MSTRAm-An accurate determination of y(x)-integral appearing in Kane's expression for the density of states is presented. Expressions of this approach are compared with other existing approximations. Mock's model for total density of states is applied to illustrate possibilities of proposed derivations. An efficient algorithm for analyses of highly doped semiconductor material properties with Kane related models is introduced. Calculated dependence of pn product and screening length versus doping is given. The influence of different approaches met in the literature and in this work on calculated semiconductor parameters of importance such as minority carrier concentration and pn product is shown.
INTRODUCTIOIIA variety of models for efficient highly doped semiconductor modeling can be found in the literature. This is a consequence of the tendency to describe heavily doped regions as accurate as possible yet to model mentioned areas sufficiently accurate, at acceptable complexity for device modeling. Band tail effect was among others described by Kane, who gave expressions for the density of states functions (1,Z). Evaluation of y(x)-integral (3) appearing in Kane's expressions is presented. Mock's model 161 for overall band description is applied to present the use of our derivations. Algorithm for pn product calculation is presented. A comparison of our derivations with approximate expressions given by Slotboom [SI is also reported.
This paper introduces a new class of advanced control algorithms for batch-reactor temperature control where a nonlinear PI controller with a feed-forward part in a cascade combination with a P controller is used. The main goal of the algorithm is to optimize production by lowering the costs of the temperature control and increasing the quantity and quality of the chemical, biological, pharmaceutical, food and beverage products produced in these reactors. The algorithm is designed to cope with the constraints and the mixed discrete and continuous nature of the process by manipulating variables for heating and cooling. The stability and robustness of the control algorithm is proven through the Popov Stability Criterion. The simulation results of the proposed algorithm show much better performance compared to a conventional cascade PI control structure, which is most commonly used in industry. Furthermore, the study also shows real-time implementation on a bioreactor using the proposed algorithm.
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