Page 196 - Microsensors, MEMS and Smart Devices - Gardner Varadhan and Awadelkarim

176 MICROSTEREOLITHOGRAPHY FOR MEMS

where I t, and I 0 are the transmitted and incident light intensities, C is the concentration of
the absorber, d is the distance the light has passed into the absorber, and is a constant
proportional to the absorption coefficient of the absorbing material at the wavelength used.
In the SL process, we consider the UV beam to have a Gaussian profile, which is
scanned in a straight line at constant velocity v s along the x-axis, which is in the surface
of the photopolymer, as shown in Figure 7.5 (Jacobs 1992).
The irradiance (radiant power per unit area), I(x, y, z) at any point within the resin
can be related to the irradiance incident on the resin surface, I (x,y, 0) using the
Beer-Lambert law

(7.2)

where d p is the penetration depth of the beam, which depends on the wavelength, the
absorption coefficient, and the initiator concentration (from Equation (7.1)). It is defined
as the depth of resin that results in a reduction in the incident irradiance by a factor
of 1/e.
Here, we assume a Gaussian radial distribution of the light intensity in the plane
orthogonal to the optical axis O-X shown in Figure 7.6. The relationship between the
power P and irradiance I of an axisymmetric Gaussian light source (i.e. laser beam) is

Figure 7.5 Mathematical representation of the line scan of a Gaussian beam. From Jacobs (1992)

H

Figure 7.6 Definition of the half-width w 0 of a Gaussian light beam