Why don't semiconductors have a Fermi surface?

[aaaa202]

My teacher told me the other day that a semiconductor does not have a fermi surface. I didn't understand this remark. As I understand it the Fermi Surface is just the surface in k-space spanned by the highest occupied energy levels. Surely in a semiconductor you will also have some highest occupied energy states sitting in the top of the valence band?

 

[DrSteve]

Technically he/she is correct. See https://en.wikipedia.org/wiki/Fermi_level, especially the figure in the section
The Fermi level and band structure