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# Resistance Calculation Through the Utilization of Monte Carlo Random Walk Algorithm

IP.com Disclosure Number: IPCOM000078774D
Original Publication Date: 1973-Mar-01
Included in the Prior Art Database: 2005-Feb-26
Document File: 3 page(s) / 48K

IBM

## Related People

Chang, AW: AUTHOR [+2]

## Abstract

This algorithm provides a computer programming approach which will calculate the resistance within a fully enclosed or bounded i.e. isolated region, given the potential at two subregions within the primary regions.

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Resistance Calculation Through the Utilization of Monte Carlo Random Walk Algorithm

This algorithm provides a computer programming approach which will calculate the resistance within a fully enclosed or bounded i.e. isolated region, given the potential at two subregions within the primary regions.

Suppose a designer is designing a P-type resistor region 10 in Fig. 1 which is fully bounded by PN junction 11. Within P region 10 there are two subregions 12 and 13 which are resistor contacts of known potential, e.g., regions 12 has a potential 0 volt and region 13 has a potential 1.0 volt. The designer may utilize the programming approach to calculate the resistance of P region 10. The present approach is particularly of value when dealing with bounded regions or subregions of irregular boundaries. In Fig. 2, which will be utilized as an illustrative example, in calculating the resistance of P region 20, isolated within PN junction or boundary 21, the potentials of subregions or contacts 22 and 23 are given. The first step is calculating the resistance of P region 20 is to calculate the field around one of the contacts, in the present example, contact 20.

This is done by determining the potential of each of a plurality of points 24 which are equidistant from contact 22.

The potential of each of these points may be calculated by the solution of the La Place Equation by a random walk technique utilizing variable increments or steps, with the size of each next step being determined by the distance between the present position in the walk and the nearest boundary, either primary boundary or subboundary.

This random walk technique is illustrated in Fig' 3, which like Fig. 2 is a resistor 30 having an irregular boundary 31, a pair of subregions or contacts 32 and 33 of known potential and, for purposes of illustration, an additional internal subregion 34.

Assume the random walk starts from a point 35. On the computer, a large number of random walks are taken from the same point, e.g., in the order of 100 walks. Then a count is kept and a determination is...