We report here transport properties measurements and theoretical results on modeling carrier charge mobility in Hg 1-xCdxTe (x =0.22). Conductivity and Hall Effect were measured in the temperature range 4.2 - 300 K. Our measurements indicate that the sample is n-type semiconductor. In intrinsic regime, the slope of the curve RH T3/2 indicates a gap of 178 meV which agree well with Eg (x = 0.22, 300 K) = 183 meV. Our theoretical calculations, according to the Kane model, show that the Fermi energy EF increases with temperature. The calculated donor state Ed is 3 meV above the conduction band at 4.2 K and agrees well with 0.67 meV of low field Hall effect measurements. Our theoretical calculations on the mobility shows that ionized impurity scattering dominate below 25 K, optical phonons scattering at high temperatures (>70K) and the mobility is generated by the both mechanisms of scattering in the intermediate temperature regime. At high temperatures, an excellent agreement between experimental and calculated scattering mobility is obtained by introducing a trial function. The detection wave length  situates the sample as medium-infrared detector

Chaib, H.

El-Abidi, A.

Nafidi, A.

Taoufik, A.

English

We report here transport properties measurements and theoretical results on modeling carrier charge mobility in Hg 1-xCdxTe (x =0.22). Conductivity and Hall Effect were measured in the temperature range 4.2 - 300 K. Our measurements indicate that the sample is n-type semiconductor. In intrinsic regime, the slope of the curve RH T3/2 indicates a gap of 178 meV which agree well with Eg (x = 0.22, 300 K) = 183 meV. Our theoretical calculations, according to the Kane model, show that the Fermi energy EF increases with temperature. The calculated donor state Ed is 3 meV above the conduction band at 4.2 K and agrees well with 0.67 meV of low field Hall effect measurements. Our theoretical calculations on the mobility shows that ionized impurity scattering dominate below 25 K, optical phonons scattering at high temperatures (&gt;70K) and the mobility is generated by the both mechanisms of scattering in the intermediate temperature regime. At high temperatures, an excellent agreement between experimental and calculated scattering mobility is obtained by introducing a trial function. The detection wave length  situates the sample as medium-infrared detector

Revues Scientifiques Marocaines

M. J. CONDENSED MATTER                     VOLUME 13, NUMBER 2                        OCTOBER 2011 MJCM, VOLUME 13, NUMBER 2                                                © 2011 The Moroccan Statistical Physical and Condensed Matter Society    Scattering mechanisms and electronic transport properties in a Hg1-xCdxTe medium-infrared detector   A. El-Abidi*1, A. Nafidi 1, H. Chaib1 , A. Taoufik 1Laboratory of Condensed Matter Physics and Nanomaterials for Renewable Energy, Department of Physics, Faculty of Sciences, BP 8106 Hay Dakhla;University Ibn Zohr, 80000 Agadir, MOROCCO.   (*) Corresponding author. E-mail: elabidiabderrahim@yahoo.fr,nafidi21@yahoo.fr  Abstract: We report here transport properties measurements and theoretical results on modeling carrier charge mobility in Hg 1-xCdxTe (x =0.22). Conductivity and Hall Effect were measured in the temperature range 4.2 - 300 K. Our measurements indicate that the sample is n-type semiconductor. In intrinsic regime, the slope of the curve RH T3/2 indicates a gap of 178 meV which agree well with Eg (x = 0.22, 300 K) = 183 meV. Our theoretical calculations, according to the Kane model, show that the Fermi energy EF increases with temperature. The calculated donor state Ed is 3 meV above the conduction band at 4.2 K and agrees well with 0.67 meV of low field Hall effect measurements. Our theoretical calculations on the mobility shows that ionized impurity scattering dominate below 25 K, optical phonons scattering at high temperatures (>70K) and the mobility is generated by the both mechanisms of scattering in the intermediate temperature regime. At high temperatures, an excellent agreement between experimental and calculated scattering mobility is obtained by introducing a trial function. The detection wave length λ = 6.89 μm  situates the sample as medium-infrared detector. PACS: Keywords: Hg1-xCdxTe, Hall Effect, conductivity, scattering, transport mobility.  I. Introduction  The level of development achieved in the growth technics of semiconductor has allowed the experimental observation of a number of fine aspects present in optical and transport properties of these structures. Among them The II-VI ternary random alloys Hg1-xCdxTe have been predicted as a stable alternative for application in infrared optoelectronic devices. Especially in the region of second atmospheric window (around 10 m) which is of great interest for communication. A number of papers have been published devoted to the band structure of this system as well as its magneto optical properties [1]. A study on the temperature dependence respectively of Hall constant, conductivity, and mobility reveals the importance of scattering mechanisms. The aim of this work is to determine the transport properties for Hg 1-xCdxTe (x =0.22) and the contribution of various scattering mechanisms by doing theoretical curve fitting on the experimental temperature-mobility plot.  II. Experimental methods  The Hg1-xCdxTe sample was grown by molecular beam epitaxy (MBE) on [111] CdTe substrate. The nominal composition (x = 0.22) was determined by density measurements with a precision of ± 0.005 in x. The Hall Effect measurements and conductivity were done in the    temperature range 4.2-300K. A weak current (I = 0.1 mA) flows along the sample under a transversal weak magnetic field  (B = 0.2 T). The Ohmic contacts were obtained by chemical deposition of gold from a tetrachloroaurric acid in methanol solution after a proper masking to form the Hall crossbar.  III. Theory and general formulation  The calculation of the Fermi energy EF at a temperature T have been done via the formula (1) giving the expression of the density n of electrons in the conduction band. We iterated on the value of EF, between 0 and Eg+10 kBT, that gives a density n near of the measured one nmes.3/21/2F c Bc c B( E - η)0BE - E 2π m*k T2 (E)n = N dE (1) where:   η = and N = 2    .k  is the  Boltzmann's constant.1+e K T h²π    The energy gap has been calculated by the empiric formula of G. Hansen et al [2]:  3 -4g  ) T (2)E (x,T)= - 0.302 + 1.93x - 0.810x² + 0.832x + 5.03510 (1-2x Here T is the temperature in Kelvin, Eg is the material band gap in eV and x is the fractional composition value. The effective mass of electron m* was obtained via Kane model band [3]. 7813 A. El-Abidi, A. Nafidi, H. Chaib, A. Taoufik  MJCM, VOLUME 13, NUMBER 2                                                © 2011 The Moroccan Statistical Physical and Condensed Matter Society 0 0g g1m* = m (3) m  is the free-electron mass2 1- 0.6+6.333 ( + )E E +1 The effective mass of hole was fixed at h 0m = 0.55 m[4]. The origin of energies is taken at the top of the valence band (Ev =0 and Ec=Eg). The carrier concentration nmes was calculated from the standard expression: HmesHrn = (4)R .e For convenience Hr  was assumed to be unity. In order to determine the energy of the donor level Ed, we iterated in the formula (5) - giving the expression of EF as a function of the temperature [5] - on values of Ed that vary between 0 and Eg+ 5 kBT. The Ed energy is therefore the one that gives the EF calculated previously. The calculation of Ed have been done in extrinsic regime (4.2 77 )K T K  . c d BB g1/2(E -E ) / k TdF d BcB gc v vBFc* For : k T < E /10N1E =E + k T Ln -1+ 1+8 e4 N *  For : k T > E /10 (5)E +E Nk TE = + Ln                                       2 2 N                The density of donor impurities in the sample was 14 -3d mesN n 5.2410 cm  in the regime of carriers freeze-out. Electron mobility has been calculated in the temperature rang 4.2 300K T K   by the solution of the Boltzmann equation with the relaxation-time approximation [6] 0kf - f1v. f F. f (6)(k)rgrad grad   We included four types of scattering processes namely, acoustic phonons scattering, piezoelectric scattering, polar optical phonons scattering and ionized impurity scattering. The Hall mobility H H 0μ = R .σ , where RH is the Hall coefficient and 0σ  the conductivity without field, will be compared to the calculated electron mobility μ . The relations between electron mobility and temperature, for various scattering processes, are given as follows: The acoustic phonons scattering mobility is given by the relation [7]:  -5lac 5/23/2ac03.10  Cμ = (7)m*T  E ²m    Where: Cl = 6.97 1010 N.m-² [8] is the longitudinal elastic constant, Eac = 9.5 eV [8] is the deformation potential for acoustic phonons.  The piezoelectric scattering mobility is given by the relation [9]:    spz 3/2 1/20μ  =  2.6 (8)m/m k'² T/100  s  is the dielectric static constant in the semiconductor and is given by the relation [4]: sε  = 20.5 - 15.5 x  + 5.7 x² (9) , 0 is the dielectric constant in vacuum and k'  is given by: pzpz 0 s lek' = (10)e ² + . .C  where pze  is the piezoelectric constant. The polar optical phonons scattering mobility is given by the relation [9]: D5opD0θexpTμ  = 2.6 10 (11)θα.(m*/m ).k'       Where Dθ  is the Debye’s temperature and α  is the coupling constant without dimension given by: B op s1 mc² 1 1α = - (12) 137 2k θ       op is dielectric optical constant. α  is 0.39 for CdTe and 0.05 for HgTe [10]. The Debye’s temperatures of HgTe and CdTe are respectively 147. 5 K [11] and 160 K [12]. When the alloy      Hg1-xCdxTe is a two mode system in which the optical modes associated with CdTe and with HgTe are both observed, the mobility was calculated from Eq. (11) by first substituting the CdTe values for the appropriate parameters, then using the values for HgTe in the expression and averaging the two results [10] with the expression: op1 x 1-x = + (13)μ μ (CdTe) μ (HgTe)  The ionized impurity scattering mobility imp  is given by the Brooks-Herring equation [13]: 15 3/2simp1/2a d 03.2810  ² Tμ = (14)b(N +N ) (m*/m ) ln (b+1)-b+1    Where:   14 0 s1.2910 m*/m  T²b = (15)N* and N* is the effective screening density given by: a d ad(n + N ) (N - N - n)N* = n + (16)N Where Na and Nd are, respectively, the concentration of acceptors and donors.  The total mobility μ  is calculated using the relation:   i i1 1= (17)μ μ  where iμ refers to the individual   calculated mobility from various scattering processes and i is the number of scattering process included.   IV. Results and discussion  The measurement of RH at different temperatures shows that the sample is an n-type semiconductor in fig.1.  13 79 = = Scattering mechanisms and electronic transport properties in a Hg1-xCdxTe medium-infrared detector  MJCM, VOLUME 13, NUMBER 2                                                © 2011 The Moroccan Statistical Physical and Condensed Matter Society 0 10 20 30 40102103104105(-)103/T (K-1)|RH| (cm3 /C)Hg1-xCdxTex = 0.22Type n Fig. 1: Temperature dependence of the Hall constant in Hg 1-xCdxTe (x =0.22).  At low temperature (in extrinsic regime), we are in presence of a carrier freeze-out and the density of the carriers is nearly independent of the temperature. After RH increases slightly according to 103/T following the diminution of the density of carriers as described by:  Bd  n A exp - ΔE /2k T   [9], d c dΔE = E - E is the full activation energy. The slope of HR = f (103/T) curve in extrinsic regime in fig.1 allow us to determinate the donor ionisation energy dΔE = - 0.67 meV . That shows the existence of a donor state at 0.67 meV above the conduction band.   3 4 5 62x1064x1066x1068x1061071,2x1071,4x1071,6x1071,8x1072x107(-)  103/T (K-1)RHT3/2  (cm3 C-1K3/2 ) Fig.2: variation of RH.T3/2 as a function of 103/T in Hg 1-xCdxTe (x =0.22).  When the temperature increases, in the intrinsic regime, the electrons go thermally from the donor level (caused by Te rather than Hg interstitials [14]) and valence band to the conduction band. So the carrier’s concentration increases and Hall constant decreases. The slope of 3/ 2HR T  (103/T) in fig.2 gives Eg =178 meV which agree well with  Eg (300K, x=0.22) = 184 meV, given by the formula of Hansen et al. The corresponding detection wave length to this small gap is λ = 6.89 μm . This   situates the sample as medium-infrared detector (MIR) as shown in the fig. 3.  0 50 100 150 200 250 300 350050100150200250300350Eg m) Eg(meV)T(K)68101214  Fig .3 Temperature dependence of the band gap Eg  and cut-off wavelength    The measured electrons concentration nmes at 4.2 K, 77 K and at the ambient temperature 300 K, and their corresponding calculated Fermi energy are given in Tab.1 and shown in the fig 4. 0 50 100 150 200 250 300 350 400050100150200050100150200Ev Ec=Eg EdEd E (meV) E (meV) T(K) EF Eg/2  Fig.4 Fermi energies versus temperature      At low temperatures (25 K-100 K), the thermal energy is sufficient to ionize all donors and one reaches a plateau of concentration of carriers. This allows us to extract the  T K   3mesn cm  EF (meV) 4 (2.5 ± 0.3) ·1014 97 77 (3.01± 0.36) ·1014 103 280 (1.03± 0.12) ·1016 151 T(K) Eg(meV) Ed (meV) 4.2 95.2 98 77 116.9 111 Tab.1 : The concentration of electrons and the energy of Fermi at different temperatures. Tab.2:  Calculated Eg and Ed at 4.2K and 77K.   13 80 = A. El-Abidi, A. Nafidi, H. Chaib, A. Taoufik  MJCM, VOLUME 13, NUMBER 2                                                © 2011 The Moroccan Statistical Physical and Condensed Matter Society density ND: 14 35.2410D A Dn N N N cm .  And to determine the donors energy level’s Ed in Tab.2.  In our calculations we found an electronic donor state approximately at 3 meV above the conduction band at T = 4.2 K. A resonant electronic state 8 meV above the conduction band at 4.2 K was observed in Shubnikov de Hass experiments in Hg 0.8Cd 0.2Te [15] which is different to 0.67 meV from our Hall experiments and the calculated 3 meV . For the intrinsic conduction  0 i hσ = e n μ (1+b)  where e hb = μ /μ . Since the intrinsic concentration ni rises exponentially with temperature to i C V g Bn N N exp( E / 2K T)  ; we obtain the temperature dependence of 0 as shown in Fig.5. When the temperature is lowered, 0σ  enters the extrinsic region where the carrier concentration is constant and 0  rises, for the simplest case 0σ-3/20 α τ α T . At still lower temperatures, there is a carrier freeze-out. 0 10 20 30 40 200 250 300100101102  Hg1-xCdxTeType n   103/T (K-1)0  (  cm ) -1 Fig.5: Temperature dependence of the conductivity in the investigated Hg 1-xCdxTe (x =0.22)  In Fig. 6 we see the effect of single-scattering mechanisms on the total electron mobility. Ionized impurity scattering is seen to dominate below 25 K, optical phonons scattering at high temperatures (>70K) and the mobility is generated by the both mechanisms of scattering in the intermediate temperature regime.   10 100104105106  T  ( K ) (cm2 /Vs) Fig.6: Temperature dependence of the mobility. The closed circles represent the experimental data points. The datched curve represent the sum of all contributions of various scattering mechanisms while the solide line represents the sum taken into account the additional term.  At lower temperatures the calculated mobility is about a factor of 10 greater than the measured value. This disagreement can be due to the impurities type acceptors and the non-parabolicity of the conduction band not taken into account in our calculations. The discrepancy is reduced at higher temperatures to a factor of 1.3.  In order to improve the agreement between theory and experiment, in the intrinsic regime, we added a term which replaces additional scattering mechanisms not discussed in this paper such as electron-hole scattering and scattering by optical transversal phonons. We tried to estimate such a term by a trial function: a 1 2μ =μ exp(μ /T) [16] where -1 -11μ = 15835 cm² V  s  and 2μ  = 239 K  are fitting parameters. These values have been determined while minimizing the sum of squares which characterizes the quality of the fit. In fig. 7, the additional term within these values gives a good agreement for temperatures higher than 70 K . 10 10010310410510610710810910101011  T  ( K ) (cm2/Vs)optpiezacouimpexp Fig.7: Electron mobility as a function of temperature. The closed circles represent the experimental data. The various other curves refer to calculated contributions of various scattering mechanisms.  V. Conclusions  We have presented transport properties measurements and theoretical results on Fermi energy, donor state energy and mobility of Hg 1-xCdxTe (x =0.22). Calculated electron mobilities are observed to be in agreement with experimental data points at high temperatures. On the contrary, a discrepancy is observed at the low temperatures what is due to the non compatibility of the singly ionized donor scattering centres model and the non parabolicity of the conduction band which is not taken into account. However, we can conclude that the ionized impurity scattering dominate below 25 K, optical phonons scattering at high temperatures (>70K) and the mobility is generated by the both mechanisms of scattering in the intermediate temperature regime. The average of Hall mobility is 2.7 105 cm²/Vs at low temperature. This agrees well with the fact that for small x the alloy had electronics 81 13 = = = Scattering mechanisms and electronic transport properties in a Hg1-xCdxTe medium-infrared detector  MJCM, VOLUME 13, NUMBER 2                                                © 2011 The Moroccan Statistical Physical and Condensed Matter Society properties near these of bulk HgTe. This sample is a medium-infrared detector. We are trying to fit such mobility in p-type Hg1-xCdxTe (x=0.204) [17] and in the two-dimensional (II-VI) p-type HgTe/CdTe superlattice [18].    References  [1] J. L. Schmit, J. Appl. Phys. 41 (1990) 2876. [2] L Hansen, J.L. Shmit, T.M. Casstleman, J. Appl. Phys. Vol 53, p7099-7101 (1982). [3] M.A. Kinch, M.J Brau, A. Simmons, J. Appl. Phys.44 (1973)1649 [4] Wenus J. Rutkowski J., Rogalski A., IEEE trans. On electron devices, vol. 48, 7, p1326-1332 (2001). [5] P. Kiéev, Semiconductor physics, (Mir, Moscou, 1975), Chap. 3, P. 213 [6] A. El-Abidi., doctorate thesis, Ibn zohr university, Agadir Morocco (2010) [7] F. J. Blatt, in Solid state physics, edited by F. Seitz and D. Turnbull (Academic, New York, 1957), vol.4, p. 332. [8] D. Chattopadhyay and B.R. Nag, Journal of applied physics, Vol. 45, N0. 3, March 1974 [9] K. Seeger, Semiconductor physics, an introduction (Springer, 2002), chap 6 p.159-221. [10] W. Scott J. Appl. Phys., Vol. 43, No. 3, March 1972 [11] J G Collins et al 1980 J. Phys. C: Solid State Phys. 13 1649-1656  [12] T F Smith et al 1975 J. Phys. C: Solid State Phys. 8 2031-2042    [13] J. D. Wiley, Semiconductors and semimetals (Vol. 10), Academic Press, New York (1975). [14] R. Dornhaus, H. Happ, K.H. Müller, G. Nimtz,  W.  Schlabitz, P. Zaplinski, G. Bauer: in proc. XIIthInt. Conf. Phys. Semicond., Stuttgart 1974, ed . by M.H. Pilkuhn (Teubner, Stuttgart 1974), p.1157. [15] R. Dornhaus, G. Nimtz, W. Schlabitz, H. burkhard : Solid State Commun. 17, 837 (1975). [16] P.Moravec, R Grill, J Franc, R Vaghova, P Höschl and E Belas..semicond.Sci. Tecghnol. 16 (2001) 7-13 [17] A. El Abidi, A. Nafidi et al, Book of Abstracts (CA:235) 10th Moroccan Meeting On the chemistry of The state Solide (REMCES 10) Meknes, Morocco, April 27, 28 and 29 (2005) [18] A. El Abidi, A. Nafidi et al, Physica B: Physics of Condensed Matter 405, (2010) pp 936-940      82 13 

Scattering mechanisms and electronic transport properties in a Hg1-xCdxTe medium-infrared detector

https://revues.imist.ma/index.php/MJCM/article/download/474/406

Scattering mechanisms and electronic transport properties in a Hg1-xCdxTe medium-infrared detector

Abstract

Similar works

Full text

Available Versions

Revues Scientifiques Marocaines