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2020 | OriginalPaper | Chapter

8. Device Parameter Variations in Microsystems Manufacturing

Author : Michael Huff

Published in: Process Variations in Microsystems Manufacturing

Publisher: Springer International Publishing

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Abstract

This chapter focuses on a major theme of this volume, namely, how to analyze the variations in device parameters that occur when using microsystems fabrication technologies. It is explained that parameter variations are important since they result in the device output differing from the expected device output behavior that is based on the design. Two different types of parameter variations are discussed: systematic (bias) variations and random variations. Bias variations are fixed amounts of offsets that occur in the device parameters, while random parameter variations are caused by non-systematic process variations. It is discussed that the magnitude of these parameter variations can significantly vary depending on the specific details of the equipment, process being performed, and the aggressiveness of the device dimensions. This chapter also covers the important concepts of precision and accuracy. Both are important for a well-controlled manufacturing process. The tools of statistical analysis are covered for both continuous and discrete probability distributions. Various examples are used to reinforce how these statistical methods can be effectively employed in analyzing the variations of the device output behavior using microsystems manufacturing. The material covered in this chapter will be used in the next chapter in explaining parametric yield analysis.

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previous chapter Microsystems Process Integration, Testing, and Packaging

next chapter Yield Analysis and Quality Assurance and Control Methods Used in Microsystems Manufacturing

There may be additional desirable characteristics, such as availability, low cost, ability to scale with demand, etc.

There can also be other types of variations (or errors) due to mistakes made in the manufacturing processes, but these types of variations and errors will be ignored in this discussion.

It should be noted that the bias variation could be due to a systematic variation in the parameter or a systematic variation in the measurement of the parameter or both. However, we are assuming in this discussion that the systematic variation is not due to the measurement instrument or method used.

The terms “micro-“and “macro-“as they relate to dimensional scales are usually meant to mean the following: “Micro-dimensional” scale refers to devices that have dimensions in the range from microns to tens of microns, sometimes even to the level of hundreds of microns. “Macro-dimensional” scale usually refers to devices that are visible and can be handled without aid. Macro-dimensional most often refers to devices that are several millimeters or larger.

It is assumed that contact photolithography is used. The variation in the width was given in Chap. 4.

It is noted that the variation of the manufacturing process used to make these micro-beams is better than that obtained with contact photolithograph and could be obtained with a higher-resolution form of lithography.

These are called “Bernoulli” trials.

Hypothesis testing can also be used on large samples wherein the procedure is the same as for small samples except that z_α is used to replace t_α,ν.

The Hagen-Poiseuille equation is derived from the more fundamental Navier-Stokes equations that are used to describe the motion of viscous fluids. The Navier-Stokes are based on application of Newton’s second law to fluid motion combined with an assumption that the stress in the fluid is the summation of a diffusing viscous term that is proportional to the fluid velocity gradient and the fluid pressure.

It may seem that the condition of a cylindrical conduit would exclude this law for use on modeling microfluidic conduits since fabrication of a cylindrical conduit would be difficult. However, it should be noted that correction factors to take into account the conduit cross-sectional shape are available. For simplicity we will ignore these correction factors in the present discussion.

The desired microchannel radius would likely be the result of a desired flow resistance value of the device, and this flow resistance value would be derived from the application specification. In other words, the 100.00 micron microchannel radius would not be arbitrarily selected but instead derived from the device output response.

The reader should recall that the tolerance interval was for 95% of the population and therefore represents 2σ.

It should be obvious to the reader that if it were desired to include the variation of the length of the microchannel, this would be a simple matter.

In Chap. 10 methods for removal of the bias variations will be examined.

This type of analysis is also sometimes referred to as “tolerance analysis.”

The deterministic sampling methods are used to directly determine the yields and therefore will be discussed in the next chapter.

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Title: Device Parameter Variations in Microsystems Manufacturing
Author: Michael Huff
Publisher: Springer International Publishing
Book: Process Variations in Microsystems Manufacturing
Print ISBN: 978-3-030-40558-8

Electronic ISBN: 978-3-030-40560-1

Copyright Year: 2020
DOI: https://doi.org/10.1007/978-3-030-40560-1_8