Modeling latent-image formation in photolithography, using the Helmholtz equation

Reformulation for latent image formation model in photolithography using numerical absorbing boundary condition

“…6 shows a result of simulation similar to that made by Urbach and Bernard [3] in their Fig. 6 shows a result of simulation similar to that made by Urbach and Bernard [3] in their Fig.…”

“…[1] cannot accurately predict the effects of lateral interference and scattering{2, 3,4]. For example, topography scattering during the exposure process of the lithography causes the redirection of light into an otherwise unexposed region of the photoresist.…”

“…In the imaging part, the aerial image formed by the imaging system and projected onto the scattering part is computed using the diffraction theory [6,7,8] . These include the finite-difference time-domain (FDTD){9, 10], waveguide [11,5], finite-difference bearri-propagation{12, 13], finite-element (FE) [2,3], and fast multipole [14,15] methods. Since the medium of the scattering part is inhomogeneous and the interaction of the light with the photoresist is basically chemical, the scattering model is not as reliable as the imaging model.…”

“…FORMULATION OF THE SACTTERING MODELBefore the scattering model is considered, simple imaging models by which the distribution of incident fields projected on the surface of the photoresist is calculated are briefly described. For convenience we use the following assumptions: the light source is monochromatic with the time dependence of e2't and transverse magnetic (TM) polarized, the mask pattern is one-dimensional, and the intensity of the lightwaves is the incoherent summation of fields produced by point sources distributed along a line in the source[3].According to the standard method of Fourier optics, the incident electric or magnetic field projected onto the resist layer is proportional to a complex field given by[13}U(x, z) = F' {T(f, Z)H(fr)F[t(Xm)}}(1) where the subscript s indicates that the field is an incident field contributed by the point source at x = x and F and F1 denote the Fourier transform and inverse Fourier transform, respectively. In the present study, since our intention is to develop a method which incorporates the imaging model for an illumination system into the scattering model, and to test its validity, the simplified optical system with Koehler illumination shown inFig.…”

Simulation of the Postexposure Bake Process of Chemically Amplified Resists by Reaction–Diffusion Equations

“…Although many exposure models are available to simulate the partially coherent radiation propagating in the resist film [31][32][33][34], the simulation of the exposure process itself is outside the scope of this article. Hence, in this work, a simple model of a plane-wave with a wavelength of 193 nm propagating in a dissipative medium is utilized [35][36].…”