Thermal Matching of a Thermoelectric Energy Scavenger with the ...

the wrist, has usually similar or less thickness, therefore, theradiator can be moved out of the convection layer and theheat transfer into the air improves.Second, if using small-size thermopiles, like, e.g.,MEMS thermopiles, the TEG becomes almost empty [3], sothat the plate-to-plate radiation heat exchange can beeffectively suppressed using the plates with low emissioncoefficient.Third, proper positioning of the TEG on human beingoffers much lower thermal resistance of the body than itsaverage value [2, 3].Forth, a small radiator instead of a cold plate effectivelyreduces the thermal resistance of ambient air [2].Finally, the thermal resistance of the body itself can bedecreased using a radiator as shown in [3] through changingthe local heat flow in humans under the device.Thermal matching of MEMS thermopilesThanks to the laws of scaling, small MEMS thermopilesFigure 4. Matching of the MEMS TEG with the ambience(squares) and parallel matching of thermopiles (circles) tothe air in a TEG (similar to points 2-3 in Fig. 2).can be as effective as commercial thermopiles. The rules ofdesigning the TEG remain the same as discussed above. Atall thermally conducting pillar, however, has to be added tothe TEG for thermal interconnection of the thermopile chipwith the well-separated plates [3]. Fig. 4 illustrates thermalmatching of 3 µm-tall BiTe micromachined thermopile with1 µm 2 leg cross section of the design reported in [4] in a3 cm × 3 cm TEG at a temperature of 22 °C. Taking intoaccount the helpful hints of the previous section, a pinfeaturedradiator [2] replaces the cold plate and provides athermal resistance in the human body of 200 cm 2 K/W.Numerical calculations show that even the TEG withone-stage 3 µm-tall thermopile on humans, can beeffectively thermally matched with the ambience, providingR TEG,0 = 1.4R amb,opt , which shows potential advantage of theMEMS thermopiles for wearable devices as compared withthe existing industrial technology. Comparing the parallelmatching of two resistors composing the TEG, Fig. 1, onecan notice that the thermal matching required (squares inFigs. 2, 4) calls for smaller thermal resistance of the TEG incase of commercial thermopiles, Fig. 2, and for the largerone in case of MEMS thermopiles, Fig. 4. One can mentionthat despite very small height of the micromachinedthermopile, a power exceeding 16 µW/cm 2 can be obtained.Thermal matching in wearable devices of tomorrowApplication of the thermal matching for designing theTEGs with different types of thermopiles gives the limit forpower generation on human beings equal to 30 µW/cm 2 (on24-hour average) at an ambient temperature of 22 °C and aZT of 1. The TEGs fabricated in 2005-2006, have alreadyclosely approached this limit producing 20 µW/cm 2 at a ZTof about 0.8 – 0.85.The modeling of advanced MEMS thermopiles withlarge aspect ratio [5] shows that in order to make universalwearable thermoelectric energy scavenger for all seasons,the thermal matching must be performed for the airtemperatures very close to skin temperature, e.g., for 35 °C.The smaller lateral size of the thermocouple legs is neededas compared with the TEG optimized to 22 °C, in addition,the number of thermocouples must be more than double. TheTEG then will produce over 2 V at an air temperature of 35°C which is more than enough to power advanced electroniccircuits. Therefore, wearable devices with such thermopileswill be powered all year round. The other approach is to uselarge rechargeable Li cell to keep self-powered devicesworking when the temperature difference minimizes insummer time. Then, the matching is to be performed for atypical ambient temperature, e.g., to 22 °C. The thermalmismatching in summer does not exceed about 10% becausethe thermal resistance of the body decreases whileapproaching 36 °C air temperature. According to themodeling, this device still produces a power of 0.5 µW/cm 2at a voltage of 1.1 V at 35 °C, however, the powerproduction becomes only periodical within the 35–37 °C; itstill occurs due to natural fluctuation of the air and skintemperatures in a real life.ConclusionsThermal matching of energy scavengers to the ambienceis required to maximize the generated power. It serves as athermal equivalent of electrical matching of a generator to itsload. The derived thermal matching equations result in aspecific design of TEGs for autonomous devices, whichinclude radiator, multi-stage commercial thermopiles or amicromachined thermopile on a tall pillar, and at leastseveral millimeters separation in between the plates of theTEG. It is shown that the thermal optimization is valid forany thermopile irrespective of its particular design. Thedesign method is extensively tested in applications on man.In a moderate climate, a power of about ZT/30 mW/cm 2 onaverage can be reached. This value is a limit imposed bythermal matching conditions and by personal acceptance ofthe device on a body. The energy scavengers fabricated in2005-2006, which are thermally matched to theenvironment, show power generation near the theoreticallimit.References1. Kishi, M., Nemoto, H., Hamao, T. et al, “Micro-ThermoelectricModules and Their Application to Wristwatchesas an Energy Source”, Proc 18 th Int Conf on Thermoelectrics(ICT), Aug. 29-Sept. 2, 1999, pp. 301-307.2. Leonov, V., Torfs, T., Fiorini, P., Van Hoof, C,“Thermoelectric Converters of Human Warmth for