hole concentrationp increaseswith decreasingT indicating that in this region the electricaproperties are dominated by an impurity band conductionthis band, the mobility increases with temperature expontially with an activation energy of about 30 meV duethermally activated hopping processes. Above about 200p was found to be dominated by a shallow acceptor lewith an activation energy of about 50 meV. The originthis level, consistent with the hydrogenic model and screing effects, is attributed to the copper vacancy. The heffective mass and the concentration of ionized impuritdetermined from the analysisp(T) curve in the high tem-perature region are found to be 0.97me and 931021cm23,respectively. From the analysis of the mobility data by asuming scattering by acoustic phonons and ionized impties, the valence band deformation potential and the st


1einrv

Z

s

d

la-

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h,aryp.


dielectric constant were calculated to be 18.5 eV andrespectively. Other two acceptor states with activation engies of around 0.12 and 0.26 eV, attributed to Seleniumterstitial, and a deeper state at 0.30 eV, were also obsefrom the optical measurements.

ACKNOWLEDGMENTS

This work was supported by theConsejo de DesarrolloCientifico y Humanı´stico ~C.D.C.H.T.! of the Universidad deLos Andes~ULA-Merida!. The authors would like to thankProfessor S. M. Wasim for valuable discussion.

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On the temperature dependence of the electrical and optical properties of Cu[sub 2]GeSe[sub 3]