Thermal analysis of surface micromachined porous silicon membranes using the 3ω method: Implications for thermal sensing

Investigations into porous silicon thermo-resistive type thermal sensors and their advantages in speed-sensitivity trade-off relative to other comparable thermal materials are presented in this work. Porous silicon films were suspended above a silicon substrate using successive patterning and micromachining steps. The 3ω method was used in both supported and suspended configurations, allowing the analysis of both cross-plane and in-plane thermal properties of the micromachined films. By utilising a low noise, broad-frequency measurement of the in-phase and out-of-phase temperature components, thermal conductivity and thermal diffusivity were simultaneously determined. The measurements showed isotropic thermal conductivity of 0.38 ± 0.02 W/m K and 0.12 ± 0.01 W/m K, and thermal diffusivity of 0.39 ± 0.04 mm²/s and 0.23 ± 0.02 mm²/s, for the surface micromachined released porous silicon films at 50 % and 77 % porosity, respectively. The implemented suspended 3ω method leveraged a thermal model that accounted for the finite length of the heater (180 µm) and membranes (400 µm × 400 µm), eliminating the millimetre scale dimensional constraints in previous works. Use of a thermal passivation technique rendered the thermal properties of the films robust against successive photolithography and micromachining. The obtained thermal properties were utilised in finite element modelling of a thermo-resistive thermal sensor with 50 µm × 50 µm × 100 nm dimensions. The modelling results suggest that a thermal time constant of 5 ms could be achieved, comparable to that of amorphous silicon based thermal sensors but with 2–4 times larger temperature sensitivity due to smaller intrinsic thermal conductivity and heat capacity in the porous silicon films, thus achieving a significant improvement in overall speed-sensitivity trade-off.