EE212 HW 3

# EE212 HW 3 - EE 212 FALL 09-10 HOMEWORK ASSIGNMENT #3...

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EE 212 FALL 09-10 HOMEWORK ASSIGNMENT #3 ASSIGNED: THURSDAY OCT. 15 DUE: THURSDAY OCT. 22 SOLUTION SHEET #1. An experimental DUV resist has a contrast of 5. It is being used with a projection imaging system that produces the aerial image shown below. Will the resist be able to resolve this image? Calculate a quantitative answer. (5 points). Answer: In order for a resist to resolve an aerial image, the resist CMTF must be less that the MTF of the aerial image. Thus we need to calculate these two values and see which is larger. MTF = I MAX " I MIN I MAX + I MIN = 0.6 " 0.2 0.6 + 0.2 = 0.5 CMTF resist = 10 1/ " # 1 10 1/ " + 1 = 10 0.2 # 1 10 0.2 + 1 = 0.584 2.584 = 0.226 Since the CMTF < MTF, the resist should be able to resolve the image. #2. This problem should give you a feeling for why e-beam tools are not used today for exposing wafers. An electron beam lithography system (like the mask making system illustrated on page 2 of the class notes on lithography), has a beam current of 1 nA, an accelerating voltage for the e-beam of 100 kV and a spot size of 50 x 50 nm square. (This size corresponds to the pixel size the machine can write in photoresist.) a). If the e-beam resist the machine is exposing requires a dose of 10 mJ/cm 2 , how long would it take to expose each pixel? (Hint: 1 Joule = 1 volt coul). (5 points).

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Answer: Each pixel will require an exposure of Exposure energy = 10 mJ cm " 2 ( ) 50x10 " 7 cm ( ) 2 = 2.5x10 " 13 J = 2.5x10 " 13 volt coul Thus the exposure time will be given by Exposure time = 2.5x10 " 13 volt coul 10 5 volts ( ) 10 " 9 coul sec # \$ % ( = 2.5x10 " 9 sec or 2.5 nsec b). How long would it take to write the pattern on an entire 12 inch diameter wafer? (5 points). Answer: The number of pixels on a 12 inch wafer is given by # pixels = Wafer area Pixel Area = " ( ) 12inches ( ) 2 /4 50x10 # 7 cm ( ) 2 2.54 cm inch \$ % ( ) 2 = 2.92x10 13 pixels Thus the total wafer exposure time is given by 2.92x10 13 pixels ( ) 2.5x10 " 9 sec pixel # \$ % ( = 73,000 sec or 20.2 hours . This illustrates why direct writing with an e-beam is not currently a practical solution to wafer level lithography. #3. A particular DUV photoresist has a contrast of 5. The post exposure bake (PEB) time
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## This note was uploaded on 06/12/2011 for the course EE 212 at Stanford.

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EE212 HW 3 - EE 212 FALL 09-10 HOMEWORK ASSIGNMENT #3...

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