S. V. Babu

Exact solution of Dill's model equations for positive photoresist kinetics

The equations of Dill for bleaching of photoactive compound in positive photoresists have been solved analytically in closed form. As an application, the contrast γ, has been evaluated explicitly in the absence of reflection from the substrate.

Simulation of Three-Dimensional Positive Photoresist Images

The least-action dissolution algorithm (LEAD) is applied to simulate three-dimensional positive photoresist images on reflective substrates. This algorithm avoids the ambiguities of the string algorithm and its modifications by utilizing the local validity of the eikonal description of the underlying diffusion equation to describe developer penetration with a moving boundary. The electric field and the concentration of the photoactive compound (PAC) within the photoresist film in the presence of standing waves in three dimensions are obtained from the numerically efficient WKB procedure proposed recently. The PAC concentration profile is combined with the LEAD algorithm to simulate a three dimensional one micron diameter contact hole in a single layer resist.

Calculation of image profiles for contrast enhanced lithography

Simultaneous bleaching of a contrast enhancing film (CEF) and the underlying positive photoresist is considered in the absence of any interface or substrate reflectivity. The intensity transmitted by the CEF is determined as a function of exposure time exactly using the absorptivity of the film in Dill’s model equations. Corresponding to this time dependent transmitted intensity, the concentration profiles in the positive photoresist have been expressed exactly in closed form. Relations, that implicitly define the developed image profile, are derived assuming that the resist development can be approximated by a two state process. Furthermore, they are solved numerically for a polysilane–AZ2400 resist system and a model CEM‐388–resist combination proposed by Mack. The predicted image profiles are in excellent agreement with the experimentally determined profiles of Hofer et al., for the polysilanes, and the predictions of prolith for the model system of Mack.

Resist development described by least action principle‐line profile prediction

A new idea is introduced requiring that each development path will be the path of least resistance to developer penetration. Consequently, minimum dissolution time is required for the development of the final line profile. This idea manifests itself in a variational calculation of the path integral along each local development trajectory, from which the dissolution profile is obtained uniquely, as a solution of a nonlinear partial differential equation (PDE). The photoactive compound (PAC) concentration is obtained from the standard Dill’s equations for the exposure–bleaching process for both monotonic as well as standing waves. The procedure has been implemented and tested. It has been found to be very accurate and it eliminates the path crossings inherent in the predictions of the string algorithm. The arbitrary elimination of unfavorable points is avoided as well for all developing times.

Three Dimensional Profile Simulation For Positive Photoresists

The least action principle algorithm is extended to model the development of a three dimensional latent image in an exposed resist The photoactive compound (PAC) concentration is determined in a model resist film from the exact solution of Dills equations for the exposure-bleaching process for the case of a matched substrate. The procedure is valid for all mask shapes and is illustrated with an elliptical symmetry imposed upon the incident light intensity. Utilizing these PAC gradients, the three dimensional least action principle algorithm is employed to compute developed resist profiles.

Exposure bleaching of nonlinear resist materials: Exact solution

Dills model equations for the exposure bleaching of positive photoresists have been solved exactly in a closed form when the bleaching characteristics are nonlinear. As an application, the simultaneous bleaching of a positive photoresist and that of a polysilane contrast-enhancing film (CEF) is solved to determine the photoactive compound (PAC) concentration.

Standing waves in optical positive photoresist films: a new approach

A new approach to the problem of standing waves in a thin positive photoresist film is given. Explicit analytic expressions are obtained in terms of the classical WKB approximation. A self-contained, convergent iteration scheme is offered for accurate determination of the fields and the concentration of the photoactive compound as functions of depth and time.

A three‐dimensional profile modeling algorithm for positive photoresists

A numerically efficient version of the WKB algorithm for determining the electric field and the concentration of the photoactive compound within a photoresist film in the presence of standing waves is implemented in three dimensions assuming normal incidence and a flat substrate. This algorithm is combined with the least‐action dissolution (LEAD) algorithm to simulate three‐dimensional developed resist profiles.

Exact solution for the kinetics of the image reversal process

The model equations describing the image reversal process with positive photoresists have been solved by extending the recently derived analytical solution of Dills equations for the exposure bleaching of positive photoresists. The solution is presented in a closed form that requires only simple numerical integrations to determine the time-dependent two-dimensional concentration profiles of the photoactive compound (PAC).