The n decreased with an increasing heat-treatment temperature of between 300 and 500 K, while the .... The temperature differential given to the specimen was.
Materials Transactions, Vol. 43, No. 3 (2002) pp. 385 to 389 Special Issue on Environmentally Benign Manufacturing and Material Processing Toward Dematerialization c 2002 The Japan Institute of Metals
Graded Design of Carrier Concentration in Thermoelectric PbTe System by Heat-treatment Yoshikazu Shinohara, Yoshio Imai and Yukihiro Isoda Energy Conversion Materials Research Group, National Institute for Materials Science, Tsukuba 305-0047, Japan In order to develop a new process of forming a carrier concentration gradient in PbTe only by using heat-treatment, the effect of heattreatment on a carrier concentration n of the p-type PbTe has been investigated, and the p-type PbTe has been heat-treated using a temperature gradient. The as-grown stoichiometric PbTe was p-type with an n of 1.0 × 1024 m−3 . Vacuum thermal exposure with Te-rich PbTe at 900 K for 1 h increased the n of the stoichiometric PbTe to 5.1 × 1024 m−3 , which indicates that hole formation was achieved by thermal exposure at this temperature and duration. The thermally exposed stoichiometric PbTe was heat-treated in the temperature range of 400 to 900 K for a period of 24 h. The n decreased with an increasing heat-treatment temperature of between 300 and 500 K, while the n increased with an increasing heat-treatment temperature of between 500 and 900 K. A minimum n was measured at 500 K, above which the formation energy of holes was determined to be 16.4 kJ/mol. On the basis of these results, a 19 mm long thermally exposed stoichiometric PbTe was heat-treated using a temperature gradient of 340–900 K for a period of 24 h. A continuous change in n was formed in the PbTe, and a minimum value of n was determined to be at a position corresponding to the heat-treatment temperature of 500 K. A continuous gradient of hole production was successfully achieved in the p-type PbTe only by heat-treatment using a temperature gradient. (Received October 22, 2001; Accepted December 27, 2001) Keywords: carrier concentration gradient, thermoelectric material, lead telluride, thermodynamic equilibrium, formation energy, heattreatment, temperature gradient
1. Introduction
Figure-of-merit, Z/K-1
Low carrier conc.
Lead telluride (PbTe) is a typical thermoelectric material for application in the temperature range of 300 to 700 K.1) It has already been used for power generating devices in special environments, i.e. space, deep sea, desert, polar regions, etc.2) Its more common applications need much higher thermoelectric energy conversion efficiency η. The higher η is achieved by the higher figure-of-merit Z (= α 2 /(ρκ)), where: α = Seebeck coefficient, ρ = electrical resistivity, and κ = thermal conductivity. For PbTe the value of Z varies with temperature, and the maximum Z is at the corresponding temperature Tm , as shown in Fig. 1. The Tm can be increased by increasing the carrier concentration n.3) When n changes gradually in PbTe, Z can be kept high in a wide temperature range up to 700 K, (as indicated by a dotted line in Fig. 1). The optimum n gradient is 2 × 1024 m−3 –1 × 1025 m−3 . The n gradient is effective in improving the η of thermoelectric material.4) Only a step-like gradient of n has been achieved by joining two segments with different values of n.5) The effective maximum power Pmax was higher by 20% than that of the constituent parts.5) To date only the two-step gradient has been effective in improving Pmax , that is η, however a continuous gradient is much more desirable. The difficulty of controlling n is, however, an obstacle to the formation of a continuous gradient which as yet has not been achieved. We need a new technique instead of the ordinary techniques such as joining, powder metallurgy and hot pressing. PbTe has been reported to change n by heat-treatment.6, 7) If n changes continuously by heat-treatment using a temperature gradient, then heat treatment using a temperature gradient may form a continuous gradient of n. In the present paper the effect of heat-treatment temperature on n of the p-type PbTe has been investigated and a heat-
High carrier conc.
FGM
Tm
Tm
300
700 Temperature, T/K
Fig. 1 Relationships between carrier concentration and figure-of-merit.
treatment process to form a continuous gradient of n has been newly developed. 2. Experimental Pb(6N) and Te(6N) were weighed at an atomic ratio of 1:1 and sealed in a quartz ampoule in a vacuum of 1 × 10−4 Pa. The contents were melted and stirred by a rocking-furnace and subsequently grown unidirectionally at a cooling rate of 4 Kh−1 under a temperature gradient of 1 Kmm−1 to obtain a stoichiometric PbTe ingot. Pb(6N) and Te(6N) were also weighed at Pb : Te = 1 : 2 and vacuum-sealed in a quartz ampoule to prepare the hole-doping source by water quenching from the melting point. The as-grown stoichiometric ingot and doping source were cut to a size of 2 mm×3 mm×30 mm
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Y. Shinohara, Y. Imai and Y. Isoda
PbTe
PbTe+Te
Quarts ampoule
20mm
Table 1 Change in electrical properties of stoichiometric PbTe by thermal exposure at 900 K for 1 h.
Before exposure After exposure
ρ( m)
n (/m3 )
µ (m2 /Vs)
7.4 × 10−5
1.0 × 1024
0.087 0.089
1.4 × 10−5
5.1 × 1024
Fig. 2 Photograph of a quartz ampoule with stoichiometric PbTe specimens and a hole-doping source (PbTe + Te).
Heating
19mm
Specimen
900K
340K
Cooling Fig. 3 Schematic view of the heat-treatment of PbTe using a temperature gradient of 340–900 K.
and vacuum-sealed together in the same quartz ampoules, as shown in Fig. 2. The ampoules were thermally exposed at 900 K for 1 h and subsequently air-cooled. The thermally exposed stoichiometric PbTe specimens were taken out from the ampoules and vacuum-sealed again one by one in quartz ampoules. These ampoules were heattreated in a temperature range of 400 to 900 K for 24 h and subsequently air-cooled to clarify the effects of a heattreatment temperature gradient on the electrical properties of the PbTe specimens. The 19 mm long thermally exposed stoichiometric specimen was heat-treated for 24 h in Ar using a temperature gradient, as shown in Fig. 3. The upper and lower temperatures were kept at 900 and 340 K during the heat-treatment process. The temperature differential given to the specimen was 560 K/19 mm. After the heat-treatment the n distribution in the longitudinal direction was evaluated. Electrical resistivity (ρ) and Hall coefficient (RH ) were measured at room temperature by the DC method at high speed and high resolution.8) A magnetic field of 0.5 T was applied during the RH measurement. The value of n was calculated from RH data assuming that the PbTe was perfectly degenerated. 3. Results and Discussion The as-grown stoichiometric PbTe showed the p-type conduction with a Hall mobility µ of 0.087 m2 V−1 s−1 and an n
Fig. 4 Thermal exposure of stoichiometric PbTe specimens in (PbTe + Te) vapor at 900 K for 1 h.
of 1.0 × 1024 m−3 . The value of µ is similar to the literature data,9) which indicates an ideal purity for PbTe. After thermal exposure with a hole-doping source at 900 K for 1 h the n of the stoichiometric PbTe had increased by a factor of 5 (as shown in Table 1). On the other hand, the µ was not changed by the thermal exposure, which means that the transport property of holes is independent of the thermal exposure. The vapor pressure of PbTe at 900 K is ∼ 13 Pa, whereas that of Te is 1.3 kPa.10) During thermal exposure, the stoichiometric PbTe is held in (PbTe + Te) vapor, as depicted in Fig. 4, however, the mixture consisted mainly of Te vapor. Since PbTe vapor has no effect on the stoichiometric PbTe, Te vapor must act as a kind of p-type dopant. From the activation energy of Te self-diffusion in PbTe,11) it seems that the thermal condition of 900 K −1 h is insufficient for Te atoms to diffuse from the surface into the 2 mm thick specimens. The hole-formation mechanism by Te vapor is unknown, but it is believed that vacancies at Pb sites of PbTe structure are closely related with hole-formation and that one vacancy forms two holes. It is probable that Te vapor induces vacancies at Pb sites. The thermally exposed stoichiometric PbTe specimens were heat-treated in a temperature range of 400 to 900 K for 24 h. The change in ρ of the specimens is shown as a function of the heat-treatment temperature in Fig. 5. ρ increased with an increasing heat-treatment temperature of between 300 and 500 K, while ρ decreased with an increasing heat-treatment temperature of between 500 and 900 K. A maximum value of ρ was measured at 500 K. Whether the heat treatment is above 500 K or not is important to determine the temperature dependence of ρ. The change in n of the specimens is also shown as a function of the heat-treatment temperature in Fig. 6. n decreased continuously with an increasing heat-treatment temperature of between 300 and 500 K, while it increased continuously with an increasing heat-treatment temperature of between 500 and 900 K. A minimum value of n was measured at 500 K, which is a critical temperature for both n and ρ.
Graded Design of Carrier Concentration in Thermoelectric PbTe System by Heat-treatment
0.0003
25
0.0002
Carrier Concentration, n/m-3
m
10
/ Electrical Resistivity,
387
16kJ/mol
24
10
0.0001 Before H.T.
452K-1050h
0 200
400
600
800
1000
Heat Treatment Temperature, T/K Fig. 5 The variations of electrical resistivity of PbTe as a function of the heat-treatment temperature.
23
10
0.001
0.002
Heat Treatment
0.003
0.004
Temperature,T-1/K-1
Fig. 7 Arrhenius plots of carrier concentration of heat-treated PbTe.
Carrier Concentration, n/1024m-3
6
1.0 × 1023 m−3 by heat-treatment at 452 K–1050 h.7) When a much longer heat-treatment time is applied during this process, the temperature corresponding to a minimum n should be shifted to a temperature below 500 K. Arrhenius plots of the n values are shown in Fig. 7. The plot is linear between 600 K and 800 K. The reported value of 1.0 × 1023 m−3 at 452 K–1050 h7) is accepted as being on the extrapolated line from the slope between 600 and 800 K. The line reveals the n to be in thermodynamic equilibrium. The formation energy of holes is generally expressed by the following equation: Q , (1) n = n 0 exp − kT
4
2
0 200
400
600
800
1000
Heat Treatment Temperature, T/K Fig. 6 The variations of carrier concentration of PbTe as a function of the heat-treatment temperature.
Figure 6 is a mirror image of Fig. 5. The µ of the specimens was almost independent of heat-treatment temperature. Heattreatment of the specimens causes the change in n, leading to the change in ρ. The change in n by heat-treatment can be interpreted as follows: the vacancy concentration n v at Pb sites (which determines n) is changed by the heat-treatment. A PbTe specimen that is thermally exposed at 900 K for 1 h contains n v almost in thermodynamic equilibrium. When this specimen is heattreated at a temperature below 900 K for 24 h, n v changes to a lower value in thermodynamic equilibrium at the heattreatment temperature. The heat-treatment time of 24 h is long enough to decrease n v in thermodynamic equilibrium at 500 K or more, while it is not enough at 500 K or less. The vacancies created in the PbTe specimen that was thermally exposed at 900 K for 1 h remain at 500 K or less without extinction. As a result, n increases by heat-treatment below 500 K and there is a minimum value of n measured at 500 K. It is reported that the n of the stoichiometric PbTe was
where n 0 , Q and k are a constant, formation energy of holes and Boltzmann’s constant, respectively. From the slope, the Q is determined to be 16.4 kJmol−1 . As was mentioned previously within this paper, one vacancy forms two holes. The equilibrium constant K of vacancy-formation can be described as follows: Pb2+ + Te2− → (Vacancy)2+ + Pb + Te2− → (Vacancy) + 2e+ + Pb + Te2− [Vacancy][e+ ]2 [Pb] [Pb2+ ] Q K = K 0 exp − , kT K =
(2) (3) (4)
where K 0 and Q are a constant and the formation energy of vacancies respectively. From eqs. (3) and (4), log[e+ ] ∝ −
Q 2k
(5)
The value of Q is estimated to be 33 kJmol−1 (0.34 eV). This value is almost equal to the band gap energy of 0.36 eV for PbTe above 450 K.12) The intrinsic conduction region affects the formation of vacancies at Pb sites. The number of vacancies at the Pb sites of a PbTe structure is closely related to excitation of electrons from the valence band. On the other
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Y. Shinohara, Y. Imai and Y. Isoda
Temperature, T/K
800
600
400
0
10
20
Distance from Cooled Edge, d/mm
hand, n above 800 K tends to be saturated as shown in Fig. 7. This result suggests that too high a value of n v is unstable in a PbTe structure. The temperature of 800 K may be the thermal stability limit of the thermoelectric properties of p-type PbTe. The 19 mm long thermally exposed specimen was heattreated for 24 h using a temperature gradient of 340–900 K. Figure 8 shows the temperature distribution inside the specimen in the longitudinal direction during heat-treatment. The temperature gradient in the specimen increases with temperature: thermal conductivity κ decreases with increasing temperature. The critical temperature of 500 K is just at the center of the specimen, 10 mm distant from the cooled edge. It is predicted that the n distribution in the longitudinal direction has a minimum about 10 mm distant from the cooled edge. A photograph of a specimen heat-treated using a temperature gradient is shown in Fig. 9. The specimen keeps its metallic luster at 0–7 mm from the cooled edge, while loses it at 7–19 mm. This is caused by PbTe evaporation from the surface. No crack formation by the heat-treatment is observed although the thermal expansion coefficient of PbTe is as high as that of stainless steel.13) The specimen was cut into 13 pieces in the longitudinal direction and six pieces, which are marked in Fig. 9, were selected for Hall coefficient measurement to determine the n distribution in the longitudinal direction. Figure 10 shows the n distribution formed by the heattreatment using a temperature gradient of 340–900 K. The n decreased continuously with increasing distance in the range of 0–10 mm from the cooled edge, while the n increased within the range 10–19 mm. A minimum n was measured at a distance of 10 mm, as is predicted above. The n changes continuously within the specimen, according to the temperature gradient. The continuous gradient of the value of n in p-type PbTe was successfully formed by heattreatment using a temperature gradient of 340–900 K. For a heat-treatment time of 24 h, a temperature gradient from 340 to 500 K can form a decreasing gradient of n, whilst the gradient from 500 to 900 K can form an increasing gradient. When the heat-treatment time is longer than 24 h, the critical temperature should be lower than 500 K. The obtained n gradient of 0.3–5 × 1024 m−3 is lower than the optimum of
Fig. 9 PbTe specimen heat-treated using a temperature gradient of 340–900 K.
6
Carrier Concentration, n/1024m-3
Fig. 8 Temperature distribution in PbTe during heat treatment.
4
2
0 0
10
20
Distance from Cooled Edge,d/mm Fig. 10 Carrier concentration distribution formed in PbTe by heat-treatment.
2 × 1024 m−3 –1 × 1025 m−3 . Increasing the thermal exposure temperature can increase the maximum value of n.6) We can therefore adjust the n gradient by adjusting the thermal exposure temperature. Figure 11 shows the variations of n as a function of temperature using a temperature gradient of 340–900 K. There is almost no difference between Figs. 7 and 11. The formation energy of holes calculated from Fig. 11 is 16 kJmol−1 , as well as from Fig. 7. Whether the temperature distribution inside the specimen is uniform or gradiated has almost no effect on n. The heat-treatment data in a uniform temperature field, such as in Fig. 7, can be applied to designing the n distribution within a temperature gradient. When the cross section area of the specimen is changed in the longitudinal direction, the temperature distribution is different from that shown in Fig. 8. The shape of the specimen can be determined on the basis of the data on the temperature dependency of κ. We will be able to design
Graded Design of Carrier Concentration in Thermoelectric PbTe System by Heat-treatment 25
Carrier Concentration, n/m-3
10
24
10
23
10
0.001
0.002
Heat Treatment
0.003
0.004
Temperature,T-1/K-1
Fig. 11 Arrhenius plots of carrier concentration formed in PbTe by heat-treatment.
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(2) The thermally exposed stoichiometric PbTe was heattreated at temperatures from 400 to 900 K for 24 h. The value of n decreased with an increasing heat-treatment temperature of between 300 and 500 K, whilst the value of n increased with an increasing heat-treatment temperature of between 500 and 900 K. The minimum value of n was measured at 500 K. (3) The formation energy of holes was determined to be 16.4 kJmol−1 . (4) The 19 mm long thermally exposed stoichiometric PbTe sample was heat-treated using a temperature gradient of 340–900 K for 24 h. The n of the heat-treated PbTe changed continuously according to the temperature distribution. (5) A continuous gradient of the value of n was successfully formed in the p-type PbTe by heat-treatment using a temperature gradient. This study was performed through Special Coordination Funds of the Ministry of Education, Culture, Sports, Science and Technology of the Japanese Government. REFERENCES
the n distribution from the κ data through the following procedure: (the κ data) → (the shape of the specimen) → (the temperature distribution) → (the n distribution). We have opened a door to the designed n distribution in the ptype PbTe on the basis of the temperature dependency of n and κ. 4. Conclusions In order to develop a new process of forming a gradient in PbTe by only using a heat-treatment process, the effects of heat-treatment on the n of the p-type PbTe have been investigated during the heat-treatment of a sample of p-type PbTe using a temperature gradient of 340–900 K. The conclusions are as follows: (1) The as-grown stoichiometric PbTe was p-type with an n value of 1.0 × 1024 m−3 . Vacuum thermal exposure with the Te-rich PbTe at 900 K for 1 h increased the n value to 5.1 × 1024 m−3 .
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