Page 402 - Sami Franssila Introduction to Microfabrication

Appendix A

Comments and Hints to Selected Problems

1. Introduction for the pool and the balls. See Figure 4.1 for
concentration-to-resistivity conversion.
1. How does this value compare with atomic sizes? 3. Into which direction will segregation work?
4. One mole of gas equals 22.4 liters. 4. What if 0.01 ohm-cm boron-doped silicon is used as
5. Chips can fail by many different mechanisms; a boron source, instead of pure boron?
E a = 0.7 eV is the activation energy for just one 5. When X = 0, 10 ohm-cm material will be pulled.
common mechanism. 6. This is an order of magnitude question. Yield
7. Extrapolation is a dangerous business: how far do strength is strongly temperature dependent: at the
you expect scaling to continue?
end of crystal-pulling, neck temperature can be, for
◦
instance 600 C, and yield strength is of the order
2. Micrometrology of 1 GPa.
7. COP size and wafer thickness must be considered.
1. Be careful with units: resistivity is usually given in
µohm-cm (=10 −8 ohm-m).
4. In Equation 2.9, kilovolts and tens of kilovolts 5. Thin-film Materials and Processes
are typical. 1. You have four degrees of freedom to work with:
6. Calculate the volume that is being probed. Express width, length, thickness and resistivity.
your answer in atomic %. 2. You can only calculate a lower-limit value based
8. Acceleration voltage and electron wavelength are on polysilicon minimum resistivity because dop-
related, as are wavelength and resolution. ing changes poly resistivity by orders of magni-
9. TaN x resistivity is not given: you could try the tude.
following: 1) ignore it completely; 2) assume the 3. This is an order of magnitude question. One signif-
same resistivity as Ta; and then see how much your icant digit is enough. C = Q/V , Q = Ne, N is the
result is affected. If you are going to surf the Internet number of electrons and e is the elementary charge.
to find TaN x resistivity, you will find a bewildering 4. See Table 5.7.
range of values, so you are no better off. 5. Which fraction of silicon atoms in the flow would
you expect to end up on the wafer as an a-Si film?
3. Simulation 6. Molar volumes (m mol /ρ) are useful; or you may
2
assume 1 cm area and calculate via the number
1S. Differences will become apparent at high doping of atoms.
levels. 8. Ni , M = 58.71 g, and set alpha = 1 for the maxi-
2+
3S. What is your criterion for penetration? mum possible rate. (≈100 µm/hr)

4. Silicon 6. Epitaxy
1. The unit cell of silicon consists of 8 silicon atoms. 1. Table 4.1.
2. This is an order of magnitude question: you just 2. Yes, and very accurately, if there is no spurious
guestimate (guess and estimate) the dimensions deposition over the edges or on the wafer backside.

Introduction to Microfabrication Sami Franssila
 2004 John Wiley & Sons, Ltd ISBNs: 0-470-85105-8 (HB); 0-470-85106-6 (PB)