Material synthesis and module fabrication

Figure 1a,b show the structure of the thermoelectric module. The thermoelectric material at the heart of the module consists of p-type 10/50 Å Bi 2 Te 3 /Sb 2 Te 3 superlattice and n-type δ-doped Bi 2 Te 3−x Se x , both of which are grown heteroepitaxially using metalorganic chemical vapour deposition18. The n-type structure is grown by periodically interrupting the growth of Bi 2 Te 3−x Se x and dosing the flow with Te and Se species. This δ-doping process can result in an increase in carrier concentration without a reduction in electron mobility. In the present experiment, 8.1-μm-thick thin films are grown and fabricated into cooling devices.

Figure 1: Cross-sectional views of a Bi 2 Te 3 -based thin-film thermoelectric module. (a) Illustration of thin-film-based thermoelectric module, showing top and bottom AlN headers, Cu traces and n-type and p-type active elements. L represents the length of the active elements, which is 8 μm in the present work. Figure is not to scale. (b) Scanning electron microscope image of the upper portion of a completed thin-film superlattice thermoelectric module. Scale bar, 250 μm. Full size image

The ZT values of the Bi 2 Te 3 /Sb 2 Te 3 superlattice materials used in this study have been previously measured by two different methods. One is the direct measurement of ZT by Harman method, which reported ZT>2 in ref. 18. The second method is the determination of individual thermoelectric properties, such as Seebeck coefficient, electrical resistivity and thermal conductivity, followed by calculation of ZT. The ZT values of representative p- and n-type materials used in the devices in the present study were estimated, using this indirect technique, to be 1.4 and 1.5, respectively. These data have been added in Table 1. These values were determined through measurement of the in-plane electrical resistivity and Seebeck coefficient of representative material along with an estimation of thermal conductivity via an in-couple-property-validation model. Details of this model are given in ref. 32. Both direct measurement and indirect measurement of ZT were conducted at T=300 K. These estimated ZT values by the indirect method are slightly less than the ZT data measured directly via the Harman method for similar materials in ref. 18.

Table 1 ZT data from representative p- and n-type thermoelectric materials. Full size table

In the device fabrication process, the top epitaxial surfaces of the p- and n-type materials are first metalized and then bonded to a common metalized AlN die header. Following chemical removal of the substrate, electrical contacts are fabricated on the exposed surface (typically with two n- and two p-type circular contacts designated as the 2N–2P configuration). This die header subassembly is then inverted and bonded to a second AlN header that contains the electrical traces used to power the module. As shown in Fig. 1b, the basic completed module structure has a 600 × 600-μm2 top header area and is 550 μm tall.

Electrical contact resistance

One significant barrier to reaching high cooling fluxes with thin-film thermoelectric modules is electrical contact resistance between the metal electrodes and the thermoelectric elements, especially for Bi 2 Te 3 -based materials with low intrinsic electrical resistivity (10−3 Ω cm)1,26. In the present experiment, two metallization methods (plated Au and evaporated Cr/Ni/Au metallization) and two different superlattice structures (standard structures and δ-doped structures) are explored to improve the electrical contact resistance. Au diffusion into the Bi 2 Te 3 lattice may very well be happening in the thermoelectric devices with plated Au contacts. The detailed effects of this potential Au diffusion need further study in the future.

Electrical contact resistivity has been measured using the transmission line measurement technique33, which measures the resistance across an annular gap as a function of gap width, fabricated on a broad area of metallization on the top surface of the thin-film superlattice material. The metalized contacts are formed on the thin-film superlattice surface as shown in Fig. 2, through the use of photoresist masks (gold is the metal contact, white is the thin-film superlattice surface) to form a set of six gaps with different gap widths. A four-wire probe is used to apply a small current across each gap (with two of the probe wires) and measure the voltage drop across the thin-film superlattice gap (with the other two probe wires). The gap resistance R g (measured ΔV over current) is a function of the gap width, governed by the relationship shown in equation (3).

Figure 2: Example of circular TLM patterns used for contact resistivity determination. In this measurement technique, six gaps of increasing widths (d=R 1 −R 0 ) are patterned onto the sample surface. The gold colour represents the metal contact, while the white is the thin-film superlattice (TFSL) surface. A four-wire probe is used to apply a small current across each gap and measure the voltage drop (ΔV). Full size image

The gap resistance R g versus gap width d data is fitted to equation (3), with R s (sheet resistance) and L T (transfer length) as fitting parameters. Contact resistivity ρ c can then be calculated as R s × L T 2 with units of Ω m2. In the present modules, plated Au was used as the contact to the source (top) side of the n-type δ-doped Bi 2 Te 3−x Se x , while evaporated Cr/Ni/Au was used as the source (top) side of the p-type Sb 2 Te 3 /Bi 2 Te 3 . Plated Au was used as the sink (bottom) side contact of both the n- and p-type elements. Electric contact resistivity for thin-film superlattice materials and selected contact metals is shown in Table 2. The R s , L T and ρ c values given in Table 2 are an average of the 6–8 experimental values measured for each material type and metallization scheme. The s.d. among these measurements is provided as well.

Table 2 Specific electric contact resistivity, as measured by transmission line model (TLM) technique, for superlattice thermoelectric elements with different structures and metallization. Full size table

Maximum temperature difference ΔT max

To evaluate the maximum temperature difference ΔT max , the thermoelectric module is placed directly on a water-cooled heat sink, maintained at 25 °C, and the T C and T H values are measured using 25 μm diameter thermocouples as a function of current supplied to the module, I. The voltage V is also monitored as a function of electric current under vacuum (pressure, P<1 mTorr), up to the current producing the maximum ΔT max , which defines the current value of I max .

The measured temperature difference and voltage behaviour of the thermoelectric module are given by28,34:

In the above equations, S is the module Seebeck coefficient, which is determined by the voltage between the two electrical leads, V, and the temperature difference between the two AIN headers, ΔT. The module electric resistance is denoted by R, and consists of the electric resistance of the n and p elements R element , the electric resistance of the metal traces R trace , and the electric contact resistance between the elements and the metal traces R contact . The module electric resistance R can be determined by the voltage between the two electrical leads, V, and the electrical current I through the electrical leads. K is the module thermal conductance between the two AIN headers. R th is the parasitic thermal resistance of the module, which is the difference between the module thermal resistance and the thermal resistance of the n and p thermoelectric element pair (Fig. 3). In the ΔT max measurements, there is no heat pumped by the module (cooling power, Q P =0) and the module parameter values can be determined by fitting equation (4) to the experimental ΔT as a function of I, V, T C and T H data, and similarly fitting equation (5) to the voltage data. The inclusion of a parasitic thermal resistance R th is necessary when considering thin-film thermoelectric modules, because the high-heat fluxes that occur within the module produce an internal element hot-side temperature T H int that is different from the externally measured value T H .

Figure 3: Thin-film thermoelectric module structure. The red and blue rectangles represent the p- and n-type active TE materials, respectively. Yellow represents the current traces and tan represents the ceramic bottom header of the module. Heat entering the module is given by Q P , while the heat being pumped out is given by Q sink . T C , T H and T H int are the cold-side temperature, externally measured hot-side temperature and internal element hot-side temperature, respectively. The green rectangles represent the parasitic thermal resistances R th , which reduce the externally observed ΔT value. Figure is not drawn to scale. Full size image

The upper portion of Fig. 4 shows ΔT versus I data for the module with the largest contact diameter (230 μm). The circles indicate the experimental external ΔT values measured with thermocouples, and the curve drawn through these points is the fit of equation (4) to the data, using a parasitic thermal resistance of R th =(3.08±1.98) K W−1. An external ΔT max value of 43.54 K is observed at an electric current of 14.8A, and the upper dashed curve shows the predicted internal ΔT (T H int −T C ) occurring inside the module, which has a maximum value of 49.3, 5.7 K higher than the external value. The difference in internal and external ΔT is caused by the internal thermal resistance R th , which reduces the external ΔT that can be measured by the thermocouples. The multidimensional fit of equation (4) to experimental ΔT external versus I data also yields the values of the ratios S/K (0.0228 μV W−1) and R/K (0.349 Ω K W−1).

Figure 4: Analysis of experimental data. (a) Experimental ΔT versus I data for the module with the largest effective contact diameter (230 μm) and the fit of equation 4 to the data. Blue dots represent experimentally measured data points, and the blue line represents the fit . The red dotted line indicates predicted internal temperature difference (T hint −T C ) versus I. (b) Corresponding V versus I data for the same module. The blue dots represent experimentally measured data points, and the red line represents the theoretical fit. Full size image

Figure 4b shows the voltage versus current data for the same module. R can be determined via a one-dimensional least squares fit of equation (4) to this experimental V versus I data, which subsequently allows for the calculation of K and S from the previously determined R/K and S/K values. The resulting values of the total Seebeck coefficient S=(450±48) μV K−1, thermal conductance K=(19.7±2.1) mW K−1 and electric resistance R=(6.87±0.01) mΩ are given in the legend of Fig. 4b. Details of this procedure have been described elsewhere34.

Maximum cooling flux q max

The cooling power for a thermoelectric module in the presence of a parasitic thermal resistance R th is shown in equation (6), where ΔT is the externally measured temperature difference28,34.

In the case of R th =0, equation (6) reduces to the standard thermoelectric heat-pumping equation35, where the maximum cooling power Q P occurs when I=ST C /R (which is I max ). To determine I max in the case of non-zero R th , the voltage dependence in equation (6) is eliminated using equation (5), and after some rearrangement the expression for Q P becomes:

Equation (7) is then differentiated with respect to I and solved numerically for the value of I that yields a zero of the resulting expression. The I max value is then substituted into equation (7), along with the individual fitted module parameter values to obtain the Q max value that is expected. The I max values calculated using equation (5) are found to agree with the experimentally observed values in these modules and are smaller than what is obtained from using the standard expression I max =ST C /R. The maximum cooling flux q max is calculated by dividing the total cooling power Q max by the top header area of the module, which is 600 × 600 μm2. The performance of four thin-film thermeoelctric modules with different contact diameters (that is, the packing fraction) is summarized in Table 3. The table shows the measured maximum cooling flux (q max =Q max /A T ), as well as the predicted value and a discrepancy of 13% is observed between the predicted and measured values. The coefficient of performance (COP) values were calculated at q max ; that is for ΔT=0 K. With the establishment of the q max value and ΔT values, the load lines can be determined, as shown in Fig. 5.

Table 3 Performance of thin-film thermoelectric modules of varying contact diameter (that is, packing fraction). Full size table

Figure 5: Load lines for each of the four measured modules of this work. The load lines are determined by the measurement of q max at ΔT=0K, and the measurement of ΔT max at q=0 W m−2. An additional data point for the case of ΔT=10 °C is included for the module with the largest contact diameter (230 μm). Full size image

In the case of the largest module, an additional data point that was obtained at ΔT=10 °C is also shown. The maximum temperature difference ΔT max should not be dependent on the module geometry, but the variation seen indicates a possible undetermined parasitic phenomenon may be present. Further studies are needed to identify this undetermined parasitic phenomenon.

It can be seen that a maximum cooling flux in excess of 250 W cm−2 is achieved in the thin-film Bi 2 Te 3 superlattice thermoelectric module with a contact diameter of 230 μm (that is, 48% packing fraction). This value is 25 times higher than is typically observed in commercial-off-the-shelf bulk thermoelectric modules (http://www.marlow.com) and more than 2.5 times better than commercial-off-the-shelf thin-film modules (http://www.lairdtech.com). The maximum cooling flux of the module was measured using two different methods, the Q-meter method by RTI and the non-contact IR method by University of Maryland.

Contact diameter and packing fraction

Figure 6 shows the dependence of maximum cooling power Q max as a function of the total element contact area A c (including both n and p contacts). The top header area A T is 600 × 600 μm2 for all of the modules tested. The packing fraction is the ratio of the total element contact area A c to the top header area of the module A T , and the module with a contact diameter of 230 μm has a packing fraction of 48%.

Figure 6: Q max versus total contact area data for the four thin-film thermoelectric modules of this work. Experimentally measured values are represented by red squares, and the corresponding theoretically predicted values are represented by blue diamonds. The dotted line represents a linear trendline fit to the experimental data. This trendline has been indexed to the origin and is expressed by the equation y=601.6x. Full size image