Hopping conduction and dielectric properties of InSb bulk crystal

Transcription

1 International Journal of Basic & Applied Sciences IJBAS-IJENS Vol: 11 No: Hopping conduction and dielectric properties of InSb bulk crystal A. A. Ebnalwaled * Physics Department, Faculty of Science, South Valley University, Qena 83523, Egypt * Corresponding author - Kh_ebnalwaled@yahoo.com Abstract. The conduction mechanism in InSb crystals has been investigated by means of dc and ac conductivity measurements. The temperature-dependent electrical conductivity analysis revealed the dominance of the thermionic emission and the variable range hopping (VRH) of charged carriers above and below 325 K, respectively. The Mott's temperature T 0, the density of states at the Fermi level N (E f ), the average hopping distance R hop and the barrier height W hop have been calculated for the obtained InSb crystals. The ac electrical conduction as a function of frequency analysis suggests that ac conduction is attributed to correlated barrier hopping (CBH) model. There is a significant increase with temperature at low frequencies in the dielectric constant due to increase in contribution from space charge polarization with temperature Keywords: Variable range hopping, Correlated barrier hopping, Electrical conductivity, Dielectric constant, InSb 1. Introduction InSb has important applications in infrared, optical, microwave, and millimeter-wave devices [1] [4]. The properties of InSb make it very suitable for high-speed devices, magnetic sensors and so on [2], [3]. By using exclusion/extraction techniques it is possible to design functional InSb MOSFET operating at 300 K with relatively low leakage currents [5]. Its extremely high mobility and saturation velocity are expected to lead to a dramatic increase in the frequency of operation, which can be used to either extend the range of operation into THz range, or can be traded off for some other critical parameter, such as reduction of power dissipation for the same level of high frequency performance [5]. In recent years, efforts have been made to provide a deeper understanding of electronic properties of semiconductor devices. These efforts have revealed that in a number of cases, the simple interpolation procedures which have been relied on for more than two

2 International Journal of Basic & Applied Sciences IJBAS-IJENS Vol: 11 No: decades break down. In bulk semiconductor alloy materials such as, for example, InAsSb and GaInAs, the effects of long-range and local ordering, and selective localization, respectively, have been clearly demonstrated. Such properties are strongly linked to bowing of the band structure states, and to the changes in the density of states and optical and transport parameters of alloys [6]. In my previous work [7], InSb crystals were grown by vertical Bridgman technique from stoichiometric melts. The results of investigations were carried out to determine the structural, electrical and thermoelectric power properties of the obtained InSb crystals. The structural parameters were calculated for the prepared crystals and the values have a good agreement with the standard InSb crystals values. Preliminary characterization indicated that the semiconducting character of the obtained crystals is P-type. The measurements reveal higher Seebeck coefficient, electrical conductivity and power factor than the published results for the same compound [8] [10]. The present work is purposed to investigate the temperature and frequency dependence of the electrical conductivity and the dielectric properties of the obtained InSb crystals in order to understand the electrical conduction mechanism in it. 2. Experimental The growth of InSb crystal took place in a modified {traveling solvent method (TSM)} technique [7], [11]. The ampoule was heated up to 750ºC for 7 hours and then kept for 24 hours to guarantee a homogeneous distribution of the materials in the melt. Lowering rates selected were in the range mm/h and the temperature gradient was near 12 K/Cm. Even after solidification, the lowering rate was maintained at the same rate till the entire ampoule was out of the furnace The EDX analysis was performed by (Elemental Analyzer EDXRF, JSX3222, JEOL, Japan). The X ray diffractograms were measured stepwise with angle / second value of 0.02 o at ambient temperature with a model D 5000 Siemens diffractometer (Germany), the analysis reveal that the grown crystal has cubic structure with lattice parameter equal to A [7]. The surface of the grown crystals was analyzed by scanning electron microscopy. Also the homogeneity of the grown crystals was investigated with the aid of melting point test and electrical conductivity measurements of many cuts of each crystal.

3 International Journal of Basic & Applied Sciences IJBAS-IJENS Vol: 11 No: For the dc electrical conductivity measurements, the sample dimension was adjusted to be 9 x 3 x 2 mm 3. The ohmic nature of the contacts was verified by recording the current voltage characteristics for forward and reverse directions. For the ac electrical conductivity measurements, the original shape of the product crystal was utilized. Only the length was adjusted by polishing processes to be 3.5 mm while the crystal natural diameter was 10 mm. A two-part calorimeter was used. The inner part acted as a holder where the crystal was mounted on a flat end of a copper cylinder. It was heated electrically (the flat end was insulated from the crystal by thin sheets of mica). The second part of the calorimeter acted as a jacket to keep the measurements under vacuum. 3. Results and discussion 3.1 Temperature dependence of dc conductivity The temperature dependence of σ dc was previously measured by the author in the range K [7], from this work the semiconducting behavior for the obtained InSb crystals was indicated. To investigate the conduction mechanism for the obtained InSb crystals the conductivity temperature dependence is analyzed according to the following three possible conduction mechanisms: (i) Thermionic emission of charged carriers [12] in which the conductivity is given by σ T = σ exp( E / K ) 1 0 σ BT where σ is the conductivity, σ 0 is the pre-exponential factor, K B is the Boltzmann constant, E σ is the conductivity activation energy. (ii) Thermally assisted tunneling [13], for which σ varies as T 2 according to expression: 2 F 2 σ = σ 1(1 + T ) 2 6 where σ 1 and F are constants. (iii) Mott s variable range hopping [14], [15], in which the expression for the conductivity at low temperatures is given by: 4 σ T = σ exp(( T / ) 1/ ) T where σ 2 is the dc conductivity at room temperature and T 0 is the Mott temperature.

4 International Journal of Basic & Applied Sciences IJBAS-IJENS Vol: 11 No: Fig. 1 shows the variation of log σ T - T -1 in the temperatures range K. As illustrated from the figure the conductivity temperature variation was found to follow the thermionic emission theory, but as we can see from the figure there are two values for the conductivity activation energy below and above 325 K. The different values of the conductivity activation energy in different temperature regions indicate that another conduction mechanism may have become more dominant than thermionic emission [16]. σ T 2 variations were examined and found to be non-linear indicating that the tunneling transport mechanism is not adequate in the studied temperature range. In the low temperature region (below 325 K), the temperature dependence of the conductivity was explained with the Mott s variable range hopping mechanism. Fig. 2 displays the variation of log σ T - T -1/ 4, which fits linearly indicates that below 325 K the Mott s variable range hopping mechanism is the dominant mechanism. At lower temperature the probability of thermal release becomes rapidly smaller, so that at a temperature below 325 K the variable range hopping mechanism dominates [17]. The change in the conduction mechanism from thermionic emission to variable range hopping was investigated previously in another crystalline semiconductor material [16]. Mott parameters (T 0, the density of states at the Fermi level N(E f ), R hop the average hopping distance and W hop the barrier height) have been calculated for the obtained InSb crystals (table 1) by using the modified Mott's theory [14], [15]. 3.2 Temperature and frequency dependence of ac conductivity Fig. 3 indicates the ac conductivity σ ac for grown InSb crystals as a function of the reciprocal temperature at fixed frequencies of 1 KHz, 2 KHz, 5 KHz, 10 KHz, 16 KHz, 20 KHz, 26 KHz and 30 KHz. the figure clearly that the σ ac increases linearly with temperature. The dependence of σ ac on temperature is given according to the well known equation: σ = σ exp( E( ω) / K ) 4 ac 0 BT where E (ω) is the electrical activation energy. The frequency dependence of ac activation energy for the investigated sample is shown in Fig. 4. The obtained activation energy at frequencies > 10 KHz is lower than the obtained dc activation energy [7]. This result was published previously in other

5 International Journal of Basic & Applied Sciences IJBAS-IJENS Vol: 11 No: semiconductors [18], [19]. It is seen from Fig. 4 that the activation energy decreases with rising frequency. The increment of the applied field frequency enhances charge carriers to jump between localized states; hence the electrical activation energy decreasing with rising frequency [18], [20]. Fig. 5 illustrates the frequency dependence of σ ac, from the figure we can notice that σ ac increases linearly with frequency at high frequencies. This increment in σ ac ascribed to hopping mechanism that occurs by the influence of an applied electrical field. At high frequencies, σ ac increases proportionally to ω s with the rise in frequency because intrawell hopping becomes active [21], [22]. The values of the exponent s were obtained from the slopes of straight lines in Fig. 5. The conduction mechanism is determined from the temperature behavior of s. In the CBH model that describes charge carrier hops between sites over the potential barrier separating them, s decreases with the increment in temperature [23] [25]. The variation of frequency exponent s as a function of temperature is shown in Fig. 6. It is worth mentioning that the values of s decrease with rising temperature and approaches to one particularly at low temperature and high frequency range, which is in good agreement with the predicted values as CBH model proposed by Elliot et al. [26]. This result suggests that correlated barrier hopping model is the most suitable model to characterize the electrical conduction mechanism of the obtained InSb crystals. The frequency exponent s in CBH model is evaluated at low temperature to be [27]: 6K T s WM where W M is the maximum barrier height. B = 1 5 The value of W M was calculated to be ev by measuring the slope from Fig. 7 and using Eq. (5). This is consistent with the calculated value from Mott's theory (table1). 3.3 Temperature and frequency dependence of dielectric properties A dielectric characteristic study of the grown InSb crystals indicates its response to an applied electric field. Variations in the dielectric constant ε may be attributed to different types of polarization, which may come into play at different stages of its responses to varying temperature and frequency of the applied alternating field.

6 International Journal of Basic & Applied Sciences IJBAS-IJENS Vol: 11 No: The dependence of the dielectric constant ε on temperature and frequency of the applied ac field is studied in the temperature range of 282 K 514 K and frequency range of 10 Hz 2 KHz. Fig. 8 shows the dielectric constant ε as a function of temperature for the obtained InSb crystals at some frequencies in the range 1 5 KHz. From these plots it can be seen that the values of ε are increase with the rise in temperature. From these plots it can be seen that the behavior of InSb crystals showing dependence of dielectric constant on temperature is almost similar at all the frequencies. Also, we can observe that the rate of increase of ε is higher for lower frequency; this behavior has been reported for other materials [28]. However, no peak in the temperature range is observed which indicates that in this range there is no symptom of ferroelectric phase transition [29], [30]. Fig. 9 shows the dielectric constant ε versus frequency plots in the range 10 Hz 2 KHz at various temperatures. From these plots it can be seen that the values of ε increase with frequency till 390 Hz and then decreased. There are four mechanisms which contribute to the dielectric polarization of a material viz. (i) electronic, (ii) ionic, (iii) space charge or interfacial and (iv) dipolar polarization. The first two contribute to the dielectric constant at higher frequencies and the latter two to that at the lower frequencies [31]. The obtained results indicate that the values of ε increase with temperature at all frequencies leads to the conclusion that rise of dielectric constant for InSb crystals with temperature may be due to increase in contribution from space charge polarization with temperature [31]. 4. Conclusion In this work the conduction mechanism of InSb crystals was investigated, the data was analyzied using thermionic emission and variable hopping of charged carrier's theories. The obtained activation energy at frequencies > 10 KHz is lower than the obtained dc activation energy. At high frequencies, σ ac increases proportionally to ω s with the rise in frequency because intrawell hopping becomes active.

7 International Journal of Basic & Applied Sciences IJBAS-IJENS Vol: 11 No: The variation of frequency exponent s as a function of temperature suggests that correlated barrier hopping model is the most suitable model to characterize the electrical conduction mechanism of the obtained InSb crystals. The obtained results indicate that the values of ε increase with temperature at all frequencies due to increase in contribution from space charge polarization with temperature. List of tables Table 1: Calculated Mott's parameters for the obtained InSb crystals. References T 0 (K) N (E f ) (cm 3 ev -1 ) R hop (Å) (300K) W hop (ev) (300 K) 1.1 x x [1] V.K. Dixit, B.V. Rodrigues, H.L. Bhat, R. Kumar, R. Venkataraghavan, K.S. Chandrasekaran, B.M. Arora," Effect of lithium ion irradiation on the transport and optical properties of Bridgman grown n-type InSb single crystals", J. Appl. Phys. 90 (2001) [2] V.K. Dixit, B.V. Rodrigues, H.L. Bhat, R. Venkataraghavan, K.S. Chandrasekaran, B.M. Arora," Growth of InSb epitaxial layers on GaAs (0 0 1) substrates by LPE and their characterizations", J. Cryst. Growth 235 (2002) 154. [3] T. Zhang, S.K. Clowers, M. Debnath, A. Bennett, C. Roberts, J.J. Harris, R.A. Stradling, L.F. Cohen," High-mobility thin InSb films grown by molecular beam epitaxy", Appl. Phys. Lett. 84 (2004) [4] T.D. Mishima, M.B. Santos," Effect of buffer layer on InSb quantum wells grown on GaAs (001) substrates", J. Vac. Sci. Technol., B 22 (2004) [5] E. Sijercic, B. Pejcinovic," Investigation of scaling of InSb MOSFETs through drift diffusion simulation", Solid-State Electronics 50 (2006) [6] M. Jaros, " Electronic properties of semiconductor alloy systems" Rep. Prog. Phys. 48 1(985) [7] A.A. Ebnalwaled, "Evolution of growth and enhancement in power factor of InSb bulk crystal", J. Cryst. Growth 311 (2009) 4385.

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10 International Journal of Basic & Applied Sciences IJBAS-IJENS Vol: 11 No: log (σ δc T 1/2 Ω -1 cm -1 K 1/2 ) / T (K -1 ) Fig. 1: The variation of log σ T - T -1 in the temperatures range K for InSb crystals log (σ δc T 1/2 Ω -1 cm -1 K 1/2 ) T -1/4 (K -1/4 ) Fig. 2: The variation of log σ T - T -1/ 4 (below 325 K) for InSb crystals.

11 International Journal of Basic & Applied Sciences IJBAS-IJENS Vol: 11 No: log (σ αc Ω -1 cm -1 ) KHz 2KHz 5KHz 10KHz 16KHz 20KHz 26KHz 30KHz /T (K -1 ) Fig. 3: Temperature dependence of ac conductivity at different frequencies E (ω) ev Ln F Fig. 4: Variation of the activation energy as a function of frequency.

12 International Journal of Basic & Applied Sciences IJBAS-IJENS Vol: 11 No: log (σ αc Ω -1 cm -1 ) K 309K 333K 373K 423K 473K Log (F [Hz]) Fig. 5: Frequency dependence of ac conductivity at different temperatures. 1.1 B S T (K) Fig. 6: Temperature dependence of the frequency exponent s.

13 International Journal of Basic & Applied Sciences IJBAS-IJENS Vol: 11 No: S T (K) Fig. 7: Variation of the parameter (1 - s) with temperature KHz 2KHz 3KHz 4KHz 5KHz Log ε T (K) Fig. 8: Temperature dependence of dielectric constant at different frequencies.

14 International Journal of Basic & Applied Sciences IJBAS-IJENS Vol: 11 No: K 309K 333K 373K 423K 473K Log ε Log (F[Hz]) Fig. 9: Frequency dependence of dielectric constant at different temperatures.