Process data shows Essay Example

Process data shows Essay Example Process data shows Essay Process data shows Essay 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. This implies that the time required to complete the etching process is exactly the time required for the buffered oxide etchant to etch to the interface between the silicon dioxide layer and the substrate. I have also completed this question with the assumption that the buffered oxide etchant is a wet etchant, and that it etches isotropically. The slide entitled Isotropic Wet Etching and Feature Size in section 5 of the notes states the time required for a perfect etch using a wet etchant, with no overetching or underetching. This time is given in the following formula: where z is the thickness of the film, r is the etch rate of the etchant and ? is the time required for a perfect etch, with no overetching or underetching. The thickness of our silicon dioxide film may vary up to 10% and the etch rate of our buffered oxide etchant may vary up to 15%. Therefore, the time required to complete the etching process may also vary. From the above equation for ? , we can see that the maximum possible time required to complete the etching process occurs when z is maximized and r is minimized. Therefore, we can slightly modify the above equation for ? to represent the maximum possible time required to complete the etching process: where ? max is the maximum possible time required to complete the etching process, with no overetching or underetching. Substituting our previously determined values for zmax and rmin into the above formula yields: with significant figures applied Therefore. Max represents the maximum possible time required to complete the etching process, with no overetching or underetching. b). I have completed this question with the assumption that the buffered oxide etchant is a wet etchant, and that it etches isotropically. For an isotropic wet etching process, undercutting will occur at the top of the silicon dioxide layer. The slide entitled Isotropic Wet Etching and Feature Size in section 5 of the notes states the amount of undercutting that would occur at the top of the silicon dioxide layer for a perfect etch, with no overetching or underetching. Since the etchant is isotropic, it must etch equally in all directions. Additionally, the etchant is always in contact with the top of the silicon dioxide layer during the etching process. Therefore, it etches horizontally along the top of the silicon dioxide layer for the entire time for which the etching process occurs. Therefore, the length of the undercut that is generated at the top of the silicon dioxide layer is simply equal to the etch rate of the buffered oxide etchant multiplied by the time of the etching process. Mathematically, Where xundercut is the length of the undercut that is generated at the top of the silicon dioxide layer. I have completed question 6-1-a with the assumption that we are etching for the maximum possible time required to complete the etching process. As a result, whatever variations in film thickness or etch rate may occur, the film of silicon dioxide will be fully etched through. The maximum undercut will be generated if the buffered oxide etchant etches at its maximum possible rate. The maximum possible etch rate of the buffered oxide etchant is 115% of its nominal value. Therefore, the maximum possible etch rate of the buffered oxide etchant can be determined through the following calculation: where rmax is the maximum possible etch rate of the buffered oxide etchant and rnominal is the nominal 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, 115% can be expressed as 1. 15. 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 the above equation for xundercut can be modified slightly to yield the length of the undercut that is generated at the top of the silicon dioxide layer after the maximum possible etch time and with the maximum possible etch rate. Mathematically, where xundercut_max is the length of the undercut that is generated at the top of the silicon dioxide layer after the maximum possible etch time and with the maximum possible etch rate. Substituting our previously determined values for rmax and ? max into the above equation yields: with significant figures applied The minimum undercut will be generated if the buffered oxide etchant etches at its minimum possible rate. 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 nominal etch rate of the buffered oxide etchant.