1 Introduction

Among all technologies photolithography holds the leading position in pattern transfer in today's semiconductor industry. The reduction of the lithographic feature sizes towards or even beyond the used wavelength and the increasing nonplanarity of the devices place considerable demands onto the lithography process. The large cost and time necessary for experiments make simulation an important and especially cost-effective tool for further improvements. However, a rigorous description of the fundamental physical effects governing sub-micrometer-photolithography places considerable demands onto the modeling, whereby a three-dimensional simulation becomes necessary. As a consequence the needed computational resources are extremely high. In three dimensions some approaches (e.g. [1] [2] [3]) are suited only for supercomputers, others are already proposed for workstation based simulation (e.g. [4] [5] [6]).

We present an overall three-dimensional photolithography simulator running on modern engineering workstations. The simulator consist of three different modules as shown in Fig. 2, whereby each module accounts for one of the fundamental processes of photolithography: imaging, exposure/bleaching and development.

Figure 2: The three basic modules of the photolithography simulator.

The lithography simulator calls these three modules sequentially. As well defined interfaces exist between these modules, they can be treated independently. Furthermore, each part requires its specific simulation approach. The individual tasks and our solutions therefore are briefly summarized as follows:

• The imaging module describes the illumination of the photomask. The light transmission through the optical system including the photomask has to be simulated. The output of the imaging module is the aerial image, which is the light intensity incidenting on top of the wafer. Our approach combines the vector valued version [7] [8] of the classical scalar theory of Fourier optics [9] with a semi-analytical algorithm for calculating the photomask's Fourier coefficients. The discretization of the distributed light source is described in larger detail as it is of crucial importance for the numerically efficient implementation of the differential method.

• The exposure/bleaching module simulates the chemical reaction of the photosensitive resist. Thereby the light propagation within the optically nonlinear resist and electromagnetic (EM) scattering effects due a nonplanar topography have to be modeled. The result of the exposure/bleaching module is the latent bulk image. Our approach is based on the novel three-dimensional extension of the originally two-dimensional differential method. An overview of the principial operation of the algorithm is presented disregarding mathematical details but focussing on a consistent description with the imaging module.

• The development module models an isotropic etching process, whereby the inhomogeneous etch or development rate is determined by the previously calculated bulk image. The final developed resist profile is the result of the overall photolithography simulator. We extended the recently proposed cellular based etching simulator [10] [11] for photolithographic applications.

The paper is organized according to the simulation flow depicted in Fig. 2. In the next three sections we discuss the imaging, the exposure/bleaching and the development module, respectively. Then we present simulation results for contact hole printing over a planar and a stepped substrate to demonstrate the capability of the simulator. We conclude with a brief summary of the main features of the simulator and the contributions of this paper.