We present measurements of the electrical conductivity of barely metallic n-type SiAs that are driven to the metal-insulator transition (MIT) by impurity concentration. The experiments were carried out at low temperature in the range (3.48 - 0.00044 K) and with impurity concentrations up to . On the metallic side of the MIT, the electrical conductivity is found to behave likedown to 0.44 mK. Physical explanation to the temperature dependence of the conductivity is given in metallic side of the MIT using a competition between two effects involved in the mechanisms of conduction, like electron-electron interaction effect, and weak localization effect

Abdia, Rachid

Biskupski, Gerard

Capoen, Bruno

Dlimi, Said

El kaaouachi, Abdelhamid

Hemine, Jamal

Limouny, Lhoussine

Narjis, Abdelfattah

Sybous, Abdelghani

English

Revues Scientifiques Marocaines

Contribution of weak localization and electron-electron interaction, in corrective term “mT1/2” of the metallic conductivity in n-type SiAs

M. J. CONDENSED MATTER                     VOLUME 13, NUMBER 2                   OCTOBER 2011 MJCM, VOLUME 13, NUMBER 2                                            © 2011 The Moroccan Statistical Physical and Condensed Matter Society    Contribution of weak localization and electron-electron interaction, in corrective term “mT1/2” of the metallic conductivity in n-type SiAs  Abdelghani  Sybous 1, Abdelhamid El kaaouachi 1,*, Abdelfattah Narjis1, Lhoussine Limouny1, Said Dlimi1, Bruno Capoen 2, Jamal Hemine3, Rachid Abdia1, and Gerard Biskupski 4   1 Research Group in ESNPS, Physics Department, University Ibn Zohr, Faculty of Sciences, B.P 8106, Hay Dakhla, 80000 Agadir, Morocco. 2 C E R L A - FR CNRS 2416, Université des Sciences et Technologies de LilleI 59 655 Villeneuve d'Ascq Cedex France. 3 Laboratoire de Physique de la Matière Condensée, Faculté des Sciences et Techniques de Mohammadia, Département de Physique, Mohammadia, Morocco. 4 Laboratoire de Spectroscopie Hertzienne ,LSH équipe des semi-conducteurs, Bâtiment P5, Université des Sciences et Technologies de LilleI 59 655 Villeneuve d'Ascq Cedex France  Corresponding author: a.saybous@yahoo.fr  ABSTRACT: We present measurements of the electrical conductivity of barely metallic n-type SiAs that are driven to the metal-insulator transition (MIT) by impurity concentration. The experiments were carried out at low temperature in the range (3.48 - 0.00044 K) and with impurity concentrations up to 316410.10 cm . On the metallic side of the MIT, the electrical conductivity is found to behave like 2/10 mT down to 0.44 mK. Physical explanation to the temperature dependence of the conductivity is given in metallic side of the MIT using a competition between two effects involved in the mechanisms of conduction, like electron-electron interaction effect, and weak localization effect.  Keywords: SiAs semiconductor, low temperature, impurity concentration, metal-insulator transition, electron-electron interaction effect, weak localization effect.   I. Introduction  Biskupski et al. [1], and El kaaouachi et al. [2] have observed the metal-insulator transition (MIT) induced by an impurity concentration in barely metallic and compensated n-type InP. Using new analysis methods, they determined the critical magnetic field CB  for which the conductivity changes from a metallic behaviour to a variable range hopping regime.  In recent years it has become clear that not too close to the MIT, the equation for the temperature dependence of the metallic conductivity [3 - 5] is: 2/1)0( mTT                                                                                                  ( 1 )  Where )0( T is the zero temperature conductivity and m is the magnitude of the correction term. )0( T  and m were obtained by standard linear  regression methods. In the absence of the magnetic field, several authors have examined the behaviour of the magnitude m in different semiconductors [6-8]. They have shown that at B=0 T, the sign of the term m depends on the difference between the Hartree and the exchange terms.    In this paper, we examine the behaviour of the magnitude m with impurity concentration n . When the MIT is    induced by an impurity concentration, several phenomena contribute to this corrective term   “ 2/1mT ” among which are the electron-electron interaction effect, and the weak localization effect.  In the absence of the magnetic field the electrical conductivity can be written as:  onlocalizatiWeakeractioneeT    int)0(                                                                                         ( 2 )   where eractionee int  and onlocalizatiweak  are respectively the contributions of  electron-electron interaction and weak localization effects of  corrective term of the electrical conductivity  .   In Fig. 1, we have plotted the electrical conductivity    versus 2/1T  for different values of  impurity concentration n  between 1610.67,8  and 31610.4,10 cm  for a metallic SiAs sample with magnetic field equal 0 T. The experiments were carried out at low temperature in the range (0.9 -0.00033 K) and in impurity concentration up to 31710.4,6 cm  . We have observed that m changes the sign in this interval of impurity concentration. 13 67Abdelghani  Sybous, Abdelhamid El kaaouachi, Abdelfattah Narjis, Lhoussine Limouny, Said Dlimi, Bruno Capoen, Jamal Hemine, Rachid Abdia, and Gerard Biskupski MJCM, VOLUME 13, NUMBER 2                                            © 2011 The Moroccan Statistical Physical and Condensed Matter Society 0.0 0.5 1.0 1.5 2.0 2.520406080100120140S cm -1 )T 1/2  ( K 1/2 )n=10.4 1016 cm-3n =9.5 n =9.05n=8.91  n=8.67  Fig. 1. Electrical conductivity  versus 2/1T for  different impurity concentration  II. Electron-electron interaction effect  The electron-electron interaction effect has been estimated by Altshuler et al. [9] and simplified by El kaaouachi et al. [2]. The simplified form of the contribution of electron-electron interaction effect to the electrical conductivity with a 2/1T dependence is given by:                                  2/1122int.23.22122),(  TekeDTkELnFFenTBBFeractionee                  (3)                                  Where  D is a diffusion parameter of the middle given by : )1/(DD 0  cnn                                                                                                            (4) cn is the critical impurety concentration. 0D  and   are a constants 320fVD   , FV and   are respectively  the speed at the Fermi level and the elastic scattering time. In other hand, following the work of Wegner [10], in the metal side of the TMI, the conductivity at zero temperature is given by:   1)0(ccnn                                                                                                       (5) In fig. 2 we plot the variation of the ))0(ln(  with the)1/ln( cnn . This allows us to access to the slope  7.0 . And Fig.3, shows the evolution of the diffusion parameter D  with the impurety concentration n .  -5 -4 -3 -2 -1 0 1 23,03,54,04,55,05,56,06,57,0ln(0)  ( s cm-1 )ln(n/nc-1) Fig. 2. Evolution of the ))0(ln(  against  )1/ln( cnn     III. Weak localisation effect  The weak localization correction has been calculated by kawabata [11] and developed by El kaaouachi et al.[2].  The expression obtained is given by: 2/122 12TDAeonlocalizatiWeak                                                                                                           (6) where A is a constant given by:  BFkEA2/3232                                                                                                                                        (7) 0,5 1,0 1,5 2,0 2,5 3,0 3,50246810D   (cm2  s-1 )n  ( cm-3 ) D(*10+19) Fig. 3. Variation of the diffusion parameter D  with impurety concentration n     IV. Results and discussion  We present in Table 1 some parameters of the SiAs sample. We have calculated the Hartree Fock constant F using two theoretical methods: the Thomas-Fermi approximation “ FTF  ”, and the Kleinman-Langreth dielectric function [12-13] “ LKF  ”  13 68 Contribution of weak localization and electron-electron interaction, in corrective term “mT1/2” of the metallic conductivity in n-type SiAs MJCM, VOLUME 13, NUMBER 2                                            © 2011 The Moroccan Statistical Physical and Condensed Matter Society   xxF FT1ln    where   22FTFKkx                                                                                                  (8)  Where Fk  is the Fermi vector and FTK   is the Thomas-Fermi scattering vector.  1lnLKF      where     22 FSkK                                                                                                  (9) where SK is the scattering parameter given by: 2/1212158.012FTFFSkkKK       and     2/12202*412FTFKnemk                                                           (10)                                                                                     We have obtained for our sample  099.0FTF  and 893.0LKF .  Table 1. Some parameters of the SiAs sample.  Parameters Symbol value Critical impurity concentration cn  3181058.8 cm  Fermi vector Fk  7.38 108m-1 Free path length l 186 Å  Thomas-Fermi scattering vector FTK   2.26 108m-1 Parameter lkF  lkF    Elastic diffusion constant 0D  4.66 10-4m2s-1 Constant FTF   FTF   0.099 Constant  LKF   LKF   0.893  Firstly, we have calculated separately the theoretical value of the magnitude m due respectively to electron-electron interaction effect, and weak localization effect using Equations (3) and (6). Then we compared these theoretical values with experimental values of m.   In Fig. 4, we plot experimental values of m and the corrective term to electrical conductivity  due only to electron-electron interaction effect Eq. (3) in the both cases when F is calculated using Thomas-Fermi approximation “FTFF  ” and using Kleinman-Langreth approximation “FTFF  ”. 0,88 0,92 0,96 1,00 1,04-50050100150200250300m  ( s cm-1 K-0.5)n  (cm-3)mexpm e-e (F=FTF)m e-e (F=FKL)(*10+19)   Fig. 4. Experimental and theoretical values with (F=FTF and F=FKL) of magnitude m versus impurity concentration (contribution of electron-electron effect).      The electron-electron interaction effect contribution to m is positive and decreases slightly with impurity concentration. This decrease is larger when F was calculated using the Kleinman-Langreth approximation. In Fig. 5, we plot experimental values of m and the corrective term to electrical conductivity  due only to weak localization effect Eq.(6). 0,88 0,92 0,96 1,00 1,04-250-200-150-100-500m  ( s cm-1 K-0.5)n  ( cm-3 ) m l_f  m exp(*10+19) Fig. 5. Experimental and theoretical values of magnitude m versus impurity concentration (contribution of weak localization effect).  The contribution to m due to the weak localization effect vary with the impurety concentration and is negative.  13 69 Abdelghani  Sybous, Abdelhamid El kaaouachi, Abdelfattah Narjis, Lhoussine Limouny, Said Dlimi, Bruno Capoen, Jamal Hemine, Rachid Abdia, and Gerard Biskupski MJCM, VOLUME 13, NUMBER 2                                            © 2011 The Moroccan Statistical Physical and Condensed Matter Society 8,5 9,0 9,5 10,0 10,5-60-40-200m  ( s cm-1 K-0.5)n (cm-3)  m( F=FTF) m( F=FKL) m exp( *10+16 ) Fig . 6. Experimental and theoretical values of magnitude m versus impurity concentration using the sum of the two effects ( e-e interaction effect and weak localization effect Eq.  (2).  Secondly, we have calculated theoretical values of m using the sum of electron-electron interaction effect, and weak localization effect Equations (2), (3) and (6). The Hartree-Fock constant F was calculated using respectively the Thomas-Fermi approximation and the Kleinman-Langreth approximation. The theoretical and experimental results of the magnitude m in corrective term “2/1mT ” of the electrical conductivity are shown in Fig. 6. We noticed that the experimental values of m are changing sign. We also noted that there is not a good qualitative agreement between experimental and theoretical results of magnitude m when LKFF  , but when the Hartree-Fock constant F was calculated in the Thomas-Fermi approximation  (FTFF  ) we observed a large discrepancy between experimental and theoretical results.    V. Conclusion       The experimental values of magnitude m are positive and vary slightly with the magnetic field. We can infer that the electron-electron interaction effect (positive contributions to m) is dominant over the weak localization effect (negative contribution to m). The summation of the three effects varies slightly with magnetic field. In previous work, El kaaouachi et al. [2] found that m changes sign from negative to positive when the magnetic field increases in InP sample. We have also obtained a better correspondence between theory and experiment forFTFF  .  References    [1]  G. Biskupski et al., J. Phys Condens Matter. 3 (1991) 8417.   [2] A. El kaaouachi et al., Phys. Stat. Sol b. 241 No 1 (2004) 155-162.    [3] A. El kaaouachi et al., Physica B Condens Matter. 226 N°3 (1998) 226- 228.      [4] A. El kaaouachi et al., Physica B Condens Matter . 304 (2001) 377-381   [5] A. El kaaouachi et al., Semiconductors Sciences and Technology.18 (2003) 69-74.   [6] G. A. Thomas et al., Phys. Rev B 26 (1982) 2113   [7] G. A. Thomas et al., M. Paalmen, and T. F. Rosenbaum, Phys. Rev B 27 (1983) 3897   [8] W. N. Shafarman et al., Phys. Rev B 40 (1988) 1216.   [9] BL. Altshuler et al., Sov. Phys –JETP. 54(1981) 411. [10] FJ. Wegner, Z. phys. B 35 (1979) 2007. [11] A. Kawabata,  solid state commun. 34 (1980) 431. [12] L. Kleiman, Phys. Rev. 160 (1967) 585. [13] DG. Langreth, Phys Rev. 181 (1967) 753.     70 13 

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Contribution of weak localization and electron-electron interaction, in corrective term “mT1/2” of the metallic conductivity in n-type SiAs

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