*3.2. Simulation Results*

The thermal analyses of the investigated MEMS structure were divided into di fferent areas. The first one, presented in this subsection, is related to the comparison between the results obtained

using the reduced and non-reduced DPL model. In this area, the dynamic of average temperature rises in the platinum heater and the temperature sensor were investigated. Moreover, the temperature distribution in an entire cross-sectional area was considered for selected time points. It is also worthwhile highlighting that all results included in this subsection were received using a 10 nm distance between mesh nodes. Additionally, a comparison with FK and the measurement results was also carried out.

A comparison of the normalized average temperature rises over the time in the platinum heater and temperature sensor obtained using the reduced and non-reduced DPL model, the FK model, as well as real measurements is shown in Figure 3. It can be seen that there are almost no di fferences between the results plotted based on the reduced and non-reduced DPL models. The black solid line, which indicates the non-reduced DPL model results for the heater, coincide almost exactly with the red dashed line, which shows the outputs of the reduced DPL approach. A similar situation is also visible for the case of the temperature sensor. The black dotted line shows the results yielded using the non-reduced DPL model, and it coincides with the dashed blue curve, which shows outputs produced by the reduced DPL approach.

**Figure 3.** Comparison of normalized average temperature rises over the time in the platinum heater and the temperature sensor obtained using the reduced and non-reduced Dual-Phase-Lag (DPL) model, Fourier–Kirchho ff (FK) model, and measurements.

For comparison purposes, the measurement results which are indicated by the green lines were also plotted. It can be seen that the volatility over the time is very similar to the simulation results obtained using the DPL model, which confirms the correctness of the proposed approach.

The FK model produces significantly di fferent outputs. The dashed and dotted black curve, which shows the temperature rise in the heater, as well as the dashed black line, which indicates the temperature changes over time in the temperature sensor, does not coincide with the DPL model or the measurement results. Thus, the FK model should not be used for temperature distribution determination at nanoscale.

In addition, an analysis of a temperature distribution inside an entire considered cross-sectional area of the MEMS structure was carried out. The results' comparison, for selected time points, is demonstrated in Figures 4–6.

**Figure 4.** Comparison of normalized temperature rise in a cross-sectional area of the investigated MEMS structure obtained using reduced and non-reduced DPL model for t = 12.023 ns.

**Figure 5.** Comparison of normalized temperature rise in a cross-sectional area of the investigated MEMS structure obtained using reduced and non-reduced DPL model for t = 19.055 ns.

**Figure 6.** Comparison of normalized temperature rise in a cross-sectional area of the investigated MEMS structure obtained using reduced and non-reduced DPL model for t = 2 μs (steady state).

For each investigated time point, i.e., at different stages of temperature rise, it can be seen that the differences between the results obtained using the reduced and non-reduced DPL model are almost unnoticeable, which also suggests a very good level of coincidence between both investigated DPL versions.
