Planar and three-dimensional thick-film thermoelectric microgenerators

Abstract

This paper describes manufacturing process as well as thermoelectric properties and long-term stability of planar and three-dimensional (3-D) thermoelectric structures made in thick-film/LTCC technology. Screen-printed thick-film thermocouples based on PdAg, Ag and Ni inks were manufactured and investigated. Seebeck coefficient and electrical output power were measured with the help of custom built automatic measuring system. Achieved results were compared with literature data and earlier authors’ results. Seebeck coefficient greater than 20 μV/K and about 5–8 μW/junction output power were measured for temperature difference of about 100 K for Ag–Ni thick-film planar thermocouple made on both used substrates. This combination of materials was chosen to create three-dimensional thick-film thermocouples (reported in the literature for the first time). We received for them Seebeck coefficient greater than 15 μV/K and the output power on level of 1 μW/junction for temperature gradient of about 60 K.

Introduction

When the ends of two different materials, A and B, are connected together and the junctions are put into different temperatures the thermoelectric force E_T, measured in Volts (or more often in mV), appears between connection points and the current flows in the circuit [1], [2]. Selection of materials with good thermoelectric parameters is important to obtain good efficiency of the thermocouple. Seebeck coefficient (α), electrical conductivity (σ = 1/ρ) and thermal conductivity (λ), measured, respectively, in V/K (usually μV/K), 1/Ω and W/K m, are combined in the so-called thermoelectric figure-of-merit, Z = α²σ/λ [K⁻¹] (the quantity W = α²σ [W/K⁻¹ m⁻¹] is called thermoelectric power factor).

In the case of a small temperature difference (several Kelvins) or for temperature independent material parameters these quantities can be used for direct comparison of thermoelectric materials, where the main target is connected with improving the figure-of-merit, Z or increasing the thermoelectric power factor, W. However, the transport properties α, σ and λ usually are temperature dependent. This results in a temperature dependent function Z(T). Thus, in any temperature range, materials with different properties have to be used in order to achieve a high figure-of-merit. Moreover, since Z varies with temperature, a more useful dimensionless figure-of-merit can be defined as Z · T.

The thermoelectric figure-of-merit of a thermocouple (thermogenerator) Z_AB is defined as

$$Z_{\text{AB}}={\alpha }_{\text{AB}}^2/(\sqrt{{\rho }_{\text{A}}{\lambda }_{\text{A}}}÷\sqrt{{\rho }_{\text{B}}{\lambda }_{\text{B}}}{)}^2$$

where α_AB = α_A − α_B denotes the relative Seebeck coefficient and α_A, α_B – Seebeck coefficients of materials used for thermocouple arms (Fig. 1b) [3].

The thermoelectric power factor of a thermocouple W_AB can be calculated from the formula

$$W_{\text{AB}}={\alpha }_{\text{AB}}^2·{\sigma }_{\text{AB}}={\alpha }_{\text{AB}}^2/{\rho }_{\text{AB}}$$

where ρ_AB = ρ_A + ρ_B (ρ_A, ρ_B – electrical resistivity of materials A and B).

In general, the application of thermocouples in sensor systems and thermoelectric microgenerators is described in the literature very often [4], [5]. Thermoelectric force, E_T depends on Seebeck coefficient α, thermal conductivity λ and structure dimensions:

$$\begin{array}{cc}\hfill E_{\text{T}}=& n·\alpha ·\mathrm{\Delta }T=n·({\alpha }_{\text{A}}-{\alpha }_{\text{B}})·(T_{\text{H}}-T_{\text{C}})\hfill \\ \hfill \mathrm{\Delta }T\sim & \frac{\lambda ·l}{t·w}\hfill \end{array}$$

where n – number of thermocouples in thermopile, ΔT = T_H − T_C – temperature difference between hot and cold junction (measured in Kelvins), l, t, w – dimensions (length, thickness and width of thermocouple arms). In order to achieve a higher thermoelectric force, E_T can effectively be multiplied by connecting the thermojunctions electrically in series and thermally in parallel.

Internal resistance depends on electrical resistivity ρ_AB and structure dimensions (we assumed that both thermocouple arms have the same dimensions)

$$R_{\text{i}}=\frac{{\rho }_{\text{AB}}·l}{t·w}[\mathrm{\Omega }]\text{,}$$

Output electrical power, P_OUT generated by such a structure is described by equation:

$$P_{\text{OUT}}=\frac{E_{\text{T}}^2}{4R_{\text{i}}}[\text{W}]\text{,}$$

where R_i is the internal electric resistance of thermopile, E_T is the thermoelectric force. Output electrical power, P_OUT is proportional to thermoelectric power factor, W_AB.