Design and Evaluation of High Precision Hybrid Resistors by Laser-Trim-Simulation

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The theoretical results of this project are reported in the following document (English abstract see below):

For short introductions see:

 Common information
 Technological problem description
 Mathematical modelation
 Numerical Simulator Package RCutSim
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Abstract:

This document discusses mathematical laser trim simulation of electrical film resistors. The functionality, capability, and reliability of modern hybrid IC's depends on precise resistor values or relations. In practice, however, high precision resistors are difficult to manufacture. Natural distribution and drift of film resistors, as well as fabrication process variations are responsible for this. Functional laser trimming became the most popular method of individually tailoring each hybrid circuit to meet precise resistor specifications. It is highly desirable to optimize the size, shape, and trim pathway of resistors to be trimmed, because of the high costs involved in the trim process step. For instance, optimized size minimizes chip real estate usage and optimized trim pathways result in reliable, automatized, high-speed laser trims. The optimization process starts at the design stage and ends at the final multiprobe stage where trimming takes place.

Laser trimming uses the dependence of resistance from the film geometry. Unfortunately analytical expressions exist for some special geometrical cases only. Resistance approximation formulas, like the so called Square Count Method, are insufficient for extreme accurate trims and don't even exist for most geometries. But nowadays it is possible to step away from resistance approximations by usage of fast differential equation solving techniques which adequately describe the current flow through an arbitrary film resistor shape. The mathematically function - who is necessary to know for trim optimizations - is the so called trim characteristic. The trim characteristic describes how a resistor changes as a function of trim pathway length. To obtain those characteristics it is necessary to compute the resistance for each little geometrical change every laser pulse causes on its trim pathway. The resistance depends on the particular current flux field in the present film domain. The stationary flux field in the resistor domain is ruled by the Laplacian-equation. In almost all geometrical cases this partial differential equation has to be solved numerically. For an entire trim characteristic the Laplacian-equation has to be computed about hundred times and more with a high accuracy by a shifting geometry. That's why a fast, accurate and robust numerical solver should be used for this. In addition, it is essential that this algorithm can easily adapt geometrical changes with a minimum of effort.

In order to do this, the study explains briefly the necessity of laser trimmings in the electronic circuit production and also the laser trim process itself, first. Afterward the required equations will be derived from Maxwell's equation system. The second part justifies the need and the choice of the numerical algorithm and gives short method introductions. The last part discusses how to use numerical trim simulations in resistor, and trim strategy design process. Furthermore, a post-trim drift model is deduced from numerical trim simulation and some conclusions will be made for design rules. Application of the resistor, and trim path design methods shown as here lead into reliable and complete laser trim process automations independent of precision requirements.

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