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When they say that we have a {1 0 0} single crystal wafer, I know that the surface normal to the wafer is oriented in the <1 0 0> family direction, but if I draw a line on the wafer, parallel to my primary flat, does it indicate a crystallographic direction family too? Like <1 0 0> or <1 0 1>. I mean it's obvious that it cannot be <1 1 1> due to the FCC lattice of Si(I am making the assumption that the thin plane of the primary flat is at exact right angles to the wafer surface, if that angle is allowed to be 54 degrees, it can also be a <1 1 1> ), but it can surely be directed at none of the crystallographic directions at all, so the question is, if I draw a line on the wafer surface parallel to the primary flat, will it be directed towards the <1 0 0> or the <1 0 1> family, or does the manufacturing process just slice an arbitrary flat out of the Si ingot before slicing it into wafers?

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The flats on Si wafers are not arbitrary. The largest, or primary flat, is perpendicular to the <110> orientation in the plane of the wafer. If it exists, the secondary flat helps identify the wafer orientation and doping type (and can easily vary based on wafer maker and the company ordering the wafers). All modern wafers (anything 200mm or bigger, almost all 150mm) are (100) and boron doped, so the secondary flat isn't used.

The primary flat has a specific orientation since the chips need to be aligned along the <110> crystallographic orientations so the wafer can be diced up. This usually uses a diamond scribe and careful breaking rather than sawing, because the saw is wider than a scribe line (so fewer chips/wafer) and dirtier .

So, you wafer has <001> pointing up, and <110> in plane towards the flat.

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