*2.3.5 Calculating the bolometer temperature distribution*

Using the above expressions for *Cvt*, *κ*, and *Hnet*, we can convert the heat flow equation above into a thermal network like that illustrated in **Figure 6** [14]. Each resistor in the figure represents the thermal resistance of the CNTs in series with the thermal resistance between adjacent CNTs. The capacitors represent the thermal capacity of the individual CNTs, while the current sources represent the net IR radiation absorbed by each CNT.

This thermal network contains thousands of nodes, where there is a specific equation relating the thermal resistance, capacitance, and net power for each node. This system of equations can be solved to determine the temperature as a function of position and time throughout the bolometer absorber.

The output data from these calculations are shown plotted in **Figure 7** for different CNT network types [16]. Here, we assume the pixel tightly packed with CNTs and *Hnet* of 1 nW. Two different thermal resistance values were modeled for the nanotubes: 5 × 108 K/W and 1 × 109 K/W, shown in **Figure 7(a)** and **(b)**, respectively.

As expected, a higher thermal resistance results in a greater temperature difference from the ambient. We note that in general the thermal resistance also rises with increasing temperature, resulting in further heating of hot spots. The color-mapped temperature gradients of the contact legs that connect the film to the readout integrated circuit (ROIC) can be clearly seen in **Figure 7**.
