Anisotropic Etching in Semiconductor Fabrication

[pj33]

TL;DR Summary

Why does the Si(111) has low etching rate

I am learning about designing semiconductors but I had some issues understanding some things about the structure of Si.

About lattice structure:
1) Why does an FCC has 8 atoms per cell? Doesnt has 14?

About wafers
1) I know you can have wafers along different surfaces. What information can I calculate for the different surfaces liek Si(101), Si(111)... and how?(is there a formula). I mean I know when etching occurs for some reason Si(111) forms a 54.7 degree angle but I don't understand why.
2)Why in anisotropic etching does the Si(111) has the lowest etching rate?
3)When etching occurs, is the Si(111) the stable state that converges everytime (if sufficient etching time is given)?

I feel that my questions above my not be that clear (for etching), but I hope with the following everything will make sense.
What does it mean to have a Si(100) wafer with sides in the <110> directions and then a groove will be etched with the sides at an angle of 54.7 degrees wrt to the surface.

Since it's a Si(100) how does it have sides of <110> direction.
Why it makes at angle of 54.7? Is this because at <111> direction is most stable and this is the corresponding angle that is formed at <111> direction?

Thank you in advance!

 

[phyzguy]

Summary:: Why does the Si(111) has low etching rate

I am learning about designing semiconductors but I had some issues understanding some things about the structure of Si.

About lattice structure:
1) Why does an FCC has 8 atoms per cell? Doesnt has 14?

About wafers
1) I know you can have wafers along different surfaces. What information can I calculate for the different surfaces liek Si(101), Si(111)... and how?(is there a formula). I mean I know when etching occurs for some reason Si(111) forms a 54.7 degree angle but I don't understand why.
2)Why in anisotropic etching does the Si(111) has the lowest etching rate?
3)When etching occurs, is the Si(111) the stable state that converges everytime (if sufficient etching time is given)?

I feel that my questions above my not be that clear (for etching), but I hope with the following everything will make sense.
What does it mean to have a Si(100) wafer with sides in the <110> directions and then a groove will be etched with the sides at an angle of 54.7 degrees wrt to the surface.

Since it's a Si(100) how does it have sides of <110> direction.
Why it makes at angle of 54.7? Is this because at <111> direction is most stable and this is the corresponding angle that is formed at <111> direction?

Thank you in advance!

(1) The FCC lattice has 4 atoms per unit cell, not 8 or 14. There are 6 atoms on the 6 faces, each of which is 1/2 in the unit cell, and 8 atoms at the corners, each of which is 1/8 in the unit cell, so there are 6*1/2+8*1/8=4 atoms in the unit cell.

(2) You might try watching this YouTube video:

.

It shows the various crystal planes. I think of it as follows. When you cut through the (100) plane, each atom is bonded to 4 atoms in that plane. When you cut through the (111) plane, each atom is bonded to 6 atoms in that plane. So it is more difficult for the etchant to remove atoms along the (111) plane, so the etch rate is lower. As to why the 54.7 degrees, this is just the geometry of the cubic lattice. Try calculating that angle and see what you get.