In a CW system, this is often the only consideration and the temperature rise is defined by total heat load to the silicon multiplied by the package thermal resistance from silicon to the backside ceramic of the package.

${∆T}_{SILICON-TO-CERAMIC}= Q_{SILICON}\times R_{SILICON-TO-CERAMIC}$

Where:

$Q_{SILICON}= Q_{ELECTRICAL}+ Q_{ILLUMINATION}$

$Q_{ILLUMINATION}$ = ( ${\alpha }_{DMD}$ x $Q_{INCIDENT}$ )

$Q_{ELECTRICAL}$ = total electrical power on DMD [from DMD data sheet]

$R_{SILICON-TO-CERAMIC}$ [from DMD data sheet]

$Q_{INCIDENT}$ = total incident average optical power to DMD

${\alpha }_{DMD}$ = DMD thermal absorptivity

${\propto }_{DMD}=\left(1-Overfill\right) * \{\left[{FF}_{MIRROR} * (1-MR)] + \left(1-{FF}_{MIRROR}\right)\right\} + \left(2 *{\propto }_{WINDOW}\right)+Overfill$

Where:

${FF}_{MIRROR}$ = fill factor of mirror array (off-state calculates highest temperature) [Table 2-2]

$MR$ = mirror reflectivity [Figure 2-1, Figure 2-2, Figure 2-3]

${\alpha }_{WINDOW}$ = absorptivity of window single pass

$Overfill=1- \frac{Array Area}{Incident\mathrm{ }Area}$

$Incident Area$ = total illuminated area on the DMD

Because the thermal time constant of the silicon is on the order of seconds, the silicon can see the pulsed heat sources as a continuous heat source equal to the average absorbed power of the optical power to the DMD.

Fill factor of the mirror array (FF_MIRROR) is higher in the on-state than the off-state [Table 2-2]. This is because mirrors tilted away from the illumination source (off-state) expose more of the silicon to illumination through the mirror gaps. For worst case thermal modeling only the off-state fill factor needs to be used.