## Abstract

PbSeTe-based quantum dot superlattice structures grown by molecular beam epitaxy have been investigated for applications in thermoelectrics. We demonstrate improved cooling values relative to the conventional bulk (Bi,Sb)_{2}(Se,Te)_{3}thermoelectric materials using a n-type film in a one-leg thermoelectric device test setup, which cooled the cold junction 43.7 K below the room temperature hot junction temperature of 299.7 K. The typical device consists of a substrate-free, bulk-like (typically 0.1 millimeter in thickness, 10 millimeters in width, and 5 millimeters in length) slab of nanostructured PbSeTe/PbTe as the n-type leg and a metal wire as the p-type leg.

Solid-state thermoelectric (TE) cooling and electrical power generation devices have many attractive features compared with other methods of refrigeration or electrical power generation, such as long life, no moving parts, no emissions of toxic gases, low maintenance, and high reliability. However, their use has been limited by the relatively low energy conversion efficiency of present thermoelectrics. Quantum dot superlattice (QDSL) structures, which have a delta-function distribution of density of states and discrete energy levels due to three-dimensional quantum confinement, a potentially more favorable carrier scattering mechanism, and a much lower lattice thermal conductivity, provide the potential for better thermoelectric devices. The molecular beam epitaxial (MBE) growth of self-assembled QDSL materials on planar substrates using the Stranski-Krastanov growth mode yields improved TE figures of merit (1, 2). Self-assembled quantum dot materials represent just one of a number of new approaches (3) being investigated in order to enhance TE performance. Here, we describe the fabrication of a cooling device in a test setup from nanostructured film materials and the device's characteristics obtained from such material. We also discuss the growth and properties of n-type and p-type QDSL film TE materials and background information on the band structure and properties of PbSnSeTe alloy materials (in which the 300 K energy gap can approach zero) [see supporting online material (SOM) Text]. Also presented in the SOM Text are results that indicate conservatively estimated intrinsic ZT values of 2.0 at 300 K have been obtained for PbSnSeTe. Further improvements are anticipated, because both the QDSL materials and devices are not optimized.

#### Characterization of thermoelectrics.

Both the efficiency and coefficient of performance of a TE device are directly related to the dimensionless materials (or intrinsic) figure of merit ZT.(1)where *T* is the temperature, S is the Seebeck coefficient or thermopower, ρ is the electrical resistivity, and κ is the thermal conductivity (which includes both the electronic and lattice contributions) used to characterize thermoelectrics. Conventional TE cooling materials are bulk solid solution alloys of Bi_{2}Te_{3}, Bi_{2}Se_{3}, and Sb_{2}Te_{3}, with the best materials having ZT room temperature values of approximately 1.0 (4). In order to enhance ZT, a high Seebeck coefficient, an increased electrical conductivity, and a decreased thermal conductivity are needed, but these materials properties often counter each other. Previously, epitaxially grown PbSeTe/PbTe (ternary) QDSL yielded estimated 300 K TE figure of merits of 0.9 (1,2). The results here indicate that our initial objective of demonstrating that high ZT values (measured in the 1.3 to 1.6 range at 300 K) are possible with QDSL materials and that PbSeTe-based QDSL materials are capable of achieving larger temperature differential values than conventional bulk (Bi,Sb)_{2}(Se,Te)_{3}solid solution alloys. It is helpful to define an extrinsic or operating device thermoelectric figure of merit as(2)Z_{d}T is reduced from the intrinsic ZT by extraneous or parasitic factors such as those listed below. S_{u} is the sum of the absolute values of the n-type and p-type Seebeck coefficients; R_{u} is the total electrical resistance and includes both the thermoelement resistances and the contact resistances; and*Κ*
_{u}is the total thermal conductance including the thermoelement thermal conductances, junction, or contact thermal conductance, as well as other parasitic effects, such as thermal radiation absorbed on the surfaces around the cold junction surface areas and heat absorption at the cold junction from the thermocouple lead wires used to measure the cold junction temperature. If the parasitics are negligible, then Z_{d}T for a standard unicouple can be optimized by adjustments in device geometry, which makes R_{u}Κ_{u} a minimum. This requirement leads to (R_{n}/K_{n}) = (R_{p}/K_{p}), where R_{u} = R_{n} + R_{p} and K_{u} = K_{n} + K_{p} (R_{n} and R_{p}are the electrical resistances of the individual n-type and p-type thermoelements, respectively; K_{n} and K_{p }are the thermal conductances of the individual n-type and p-type thermoelements, respectively). The intrinsic ZT for a unicouple with negligible parasitics can be written as(3)Bi_{2}Te_{3}-alloys are not competitive with large-scale commercial cooling and power generation applications based on fluids and gases. TE ZT values greater than 3.0 are needed to have the potential to compete even in a small part of this market. Nevertheless, niche applications for bulk TE devices have developed, such as small portable refrigerators and picnic coolers and the cooling and temperature stabilization of diode lasers.

#### Performance characteristics of a TE cooler device.

The net rate of transfer of heat or cooling rate (5), E_{c}, out of the cold junction region of a unicouple device structure with electrical current flowing is defined as(4)ΔT is the difference in temperature between the hot junction temperature, T_{h}, and the cold junction temperature, T_{c}; i.e, T_{h} – T_{c}. I is the electrical current flowing through each TE element of the device. The thermoelements are connected electrically in series and thermally in parallel. If Eq. 4 is solved for ΔT, it is seen that the ΔT is increased upon adjusting experimental conditions such that E_{c} ∼ 0 and I is increased until ΔT reaches a maximum. The maximum attainable temperature difference, ΔT_{max}, may be determined by maximizing Eq. 4 with respect to I_{u}. This leads to the condition(5)By inserting Eq. 5in Eq. 4 and using *E*
_{c} = 0, we obtain the well-known result(6)Upon using Eqs. 2 and 6, we obtain(7)Quadratic Eq. 7 can be solved for T_{c} to yield the minimum attainable temperature. The above equations assume that S_{u},R_{u}, and K_{u} are averaged quantities over the entire ΔT range.

#### Fabrication and characteristics of the film TE cooling device.

For the device demonstration performed, n-QDSL sample B (Table 1) which was MBE grown on a 18 mm by 18 mm BaF_{2} substrate wafer, was used as the starting material. On another wafer from the same n-QDSL growth run B, a Seebeck coefficient of –208 μV/K and an electrical resistivity of 1.71 mΩ-cm were measured (Table 1). n-QDSL B has an unknown thermal conductivity that is determined in the device test setup described here. The n-QDSL B film/BaF_{2} substrate wafer was cleaved to size and the 11 mm by 0.104 mm ends immediately metallized in a glove box that contained an inert atmosphere so that oxide formation on the cleaved sample surfaces was minimized. After cleaving, the measured dimensions of the n-QDSL B film were a thickness of 0.104 mm, length of 5.0 mm, and width of 11.0 mm for the n-type TE leg. Then the BaF_{2} substrate was removed by dissolution. A gold ribbon 25 μm thick and 250 μm wide with a length of 5 mm was used in place of the conventional p-type TE leg. Gold is a p-type metal (an n-type metal wire would have worked as well) with a 300K Seebeck coefficient of +2.9 μV/K, electrical resistivity of 2.4 μΩ -cm, and a thermal conductivity of 2800 mW/cm-K with a ZT of 0.0.

A schematic of the generic one-leg TE refrigerator test setup is shown (Fig. 1). The bulk thermoelectric device made from a thick film of n-type PbSeTe/PbTe QDSL material (current flow in-plane of QD superlattice) is displayed as a photograph (Fig. 2). Not shown is the enclosure of the test device, which enables a good vacuum of about 10^{−5} Torr to be achieved within the chamber containing the device. ΔT versus I data was collected and is shown in graphical form (Fig. 3). The TE demonstration test device cooled the cold junction region to a temperature T_{c} = 43.7 K below the hot junction temperature, which was maintained at approximately T_{h}=299.7 K by large copper heat sinks. (Good metal plating and good soldering techniques are necessary in order to obtain high ΔT_{max} values). The T_{c} thermocouple (TC) is embedded in the liquid solder used to join the T_{c} TC to the thermoelement and positioned as close to the metallized layer as possible (Fig. 2). The T_{h} TC was also embedded in liquid solder. Chromel/alumel thermocouples (type K) with a wire diameter of 0.015 cm and a length of 17 cm were used to measure T_{h} and T_{c}. Care was taken to ensure that the electrical current had no influence on the TC measurements. Tests were performed on the demonstration device to monitor the TC reading with and without electrical current flowing, and zero voltage pickup by the TC was confirmed. TCs were soldered to both the T_{c} and the junction with the heat sink to measure T_{c} and T_{h}. The electrical current for ΔT_{max} = 43.7 K was 700 mA, and the electrical power input was 87 mW. The ΔT_{max} = 43.7 K temperature differential (without any forced heat removal by blowing air or running water) was much greater than the recently reported value of ΔT_{max} = 32.2 K for a similar single one-leg Bi_{2}Te_{3}/Sb_{2}Te_{3}superlattice device (cross-plane current flow of superlattice and no quantum dots) that has an equivalent hot junction temperature (6).

To obtain an indication of the parasitic heat flows in our test setup, we used a n-type bulk (Bi,Sb)_{2}(Se,Te)_{3}solid solution alloy material (7, 8). The (Bi,Sb)_{2}(Se,Te)_{3} alloy sample has a measured 300 K Seebeck coefficient of –228 μV/K, electrical resistivity of 1.24 mΩ-cm, and a thermal conductivity of 13.6 mW/cm-K with a 300 K materials ZT = 0.9 (Eq. 1). A gold ribbon was again used for the p-type leg. Because all materials properties have been measured for this unicouple, the intrinsic (ZT)_{one-leg} = 0.34 (Eq. 3) for the (Bi,Sb)_{2}(Se,Te)_{3} alloy/Au unicouple. If we made a unicouple of the n-type thermoelement and an identical p-type thermoelement, then (ZT)_{two-leg} = 0.9 (Eq. 3); i.e., the intrinsic (ZT)_{two-leg} of the latter device would be a factor of 2.65 larger than the former (ZT)_{one-leg}device. For the case of no parasitics, the intrinsic ΔT_{max} = 38.8 K (Eq. 6) for the one-legged (Bi,Sb)_{2}(Se,Te)_{3} alloy/Au unicouple device (5). If we made a unicouple of the n-type thermoelement and an identical p-type thermoelement, then the intrinsic ΔT_{two-leg max }= 75.6 K (Eq. 6); i.e., the intrinsic ΔT_{one-leg max }of the latter device would be a factor of two larger than the former ΔT_{one-leg max }device. The (Bi,Sb)_{2}(Se,Te)_{3} alloy material was cleaved to approximately the same aspect ratio L/A as the QDSL material (where A is the cross-sectional area and L is the length of a TE leg) from a bulk, homogeneous single crystal quaternary alloy, which was grown and characterized at the University of Virginia (8), the contacts metallized, and the ΔT versus I data was collected. The test device cooled the cold junction region to a temperature (*T*
_{c}) 30.8 K (lower arrow in Fig. 3) below the hot junction temperature (T_{h}), which was maintained at 297.7 K by large copper heat sinks. It is believed that the extrinsic ΔT_{one-leg max} = 30.8 K is 8 K lower than the intrinsic ΔT_{one-leg max} primarily because of parasitics.

Calculations for n-QDSL A (Table 1) using Eq. 3 indicate that a p-type QDSL leg with TE properties identical to the n-type would yield a QD unicouple with an intrinsic ZT of approximately 1.6, which corresponds to intrinsic ΔT_{two-leg max} = 103 K with T_{h} = 300 K. We expect greater cooling differential to be obtained in the future, as compared to our present unoptimized device made from the first bulk-like thick film of PbSeTe/PbTe nanostructured material, by using quaternary QDSL material for n-type and a similarly high ZT p-type leg. The calculated maximum cooling values from 300 K for a standard intrinsic two-leg TE “refrigerator” versus the 300 K intrinsic ZT values are displayed (Fig. 4). The thermal conductivity of the QDSL material was calculated as follows: First, Z_{d}T = 0.40 was calculated using Eq. 7 from ΔT_{max} = 43.7 K and*T*
_{c} = 256 K measurements. Then, using extrinsic Z_{d}T = 0.40 and assuming Z = Z_{d} in Eq. 3, we calculate the only unknown, i.e., κ of the QDSL material, as κ = 5.8 mW/cm-K. Z cannot be less than Z_{d}. A higher Z than Z_{d} would result in an even lower κ. Upon subtracting the electronic part, we obtain 3.3 mW/cm-K for the lattice thermal conductivity of the QDSL sample. For the (Bi,Sb)_{2}(Se,Te)_{3} solid solution alloy sample,Eq. 7 yields extrinsic Z_{d}T = 0.26. Assuming Z = Z_{d} in Eq. 3, we calculate κ = 20.6 mW/cm-K, which does not agree with the κ value measured on the material at the University of Virginia using a comparison method (with quartz as a reference material) due to parasitics. A second method was used to measure the total thermal conductivity for the two devices. This method (9, 10) uses ΔT versus I data (Fig. 3) at low electrical currents (0 to 25 mA for both polarities of the current). The defining equation is(8)where T_{av} is the average temperature. The I^{2}R term can be ignored in Eq. 4 because Joule heating is negligible at such small electrical currents. There are advantages of this method, even when one end of the sample is held in contact with a heat sink (11), as in these experiments. The average values (for both polarities of the electrical current) for the I and ΔT data for the n-QDSL B sample are 0, 10.2, 25.2 mA and 0, 1.3, 3.2 K, respectively. The average values (for both polarities of the electrical current) for the I and ΔT data for the Bi_{2}Te_{3}-based alloy sample are 0, 10.2, 25.2 mA and 0, 1.0 , 2.45 K, respectively. Applying the data to Eq. 8, we obtain κ = 6.2 mW/cm-K for the n-QDSL B sample. Similarly, κ =15.9 mW/cm-K is derived for the n-type bulk (Bi,Sb)_{2}(Se,Te)_{3} solid solution alloy sample. The second method needs high ZT's and good contacts in order to obtain reasonable values for κ. Also, the above κ values are uncorrected for K dependent parasitics (4, 10,11). An estimate of the *K*s and *R*s of the two test devices was obtained by calculating the intrinsic or materials values of K_{uQDSL/Au} = K_{QDSL}+ K_{Au}, K_{u(Bi,Sb)2}
_{(Se,Te)3}
_{/Au}= K_{(Bi,Sb)2}
_{(Se,Te)3}+ K_{Au}, R_{uQDSL/Au} = R_{QDSL} + R_{Au}, and R_{u(Bi,Sb)2}
_{(Se,Te)3/Au}= R_{u(Bi,Sb)2}
_{(Se,Te)3}+ R_{Au}, from the measured thermoelectric properties of the individual thermoelements and their dimensions for the two devices as 0.00044 W/K, 0.00061 W/K, 0.094 Ω, and 0.074 Ω, respectively. The calculated K_{u}'s and R_{u}'s are first-order estimates of the actual values, and many factors may change their values, such as the quality of the plating and soldering techniques used to form electrical contacts.

#### Conclusions.

TE cooling test devices have been made from PbSeTe/PbTe QDSL material. 43.7 K of cooling below room temperature was measured, even though one leg was a zero ZT gold wire. This compares to 30.8 K of cooling for the conventional (Bi,Sb)_{2}(Se,Te)_{3} material in the same test setup and the same hot junction temperature and about the same aspect ratio. We believe a TE material has been found that is a better room temperature cooler material than bulk (Bi,Sb)_{2}(Se,Te)_{3} solid solution alloy material. Device measurements indicate the attainment of device Z_{d}T and a materials or intrinsic ZT in the range of 1.3 to 1.6 at room temperature. The enhanced TE device performance at 300 K of the PbSeTe/PbTe QDSL material is believed to be (at this point in time) almost entirely due to a high density of quantum nanodots with essentially 100% PbSe composition embedded in a three-dimensional slab matrix of PbTe. As described in the SOM, the first quaternary PbSnSeTe QDSL TE materials have been grown by MBE and have conservatively estimated intrinsic ZT values of 2.0 at 300 K. Further improvements are anticipated, as both the materials and devices are not optimized.

## Supporting Online Material

www.sciencemag.org/cgi/content/full//297/5590/2229/DC1

SOM Text

References and Notes

Fig. S1

Tables S1, S2, S3