## thermalex08.in : Infrared Heat Lamp Annealing in Vacuum with Radiative Cooling

Requires: Thermal3D

Minimum Versions: Atlas 5.28.1.R

When a wafer is clamped only at it edges and is heated with an infra-red source in a vacuum, the majority of the heat loss occurs through ** black body radiation.** The vacuum prevents thermal conduction mechanisms for the majority of the wafer area. It is also important to realize that if both sides of the wafer are exposed to the vacuum without contact to a conductive heat sink, both the front and back sides of the wafer will radiate heat and so black body heat radiation must be simulated from both surfaces for accurate results.

In Atlas, black body radiation is simulated with an additional logical parameter, ** "BLACKBODY"** added to the ** "THERMCONTACT"** statement. This allows the user to set up multiple thermally radiative boundary conditions in their structure.

The power per unit area lost to black body radiation for an ideal radiator, is known absolutely for any given temperature, K. The power absorbed by that same body from it's surroundings, is also known absolutely from the temperature of those surroundings. The nett power loss or gain, to or from, any body by infra-red radiation, is therefore simply the difference between the power lost to it's surrounds and the power absorbed from it's surroundings.

The formula in Atlas is given by:

{bold} { ALPHA (T - EXT.TEMP) } + { STEFAN ( T^4 - EXT.TEMP^4) } W/cm^2

Where:-

** "ALPHA"** is the coefficient to take account of thermal conductivity to the wafer holder, and should be set to zero if all the heat loss is through radiative processes only,

** "T"** is the temperature of the surface calculated by Atlas,

** "EXT.TEMP"** is the external temperature of the surroundings, usually 300K if the equipment in normal laboratory conditions,

** "STEFAN"** is the black body radiation constant.

For reflective surfaces, the ** surface emissivity** correction can be taken account of by reducing the value of the ** "STEFAN" ** parameter from the ideal black body radiation value of 5.67051x10^-12 W/cm2/K^4, which is the default value. The area of the thermal contact is also calculated by Atlas by integration of the area of all mesh points in contact with the user defined thermal contact.

So in summary, for an ideal black body radiator, only the background temperature ** "EXT.TEMP" ** need be specified on the ** "THERMCONTACT" ** statement,the rest will be calculated by Atlas. For reflective surfaces, with less than ideal radiation characteristics, the ** effective emissivity coefficient ** can be taken account of by using the appropriate value of the ** "STEFAN"** parameter. Simply multiply the default value of "STEFAN" by the emissivity coefficient. For pure radiative cooling, also set the thermal conductivity coefficient, ** "ALPHA" ** to zero.

To load and run this example, select the ** Load** button in DeckBuild > Examples. This will copy the input file and any support files to your current working directory. Select the ** Run** button in DeckBuild to execute the example.

## Input Deck

# (c) Silvaco Inc., 2019 go atlas mesh three.d x.mesh location=0 spacing=20 x.mesh location=200 spacing=20 y.mesh location=0 spacing=0.1 y.mesh location=200 spacing=20 z.mesh location=0 spacing=20 z.mesh location=200 spacing=20 region number=1 silicon thermcontact number=1 BLACKBODY ext.temp=300 alpha=0 \ x.min=0 x.max=200 y.min=0 y.max=0 z.min=0 z.max=200 thermcontact number=2 BLACKBODY ext.temp=300 alpha=0 \ x.min=0 x.max=200 y.min=200 y.max=200 z.min=0 z.max=200 models thermal probe thermal lat.temp x=100 y=20 z=100 name=front_temp probe thermal lat.temp x=100 y=180 z=100 name=back_temp output opt.intens beam number=1 power.file=thermalex08.lum thermal angle=90 \ x.origin=100 y.origin=-1 z.origin=100 nx=10 nz=10 method direct solve b1=0 t1=300 log outfile=thermalex08.log solve b1=100 ramp.lit ramptime=0.1 tstep=1e-3 tstop=5 \ outfile=thermalex08.str onefileonly solve b1=0 ramp.lit ramptime=0.1 tstep=1e-3 tstop=60 tonyplot thermalex08.log -set thermalex08.set quit