Material representations and algorithms are presented for simulation of nanometer lithography. Organic polymer resists are modeled as collections of overlapping spheres, with each sphere representing a polymer chain. Exposure and post-exposure bake steps are modeled at the nanometer scale for both positive and negative resists. The development algorithm is based on the Poisson removal probability for each sphere in contact with developer. The Poisson removal rate for a given sphere is derived from a mass balance relationship with a macroscopic development rate model. Simulations of electron beam lithography with (poly) methyl methacrylate and Shipley SAL-601 reveal edge roughness standard deviations from 2 to 3 nm, leading to linewidth peak-to-peak 3σ variation of 15 to 22 nm. Typical simulations require about 2 MBytes and under 5 minutes on a Sun Sparc 10/41 engineering workstation.

In the direct product space of a complete metric linear space X and its related space Y, a fuzzy mapping G is introduced as an operator by which we can define a projective fuzzy set G(x,y) for any xX and yY. An original system is represented by a completely continuous operator f(x)Y, e.g., in the form x=λ(f(x)), (λ is a linear operator), and a nondeterministic or fuzzy fluctuation induced into the original system is represented by a generalized form of system equation xβG(x,f(x)). By establishing a new fixed point theorem for the fuzzy mapping G, the existence and evaluation problems of solution are discussed for this generalized equation. The analysis developed here for the fluctuation problem goes beyond the scope of the perturbation theory.

This paper describes the higher-order moment analysis of superposed Markov jumping processes. A superposed Markov jumping process is defined as a linear superposition of a finite number of piecewise constant real valued stochastic process whose value changes are associated with state transitions in an underlying descrete state continuous time Markov process. Some phenomena are modeled well by the process such as membrane current fluctuations observed at bio-membranes or load fluctuations in electrical power systems. Theoretical formula of the moment function of any order k is derived and the parameter estimation problem utilizing higher-order moment functions is discussed. A new method of estimating the kinetic parameters of membrane current fluctuations is proposed as a possible application.

The composition of CMOS control circuit and Vertical-Double-Diffused-MOS (VDMOS) power device on a single chip by using Silicon-On-Insulator (SOI) structure is formulated. Because all the MOS transistors in the CMOS control circuit are not isolated by the trenches, the interference phenomenon between SOI and the substrate is studied. Latch-up is detected thus, the construction of a mechanism to prevent latch-up is also studied. To evaluate the SOI CMOS characteristics the effects of voltage fluctuation on the substrate is analized. The latch-up mechanism is also analized by transient device simulation. As a result of this study a guideline for the immunity of latch-up is established, the features of the mechanism are as follows. First, the latch-up trigger is the charging current of the condenser composed of the oxide layer in the SOI structure. Second, latch-up is normally caused by positive feedback between the parasitic PNP-transistor and the parasitic NPN-transistor. However, in this case, electron diffusion toward the P-well is dominant after the parasitic PNP-transistor falls into high level injection. This feature is different from the conventional mechanism. The high level injection is caused by carrier accumulation in the N- region. Considering the above, it is necessary to; (1) reduce the charging current of the condenser, (2) reduce the parasitic resistance in the N- region of SOI, and (3) reduce the carrier accumulation in SOI for immunity from latch-up.