semimetal-semiconductor transition in bi-in...

Indian Journal of Pure & Applied Physics Vol. 40, June 2002, pp. 407-416

Semimetal-semiconductor transition in Bi-In system Sanjeeta Rani

Acharya Narendra Dev College, Delhi University, New Delhi 110019

and

G K Chadha

Department of Physics and Astrophysics, Delhi University, New Delhi 110007

Received 25 February 2002; accepted 18 April 2002

Semimetal-semiconductor transition in Bi-doped with 4 at. % In single crystal is reported for the first time. Resistivity and Hall coefficient measurements performed on single crystalline sample of Bi-In (4at.%) system for an extensive range of temperature from 4.2-300 K, reveal semiconducting behaviour explicitly in the range 30-130 K. Electronic parameters, i.e. carrier concentration and Hall mobility are calculated for the entire temperature range of 4.2-300 K. The pair of light mass bands at Lc and Lv moves up relative to the Tv band resulting in the disappearance of the overlap between the Lc band and the Tv band and an energy gap of the order of 37.3 MeV is introduced between the light electron (Lc) and heavy hole (Tv) band. Further, the direct band gap between Lc and Lv bands is narrowed to a value of 10.9 MeV in comparison to pure bismuth. An impurity level is also reported on account of doping corresponding to activation energy of 4.1 MeV. Results from microhardness measurements and XRD studies of pure Bi and Bi-In (4 at. %) alloy reveal that In makes complete solid solution with Bi and gains effective entry into the lattice, altering the periodicity of Bloch Potential and modifying the band structure of Bi. This seems to be the reason that the transition from semi metal to semiconductor takes place in the Bi In alloy.

1 Introduction

Bismuth (Bi), a soft, heavy, brittle, and silvery white metal with a pinkish tinge, located in Group V A of the periodic table of elements, is an element with a surprisingly broad range of applications. With few exceptions, a little amount of Bi goes a long way towards the improvement of material characteristics, most often in highly technical and industrial applications. From the point of view of electronic properties, it occupies a position intermediate between a metal and a semiconductor. The crystal structure and the band structure of Bi have been discussed in detail in the literature 1. 7 . A great deal of information about the band structure in Bi can be obtained from the electrical and magnetic properties of its alloys. It was realized by JonesR that alloying bismuth with small amounts of elements with different valency might permit the study of either an electron band or a hole band separately. Thompson9 indeed carried out above 15 K extensive measurements of the electrical properties of bismuth alloys containing Pb, Sr, Se, Te. The group IV elements Pb and Sn act as acceptors, much as do group ill elements in the silicon germanium type of

semiconductors. Similarly, group VI elements act as donors.

Noothoven Van Goor et al.w established that at 4.2 K, tin is a monovalent acceptor in Bi . The carrier density in pure Bi is of the order of 10.5

carriers/atom, and tin concentration of this order is sufficient to shift the Fermi-level through an appreciable part of the band-structure. Bate et al. II concluded that tin doping had little effect on the Lpoint band separation. However, Misu et al. 12 made magneto resistance studies at 20 K and found that the L-point energy gap increased from 13 .8 MeV in pure Bi to 17 .2 MeV. Hermans et al. 13 observed that the excess charge density P-N is observed to be an order of magnitude larger at 300 K than at 4.2 K. They attributed it to increase in pseudo-parabolic Fermi energy of pure Bi with temperature. Boxus et al.14 concluded that for tin concentration < 0.04 at. %, the addition of acceptor affects the location of Fermi level.

Abeles & Meiboom l5 a lso studied gal vanomagnetic effects and Hein 16 analyzed the measurements of Shoenberg & Uddin 17 on magnetic susceptibility of Bi-Sn, Bi-Pb and Bi-Te alloys at

408 INDIAN J PURE & APPL PHYS, VOL 40, JUNE 2002

(0)

90 eo

(b)

eo 70 60 50

· ~29

40 30

30 20

' ..... 20

Fig. 1- (a) XRD pattern of pure Bi; (b) XRD pattern ofBi-In (4 at. %) alloy

E

_--+-. --'-~"""" ......... -,. :JII'_ •••••••••• I ~ -

u

t .s. 100

f 1~Bl--I" ( .... "'> -__=_86-1" (3C.~ .

1 10 100 1000 Temperature, K

Fig. 2 - Plot of resistivity versus temperature for Bi-In (3 at. %) alloy and Bi-In (4 at. %) alloy (logarithmic scale)

low temperatures. The addition of donors and acceptors can be expected to modify the band structure of Bi as well as change the carrier concentration. The addition of group V elements, however, can be expected to modify the band structure without destroying the equality of electron and hole concentration. Thus, a comparison of the properties of alloys containing group V elements with those containing group IV or VI should help to unravel the effects on the band structure. Of the

group V elements, antimony (Sb) goes into solid solution .. with Bi in different percentages of composltlOnIR.21

• It may be noted that in Bi-Sb alloys, the crystal structure has the same symmetry as that. of pure ~i. Bi-Sb alloy shows interesting propertIes, whIch vary significantly with composition. At lower concentration of Sb (5% 8.5%>, it. is semi-metallic, while at highe; concentrations of Sb (- 40 at. %) it is semi· conducting IR-211

• The fixed band-gap is 14 MeV according to JainlR, and 20 MeV according to Yim et

RANI & CHADHA: Bi-In SYSTEM 409

100 . 1150 200 \

~20~--------------------------------~----~----~~----------------------~ lOOOIT. K-1 .

Fig. 3 - Plot of Hall coefficient RH versus IOOOIT Bi-In (4 at. %) alloy

120

100

7~ ...... -'= 80

a .~ 80

~ 0

U ..a ~

~ 20

0 0 100 ,eo 200

Tetnpera.rure. K

Fig. 4 - Plot of carrier concentration versus temperature Bi-In (4 at. %) alloy

allY. In the samples studied by Jain, the majority carriers are holes, whereas, the observations made by Yim et al.'Y, show that the majority carriers are electrons.

The electrical resistivities of a series of Bi-Sb alloys have been measured by Fenton et al. 22

Shoenberg & Uddin '7 suggested from de-Haas Van Alphen measurements on this alloy that Fermi energy decreases with addition of Sb. A decreased Fermi energy implies a decreased overlap l6 and

consequently Bi-Sb alloy becomes semiconducting at concentrations greater than 4.8 at. %. Sunglae Cho et al.2J also reported semi metal-semiconductor transition in Bi-Sb super-lattice alloys. This feature of semiconducting behaviour has also been observed for Bi-Sn alloys in the concentration range 0 .04-0.2 wt % by Abeles and Meiboom '5 . Moreover Uher et al. 24 reported superconducting behaviour of this BiSn system (cone. 0 .02-0.23 at.% Sn) below 1 K. Similar behaviour has been reported by Dey & Chaudhuri25 and Subramaniam & Chaudhuri 26

, when


bismuth is doped with appropriate concentration of either thallium or lead. Another interesting observation was made by Brandt et aPI, when they found that by the application of a magnetic field, a semiconductor-metal transition takes place. Huber et ai.27 reported semi metal-semiconducting transition in Bi wires from 0.3 to 300 K. This semi metalsemiconducting transition was further confirmed by Heremans et ai.2X.

Although, a considerable amount of work has been done on Bi doped with group IV, V, and VI elements, indium (In), a group IlIA element, as a dopant has missed the attention of all the workers. In, which has an atomic mas of 114.8 and atomic

number 49 is a very suitable dopant, which can enter the Bi lattice very easily. The extent of solubility largely depends on the atomic radius. There can be two types of primary solid solution - (i) interstitial and (ii) substitutional. In general, because of the restricted size of the interstices, only rather small atoms dissolve interstitially. The radii of atoms known (or likely) to form interstitial solutions2~ are less than 1.0 A. It may be noted curiously, that atomic/metallic radii2~ ofBi (= 1.55-1.74 A) and In (= 1.62-1.69 A), are quite comparable. The possibility of In to make interstitial solid solution, in the present case, seems to be little, since the atomic radius of In is considerably greater than 1.0 A. However, substitutional solid solution, in which

10~----------------------------------------------------------------'---'

------x

O.14-----------------.----------------,---------------~----------------~ o 100 H50 200

lOOOIT

Fig. 5 -- Plot of Ln ( IlT3/2

) versus I OOOIT Bi-In (4 at. %) alloy

(a) PureBi (b) Bi-In (4at.%)

Lv Lv

k k

Fig. 6 -- E versus k diagram for Bi and Bi-In (4 at. %) alloy


impurity atoms occupy the lattice sites of the solvent lattice , seems to be possible in the present case. Generally, substitutional solid solution is possible when the sizes of the atoms of the solvent and impurities differ2~ by no more than about 15%. However, no solid solubility data of In in Bi is available, though differing values of solubilities of other elements in Bi are reported in literature 13

·3u

.".

In view of the above and to understand the general behaviour of the changes in the band structure of bismuth doped samples, the authors have undertaken for the first time the measurements of the resistivity and Hall coefficients for an extensive range of temperature from 4.2 to 300 K of bismuth doped with In, where the concentration of the dopant is 3 at. % and 4 at. %.

2 Experimental Details

Single crystal specimens of Bi doped with 3 at. % In and 4 at. % In were grown by Bridgman technique30

f> using Johnson Matthey spectrographically standardized material (99.9999%). Detail s regarding the growth conditions have been given in the literature37

.4o

•

Single crystalline nature and symmetry of the samples were ascertained through Laue back reflection photographs, when X-rays were directed along the trigonal axis. The specimen for galvanomagnetic measurements were then, cut from the grown crystal using spark erosion technique41

and were given a rectangular parallel geometry in such a way that the trigonal axis was perpendicular to the surface of the parallelepiped. The specimen was then subjected to a slow lapping process using fine mesh carborundum powder. Each surface was lapped in tum until both the surfaces were parallel to each other.

The specimen of dimensions 20 x 3 x 1 mm) was finally annealed for about 80 h at 140°C (which is about half the melting point of Bi) to remove strains introduced during cutting and handling. Six probes were attached to the sample using silver paste for the measurement of resistivity , and Hall voltage. The electrical measurements in the range 4.2-300 K were then, carried out in a liquid helium cryostat. A Keithley 181 nano-voltmeter was used to measure the voltages and an electronic temperature controller (sensitivity = ± 0 .01 K) was used to control the temperature. Temperatures were measured using a gold + 0.07% iron-chromel

thermocouple for temperatures between 4.2 and 77K and a chromel-constantan thermocouple for temperatures between 77 and 300 K.

3 Microhardness Measurements

The specimens were mounted on Soviet microhardness meter n_MT-3 with a diamond pyramid indenter for micro hardness measurement. The diamond pyramid indenter, which was a standard square based pyramid with 136° apex angle, was pressed into the specimen under a known load, P (20 g) for a known time (20 s) and then removed. The mean diagonal of the indentation print, which is square in shape, was measured under a microscope with a built-in micrometer. The following formula is used for calculating the microhardness number H in kg/mm2:

H = 1854 PIC-

where P is load In g and C is the diagonal of indentation print in microns. Table I represents Vicker's hardness number measured at different locations on Bi and Bi-doped with 4 at. % In . The hardness was measured at various regions of the surface of the Bi-In (4 at. %) doped specimen and it reveals that it is constant and uniform, over a large area of the surface and hence a uniform phase comprises the bulk of the surface of the doped system.

Table I - Vicker' s hardness number for Bi and Bi-In (4 al. %)

S.No. System Vicker's hardness number

1 2

Bi (pure) Bi-In (4at. %)

4 X-ray Studies

12.4 10.7 (No other phase present)

In the present study, X-ray powder diffraction pattern of pure Bi and Bi-doped with 4 at. % of In samples were obtained on a Philips PW 1840101111 compact X-ray diffractometer system in conjunction with Philips PW 1830 X-ray generator (operating voltage 30 kV and current 20 rnA) with copper target, using Cu-K, radiation (I-. = 1.5405 A) . A Ni filter was used in the diffracted beam to eliminate Cu-K~ radiation. The intensities of X-ray reflections were recorded by scintillation counter and denoted by the peak heights (in arbitrary units). It may be noted from XRD patterns of doped Bi systems [Figs I(a) and J(b)] that there is a slight shift in the


position of peaks in of Bi-In (4 at.%) system with respect to the pure bismuth, indicating change in the size of the bismuth lattice due to doping. However, the peaks are characteristic of a bismuth lattice.

Table 2 - Diffraction angle 8 and lattice spacing d for Bi and Bi-In (4 at. %)

S. No Miller Bi (Pure) Bi- In (4 at. %) indices hkl 28 (fA) 28 f/A)

003 22.60 2.0043 2 102 27.20 1.6851 27.00 1.6966 3 014 38.00 1.25 II 37.66 1.2607 4 110 39.60 1.2084 39.25 1.2174 5 105 44.60 1.0970 44.38 1.1013 6 006 45.80 1.0744 45 .60 1.0781 7 11 3 45.95 1.0717

8 022 48.70 1.0253 48.54 1.0278 9 204 56.00 0.9291 55.78 0.9315 10 017 59.20 0.8967 II 116 62.10 0.8716 61.88 0.8733 12 212 64.50 0.8534 64.18 0.8557 13 108 67.40 0.8343 67.20 0.8355 14 124 70.70 0.8161 70.42 0.8 175 IS 300 71.90 0.8103 71.54 0.8120 16 207 73.60 0.8029 73 .40 0.8037 17 215 75.30 0.7963 18 028 80.90 0.7801 80.78 0.7803 19 119 85.15 0.7730 85.22 0.7729 20 127 86.90 0.7714 21 306 89.60 0.7703 89.47 0.7703 22 132 91.80 0.7706 91.31 0.7705 23 314 97.60 0.7771 97.07 0.7762

This clearly shows that, the lattice essentially consists of bismuth atoms for the doped system. The presence of any other phase is not revealed in XRD pattern. Table 2 represents the diffraction angles (8), the corresponding lattice spacings (d) and the Miller indices H, K, L, of the planes involved in reflections. The accuracy in d value measurements is about 1 in 20,000. It can also be noted that, the Miller indices H, K, L, satisfy the condition H - K + L = 3 n, where n is an integer. This implies that the lattice is R (rhombohedron) in reverse setting.

Lattice Parameters - Further, Cohen's42 method of least square refinement was employed for the precise calculation of lattice parameter using the X-ray powder diffraction pattern, in order to find out changes, if any, due to doping. It is evident from Table 3 that, lattice parameters have changed due to doping, indicating increase in the size of the unit cell of Bi-In (4 at. %) alloy in comparison to the size of the unit cell of pure Bi. Laue back reflection

photographs of the doped system were also taken and 3-fold symmetry was ascertained by directing' X-rays along the trigonal axis. Laue back-reflection photographs show that 3-foJd symmetry of pure bismuth lattice is retained after doping also.

Table 3 - Lattice parameters (hexagonal axes) of Bi and

Bi-In (4 at. %)

S.No. System Lattice const. a(A) Lattice cons!. c (A)

I Bi 4 .5506 11 .8787 2 Bi-In 4.6043 12.5883

5 Results and Discussion

5.1 Resistivity

Figs 2(a) and 2(b) represent the vanatlon of electrical resistivity as a function of temperature in the range of 4.2-300 K for Bi doped with 3 at. % lin and 4 at. % In . The variation of resistivity with temperature for both the samples can be divided in the following well-defined regions.

(A) Bi-In (3 at. %)

(a) 4.2-6.6 K - The impurity scattering region where p is constant.

(b) 6.6-90 K - After 6.6 K, the resistivity starts rising slowly as P, where x lies between 0.1-0.26.

(c) 90-130 K-In this region, the resistivity is almost constant.

(d) 130-270 K-For T> 130 the res istivity, again starts rising with temperature as TlJ7 . This continues up to 270 K.

(e) 270 - 300 K - The resistivity rises lineariy - ]1 24 up to 300 K, a behaviour characteristic of lattice scattering.

(B) Bi-In (4 at. %)

(a) 4.2-30 K - The impurity scattering region, where resistivity p is constant extends up to 30 K in this case.

(b) 30-130 K - For temperature in the range 30 :<:; T:<:; 130 K the p starts decreasing with temperature, characteristic of semiconducting behaviour, indicating the presence of a band-gap. It may be noted, that, the resistivity of Bi-In (3 at. %) system also stopped rising near this region and became constant. However, the semiconducting behaviour


1oo~---------------------------------------------------------------------.

'" <: "'6 <""l = . .......

.~ 10

:.E 0 ::;s ~

. :::t::

10 . 100

Temperature, K ' 1000

Fig. 7 - Plot of Hall mobility ~H versus temperature Bi-In (4 at. %) alloy

could be clearly visible, only when doping of In is increased to 4 at. %. It is shown in Section 5.3, with the help of calculation of carrier concentration that, this semiconducting behaviour is due to a band gap of the order of 10.9 MeV between the light mass bands, i.e. conduction band and valance band at the L point (tc and Lv bands).

(c) 130-300 K - For T> 130 K the resistivity starts rising slowly as r S3 . The above behaviour of Bi-In system can be explained very easily in the light of electronic parameters calculations, i.e. carrier concentration n and carrier mobility IlH . For thi s purpose Hall measurements were performed on the semiconducting sample, i.e. Bi-In system doped with 4 at. % In.

5.2 Hall measurements

Fig. 3 represents a plot of the Hall coefficient RH as a function of temperature in the temperature range of 4 .2 ~ T ~ 300 K, for Bi-doped with 4 at. % of In . The Hall coefficient RH is found to be negative indicating electrons as the major charge carriers. Further, RII is found to be decreasing with increase in temperature, indicating an increase in the carrier concentration with temperature and presence of an energy gap .

In order to properly understand the semiconducting behaviour of Bi-In (4 at. %) system,

both the electronic parameters, i.e. carri er concentration n and carrier mobility 1lI'I were calculated as mentioned in the following section .

5.3 Electronic parameters

(A) Carrier concentration

Fig. 4 represents a plot of carrier concentration n as a function of temperature in the range 4 .2 ~ T ~ 300 K. The graph reveals an exponential ri se in the carrier concentration n with rise in temperature, confirmjng the semiconducting nature of the alloy . Further, Fig. 5 represents a plot of In (/'lj3l2 ) as a function of 1000lT in the temperature range 4.2-300 K. The graph reveals presence of three band gaps of the order of 4 .3 MeV, 10.9 MeV (at low temperatures) and 37.3 MeV (at high temperatures) .

Thi s behaviour is si milar to the Bi-Sb system, when concentration of Sb is greater than 5 at. %, It is already known that Sb makes a complete sol id solution with Bi lattice and doping of Bi with Sb in the concentration range 5 ~ Sb ~ 40 at. % causes the semiconducting behaviour. Moreover, indium, like Sb also appears to be making a substituti onal solid solution with Bi , as revealed through microhardness measurements and X-ray studies . The microhardness studies performed on Bi-In sys tems showed that In has fairly good solubility in Bi . Further, from atomic radii considerations also the


atom size of Sb (- 1.45-1.68 A) and In (-1.62-1.69 A) are favourable for making a good solid solution by substituting for Bi atoms (-1.55-1.74 A) at lattice sites in a bismuth matrix. These impurity atoms, however, may alter the periodicity of the Blochpotential and modify the band structure in addition to introducing impurity levels.

In view of the above, doping of Bi with In has direct re levance and the electrical resistivity and the Hall effect data reported above can be satisfactorily explained in terms of the model proposed by Blount & Cohen IX (Fig. 6) . According to this model, the essential part of the band structure of pure bismuth consi sts of a pair of light mass bands Lc and Lv at six symmetrically located positions in k-space and a heavy mass hole band Tv at two positions in k-space. In pure bi smuth, the upper band Lc overlaps slightly upon the heavy mass hole band Tv. so that , there is a very small number of light electrons and an equal number of heavy holes even at absolute zero in contrast to semiconducting material.

It appears that, doping with indium causes the following changes in the band structure of bismuth.

(i) An impurity level is introduced on account of doping corresponding to activation energy of 4.1 MeV.

(ii ) The pair of light mass bands moves up relative to the Tv band, resulting in the di sappearance of the overlap between the Lc band and the Tv band and an energy gap of the order of 37.3 MeV is introduced between the light electron (Lc) and heavy hole (Tv) band at a concentration of 4 at. % of In .

(iii) The band-gap between Lc and Lv, the light mass bands also decreases to a value of 10.9 MeV in comparison to experimentally determined value43 of direct energy gap of pure Bi, which is 13.53 MeV.

Using the above model, the behaviour of the system can be explained in the following manner. On account of narrow gap between Lc and Lv thermal excitation of electrons (say nc) begins at rather low temperature from the light mass band Lv resulting in PI holes in Lv band. However, the impurity band traps a fraction anc of these electrons, ionizing the impurity atoms . Only bnc (= nc - anJ numbers of electrons manage to reach the conduction band and participate in the conduction process, causing therefore, the Hall coefficient to be

negative. The conduction process in this region is a mixed conduction process consisting of both the impurity band conduction and intrinsic conduction. This continues up to a temperature of 55 K (Fig. 5). Hereafter, as the temperature rises further, Ie ser number of electrons are trapped into the impurity band, as most of impurity atoms are ionized and tend to reach the saturation value and more and more electrons are able to reach the conduction band and as a result b > a . The conduction process at thi s stage is mainly intrinsic and a band-gap of the order of 10.9 MeV is distinctly observed. In fact , by extrapolating the carrier concentration graph of this region, towards the lower temperature, the position of impurity band could be easily determined. Thi s can be done in following manner.

Let n Il be the number of electrons, which are observed through Hall measurements and nc , is the actual number of electrons excited from the Lv band at low temperatures in the range 4.2 ::; T ::;55 K. Then, the difference nc-n" is the number of e lectrons trapped in the impurity band and is equal to the P number of holes created in Lv band on account of impurity band conduction. A plot In pr-:'/2 versus liT gives an energy gap of the order of 4.5 MeV, which is in agreement to the experimental value of 4.1 MeV obtained as activation energy in region I.

The second region, dominated by the intrinsic conduction across a band gap of 10.9 MeV between Lv and Lc band, continues up to - 150 K (Fig. 5) . As the temperature is raised beyond 150 K , the electrons from the heavy mass band Tv also gain enough energy to jump across the gap between Lc and Tv band and start participating in conduction process, leaving P2 number of heavy holes in the Tv band . A plot of In nT3/2 versus liT gives an energy gap of 37.3 MeV in this temperature range. The conduction process in this region involves three types of carriers, namely nc electron in Lc band, light PI and heavy P2 holes in Lv and Tv bands, respectively. The expression for Hall coefficient fo r such a process should be the following:

The electrons however being much faster in comparison to other carriers, the effective carriers are negative, causing RH to be negative throughout


the entire temperature range and can be best approximated to:

I RH=-

ene

(B) Carrier mobility

Fig. 7 represents variation of Hall mobility flH as a function of temperature for Bi doped with 4 at. % In . The graph can be distinctly divided in the following regions.

(i) 4 .2-16 K - The mobility is constant. This may be understood in terms of scattering .due to neutral impurities at low temperatures, which are quite independent of temperature.

(ii ) 16-140 K-The mobility flH ex: J Osx, which is characteri stic of impurity scattering (dominant mechanism) along with the acoustical phonon scattering.

(iii) 140-300 K - In this range of temperature II ex: J 22R which may be due to combined scattering rH ,

on account of acoustical, optical and carrier-carrier scattering (dominant mechani sm). The resultant mobility at any temperature obeys the following rule.

I

!l !l 1 +!l2+!l~

It may be understood that, the res istivity varies with temperature in accordance with the individual variation of mobility and carrier concentration with temperature. The semiconducting behaviour of Bi-In (4 at. %) is visible on ly in the temperature range 30-130 K, as flH falls faster at higher temperature (- T - 2

dependence) in compari son to the rise in carrier concentration and as a result the res istivity ri ses beyond 130 K.

6 Conclusions

It is found that, In makes substi tut ional solid solut ion with bi smuth. It may be noted curiously, that atomic/metallic radii of Bi (= 1.55-1.74 A) and In (= 1.62-1.69 A), are quite comparable. Hence, In is suited to make solid solution with Bi . Thi s is evident from microhardness and X-ray studies. Microhardness and XRD pattern reveal that In makes complete solid so lution with Bi and no traces of any other phase are found. Further, XRD pattern

shows that, the lattice remains that of pure Bi , but there is an increase in the size of the unit cell in case of Bi-In (4 at. %) alloy in comparison to the size of the unit cell of pure Bi . The fact that In makes good solid solution with Bi has a bearing on the fact that it is capable of entering into Bi lattice effective ly and is not rejected by the lattice. Once it gains an effective entry into the lattice, it is in a position to alter the periodicity of the potential and modify the band structure of Bi lattice. A transition from semi metal to semiconductor in Bi-In (4 at. %) alloy is reported with the help of resistivity and Hall coefficient measurements performed for an extensive range of temperature from 4 .2-300 K. It is found that, this semkonducting behaviour is di stinctly visible for 30 ~ T ~ 130 K. A direct bandgap of 10.9 MeV is reported between Lo and Lv bands, which show narrowing of the band-gap due to doping in comparison to the pure Bi .

Different conduction processes invol ved are explained with the help of calculation of electronic parameters from 4 .2 K to 300 K. The pai r of li ght mass bands at Lo and Lv moves up relative to the Tv band due to doping. This results in di sappearance of the overlap between Lo and Tv bands, responsible fo r the semimetallic behaviour of pure Bi . From carrier concentration an energy gap of 37.3 MeV is est imated between Lcand Tv bands in Bi-In (4 at. %) alloy, making it a semiconductor. An impurity level at 4 .1 MeV is also reported on account of doping. In addition, Hall mobility is also calculated and it is found that for T> 130 K the mobility fall s faster as a function of temperature than the carrier concentration rises as a function of temperature. This behaviour is attributed to a combined scattering of charge carriers on account of.acoust ical, optical and carrier-carrier scattering.

Acknowledgements

The authors are deeply indebted to late Prof K D Chaudhury of Department of Physics and Astrophysics , Delhi Uni versity, Delhi for his va luable suggestions and di scussions on various results. The authors acknowledge the faciliti es rendered by the Department of Physics and Astrophysics, Delhi University, National Physical Laboratory, New Delhi and Solid State Physics Laboratory, New Delhi, where the experi mental work was carried out.


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