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Introduction

Andy Somody 97300-6222 ENSC 495 Assignment #3 6-1). a). A 0.60 um film of silicon dioxide is to be etched with a buffered oxide etchant of etch rate 750 A min-1. Process data shows that the thickness may vary up to 10% and the etch rate may vary up to 15%. The maximum possible thickness of the silicon dioxide film is therefore 110% of its nominal value. Therefore, the maximum possible thickness of the silicon dioxide film can be determined through the following calculation: where zmax is the maximum possible thickness of the silicon dioxide film and znominal is the nominal thickness of the silicon dioxide film. Therefore, znominal = 0.60 um. Any number expressed as a percentage can alternatively be expressed as a decimal. For example, 110% can be expressed as 1.1. Using this decimal format, the above formula can be rewritten in the following manner: Substituting our previously determined value for znominal into the above formula yields: with significant figures applied Similarly, the minimum possible etch rate of the buffered oxide etchant is 85% of its nominal value. Therefore, the minimum possible etch rate of the buffered oxide etchant can be determined through the following calculation: where rmin is the minimum possible etch rate of the buffered oxide etchant and rnominal is the minimum possible etch rate of the buffered oxide etchant. Therefore, rnominal = 750 A min-1. Using the conversion factors 1 A = 10-10 m and 1 um = 10-6 m, rnominal can be converted to um min-1 in the following manner: with significant figures applied As was demonstrated above, this percentage value can alternatively be expressed as a decimal. Therefore, 85% can be expressed as 0.85. Using this decimal format, the above formula can be rewritten in the following manner: Substituting our previously determined value for rnominal into the above formula yields: with significant figures applied I have completed this question with the assumption that the etching process is perfect, with no overetching or underetching. ...read more.

Middle

The etch rate of the CVD oxide layer is represented by the symbol rCVD. The above formula for xundercut can therefore be modified slightly to represent the quantity of the undercutting at the top of the CVD oxide layer in this particular question. This has been done below: Substituting our previously determined values for rCVD and t into the above formula yields: with significant figures applied Using the conversion factors 1 A = 10-10 m and 1 um = 10-6 m, xundercut can be converted to um in the following manner: with significant figures applied Since the etchant is isotropic, it must etch equally in all directions. Therefore, each of the original sides of the windows must now be located a distance xundercut away from their initial positions, as defined by the patterning process. Therefore, the total distance between two opposite sides in the expanded window must be equal to: with significant figures applied where dsides is the total distance between two opposite sides in the expanded window. This length dsides is equal to the dimension of the expanded window after the etching process is complete. Additionally, the corners of the original windows would also have etched isotropically. These corners must link the four original sides of the windows at their new locations. Therefore, after the isotropic etching process, these corners should each be quarter-circles. Since these corners must also have etched a distance xundercut further into the CVD oxide film, the radius of the quarter-circles must be equal to xundercut. Therefore, the final dimensions of the window, as measured at the top of the CVD oxide layer, after ideal isotropic etching using a wet etchant is complete is represented in the following diagram: e). Before we can calculate the average slope of the window after a 30% overetch time, we must determine dimensions of the window as measured at the bottom of the film after a 30% overetch time. ...read more.

Conclusion

In question 7-1-a, we obtained an expression for the junction depth of a Gaussian distribution. This expression was given to be: In question 7-1-a, we also introduced an equation for the impurity concentration in a Gaussian distribution: The surface concentration, CS, is defined as being located directly on the surface of the wafer. Therefore, we may simultaneously substitute both x = 0 and N(0,t) = CS into the above expression for N(x,t) in a Gaussian distribution. Performing this substitution yields: This expression can be simplified to the following equation: It can be readily seen from the above equation that if we alter the diffusion coefficient, D, in a system, at least one of the factors CS, t or Q must change as well. However, question 7-2-b gives no information about which (if any) of the CS, t ,or Q variables must retain the same values they had in earlier portions of question 7. As a result, I have completed this question with the assumption that up to two of these variables may retain the same values they had in earlier portions of question 7, as long as all three are not forced to retain their old values. I have chosen to keep the values of Q and t at the same levels they were solved to be at in question 7-2-a. This implies that, when D is changed to its new value, the surface concentration CS must change to accommodate this variation in D. In section 6 of the notes, the slide entitled "Limited Source Diffusion Solutions" also supports the concept that, as the D*t product is altered, the surface concentration changes correspondingly. I have also completed this question with the assumption that the substrate doping level will retain the same values that it had in question 7-1-b. Having made these assumptions, I can now substitute the previously determined values for Q, t and Csub into my above expression for xj. After performing these substitutions, I obtain the following result for xj: with significant figures applied 1 ...read more.

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