Hall Coefficient Measurements of Moderately Doped N-In Sb at Low Temperatures

Hall coefficient (RH) measurements of moderately doped n-InSb system were carried out at low temperatures (T) down to 18 K. An exponential increase in RH was initially observed when T was reduced. This increase of R H is due to the expected reduction in the free carrier concentration. At low enough temperatures, R H tends to a constant value. This is explained as due to band tailing taking place in this system. On the other hand, Hall mobility ( H) was studied as a function of temperatures down to 18 K. H is increased as T is reduced at the high and intermediate temperature regimes down to 50 K. This increase is followed by a decrease at low temperatures. The decrease of H may be attributed to the ionized impurity scattering which is probably dominant at this range of temperatures. Introduction Transport properties of III-V compound semiconductors have been of considerable interest over the last few decades from both experimental and theoretical points of view [1-5]. Hall coefficient measurements of semiconductors are of great importance because many of physical properties could be determined. Among these physical properties it is possible to determine the carrier concentration, mobility as well as investigation of the behavior of various impurities in the system. The dependence of Hall coefficient on the temperature enables the ionization energy of an impurity or the width of the forbidden band to be estimated. Hall coefficient RH depends, in a complex way, on the magnetic flux density ( B), the charge carrier concentration ( n) and the carrier mobility ( μ). When we have one type of carrier and spherical constant energy surfaces, Hall coefficient may be written as; 70 K. Alfaramawi, S. Abboudy and L. Abulnasr ne r ne R H H = 〉 〈 〉 〈 = 2 2 1 τ τ ZKHUH 2 LV WKH VFDWWHULQJ WLPH DQG 2 2 〉 〈 〉 〈 = τ τ H r is the Hall factor. In the weak magnetic field at which the condition 1 2 2 << B μ is satisfied, the quantity H r is dependent on the scattering mechanisms [6]. For non-degenerate semiconductors and scattering by impurity ions it was found that H r =1.93; for scattering by lattice vibrations H r =1.18 [6]. For degenerate semiconductors and metals H r =1 . In strong magnetic field, i.e. if the condition 1 2 2 >> B μ is satisfied, it was found that H r =1 , therefore the Hall coefficient is independent of the scattering mechanisms. In addition, Hall mobility of charge carriers could be estimated from Hall coefficient as: H o H R σ μ = where o σ is the sample conductivity at zero magnetic field. In the present work we study the Hall coefficient and Hall mobility of n-InSb system from room temperature down to 18 K and magnetic fields up to 4.8 kG. For moderately doped InSb of typical impurity concentration of the order of 10 20 m the degenerate temperature is around 10 K. In this case one may observe the intrinsic, lattice as well as the ionized impurity scattering mechanisms under non-degenerate conditions down to 10 K. It is well documented that In Sb with an excess donor centers does not exhibit thermal freeze-out of conduction electrons onto the donor centers as the temperature is reduced [7]. This is supposed to be a result of a large effective Bohr radius (as o B A a 650 = for this system) and a vanishing donor activation energy so that donor levels merge completely with the conduction band. Experimental Barshaped n-type InSb specimen of nominated concentration of 9.5 x 10 19 m was used in the present study. The sample dimension is 8 mm long with a square crosssection of side 1.2 mm. The sample was chemically etched with CP4 solution to remove surface damage and for extra cleaning of the specimen. After the chemical etching, the sample was washed by a flow of water for at least 12 hours to remove the residual CP4. After being etched, the sample was provided with the appropriate leads for the Hall coefficient measurements. The sample was cooled down to 18 K via a closed cryogenic refrigeration employing helium as a working medium. A thermocouple thermometer of type Chromel vs. Gold with 0.07 at. % iron is used to measure the temperature. The source of the magnetic field was an electromagnet with flat pole faces. The maximum magnetic field obtained was 4.8 kG. Hall Coefficient Measurements of Moderately Doped 71 Results and Discussion Fig. (1) shows the variation of RH with the temperature ( T) at two values of magnetic field, namely 2.3 kG and 4.42 kG. It is evident that RH increases exponentially by lowering down the temperature until T=100 K, then it takes a constant value of 6.98 x 10 -2 and 6.68 x 10 -2 m/C at 2.3 kG and 4.42 kG respectively. 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.0 2.0x10 -2 4.0x10 -2 6.0x10 -2 8.0x10 -2 B = 4.42 kG B = 2.3 kG R H ( m 3 / C ) 1/T Figure 1: Hall coefficient versus 1/T at two magnetic fields. One can confirm the preceding results by plotting the carrier concentration versus 1/T for the two magnetic fields [see Fig. (2)]. In contrast to RH the carrier concentration decreases exponentially by lowering T then it tends to a finite value. At high temperature range (greater than 100 K) the decrease of n with 1/ T is due to the reduction of the carrier concentration as a normal behavior of semiconductors in the intrinsic region of conduction [8]. The slope of the linear part of the curve equals to ) 2 / ( k Eg − where Eg is the width of the forbidden gap and k is the Boltzmann constant. Estimation of the slope from the results yields a value of Eg = 0.21 eV which is in a good agreement with the theoretical prediction [5]. By further decrease of T the behavior is no longer intrinsic. The conduction electrons of the extrinsic donor centers do not exhibit thermal freeze-out and this leads to a vanishing activation energy of the donors. A formation of an impurity band merged with the bottom of the conduction band (band tailing) leads to such behavior [9]. One can expect a constant value of the carrier concentration of an electron gas at the temperature regime below 100 K. In Fig. (2) it is demonstrated that the carrier density is constant below 100 K which approximately equals the nominated concentration of the specimen. Application of the magnetic does not change the concentration of the confined electron gas. The available magnetic fields seem to be 72 K. Alfaramawi, S. Abboudy and L. Abulnasr weak to separate the impurity band from the bottom of the conduction band. Higher magnetic field may shrink the wavefunctions of the adjacent donor atoms leading to a decrease in the concentration of the conduction electrons [10]. Fig. (3) shows the variation of the Hall mobility with the inverse of temperature at two magnetic fields. 0.00 0.01 0.02 0.03 0.04 0.05 0.06 10 10 10 B = 2.3 kG B = 4.42 kG