# Silicon wafer crystal orientation

I'm confused about how [110] direction is determined for (100), (110) or (111) wafers. I found a book chapter which just confused me even more. From the image below, I understand how [110] is determined on the (110) wafer but not the other two. I'm also having a hard time understanding what different planes would look like on the (111) and (110) wafer. I would appreciate a resource for silicon wafers specifically (not necessarily crystallography). Here are things I'm not understanding.

1. How is the [110] direction determined and why is it different for each of the three wafers below? For the (110) wafer [110] is between x and y axis which makes sense. But for (100) it seems to go from z to y and for (111) it's between x and z. From my understanding [110] intercepts x and y axis at 1 and doesn't intercept z axis but that doesn't seem to be the case for (100) and (111) wafers.

2. Does the definition of x,y and z axis change when we're talking about (100), (111) or (110) wafers? I know that whichever wafer it is, that direction will be pointing out from the wafer surface but when I draw planes with respect to [110] and [111] (for (111) wafer), I don't know where the (100) plane should be. (110) plane would be perpendicular to the [110] direction and would be normal to the surface and (111) would be 35° from it. I can't find a drawing for it which makes me think we don't need to show the (100) plane? But if not then what if I need to align my mask to (100) plane on (111) wafer?

3. How would I define higher miller index planes on the 3 wafers? For example I need to align my mask to (122) or (411) plane, how would I start with it? I understand that this might become clear once I learn about the primary planes on the wafers.

• Saying that you are confused is unhelpful. Asking for resources is probably off-topic. Why are you confused? Commented Dec 1, 2022 at 19:27
• You're right I'll edit to add my confusion
– JOHN
Commented Dec 1, 2022 at 19:45

You are mixing things up. Read up on Miller index notation.

The [110] direction (note the brackets) is always pointing towards the front right (midway between the X and Y axes).

This is why the (110) plane wafer (note the brackets) is facing exactly in this direction.

In a silicon crystal (which has cubic symmetry), there are 6 axes with equivalent symmetry to the [110] direction. These are collectively called <110>. I.e. <110> will refer to any one of them. Namely these are: [1,1,0], [1,-1,0], [1,0,1], [1,0,-1], [0,1,1], [0,1,-1]

This means:

• the (100) wafer will have <110> edges on 4 sides, each 90° apart.
• the (110) wafer will have <110> edges only on 2 sides, 180° apart.
• the (111) wafer will have <110> edges on 6 sides, 60° apart.

I show each of these possibilities of forming equivalent flats in the edited image below:

## How to align your structures with other planes?

Any (plane) that is different from the (face plane) of your wafer will intersect with the facing plane along one specific [direction]. This direction can be at pretty odd angles, so it is best to pull out a calculator. Note again, due to cubic symmetry you will have several planes that are equivalent to both your facing plane and to your desired alignment plane. The set of planes equivalent to (111) - called {111} - contains 8 different planes. Any fully indexed plane will have a set of 8 equivalent planes. So in the end there can be countless directions that make any pair of these intersect.

My understanding is that, after the wafer is processed, there is no way to visually identify the crystal orientation from the appearance. By grinding a segment of the wafer's circular arc into a straight line along the <110> direction, the crystal orientation can be visually determined from the exterior. The direction parallel to this straight line segment would indicate the <110> crystal orientation.

• How does this answer anything that's been asked? Commented Apr 4 at 7:59