Ariponnammal, S

Natarajan, S

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Indian J. Phys. 70A (5), 557-562 (1996)I J P  A- an international journalTheoretical method for calculating the electrical properties of rare  earth chalcogenide compoundsS Ariponnammal and S NatarajanDepartment of Physics, Anna University, Madras-600 025, IndiaR eceived  27  M arch 1996, accepted  22 April 1996Abstract : A simple theoretical model is developed for determining the electrical transport properties of the rare earth chalcogenide compounds. This method requires only two parameters, namely, lattice constant and activation energy to calculate the electrical properties such as earner concentration, carrier effective mass, earner mobility, dielectric constant and electrical resistivity at different pressures. It also provides information on the type of conductivity. The results are in fair agreement with the experimental results.Keywords : Electrical resistivity, lattice constant, chalcogenide compounds PACSNo. : 72 15.Eb1. IntroductionA simple theoretical model is developed for determining the electrical properties of the rare earth chalcogenide compounds under pressure. The model correlates the lattice parameter with the electrical properties. This method requires only two parameters, namely, lattice constant and activation energy. It calculates the important electrical properties involved in transport mechanism such as carrier concentration, carrier mobility, carrier effective mass, electrical resistivity and dielectric constant. The validity of this method is tested by calculating these parameters for samarium and ytterbium monochalcogenides and compared with the available experimental results.2. Theoretical methodologyBefore going into detail, some important aspects involved in these compounds are discussed. The atoms of all rare earth elements except Eu, Sm and Yb exist in trivalent state. The divalent Eu, Sm and Yb are particularly ideal as most of them are semiconducting [1] and ionic [2]. The notable property of the rare earth chalcogenides is© 1996IACS558 S  A r ip o n n a m m a l a n d  S  N a ta r a ja nthat they are found to be in a semiconducting state when the rare earth ion is divalent and metallic when it is trivalent [3]. It is reported from the magnetic susceptibility studies that for the compounds containing dipositive metal ions, the third valence electrons are highly localized in 4/ levels. This would result in a full 4 / shell for the ytterbium ions, half full for the europium ions and nearly half full for the samarium ions [4]. The highly localized /  electrons do not contribute to the electrical conductivity [5]. Experimental results show that the compounds of Sm, Yb and Eu have no conduction electrons in ground state. The most likely process which gives carriers for conduction is thermal activation of electrons from the 4f  shell to the conduction band. Such a mechanism would give n-type conductivity [5]. Here, the question of which type of scattering is dominant arises. The answer is in favour of acoustic scattering. In the case of acoustic scattering, electrical conductivity 'o ' can be calculated by using the formula [6-9]<j = neu = U p , (1)where n is the carrier concentration, e is the electronic charge, u is the carrier mobility and p is the electrical resistivity.The carrier concentration [10] can be calculated from the carrier effective mass m and activation energy A E  by using the expression2{2mn*kTW  T A E ]" *  — p —  “ * [ -  2 i r }  ®where k is the Boltzmann's constant, h Planck's constant and T is the temperature.Now, the unknown effective mass m* can be deduced [11] from the lattice parameter a and activation energy AE  by the formula=  , .m* m0a2A E  ’ (3)where m0 is the electron rest mass and the A E  is the activation energy which can be calculated byA E  = ap0. (4)Here, a  is the rate of closing of the energy gap with pressure and p 0 is the transition pressure.The monochalcogenides of samarium and ytterbium are ionic semiconductors [12]. In ionic lattices, thermal motion and diffusion always give rise to vacant sites abandoned by one of the lattice ions or excess ions diffusing between the lattice cells. In this case, the ion is surrounded by electrostatic Coulomb field, which is weaker than that in a vacuum by a factor £ representing the dielectric constant of the lattice [10]. An electron moving in this field is deflected from its initial path more strongly, the closer it approaches the ion, theT h e o r e t ic a l  m e th o d  f o r  c a lc u la tin g  th e  e le c tr ic a l  p r o p e r t ie s  e tc  559longer it remains in the field which slows down its motion. So, the electron mobility (u) is given byu ____________3ef____________[ h f\6 n 2m* [ln(l + x) -  */(! + .*)] L ' J (5)The value of x  is calculated by using the formula1/3(6 )where N represents the impurity concentration which is given byN =f 2nm *kT^'A '  AE 1* [  #  1 exp 2kTj(7)The dielectric constant e [10] is calculated using the expression2 1 3 .5 3  m*€ AE m0 (8)Thus, the electrical properties at various pressures have been calculated using the lattice parameter and activation energy at that pressure. The activation energy at different pressures 'AEp is obtained as follows.AEp = (AE  -  ap) (9)where AE represents the activation energy at ambient temperature and pressure and ‘p’ is the pressure at which the activation energy is to be calculated. The validity of this theoretical model is tested by calculating these electrical properties of SmX and YbX with X = S, Se, Te under pressure and compared with available experimental values.3. ConclusionsA simple theoretical model is developed for determining the electrical properties under pressure. This method requires only two parameters namely the lattice constant and activation energy (Table 1) to calculate the electrical properties such as carrier concentration, carrier mobility, carrier effective mass, dielectric constant and electrical resistivity under pressure (Table 2). The variation of theoretical electrical resistivity with pressure for SmX and YbX (X = S, Se and Te) is compared with the reported experimental result [13,141 as shown in Figures 1 and 2. They are found to be in fair agreement with each other. The sign of the carrier mobility is of negative sign which implies that the samples are having n-type conductivity which agrees with the reported experimental result [1,14,15]. The limitation of this method is that it can be applied only to semiconductors and not to metals because of the dependence of the activation energy on the energy gap. So the present study' has been done only in the domain of semiconductor region. SmS becomes metallic at 6.5 kbar whereas SmSe and SmTe become metallic at about 30 kbar and 50 kbar560 S  A r ip o n n a m m a l a n d  S  N a ta ra ja nTable 1. The values of lattice constant (a ) and activation energy (AE) used for the present study at different pressures (P) [3,13,14].Compound P  in kbar ain A AE inev Compound Pin kbar ain A AE inev0 5.970 0.080 0.0 5.680 0.400SmS 2 5.930 0.060 YbS 5.0 5.122 0.3854 5.900 0.030 10.0 4.932 0.370- - - 15.0 4.553 0.3600 6.200 0.440 0.0 5.930 0.4005 6.173 0.366 4.5 5.912 0.390SmSe 10 6.144 0.292 YbSe 9.1 5.905 0.37015 6.120 0220 13.6 5.900 0.36020 6.108 0.140 - - -0 6.594 0.360 0.0 6.360 0.4605 6.570 0.350 5.0 6.274 0.405SmTe 10 6.539 0.334 YbTe 10.0 6.189 0.35015 6.505 0.321 15.0 6.147 0.30020 6.482 0 122 - - -25 6.413 0.0625 - - -Table 2. The calculated values of earner concentration (n ), carrier effective mass ( m ), dielectric constant (e) and earner mobility (u) at different pressures (P).CompoundPin kbar n*mx 10"3* kg e 2u inn^V 'Sec"10 3.276 xlO23 1.437 26.680 -  1.291 xlO-3SmS 2 3.277 xlO23 1.109 27.440 -2.667 xlO '34 2.251 x 1023 0.585 28.950 -6  315 x 10"30 1.805 x 10 21 4.794 16.180 -2.403 xlO*45 6.598 x I02' 4.355 17.670 -1.187 xlO-4SmSe 10 2.000 x 1022 3.825 19.460 -4.660 XlO"315 7.127x10 22 3.199 21.600 -2.000 xlO"320 2.100 xlO23 2.327 24.680 -2.053 xlO"20 8097 xlO21 4.618 19.050 -1.018 xlO"45 9.580 xlO21 4.537 19.250 -9.140 xlO"5SmTe 10 1.253 xlO22 4.409 19.610 -1.392 xlO"415 1.552 xlO22 4.295 19.870 -1.966 xlO"420 2.918 xlO23 2.294 27.930 -2.210 xlO"425 4.036 x 1023 1.316 31.270 -4.281 xlO"4T h e o r e tic a l m e th o d  f o r  c a lc u la tin g  th e  e le c tr ic a l p r o p e r t ie s  e tc 561Table 2. (C ant'd )CompoundPin kbar n*mx 10"31 kg e2u inm2\Hsec _10 2.100 xlO21 4178 15.514 -6436 xlO-5YbS 5 2.361 xlO21 3 633 14015 -5  814 xlO"510 2.878 x 10 21 3 384 13.585 -6171 x 10'515 2.938 x 1021 2 996 12.362 -  8 785 x 10-50.0 2.321 xlO21 4.400 16.339 -6.320 xlO '5YbSe 45 2.749 xlO21 4.303 16 388 -  1.207 xlO-491 3.949 x I021 4.178 16 773 -8  459 xlO-5136 4.724 x 1021 4.112 16 968 -  8.774 x 10'50 8.336 xlO20 5.010 16.176 -  5 775 x 10~5YbTe5 2 284 x I021 4 659 17 088 -  6 396 x I0~5id 6.113 xlO21 4 265 18.100 -8  971 xlO '515 1.468 x 1022 3.888 19.247 -1  117 xlO"4respectively |13| Regarding the transition pressure of Yb monochalcogenides, there is contradiction between the electrical resistivity study and pressure-volume data. AccordingFigure 1. Theoretical (- -) and reported [17]experimental (— ) resistivity variation as a function of pressure for SmX (X as S, Se, Te).—  Theoretical—  Reported [l4 ]Experimental151.00 5 10 15Pressure kbarFigure 2. Theoretical (- -) and reported [14]experimental (— ) resistivity variation as a function of pressure for YbX (X = S, Se, Te).562 S  A rip o n n a m m a l a n d  S  N a ta ra ja nto the electrical resistivity study upto 15 kbar, the valence transition as well as semiconductor to metal transition, is expected near 40 kbar [14]. The optical absorption study [16] supports the pressure volume data [13] which predicts that the energy gap must vanish at about 175 kbar. According to this theoretical electrical resistivity calculation, the valence transition seems to be at about 40 kbar, which supports strongly the experimental electrical resistivity data. Thus, this simple two parameter model gives a reasonably good description of electrical properties as a function of pressure.AcknowledgmentAuthors are thankful to the Council of Scientific and Industrial Research, Government of India, for financial support.References[1] A V Golubkov, E V Goncharova, V P Zhuze and IG Manoilova Sov. Phys. Solid Stale 7 1963 (1966)P] CM VarmaRev. Modern Phys. 48 219(1976)[3] A Chatteijee, A K Singh and A Jayaraman Phys. Rev B6 2285 (1972)[4] F J Reid, L K Matson, J F Miller and R C Himes J. Phys Chem. Solids 25 969 (1964)[5] J W McClure l  Phys. Chem. Solids 24 871 (1963)[6] D R Lovett Semimetals and Narrow Band Gap Semiconductors (Great Britain . Pion Ltd) p 72 ( 1977)[7] J Neuenschwander and P Wachter Physica B160 231 (1990)[8] David Adler CRC Amorphous Semiconductors (South Africa Butterworth) p 2 (1972)[9] S Ariponnammal and S Natarajan Pramana-J. o f  Physics 42 421 (1994)[10] A F Ioffe Physics o f  Semiconductors (Moscow : Publishing house of USSR academy of sciences) p 176, p 333, p 362 (1960)[11] W A Harrison Solid State Physics (USA : McGraw Hill) p 142 (1970)[12] A Jayaraman, V Narayanamurti, E Bucher and R G Moines Phys. Rev L ett. 25 368 (1970)[13] A Jayaraman, A K Singh, A Chatteijee and S Usha Devi Phys. R ev . B9 2513 (1974)[14] M Francillon, D Jerome, J C Achard and G Malfait J. de Physiq. 31709 (1970)[15] B Batlogg, E Kaldis, A Schlegel and P Wachter Phys. R ev . B14 5503 (1976)[16] V Narayanamurti, A Jayaraman and E Bucher Phys. Rev. B9 2521 (1974)[17] J B Goodenough, E Bucher, V Narayanamurti and A Jayaraman J. Appl. P h ys. 421741 (1971)

Theoretical Method for Calculating the Electrical Properties of Rare Earth Chalcogenide Compounds

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Theoretical Method for Calculating the Electrical Properties of Rare Earth Chalcogenide Compounds

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