larger wafers are used presently because the cost per wafer remains basically the same for small and large wafers, thus the cost per die gets smaller if we can put more dies on the same wafer.
3 inch 76 mm
4 inch 100 mm
5 inch 125 mm
6 inch 150 mm
8 inch 200 mm
12 inch 300 mm
16 inch 400 mm 2.54 cm = 1 inch
Other properties
Mechanical specifications
Type of crystal growth (CZ, FZ, epitaxial)
Thickness - (they might break if too thin)
Bow - a concavity appears due to sawing
Chemical properties/Surface
Oxygen and carbon content - important for some applications (ICs)