RESEARCH PAPER CONDUCTION MECHANISM IN AMORPHOUS As 2 S 3. R. K. Nkum, F. K. Ampong and F. Boakye Department of Physics, KNUST, Kumasi, Ghana

Transcription

1 Jurnal f Science and Technlgy, Vl. 32, N. 3 (2012), pp Kwame Nkrumah University f Science and Technlgy (KNUST) RESEARCH PAPER CONDUCTION MECHANISM IN AMORPHOUS As 2 S 3 R. K. Nkum, F. K. Ampng and F. Bakye Department f Physics, KNUST, Kumasi, Ghana ABSTRACT The cnductin mechanism in amrphus As 2 S 3 has been studied by investigating the variatin f the electrical resistivity ver the temperature range K. The electrical resistivity is characterised by a mbility gap f 2.15 ev ver the temperature range investigated. The dc cnductivity prvides evidence f cnductin by excitatin f charge carriers int the band edges near the mbility edges. The results als give the pssibility f cnductin by a phnn-assisted hpping f plarns between lcalised states. Keywrds: Amrphus semicnductr, hpping, mbility edge INTRODUCTION Discvery and study f different chalcgenide materials, whse prperties can be tailred, cnstitute the base f develpment f the slid state technlgy. Electrnic cnductin in amrphus slids has received cnsiderable attentin in recent years because f its imprtance in electrnic devices (Anwar et. al., 2005). Arsenic sulphide, As 2 S 3, and arsenic selenide, As 2 Se 3, are typical representatives f chalcgenide glassy semicnductrs, with a wide range f applicatins in ptelectrnics, infrmatin strage and acustic-ptics (Seddn, 1977; Madan and Shaw, 1988; Ppescu et al., 1996; Andriesh, 1998). Charge transprt measurements in disrdered semicnductrs and insulatrs can prvide infrmatin abut the electrnic structure f these materials. The disrder in the atmic cnfiguratin is thught t cause lcalised electrnic states r grups f states within the material. Amrphus semicnductrs are materials with particularly lw mbility. This feature certainly can be assigned t the lack f lng-range rder typical fr these substances, but the details f the transprt mechanism are nt yet well understd. One reasn fr this state f knwledge is the difficulty in btaining reliable infrmatin abut the mbility fr certain amrphus semicnductrs. Measurements f Hall effect are nt nly experimentally difficult, but interpretatin is prblematic (Stuke, 1971). Anther methd f determining the mbility is the cmbinatin f thermelectric pwer and cnductivity measurements. This is better suited fr

2 12 Nkum et al. the type f determinatin f the type f carrier invlved. First hand infrmatin n the mbility, hwever, is btained by measurement f the drift mbility. Unfrtunately, these are restricted t rather lw cnductivity values, and, therefre, such results exist nly fr a few amrphus materials and here als in a restricted temperature range. Mrever, the temperature dependence f the mbility btained by this nn-equilibrium methd is strngly influenced by traps which are irrelevant fr the equilibrium cnductivity ne is mstly interested in. There have been tw basic appraches twards an understanding f the electrical transprt in nn-crystalline systems. The first apprach is apprpriate fr cases in which the mean free path between scattered events is large cmpared t the average interactmic spacing, first develped fr the calculatin f electrical cnductivity f liquid crystals (Ziman, 1961, 1966). This apprach, thugh successful fr many liquid metals, breaks dwn in situatins where the mean free path is shrt and appears inapprpriate fr amrphus and liquid semicnductrs. Anther apprach, which has been used in calculating cnductin via the randm array f centres fund in a heavily dped crystalline semicnductr (impurity cnductin), starts with a lcalised descriptin f the charge carriers. Transprt between lcalised states ccurs by a phnn-assisted tunnelling prcess and at the abslute zer, the cnductivity is zer. A case intermediate between these tw extremes is that f cnductin in delcalised r extended states with a mean free path f the rder f the average inter-atmic spacing (Davis, 1971). The cncept f lcalised states is used extensively fr crystalline semicnductrs in which impurity atms and pint defects give rise t lcalised levels r traps in the frbidden energy gap. What is less familiar is the cncept f a cntinuus range f energies in which all electrnic states are lcalised. Lcalisatin can ccur fr a variety f reasns: (i) Strng interactin between a carrier and a plar lattice can lead t lcalisatin by plarn frmatin (Adler, 1971). (ii)in mlecular slids a similar lcalisatin can be achieved by distrtin f a mlecule. (iii) A third cause f lcalisatin is disrder, the effects f which n the electrnic states have been discussed by Andersn (1958) and Mtt (1968, 1969, 1970). It is this type f lcalisatin which seems mst apprpriate in amrphus and liquid semicnductrs. In this wrk, the resistivity variatin with temperature ver the temperature range K fr amrphus As 2 S 3 has been investigated and the mde f cnductin discussed. The mbility gap f the material has als been studied. MATERIALS AND METHODS The methd f sample preparatin is similar t that described in an earlier wrk (Nkum, 1999). Arsenic xide, As 2 O 3, f % purity was disslved in hydrchlric acid (with sme heating). Hydrgen sulphide gas was passed thrugh the slutin and a yellwish precipitate f arsenic sulphide, As 2 S 3, was frmed. The precipitate was washed, filtered ut and dried. 15 gm f the As 2 S 3 thus prepared was put int a quartz vial, which was evacuated at a pressure f abut 10-3 trr and sealed. The vial was placed in a furnace fr 5 hr at 500 C, and then at 600 C fr 3 h. At this temperature the vial was rtated cntinuusly t ensure a gd hmgeneity f the melt. Quenching was dne by immersing the vial in iced water. The sample frmed culd be identified as glass by a simple visual examinatin. This was cnfirmed by X- ray diffractin examinatin in which the diffractin pattern shwed n lines. A piece f the arsenic sulphide prepared as described abve was cut ff and shaped int a thin rectangular frm f dimensins 1 mm x 1 mm x 6 mm. Fur electrdes were made at the ends. Silver amalgam was used in making the

3 cntacts t avid plarisatin. A wheatstne bridge methd is nt suitable fr determining high resistances as it becmes insensitive at high resistances. High resistances are determined either by methds f substitutin prvided ther resistance f that rder is available r by the methd f leakage. The substitutin methd was applied in this experiment. The resistance f amrphus As 2 S 3 was fund by measuring the vltage acrss the sample and the current thrugh it. By adding a very high resistance ( Ω) f knwn value in series with the sample, the current (~ 10-9 A) culd be fund by measuring the vltage acrss the series resistance using a valve vltmeter. The vltage acrss the sample and the series resistance was measured with a vernier ptentimeter. RESULTS AND DISCUSSION The temperature dependence f the electrical resistivity f amrphus As 2 S 3 is demnstrated in Fig. 1. In rder t interpret the electrical data btained n the amrphus As 2 S 3 sample, it is necessary t assume a mdel fr the electrnic density f states in amrphus semicnductrs. Until nw much cntradictin exits abut the fundamental questin whether the salient characteristic f the band structure f crystalline slids, i.e. the sharp edges in the density f states frming the well-defined energy gap between valence and cnductin bands, is als valid fr the amrphus case. One f the current mdels f the band structure f disrdered lattices assumes that, due t the absence f lng -range rder, there is a range f lcalised states at the extremities f the bands (Mtt, 1969). The densities f lcalised states decrease gradually int the frbidden gap, destrying in this way the sharpness f the valence and cnductin bands. Since these lcalised states have lwer energies than the band states, carriers will tend t fall int them and becme trapped ; the trapped carriers then cannt take part in cnductin unless activated (thermally r ptically) int the band states r unless they Cnductin in amrphus As 2 S hp directly t neighburing lcalised states (Owen, 1970; Nagel et al., 1974). Hpping f carriers in the lcalised states takes place at lwer temperatures (Davis, 1971). The semicnducting behaviur f the ρ-t curve f amrphus As 2 S 3 fllws the equatin ρ = ρ exp [( T / T ) ] n where T and n are cnstants. The value f the expnent n determines the nature f the cnductin mechanism in the semicnducting sample. Over the temperature range K, the resistivity f amrphus As 2 S 3 is fund t bey the semicnductr equatin ρ = ρ = ( T / T ) ρ exp ( E / kt ) exp g 2 as demnstrated by the lnρ vs 1/T plt in Fig. 2, with T 0 = Eg/2. Eg is the mbility gap and has the same value (2.15 Ev) ver the whle measured temperature range. This indicates that the cnductin in amrphus As 2 S 3 is intrinsic ver the temperature range, and may therefre be assumed that the Fermi level is pinned very clse t the middle f the frbidden gap. The resistivity due t excitatin f carriers int the band states is described by the expnential temperature dependence (Davis, 1970) fund als fr amrphus As 2 S 3. There is therefre evidence that cnductin in amrphus As 2 S 3 ver the temperature range cnsidered is due t excitatin f charge carriers int the band edges. The dynamical electrn-phnn interactins in amrphus As 2 S 3 cause the frmatin f plarns which nce lcalised als cntribute t cnductivity by means f hpping between equivalent sites. The cnductivity f such a hpping prcess is als described by the expnential temperature dependence bserved experimentally fr amrphus As 2 S 3 (Adler, 1971). Thus cnductin by a phnn assisted hpping f plarns may als be pssible in amrphus As 2 S 3. It is reasnable, therefre,

4 14 Nkum et al. 1E+14 1E+13 Resistivity /(Ω-cm) 1E+12 1E+11 1E+10 1E Temperature/(K) Fig. 1 : Temperature dependence f resistivity fr amrphus As 2 S ln ρ /T(K) Fig. 2 : lnρ as a functin f reciprcal temperature fr amrphus As 2 S 3 t suppse that the cnductivity in amrphus As 2 S 3 results frm a cmbinatin f excitatin f carriers int the band edges and phnn assisted hpping f plarns in the lcalised states. Accrding t Mtt (1986d) ρ = hl 2πAe 2 where l is the inelastic diffusin/lcalisatin length, and A is a cnstant f the rder f 0.1. Frm Fig. 2, ρ = 2.89 x 10-5 Ω cm. Thus the value f l is 0.07 Å. This value is quite small cmpared t the value f the diffusin/ lcalisatin lengths btained fr ther nncrystalline materials (Nkum and Datars, 1992; Nkum, 1994). It has been bserved by Nkum

5 (1994) that the lcalisatin length f nncrystalline slids decreases with increasing amunt f impurity. It appears that disrder leads t sme tailing f the bands int the frbidden gap. Opinins vary as t the extent f this tailing. Chen et al. (1969) have prpsed a mdel fr multicmpnent systems in which the valence and cnductin bands verlap in the middle f the gap (Fig. 3a). A nice feature f this mdel is that it ensures self cmpensatin and a Fermi level pinned clse t the centre f the gap. David and Mtt (1970) have suggested a much smaller degree f tailing and prpsed the existence f a defect band, near the gap centre (Fig. 3b). Bth mdels, hwever, use the cncept f lcalised states in the band tails leading t the existence f mbility edges. Amrphus As 2 S 3 is fund t be s resistive (resistivity at 300 K ~ Ωm) that measurements are nly pssible ver a limited range f high temperature. Similar bservatins have Cnductin in amrphus As 2 S been made by Owen (1970) fr amrphus As 2 Se 3 and sme sulphide glasses. The high resistivities f sulphide glasses may be attributable t the very lw electrnic mbilities f sulphur grup glass frmers such as arsenic sulphide, germanium sulphide, and phsphrus sulphide. It may therefre be pssible t btain in cnducting chalcgenide glasses in systems in which inisable elements cmbine with the sulphur glass frmers. In fact, sulphide glasses exhibiting predminantly inic cnductin have been fund by Plumat (1968) in the systems GeS 2 -Na 2 S and thers by Kawamt et al (1974, 1976) in the systems As-S-Ag, Ge-S- Ag and P-S-Ag. The mbility gap is fund t be 2.15 ev. This value agrees quite well with the range f values 2.1 ev t 2.3 ev fund by Owen (1970). The mbility gap is less than the ptical energy gap f 2.4 ev and 2.36 ev bserved by sme wrkers (Klmiets, et al., 1972; Tauc and Menth, 1972). This is pssibly due t the fact the mbility rises abruptly in a regin f energy where (a) (b) Fig. 3: (a) Density f states in multicmpnent glasses accrding t Chen et al. (1969), (b) density f states accrding t Davis and Mtt (1970). The rdinate in all cases is electrn energy.

6 16 Nkum et al. the states are nt cmpletely delcalised, whereas the ptical absrptin ccurs between delcalised bands (Weiser, 1969). CONCLUSION The electrical resistivity f bulk glassy As 2 S 3 has been fund be characterised by a single activatin energy, E a, equal t 1.08 ev (E a = E g /2) ver the temperature range K. The dc cnductivity prvides evidence f cnductin by excitatin f charge carriers int the band states near the mbility edges and cnductin by a phnn assisted hpping f plarns. It is reasnable, therefre, t suppse that the cnductivity in amrphus As 2 S 3 results frm a cmbinatin f excitatin f carriers int the band edges and phnn assisted hpping f plarns in the lcalised states. REFERENCES Adler, D. (1971). Amrphus semicnductrs, The Chemical Rubber C. Press, Cleveland. Andersn, P. W. (1958). Absence f Diffusin in Certain Randm Lattices, Phys. Rev. 109: Andriesh, A. M. (1998). Chalcgenide Glasses in Optelectrnics, Sv. Semicnductrs 32: 867 Anwar, M., Ghauri, I. M. and Siddiqi, S. A. (2005). The Electrical Prperties f Amrphus Thin Films f Al-In 2 O 3 -Al Structure Depsited by Thermal Evapratin, Rm. Jurn. Phys. 50: 763 Chen, N. H., Fritzshe H. and Ovshinsky, S. R. (1969). Simple band Mdel fr Amrphus Semicnducting Allys, Phys. Rev. Lett. 23: Davis, E. A. (1971). Cnductin in Lw- Mbility Materials, (Taylr and Francis, Lndn,): p. 175 Davis, E. A. and Mtt, N. F. (1970). Cnduc tin in Nn-Crystalline Systems V: Cnductivity, Optical Absrptin and Phtcnductivity in Amrphus Semicnductrs, Phil.Mag. 22: Kawamt, Y., Nagura, N. and Tsuchihashi, S. (1974). Dc Cnductivity f Ge-S-Ag and As -S-Ag Glasses, J. Amer. Ceram. Sc. 57: Kawamt, Y. and Nishida, M. (1976). Inic Cnductin in As 2 S 3.Ag 2 S, GeS 2.GeS.Ag 2 S and P 2 O 5.Ag 2 S glasses, J. Nn-Cryst. Slids 20: Klmiets, B. T., Lyubin, Y. M., Shil, V. P. and Averjanv, V. L. (1972). Plymeric Structure and Energy Spectrum f Lcal States f Vitreus Arsenic Selenide, J. Nn- Cryst. Slids 8-10: Mtt, N. F. (1968). Cnductin in Nn- Crystalline Systems, Phil. Mag. 17: Mtt, N. F. (1969). Cnductin in Nn- Crystalline Materials. III. Lcalized States in a Pseudgap and Near Extremities f Cnductin and Valence Bands, Phil. Mag. 19: Mtt, N. F. (1970). Cnductin in Nn- Crystalline Systems IV: Andersn Lcalizatin in a Disrdered Lattice, Phil. Mag. 22: 7-29 Mtt, N. F. (1986). Cnductin in Nn- Crystalline Materials, Clarendn, Oxfrd. Nagels, P., Callaerts, R. and Denayer, M. (1974). Amrphus and liquid semicnductrs, (Taylr and Francis, Lndn,): 867. Nkum, R. K. and Datars, W. R. (1992). Supercnducting and Semicnducting Prperties f the Bi 2 Sr 2 Ca 1-x Ga x Cu 2 O y System, Phys. Rev. B46: 5688 Nkum, R. K. (1994). Lcalizatin and hpping cnductin in the Sn-dped (Bi,Pb)Srr 2 Ca 2 C u

7 3O y system, Tr. J. f Physics 18: Nkum, R. K. (1999). Effect f Ag as an impurity n the dielectric cnstant f amrphus As 2 S 3, J. Applied Sci. Technl. 4: 1 Owen, A. E. (1970). Semicnducting Glasses (Part I), Cntemp. Phys. 11: 227 Plumat, E. R. (1968). New Sulfide and Selenide Glasses: Preparatin, Structure, and Prperties, J. Amer. Ceram. Sc. 51: Ppescu, M., Andriesh, A., Chumash, V., Ivu, M., Shutv, S. and D. Tsiuleanu. (1996). The Physics f Chalcgenide Glasses, Ed. Stiintifica Bucharest Ed. Stiinta Chisinau Seddn, A. B. (1977). In: Physics and Applicatins f Nn-Crystalline Semicnductrs in Cnductin in amrphus As 2 S Optelectrnics, Ed, by A. Andriesh and M. Bertltti, Kluwer Academic Publishers, NATO Series 3 High Technlgy 36: 327 Stuke, J. (1971), Cnductin in Lw-Mbility Materials, (Taylr and Francis, Lndn), 193 Tauc, J. and Menth, A. (1972). States in the Gap, J. Nn-Cryst. Slids 8-10: Weiser, K. (1969). Prc. 3 rd Int. Cnf. Liquid and Amrphus Semicnductrs, Cambridge Ziman, J. M. (1961). A Thery f the Electrical Prperties f Liquid-Metals. I: The Mnvalent Metals, Phil. Mag. 6: Ziman, J. M. (1966). The Prperties f Liquid Metals, (Taylr and Francis, Lndn), 551