EE6615 Assignment 1
1. Considering the following solid materials, write down their relevant solid forms: single- crystal, poly-crystalline, or amorphous. (10 marks)
a. Metallurgical Grade Si (MGS)
b. Si ingot
c. Diamond in a ring
d. Sand
2. In class we discussed the Miller index notation system to describe crystal planes. We also
mentioned that sometimes the norm direction of a complicated crystal plane may not be straightforward. Here we introduce a good way to calculate the crystal plane index: consider the crystal plane shown in Fig. 1(a), we first calculate the intercepts of this plane with the three axes, which in this case are: (1, 1, 1⁄2). We then calculate the reciprocals of the three numbers, which in this case are: (1, 1, 2). Finally, after possible reduction of the three numbers to the smallest integer numbers [e.g. (2, 2, 4) should be reduced to (1, 1, 2)], we get the Miller index for this plane: (112).i
Using the above method, calculate the Miller indices for the crystal planes shown in Fig. 1(b-d). (15 marks)
Figure 1. Crystal plane notation system
3. Apart from the ones discussed in class, Zincblende is another cubic-related crystal structure commonly found in nature (e.g. ZnS). Zincblende structure essentially takes the same form as the diamond lattice structure, but with two types of atoms (blue and green atoms shown in Fig. 2). (10 marks)
(a) (b) (c) (d)
i This method is valid for cubic and cubic-related crystals.
a. Using the above information, calculate the number of blue and green atoms inside the unit cell shown in Fig. 2. (5 marks)
b. Calculate the ratio between blue and green atoms. (5 marks)
Figure 2. Zincblende crystal structure
4. In 2018, the annual average PM2.5 level recorded at Causeway Bay roadside station is 30 μg/m3.ii This value is defined as the mass density of fine particles with a diameter of 2.5 μm or less. (20 marks)
a. Assume that all particles are of the exact size of 2.5 μm in diameter, have a perfect
spherical shape, and have a density same as water, calculate how many particles
would be present per cubic foot for a PM2.5 level of 30 μg/m3. (10 marks)
b. From the clean room classification chart introduced in class, what class would the
average air quality at Causeway Bay fall into? How many orders of magnitude is it
different from a Class-10000 clean room? (10 marks)
5. Consider the photomask pattern shown in Fig. 3, where the dark region blocks light and
white region is transparent, (20 marks)
a. Draw the photoresist pattern after development for a negative-tone resist. (10 marks)
b. Repeat a) for a positive-tone resist, but is over-exposed. (10 marks)
ii https://www.aqhi.gov.hk/api_history/english/report/files/AQR2018e_final.pdf
Figure 3 Photomask pattern
6. Considering a DUV photolithography system with 193-nm ArF light source, if NA = 0.6 and k1 = 0.25, (15 marks)
a. Calculate the theoretical spatial resolution of the system. (10 marks)
b. If the same system is immersed in Ultra-Pure Water (θ stays unchanged), calculate the
theoretical spatial resolution of the system. (5 marks)
7. Considering an alternating phase-shifting mask (PSM) with etched quartz to provide the
phase shift, calculate the required etching depth for a 193-nm ArF photolithography system. (10 marks)