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Hints Problem Set #6

Problem #1

In 1(c), what is meant by the conductor passing over steps?
> Should I just use 10% of the length (1/10 mm) and 50% of the
>thickness (5000/2 Angstroms)?

There is some topography such that the insulator separating the metal from the ground plane is the same thickness. When metal is deposited over these steps, it is not equal to the thickness over flat (non-step features). Section 9.1 of Plummer discusses these step coverage problems. You're right 10% of the line length is only 1/2 as thick as the other 90% of the metal line.

> The equation I have is: Rsquare*thickness=Pi/ln(2) V/I, which doesn't > depend on length (just thickness which is also in the I=J*Area).

This equation is strictly for measuring Rsquare from the Van der Pauw structure. The always applicable equation for Rsquare is

Rsquare equals (sheet resistivity/thickness)

Given all the dimensions and the maximum current density, it is possible to solve for the max voltage.



Problem #3

The problem with Al and Si is that Si is partially soluble in Aluminum. When heated up the silicon diffuses quickly up into the aluminum. A way to work around this problem would be to deposit an alloy such that the alloy already has the small soluble (1%) percentage of silicon in Aluminum, so that the substrate will not be drawn up into the Al. Problem 3 addresses the problem in another way. Deposit a film of silicon so that this is the silicon that is absorbed into the Al, not the active or pn junction region of the silicon. Find the % of Si soluble in Al at 450 degrees C.

You can assume uniform penetration of the Al into the Silicon (i.e., spiking). So, how thick does the silicon film need to be given the max solubility of Si in Al and the fact that the Al film is 1 um thick?

It is true that the Al will not likely penetrate uniformly into the silicon. You should acknowledge this so that you realize the thickness you calculated assuming uniform penetration is the minimum thickness of silicon required.

Problem #4

For the formation of silicide, the numbers should be given

1 nm of Ti reacts with 2.27 nm of Si to form 2.51 nm of TiSi2.

These are the numbers you see in the book as well as in the literature as well. The process given for this problem is

1.) Ion Implant -- You are given energy and dose. From these numbers you can find the range and the standard deviation of the range and the concentration profile.

2.) Metal deposition – We are trying to form TiSi2. We have the silicon from the wafer, but we need the titanium. So here we deposit titanium.

3.) Anneal – The silicon from the surface of the wafer and the deposited Titanium react to form 550 Angstroms of TiSi2 (titanium silicide).

How much Si was consumed to form this much TiSi2? Neglecting dopant diffusion during the anneal, I think you should have an idea of figuring out the peak As concentration now in the silicon.

Please email me if you have any questions.

Thanks,
Joe