A lens is used to focus the illumination energy (i.e., radiation) that is required to develop the resist in a lithograph
Posted: Sun May 15, 2022 10:27 pm
A lens is used to focus the illumination energy (i.e.,
radiation) that is required to develop the resist in a
lithographic manufacturing process, as shown in the Figure. The
lens can be modeled as a plane wall with
thickness L = 1.0 cm and thermal conductivity k = 1.5 W/mK. The
lens is not perfectly transparent but
rather absorbs some of the illumination energy that is passed
through it; the absorption coefficient of the lens
is α = 0.1 mm−1. The flux of radiant energy that is incident at the
lens surface (x = 0) is q′′rad = 0.1 W/cm2.
The top and bottom surfaces of the lens are exposed to air at T∞ =
20 C and the average heat transfer
coefficient on these surface is ̄h = 20 W/m2K.
The volumetric rate at which absorbed radiation is converted to
thermal energy in the lens ()q′′′ ) is pro-
portional to the local intensity of the radiant energy flux, which
is reduced in the x-direction by absorption.
The result is an exponentially distributed volumetric generation
that can be expressed as:
q′′′ = q′′radαe−αx (1)
(a) Determine and plot the temperature distribution within the
lens.
(b) Determine the location of the maximum temperature (xmax) and
the value of the maximum temperature
(Tmax) in the lens.
(c) Determine the het flux at x = 0 and at x = L.
incident radiant energy, qrad = 0.1 W/cm² T. = 20°C ģconv,t=0 h = 20 W/m²-K - x0 X & cond,x=0 dx g L = 1.0 cm qx+dx q cond ,x=1 -- k= = 1.5 W/m-K conv.x=1 a=0.1 mm-1 T = 20°C h = 20 W/m²-K transmitted radiant energy Figure 1:
radiation) that is required to develop the resist in a
lithographic manufacturing process, as shown in the Figure. The
lens can be modeled as a plane wall with
thickness L = 1.0 cm and thermal conductivity k = 1.5 W/mK. The
lens is not perfectly transparent but
rather absorbs some of the illumination energy that is passed
through it; the absorption coefficient of the lens
is α = 0.1 mm−1. The flux of radiant energy that is incident at the
lens surface (x = 0) is q′′rad = 0.1 W/cm2.
The top and bottom surfaces of the lens are exposed to air at T∞ =
20 C and the average heat transfer
coefficient on these surface is ̄h = 20 W/m2K.
- A Lens Is Used To Focus The Illumination Energy I E Radiation That Is Required To Develop The Resist In A Lithograph 1 (359.91 KiB) Viewed 61 times
thermal energy in the lens ()q′′′ ) is pro-
portional to the local intensity of the radiant energy flux, which
is reduced in the x-direction by absorption.
The result is an exponentially distributed volumetric generation
that can be expressed as:
q′′′ = q′′radαe−αx (1)
(a) Determine and plot the temperature distribution within the
lens.
(b) Determine the location of the maximum temperature (xmax) and
the value of the maximum temperature
(Tmax) in the lens.
(c) Determine the het flux at x = 0 and at x = L.
incident radiant energy, qrad = 0.1 W/cm² T. = 20°C ģconv,t=0 h = 20 W/m²-K - x0 X & cond,x=0 dx g L = 1.0 cm qx+dx q cond ,x=1 -- k= = 1.5 W/m-K conv.x=1 a=0.1 mm-1 T = 20°C h = 20 W/m²-K transmitted radiant energy Figure 1: