Step 1: Eliminate large gaps
Gaps of $5$-$6\ \text{eV}$ or $10$-$11\ \text{eV}$ belong to insulators, where electrons cannot be excited easily.
Step 2: Eliminate zero gap
A zero gap means the bands overlap, which is the case for metals.
Step 3: Conclusion
So the semiconductor gap is small but non-zero, about $1\ \text{eV}$ or less.
Final Answer:
A semiconductor has a small non-zero gap of about 1 eV or less.
\[ \boxed{\text{(C) }1\ \text{eV or less but greater than zero.}} \]