Lithographic simulators

For the more realistic situation where intensity within the resist varies as a function of exposure as well as on account of standing waves, the solution to Eq. (12.32) becomes extremely difficult to obtain. The approach employed in modern lithographic simulators such as PROLITH is to use the standing wave equations [Eqs. (12.13)-(12.30)] to determine the intensity within the resist as a function of m(x, y, z, t). Initially, the PAC distribution is given by m x, y, z, 0) 1, and the standing wave equation gives the intensity distribution... 

To account for the effect of postexposure bake in reducing standing waves through thermally driven diffusion of the photoacid, lithographic simulators employ models... 

The evaluation of Eq. (12.81) typically involves the replacement of the integrals by summations over intervals Ax and Az, with the restrictions that Ax < Sc and Az < Sc. Alternatively, the diffusion equation shown in Eq. (12.69) can be solved directly, using finite difference methods. In lithographic simulators, either Eq. (12.81) or Eq. (12.69) is solved, with the specification of the diffusion length O, or equivalently, the diffusion coefficient D, which in tiun can be determined from appropriate functional models that account for the dependence of diffusion on bake temperature T (discussed in the next section). 

The temperature dependence of diffusivity is accounted for in lithographic simulators in terms of the Arrhenius expression ... 

The effects of acid loss due to atmospheric-based contaminants are accounted for in standard lithographic simulators in a simple way. The assumption is made that the concentration of the base contaminant in contact with the top of the resist remains constant, such that the diffusion equation can be solved for the concentration of the base B as a function of depth into the resist as... 

Thus the application of the enhanced Mack model of development rate in lithographic simulators calls for the specification of these five expression parameters . max>. min resim tl, and 1. 

Perhaps the first numerical investigation of lithographically patterned electrodeposition was published by Alkire et al. [46]. In this work, the finite-element method was used to calculate the secondary current distribution at an electrode patterned with negligibly thin insulating stripes. (This is classified as a secondary current distribution problem because surface overpotential effects are included but concentration effects are not.) Growth of the electrodeposit was simulated in a series of pseudosteady time steps, where each node on the electrode boundary was moved at each... 

Lithographic modeling simulates several key steps in the lithographic process comprising image formation, resist exposure, postexposure bake diffusion,... 

Lithographic modeling and simulation have found wide applications, spanning research, process development, manufacturing process optimization and control, and even education within the semiconductor industry. A few notable examples of these applications and their roles in shaping the evolution of lithography are outlined helow. 

Lithographic modeling has found widespread applications in the development of new lithographic processes and equipment. Such applications include the optimization of dye loadings in resists, the simulation of substrate reflectivity, the applicability and optimization of top and bottom antireflection coatings, and the simulation of the effect of bandwidth on swing curve amplitude. " ... 

From our numerical studies, we find that om scheme of 2D localization provide a potential application in atom nano-lithography. With a setup illustrated in Fig. 9, we can lithograph the atoms on a substrate, and fabricate periodic refractive index structures. The numerical simulations of the resulting patterns via 2D atom nano-lithography achieved by our localization method are shown in Fig. 10(a)-(d). The patterns are fabricated on a substrate in the the plane and grow in the z direction (in arbitrary units). In Fig. 10(a), we achieve nanorod arrays disposed on a... 

As printed feature sizes have continued to decrease, it has been well documented using both experimental investigations and simulations that simple CAR designs and their associated processes generally lack the ability to meet futrrre lithographic requirements as set forth in the For a wide variety of... 

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