DLPA027B January   2024  – April 2024 DLP500YX , DLP5500 , DLP6500FLQ , DLP6500FYE , DLP650LNIR , DLP670S , DLP7000 , DLP7000UV , DLP9000 , DLP9000X , DLP9000XUV , DLP9500 , DLP9500UV

 

  1.   1
  2.   Abstract
  3.   Trademarks
  4. 1Heating of a DMD Micromirror
    1. 1.1 Mirror Surface to Bulk Mirror Delta (ΔTMIRROR_SURFACE-TO-BULK_MIRROR)
    2. 1.2 Bulk Mirror to Silicon Delta (ΔTBULK_MIRROR-TO-SILICON)
    3. 1.3 Silicon to Ceramic Delta (ΔTSILICON-TO-CERAMIC)
  5. 2Calculating Mirror Surface Temperature With Pulsed Optical Sources
    1. 2.1 Mirror Surface to Bulk Mirror Delta (ΔTMIRROR_SURFACE-TO-BULK_MIRROR)
    2. 2.2 Bulk Mirror to Silicon Delta (ΔTBULK_MIRROR-TO-SILICON)
    3. 2.3 Silicon to Ceramic Delta (ΔTSILICON-TO-CERAMIC)
    4. 2.4 Calculating Mirror Surface to Ceramic Delta (ΔTMIRROR_SURFACE-TO-CERAMIC)
  6. 3Sample Calculations
  7. 4Summary
  8. 5References
  9. 6Revision History

2.1 Mirror Surface to Bulk Mirror Delta (ΔTMIRROR_SURFACE-TO-BULK_MIRROR)

Absorbed heat load must be transferred from the top of the mirror to the bottom of the mirror before it can be conducted from the bulk mirror to the silicon. Heat conduction through the mirror thickness is normally very efficient since the aluminum mirror is thin and has a high thermal conductivity, however pulsed illumination can create a condition where the mirror surface temperature is much higher than the bulk mirror temperature.

Since these short pulses heat the mirror surface very quickly without affecting the bottom surface of the mirror, the mirror can be treated as a semi-infinite solid. The equation for temperature of a semi-infinite solid with a constant heat flux is shown in Equation 1.

Equation 1. T x , t = T i   +   2 q * α t π 1 2 k * e x p - x 2 4 α t - q x k * e r f c x 2 α t

Where:

T ( x , t ) = temperature at depth = x, and time = t

T i = initial mirror temperature

q = absorbed heat flux on mirror surface [W/m2]

α = Mirror thermal diffusivity = 6.4667 x 10-5 m2/s

k = Mirror thermal conductivity = 160 W/m-ºC

e r f c (x) = complementary error function

Because we are only interested in the mirror surface temperature,

depth (x) = 0 in the equation above simplifies to Equation 2.

Equation 2. T t = T i   +   2 q * α t π 1 2 k

To calculate the mirror surface temperature at the end of the pulse where it is at a maximum, t = duration of the pulse. The temperature rise is only a function of the absorbed heat flux on the mirror surface (q) and the pulse duration (t). All other variables are constant for an aluminum mirror. Therefore, the temperature rise is proportional to qt1/2. As pulse duration becomes smaller with a constant average power density, the peak pulse power increases and causes a large temperature rise at the mirror surface. Also, the mirror surface temperature rise is not a function of mirror pitch because the mirror thickness can be treated as a semi-infinite solid, and the area of the pixel does not affect this 1-dimensional heat flow.