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EE 5171 – Midterm #2 Fall, 2004

1) The Nikon S306C is a current state of the art exposure system for making deep submicron integrated circuits. It uses an ArF excimer laser as the source and has a numerical aperture of 0.78. If this system is being used to expose a diffraction grating using a resist with a contrast of 4.0, what is the minimum size line (in microns) that you can expect to be able to resolve? You can assume a spatial coherence of 0.5. What is the depth of field (in microns) for this system?

2) One can etch SiO2 using HF vapor. In this technique, the wafer is suspended above a

bath of HF and the vapor comes off of the surface of the liquid, and then diffuses thrugh the air to the surface of the wafer where it reacts with the oxide.

a. Assume that the process is limited by the flux of HF molecules to the surface of the wafer, and that, for the conditions used, the partial pressure of HF near the wafer is 100 torr. If it takes four HF molecules to be incident on the surface to remove a single silicon atom from the SiO2 and the density of silicon atoms in SiO2 is 2x1022 cm-3, determine the expected etch rate at room temperature. (You can assume that the oxygen immediately volatizes once the silicon is removed).

b. The measured etch rate is many orders of magnitude less than the answer from part a. It is found to be a sensitive function of the wafer temperature with higher wafer temperatures resulting in higher etch rates. List two possible explanations for the lower etch rates that would be consistent with the observed temperature dependence.

3) One wafer to minimize As out diffusion from a GaAs wafer during an implant activation

anneal is to put the wafer into a holder made from larger wafers (see Figure 6.12 for a photograph of such a “capless annealing” system”). The holder is then placed in a rapid thermal annealing system. You can assume that the lamps are perfect black bodies with an emissivity of one.

a. If the RTA lamps are operating at 3000 K, what is the wavelength at which the spectral exitance from the lamps is a maximum?

b. What is the spectral exitance at the wavelength corresponding to the energy of the silicon bandgap (1.12eV)? Recall that for photons, Energy = hν = hc/λ where h is Plank’s constant and c is the speed of light in a vacuum.

c. Assume that such a system was made from silicon wafers, but a GaAs wafer was placed inside. Sketch the spectral exitance as a function of wavelength. Indicate the part of the spectrum that would be strongly absorbed by Si and the part that would be strongly absorbed by GaAs.

d. Would silicon system absorb more light than a GaAs system or less light from these lamps? Justify your answer.

EE 5171 Microelectronic Fabrication Midterm Exam #2 – Fall 2003

1) An early generation g-line projection lithography system has the following parameters:

S=0.5 and NA=0.16. For a resist with a contrast of 2.5, what is the minimum feature size in microns? (30 pts)

2) Water in a pan is heated to the boiling point, 100 oC, where the water vapor pressure is 1

atmosphere. a. Find the flux of water molecules in cm-2 – sec-1 coming out of the pan. (15 pts) b. Find the mean free path of water molecules under this condition in cm – Assume

that the diameter of the water molecule is 2x10-10 m , there is no other molecule in the atmosphere except water., and T=100 oC. (15 pts)

3) The figure below shows the areal image

resist. The resist has a D0 of 30 m of the resist lin sure

ne width for exposure

timpo

of a line that is being exposed in a positive tone J/cm2 and a D100 of 80 mJ/cm2. Assume that the width

d as show at right, as the distance between the two bottom corners.

a. Find the MTF of the image (10 pts)b. Find the li

e is mea

` Resist es of 1 sec, 2 sec, 3 sec, and 4 sec. Hint: the

ints at which the line width is measured are the zero resist thickness points. This corresponds to an exposure dose of D100. (30 pts) Width

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5

Inte

nsity

(mW

/cm

2 )

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Position (microns)