Another important factor is a response time (τ_P) of Peltier effect. Most of power devices release heat with high fluctuations. To flatten the time dependence of the temperature of the power chip, the τ_P should be small enough to follow the heat fluctuations. However, even for well-known Bi₂Te₃ systems, only a few reports have discussed its τ_P. Therefore, we studied a transient state of Peltier effect for a piece of n-type single crystalline Si, within a few seconds after the device was switched on.

For estimating transient behavior, we used the single crystalline n-Si (100) (100 mm² × 0.625 mm) with both of surfaces covered with Al/Pt/PtSix films. Silicon crystal (Si) has a large Seebeck coefficient and a high thermal conductivity.
During measurements, the n-Si was sandwiched by a couple of gold blocks connected to a current source. Voltage and temperature were measured near an interface between the block and the n-Si. One of the blocks was connected to ceramic heater and the other to a refrigerator. In addition, to estimate an operation of the n-Si on a 4H-SiC-based power device, the Peltier effect with a 4H-SiC substrate was tested. A 4H-SiC substrate (100 mm²  × 0.35 mmt) and a strip of Cu were inserted between the gold block at the heat source and the n-Si. Because this 4H-SiC is an electric insulator, the current path is through the right Cu strip, right gold block, the n-Si, and the center Cu strip. InGa-based liquid metal was painted between all of the components.

For deriving thermoelectric parameters, we analyzed time dependence of the difference between both sides of the n-Si, ΔT_P(t) (≡ T_D(t) − T_S(t) − ΔT(0); where T_D(t) and T_S(t) denote the temperatures of heat drain and source, respectively), based on a series thermal circuit. We employed the expression of ΔT_P(t) ≈ q_PR_HSi{1−exp(−t / τ_P)} + q_UR_HU{1−exp(−t / R_HUC_HU)} − (q_D / C_HD)t, where q_P (≡ STI_P) and τ_P denote an active heat transport and a response time by the Peltier effect, respectively. The second and third terms show an expansion and a reduction of ΔT_P(t) by thermal diffusion, respectively. We found the equation of ΔT_P(t) successfully represented all of the experimental ΔT_P(t). The fitted parameters were summarized in Fig 1 (a) and (b). The Seebeck coefficients derived without and with SiC were −490 ± 20 μV/K and −571 ± 12 μV/K, respectively, which were consistent with that reported previously. The response time τ_P obtained experimentally without and with SiC were ~ 0.1 sec and 0.15 sec, respectively. These short response time would enable a quick cooling of a heat source such as inverters. Finally, a simple simulation revealed that the parameters of ΔT_P(t = 5 sec) and τ_P for a bulk Bi₂Te₃ with the same arrangement in this work were 10 K and 2.5 sec, respectively. This shows that Bi₂Te₃-based Peltier device is not suitable for cooling a power device.

Furthermore, as the second stage, the influence of metal electrodes on the thermoelectric properties of silicon has been evaluated. Titanium, aluminum, and platinum were used as an electrode of n-Si. Some of them were sintered to form films of silicides. A conventional measurements of voltage/temperature difference during steady state revealed that their Seebeck coefficient strongly depends on all of the composition, thickness, and sintering temperature.

This research is supported by “Thermal Management Materials and Technology Research Association (TherMAT)” in New Energy and Industrial Technology Development Organization of Japan.