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Electrical properties of bismuth doped with tin and lead
Journal
of the Less-Common
ELECTRICAL AND LEAD
Metals,
PROPERTIES
144
(1988) 15
OF BISMUTH
DIPALI BANERJEE, DIBYENDU TALAPATRA BHATTACHARYA Department of Solid State Physics, Indian Jadavpur, Calcutta - 700032 (India)
15
22
DOPED WITH TIN
and RAMENDRANARAYAN
Association
for the Cultivation
of Science,
(Received October 8, 1987; in revised form February 23, 1988)
Summary The electrical conductivities and Hall effects of single crystals of bismuth doped with different percentages of tin and lead (0.17% and 0.56% lead; 0.3% and 0.71% tin) were determined in the temperature range 100 300 K. Tin and lead, both of which belong to group IV of the periodic table, have different effects on the band structure of bismuth. It was found that tin was more effective than lead in producing a change in band structure. Semiconducting properties were observed in the samples doped with lead, However, those doped with tin exhibited semimetallic and semiconducting properties depending on the percentage of dopant.
1. Introduction Bismuth is a group V element. It has overlapping valence and conduction bands and behaves as a metal having two types of carriers, electrons and holes. The properties of bismuth have been investigated by various workers. However, the results obtained are not in satisfactory agreement. The addition of impurities plays a very interesting role. It has been found that when antimony is added to bismuth the properties are changed substantially. The semimetal becomes a semiconductor. This property is attributed to a drastic change in the band structure - the overlapping bands become separated producing a small energy gap between them. A study of the properties of bismuth on addition of impurities is therefore interesting and can be used to investigate band characteristics. A systematic approach to such a study would be to add impurities: (i) that are acceptors, (ii) that are donors, (iii) that are of the same group. In this paper we report the results of investigations on single crystals of bismuth doped with acceptor impurities - lead and tin. The single crystals were prepared in our laboratory. Many workers have investigated the properties of bismuth doped with various percentages of lead and tin [ 1 - lo]. In particular, it is known that @ Elsevier Sequoia/Printed
in The Netherlands
16
small traces of tin and possibly lead can produce a temperature coefficient of resistance less than zero at room temperature [ 11. Thompson’s results [2] on the temperature variation of the specific resistance perpendicular to the principal axis in a Bi-Pb alloy are shown in Fig. 1. He stated that the smallest amounts of lead and tin required to produce alloys which have a negative temperature coefficient at room temperature are about 0.1% of lead and about 0.03% of tin. According to Abeles and Meiboom [3], the specific resistance perpendicular to the trigonal axis in Bi-Sn alloys decreases with a decrease in temperature. However, the specific resistance parallel to the trigonal axis first increases and then decreases showing a peak. They obtained a negative Hall coefficient for bismuth doped with tin at room temperature which became positive at low temperature for a current parallel to the trigonal axis. Tanaka [4] observed that for dilute alloys of Bi-Sn the electrical resistivity increased with temperature. A peak was observed which shifted to a higher temperature as the tin concentration increased. According to Tanaka pure bismuth shows a negative Hall voltage, whereas Bi-Sn alloys show a positive Hall voltage for magnetic fields parallel to the trigonal axis. The Hall coefficient remains constant below about 70 K and decreases rapidly after reaching a peak near 100 K. Smith [5] found a negative Hall coefficient for bismuth doped with small percentages of tin and lead at room temperature. However, in his experiment the direction of the magnetic field with respect to the crystal axis was not noted. Champman [6] observed a positive Hall coefficient for a Bi-Sn alloy at room temperature. According to Connell and Marcus [7] the Hall coefficient was positive for unpurified crystals of bismuth for a magnetic field parallel to the trigonal axis. It is evident from the above discussion that observations made by various workers are diverse in nature and sometimes even contradictory. No explanation has been given which can simultaneously account for all these observations. We have therefore undertaken a study of the properties of bismuth doped with lead and tin. Many reports are available on the investigation of bismuth crystals doped with small percentages of impurities (approximately
0.
I
400
I
200 “A +
Fig. 1. Resistivity-temperature axis.
I
300
I
400
relation for Bi-Pb alloys perpendicular to the principal
17
10p2% - 10p3%) [2 - 61. Early reports on crystals containing higher percentages of lead and tin impurities (greater than or equal to 1%) are also available [ 2, 5, 6, lo] ; however, it was found that the solid solubilities of lead and tin in bismuth are limited to within 1%. If higher percentages are added, segregation of the dopant results [8]. To observe the effect of the maximum amount of dopant which can be added to bismuth, we prepared two sets of crystals doped with lead and tin. The percentages of lead used were 0.17% and 0.56% and those of tin were 0.3% and 0.71%.
2. Sample preparation Single crystals of Bi-Sn and Bi-Pb were prepared by the vertical Bridgman technique using a modified Bridgman furnace. Figure 2 shows the schematic diagram of a modified Bridgman furnace and the temperature ~ /
SLOW SPEED MOTOR
P
SUSPENSION
ALUMINIUM KANTHAL
WIRE
COVER
A
WINDING
r
MOLTEN
CHARGE
25cms TERMINAL ALUMINA
POWDER
TAPERED
PYREX
SILLIMINITE
c 10 cmr
J-
WOODEN
.
BOX
-0 L
$J 400 g
30
$2 5
l-m
./\; 0
5
10
I5
DISTANCE
Fig. 2. Bridgman
furnace
20
25
(Cm)
and its temperature
50
-
profile.
MUFFLE
18
profile used for growth. A tapered Pyrex ampoule (length, 10 cm; inner diameter, 8 mm) was more than half filled with bismuth (purity, 99.99%) and the required amount of tin or lead (both purity, 99.99%) was added. The ampoule was alternately flushed with argon and evacuated four to five times and was finally sealed under vacuum. It was then held vertically in the hot zone of the furnace for 20 days at 350 “C to obtain a homogeneous distribution of tin or lead in the sample. The ampoule was then gradually lowered at a speed of 2 mm h-’ by a specially geared slow drive motor. The gradient of the furnace just below the hot zone was maintained at 2 “C mm-‘. The crystal was then annealed for 2 days to remove any imperfections. Four crystals were made. The single crystals of Bi-Sn and Bi-Pb thus obtained were then analysed by atomic absorption spectrometry; the percentage compositions are given in Table 1. TABLE 1 Prepared specimens and their impurity concentration Alloy
Bi-Sn Bi-Pb
Specimen
Sl
SZ Pl p2
3. Experiments
number
Impurity concentration lead (analysed) (at.%)
of tin or
0.71 0.3 0.56 0.17
and results
The samples were cleaved very easily and the cleavage planes were perpendicular to the trigonal axis. It was found that the trigonal axes were inclined to the direction of growth. The angles of inclination varied for the different crystals. The sides of the cleaved samples were cut to produce rectangles. The electrical conductivity u and the Hall effect RH were measured for all four crystals with the current perpendicular to the trigonal axis. Since the melting point of bismuth is low (271 “C), measurements were confined are to low temperature (100 - 300 K). The results of the measurements shown in Figs. 3, 4 and 5. The values of u for the different samples vary from 150 to 1400 a-’ cm-‘. To compare the variation in u with temperature for the different samples we plotted lg(R,/R) us. l/T instead of lg u us. l/T in Fig. 3, where R. is the resistance at room temperature. When lead is added as impurity (0.17% and 0.56%) the material becomes a semiconductor (Fig. 3); however, when tin is added as impurity (0.3% and 0.71%) the picture is different. For the sample containing 0.3% tin, u decreases with an increase in temperature until a temperature of 165 K is attained. Then u increases logarithm-
19
z9im
,
v
t
i.955t
4= 3
A-
52
o-
P,
? -
P*
t o- !i,
\
II.2 -
/l--L 0.03
t
,1&02
XL-9
i.930-
H0.0,
t
n’lcc
.I -
2
-i.905,
5
$(p)+
.
i
PP
1.O_-
5
$(yp)_
Fig. 3. Plot of lg(Ro/R) vs. l/T in semiconducting ST, PI, Pt) perpendicular to the trigonal axis. Fig. 4. Plot of Ro/R trigonal axis.
us. l/T
in semimetallic
200
alloy
and
(sample
Bi-Sn
S,)
alloys
perpendicular
(samples
to the
L
I
10
Bi-Sn
Bi-Pb
3c
T(‘K)-)
Fig. 5. Plot of RH vs. l/T in Bi-Sn
and Bi-Pb
alloys.
ically with an increase in temperature. For the sample containing 0.71% tin the decrease in u with temperature continues throughout the range of our measurements (Fig. 4). The conductivity obeys the relation u 0: T-’ up to
20
240 K; therefore up to this temperature the material behaves as a semimetal. After this and up to 300 K the decrease in u no longer obeys the relation u a T-l. Both samples of the Bi-Pb alloy (0.17% and 0.56% lead) show a logarithmic increase in u with temperature, i.e. they obey the relation u = -AE’kT (the symbols have their usual meaning). In the low temperature iliion these two samples show a very small energy gap of 0.003 eV. At higher temperature (T > 200 K) the value of AE is 0.0116 eV. Figure 5 shows the variation in R H with temperature for a magnetic field parallel to the trigonal axis and a current perpendicular to the trigonal axis. The magnetic field applied was 6.75 kG. The variation of RH with temperature has similarities in all four samples, e.g. at low temperature all four samples show a positive RH value. The positive RH value decreases with an increase in temperature. The dissimilarities are also important to note. In the sample containing 0.17% lead the positive RH value decreases as the temperature is increased. This decrease in positive value continues until it becomes negative, and then the negative value increases until room temperature is reached. In the sample containing 0.56% lead the positive RH value, after a slight initial increase, starts to decrease. The rate of decrease increases after a temperature of 210 K and it ultimately becomes negative. In the sample containing 0.3% tin the positive R H value first increases and then decreases above 200 K; however, the rate of decrease is much slower than in the lead-doped samples. In this case the RH value never becomes negative. In the sample containing 0.71% tin the positive RH value increases up to 225 K; it then starts to decrease until room temperature is reached but at a slower rate than in the lead-doped samples. The sign of RH always remains positive.
4. Discussion From the results of our experiment, it can be seen that of the four samples studied the two containing lead (0.17% and 0.56%) show a change in sign of the Hall coefficient. The sign of RH indicates that holes are predominant at low temperature and electrons at higher temperature. Since the impurity levels are acceptor levels (Fig. 6) the positive RH value at low temperature indicates that they lie at a lower energy than the top of the valence
(a)
(b)
Fig. 6. Schematic diagram of energy bands of (a) bismuth and (b) Bi-Sn and Bi-Pb alloys.
21
of electrons at higher temperature (negative band Tv. The predominance Ru value) suggests that in the intermediate temperature range the decrease in the positive RH value is a result of the fact that more and more electrons are taking part in the transport property. The variation of (I with temperature in this region shows a logarithmic increase which corresponds to an energy gap of 0.003 eV. This is much smaller than the energy gap between L, and Lv. Hence we may infer that a separation between the overlapping bands Tv and L, is caused by the addition of impurities. Semiconducting behaviour is observed in this region of temperature owing to the excitation of electrons from TV to L,. At higher temperatures the electrons are excited from Lv to L,, where the variation in u with temperature corresponds to an energy gap of 0.0116 eV, and this causes a rapid decrease in the positive RH value, ultimately making it negative. In the two samples containing 0.17% and 0.56% lead the only difference observed in the variation of RH with temperature is that the latter shows an initial small rise in positive RH. In the samples doped with tin (0.3% and 0.71%) the Hall effect maintains a similar trend as in the sample containing 0.56% lead; however, in the samples containing tin the initial rise in the positive value of RH is extended up to higher temperatures which depend on the percentage of tin (Fig. 5). The sample containing 0.3% tin is a semiconductor. The value of AE as calculated from the lg u US. l/T curve is 0.0099 eV in the temperature range 217 - 300 K. At lower temperatures the variation in u with T shows a tendency to deviate from semiconducting behaviour; u increases as the temperature decreases. In the sample containing 0.71% tin completely different behaviour is exhibited (Fig. 4). At low temperature the material behaves as a semimetal up to a temperature of 240 K. However, this behaviour is not the same as that of pure bismuth as can be seen from the fact that the Hall constant in this region is positive. This shows that the majority of carriers in this case are holes, whereas in bismuth they are electrons. The semimetallic behaviour is therefore exhibited by the holes created in Tv by the tin dopants. Therefore even if there is excitation of electrons in this region of temperature the electrons are much smaller in number than the holes and cannot make their presence felt (at least in the phenomenon of conductivity). At higher temperature (above 240 K) u decreases with temperature but does not obey the relation u a l/T. Here the decrease in conductivity with temperature is exponential. Although this is not a semiconducting property, the exponential variation in u suggests that the excitation of carriers is taking place. A plot of lg u us. l/T gives a straight line with a negative slope. The value of AE in this region is 0.009 eV. In the low temperature region (below 240 K) the material is semimetallic. The Hall coefficient is positive and does not show any tendency to decrease. Rather a small increase can be observed. We may therefore consider that only one type of carrier is present in this region of temperature. From the Hall effect measurement the carrier concentration in this region can be calculated using the relation
22
RH=
+
ne A value of approximately 10” cm-3 is obtained. Putting this value of n in the conductivity relation (I = nep, the mobility p of the carriers is calculated as approximately lo3 cm* V-’ s- ‘. Tanaka [4] also observed an increase in Rn and attributed the cause to a change in the ratio of the density of heavy holes and light holes. In his case the total number of holes would remain constant in this region of temperature. The above discussion leads to the following conclusions. (i) The overlap between T v and L, is very sensitive to the purity of bismuth. It appears that the addition of tin and lead causes a change in the overlap between Tv and L, and at the same time produces p-type material. The temperature at which RH starts decreasing in the sample containing 0.3% tin is higher than in the sample containing 0.56% lead. This shows that tin is more effective in producing a change in band overlap than lead. This may be due to the atomic size of tin, which is very different from that of bismuth; those of lead and bismuth are quite similar. (ii) When all other samples behave as semiconductors the sample containing 0.71% tin shows semimetallic behaviour. This is not a result of the fact that the property of bismuth is retained, but is due to the creation of a large number of holes by the tin impurities in Tv (in addition to the effect mentioned in (i) above). Therefore at low temperature the change in the number of carriers caused by the change in temperature is rather small. Thus although the behaviours of these samples are apparently different the reasons for their behaviours seem to be the same, i.e. the change in the overlap of Tv and L, and the production of holes.
References 1 2 3 4 5 6 7 8 9 10
C. W. Ufford, Proc. Am. Acad. Arts Sci., 63 (1928) 309. N. Thompson, Proc. R. Sot. London, Ser. A, 155 (1936) 111. B. Abeles and S. Meiboom, Phys. Rev., 101 (1956) 544. K. Tanaka, J. Phys. Sot. Jpn., 20 (1965) 1633. A. W. Smith,Phys. Rev., 10 (1917) 358. A. K. Champman, Philos. Msg., 32 (1916) 303. R. A. Connell and J. A. Marcus, Phys. Rev., 107 (1957) 940. W. S. Boyle and G. E. Smith,Prog. Semicond., 7 (1963) 39. 0. S. Es-Said and H. D. Merchant, J. Less-Common Met., 102 (1984) W. R. Thomas and E. J. Evans, Philos. Mug., 16 (1933) 329.
155.
of the Less-Common
ELECTRICAL AND LEAD
Metals,
PROPERTIES
144
(1988) 15
OF BISMUTH
DIPALI BANERJEE, DIBYENDU TALAPATRA BHATTACHARYA Department of Solid State Physics, Indian Jadavpur, Calcutta - 700032 (India)
15
22
DOPED WITH TIN
and RAMENDRANARAYAN
Association
for the Cultivation
of Science,
(Received October 8, 1987; in revised form February 23, 1988)
Summary The electrical conductivities and Hall effects of single crystals of bismuth doped with different percentages of tin and lead (0.17% and 0.56% lead; 0.3% and 0.71% tin) were determined in the temperature range 100 300 K. Tin and lead, both of which belong to group IV of the periodic table, have different effects on the band structure of bismuth. It was found that tin was more effective than lead in producing a change in band structure. Semiconducting properties were observed in the samples doped with lead, However, those doped with tin exhibited semimetallic and semiconducting properties depending on the percentage of dopant.
1. Introduction Bismuth is a group V element. It has overlapping valence and conduction bands and behaves as a metal having two types of carriers, electrons and holes. The properties of bismuth have been investigated by various workers. However, the results obtained are not in satisfactory agreement. The addition of impurities plays a very interesting role. It has been found that when antimony is added to bismuth the properties are changed substantially. The semimetal becomes a semiconductor. This property is attributed to a drastic change in the band structure - the overlapping bands become separated producing a small energy gap between them. A study of the properties of bismuth on addition of impurities is therefore interesting and can be used to investigate band characteristics. A systematic approach to such a study would be to add impurities: (i) that are acceptors, (ii) that are donors, (iii) that are of the same group. In this paper we report the results of investigations on single crystals of bismuth doped with acceptor impurities - lead and tin. The single crystals were prepared in our laboratory. Many workers have investigated the properties of bismuth doped with various percentages of lead and tin [ 1 - lo]. In particular, it is known that @ Elsevier Sequoia/Printed
in The Netherlands
16
small traces of tin and possibly lead can produce a temperature coefficient of resistance less than zero at room temperature [ 11. Thompson’s results [2] on the temperature variation of the specific resistance perpendicular to the principal axis in a Bi-Pb alloy are shown in Fig. 1. He stated that the smallest amounts of lead and tin required to produce alloys which have a negative temperature coefficient at room temperature are about 0.1% of lead and about 0.03% of tin. According to Abeles and Meiboom [3], the specific resistance perpendicular to the trigonal axis in Bi-Sn alloys decreases with a decrease in temperature. However, the specific resistance parallel to the trigonal axis first increases and then decreases showing a peak. They obtained a negative Hall coefficient for bismuth doped with tin at room temperature which became positive at low temperature for a current parallel to the trigonal axis. Tanaka [4] observed that for dilute alloys of Bi-Sn the electrical resistivity increased with temperature. A peak was observed which shifted to a higher temperature as the tin concentration increased. According to Tanaka pure bismuth shows a negative Hall voltage, whereas Bi-Sn alloys show a positive Hall voltage for magnetic fields parallel to the trigonal axis. The Hall coefficient remains constant below about 70 K and decreases rapidly after reaching a peak near 100 K. Smith [5] found a negative Hall coefficient for bismuth doped with small percentages of tin and lead at room temperature. However, in his experiment the direction of the magnetic field with respect to the crystal axis was not noted. Champman [6] observed a positive Hall coefficient for a Bi-Sn alloy at room temperature. According to Connell and Marcus [7] the Hall coefficient was positive for unpurified crystals of bismuth for a magnetic field parallel to the trigonal axis. It is evident from the above discussion that observations made by various workers are diverse in nature and sometimes even contradictory. No explanation has been given which can simultaneously account for all these observations. We have therefore undertaken a study of the properties of bismuth doped with lead and tin. Many reports are available on the investigation of bismuth crystals doped with small percentages of impurities (approximately
0.
I
400
I
200 “A +
Fig. 1. Resistivity-temperature axis.
I
300
I
400
relation for Bi-Pb alloys perpendicular to the principal
17
10p2% - 10p3%) [2 - 61. Early reports on crystals containing higher percentages of lead and tin impurities (greater than or equal to 1%) are also available [ 2, 5, 6, lo] ; however, it was found that the solid solubilities of lead and tin in bismuth are limited to within 1%. If higher percentages are added, segregation of the dopant results [8]. To observe the effect of the maximum amount of dopant which can be added to bismuth, we prepared two sets of crystals doped with lead and tin. The percentages of lead used were 0.17% and 0.56% and those of tin were 0.3% and 0.71%.
2. Sample preparation Single crystals of Bi-Sn and Bi-Pb were prepared by the vertical Bridgman technique using a modified Bridgman furnace. Figure 2 shows the schematic diagram of a modified Bridgman furnace and the temperature ~ /
SLOW SPEED MOTOR
P
SUSPENSION
ALUMINIUM KANTHAL
WIRE
COVER
A
WINDING
r
MOLTEN
CHARGE
25cms TERMINAL ALUMINA
POWDER
TAPERED
PYREX
SILLIMINITE
c 10 cmr
J-
WOODEN
.
BOX
-0 L
$J 400 g
30
$2 5
l-m
./\; 0
5
10
I5
DISTANCE
Fig. 2. Bridgman
furnace
20
25
(Cm)
and its temperature
50
-
profile.
MUFFLE
18
profile used for growth. A tapered Pyrex ampoule (length, 10 cm; inner diameter, 8 mm) was more than half filled with bismuth (purity, 99.99%) and the required amount of tin or lead (both purity, 99.99%) was added. The ampoule was alternately flushed with argon and evacuated four to five times and was finally sealed under vacuum. It was then held vertically in the hot zone of the furnace for 20 days at 350 “C to obtain a homogeneous distribution of tin or lead in the sample. The ampoule was then gradually lowered at a speed of 2 mm h-’ by a specially geared slow drive motor. The gradient of the furnace just below the hot zone was maintained at 2 “C mm-‘. The crystal was then annealed for 2 days to remove any imperfections. Four crystals were made. The single crystals of Bi-Sn and Bi-Pb thus obtained were then analysed by atomic absorption spectrometry; the percentage compositions are given in Table 1. TABLE 1 Prepared specimens and their impurity concentration Alloy
Bi-Sn Bi-Pb
Specimen
Sl
SZ Pl p2
3. Experiments
number
Impurity concentration lead (analysed) (at.%)
of tin or
0.71 0.3 0.56 0.17
and results
The samples were cleaved very easily and the cleavage planes were perpendicular to the trigonal axis. It was found that the trigonal axes were inclined to the direction of growth. The angles of inclination varied for the different crystals. The sides of the cleaved samples were cut to produce rectangles. The electrical conductivity u and the Hall effect RH were measured for all four crystals with the current perpendicular to the trigonal axis. Since the melting point of bismuth is low (271 “C), measurements were confined are to low temperature (100 - 300 K). The results of the measurements shown in Figs. 3, 4 and 5. The values of u for the different samples vary from 150 to 1400 a-’ cm-‘. To compare the variation in u with temperature for the different samples we plotted lg(R,/R) us. l/T instead of lg u us. l/T in Fig. 3, where R. is the resistance at room temperature. When lead is added as impurity (0.17% and 0.56%) the material becomes a semiconductor (Fig. 3); however, when tin is added as impurity (0.3% and 0.71%) the picture is different. For the sample containing 0.3% tin, u decreases with an increase in temperature until a temperature of 165 K is attained. Then u increases logarithm-
19
z9im
,
v
t
i.955t
4= 3
A-
52
o-
P,
? -
P*
t o- !i,
\
II.2 -
/l--L 0.03
t
,1&02
XL-9
i.930-
H0.0,
t
n’lcc
.I -
2
-i.905,
5
$(p)+
.
i
PP
1.O_-
5
$(yp)_
Fig. 3. Plot of lg(Ro/R) vs. l/T in semiconducting ST, PI, Pt) perpendicular to the trigonal axis. Fig. 4. Plot of Ro/R trigonal axis.
us. l/T
in semimetallic
200
alloy
and
(sample
Bi-Sn
S,)
alloys
perpendicular
(samples
to the
L
I
10
Bi-Sn
Bi-Pb
3c
T(‘K)-)
Fig. 5. Plot of RH vs. l/T in Bi-Sn
and Bi-Pb
alloys.
ically with an increase in temperature. For the sample containing 0.71% tin the decrease in u with temperature continues throughout the range of our measurements (Fig. 4). The conductivity obeys the relation u 0: T-’ up to
20
240 K; therefore up to this temperature the material behaves as a semimetal. After this and up to 300 K the decrease in u no longer obeys the relation u a T-l. Both samples of the Bi-Pb alloy (0.17% and 0.56% lead) show a logarithmic increase in u with temperature, i.e. they obey the relation u = -AE’kT (the symbols have their usual meaning). In the low temperature iliion these two samples show a very small energy gap of 0.003 eV. At higher temperature (T > 200 K) the value of AE is 0.0116 eV. Figure 5 shows the variation in R H with temperature for a magnetic field parallel to the trigonal axis and a current perpendicular to the trigonal axis. The magnetic field applied was 6.75 kG. The variation of RH with temperature has similarities in all four samples, e.g. at low temperature all four samples show a positive RH value. The positive RH value decreases with an increase in temperature. The dissimilarities are also important to note. In the sample containing 0.17% lead the positive RH value decreases as the temperature is increased. This decrease in positive value continues until it becomes negative, and then the negative value increases until room temperature is reached. In the sample containing 0.56% lead the positive RH value, after a slight initial increase, starts to decrease. The rate of decrease increases after a temperature of 210 K and it ultimately becomes negative. In the sample containing 0.3% tin the positive R H value first increases and then decreases above 200 K; however, the rate of decrease is much slower than in the lead-doped samples. In this case the RH value never becomes negative. In the sample containing 0.71% tin the positive RH value increases up to 225 K; it then starts to decrease until room temperature is reached but at a slower rate than in the lead-doped samples. The sign of RH always remains positive.
4. Discussion From the results of our experiment, it can be seen that of the four samples studied the two containing lead (0.17% and 0.56%) show a change in sign of the Hall coefficient. The sign of RH indicates that holes are predominant at low temperature and electrons at higher temperature. Since the impurity levels are acceptor levels (Fig. 6) the positive RH value at low temperature indicates that they lie at a lower energy than the top of the valence
(a)
(b)
Fig. 6. Schematic diagram of energy bands of (a) bismuth and (b) Bi-Sn and Bi-Pb alloys.
21
of electrons at higher temperature (negative band Tv. The predominance Ru value) suggests that in the intermediate temperature range the decrease in the positive RH value is a result of the fact that more and more electrons are taking part in the transport property. The variation of (I with temperature in this region shows a logarithmic increase which corresponds to an energy gap of 0.003 eV. This is much smaller than the energy gap between L, and Lv. Hence we may infer that a separation between the overlapping bands Tv and L, is caused by the addition of impurities. Semiconducting behaviour is observed in this region of temperature owing to the excitation of electrons from TV to L,. At higher temperatures the electrons are excited from Lv to L,, where the variation in u with temperature corresponds to an energy gap of 0.0116 eV, and this causes a rapid decrease in the positive RH value, ultimately making it negative. In the two samples containing 0.17% and 0.56% lead the only difference observed in the variation of RH with temperature is that the latter shows an initial small rise in positive RH. In the samples doped with tin (0.3% and 0.71%) the Hall effect maintains a similar trend as in the sample containing 0.56% lead; however, in the samples containing tin the initial rise in the positive value of RH is extended up to higher temperatures which depend on the percentage of tin (Fig. 5). The sample containing 0.3% tin is a semiconductor. The value of AE as calculated from the lg u US. l/T curve is 0.0099 eV in the temperature range 217 - 300 K. At lower temperatures the variation in u with T shows a tendency to deviate from semiconducting behaviour; u increases as the temperature decreases. In the sample containing 0.71% tin completely different behaviour is exhibited (Fig. 4). At low temperature the material behaves as a semimetal up to a temperature of 240 K. However, this behaviour is not the same as that of pure bismuth as can be seen from the fact that the Hall constant in this region is positive. This shows that the majority of carriers in this case are holes, whereas in bismuth they are electrons. The semimetallic behaviour is therefore exhibited by the holes created in Tv by the tin dopants. Therefore even if there is excitation of electrons in this region of temperature the electrons are much smaller in number than the holes and cannot make their presence felt (at least in the phenomenon of conductivity). At higher temperature (above 240 K) u decreases with temperature but does not obey the relation u a l/T. Here the decrease in conductivity with temperature is exponential. Although this is not a semiconducting property, the exponential variation in u suggests that the excitation of carriers is taking place. A plot of lg u us. l/T gives a straight line with a negative slope. The value of AE in this region is 0.009 eV. In the low temperature region (below 240 K) the material is semimetallic. The Hall coefficient is positive and does not show any tendency to decrease. Rather a small increase can be observed. We may therefore consider that only one type of carrier is present in this region of temperature. From the Hall effect measurement the carrier concentration in this region can be calculated using the relation
22
RH=
+
ne A value of approximately 10” cm-3 is obtained. Putting this value of n in the conductivity relation (I = nep, the mobility p of the carriers is calculated as approximately lo3 cm* V-’ s- ‘. Tanaka [4] also observed an increase in Rn and attributed the cause to a change in the ratio of the density of heavy holes and light holes. In his case the total number of holes would remain constant in this region of temperature. The above discussion leads to the following conclusions. (i) The overlap between T v and L, is very sensitive to the purity of bismuth. It appears that the addition of tin and lead causes a change in the overlap between Tv and L, and at the same time produces p-type material. The temperature at which RH starts decreasing in the sample containing 0.3% tin is higher than in the sample containing 0.56% lead. This shows that tin is more effective in producing a change in band overlap than lead. This may be due to the atomic size of tin, which is very different from that of bismuth; those of lead and bismuth are quite similar. (ii) When all other samples behave as semiconductors the sample containing 0.71% tin shows semimetallic behaviour. This is not a result of the fact that the property of bismuth is retained, but is due to the creation of a large number of holes by the tin impurities in Tv (in addition to the effect mentioned in (i) above). Therefore at low temperature the change in the number of carriers caused by the change in temperature is rather small. Thus although the behaviours of these samples are apparently different the reasons for their behaviours seem to be the same, i.e. the change in the overlap of Tv and L, and the production of holes.
References 1 2 3 4 5 6 7 8 9 10
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155.