dear Nayab,

The Fermi energy level is that level with probability of occupation with an electron is equal to one half at a temperature T greater than zero kelvin. So, At zero kelvin the energy levels above the Fermi level is zero. Once the temperature is increased electrons occupying the allowed energy levels under Ef will acquire thermal energy enabling them to be emitter above the Fermi level.

If you speak about the transmission coefficient as the probability to find an electron above the Fermi level, the P(E>= Ef)= integral f(E) dE from Ef to infinity.

This my my own understanding to your question otherwise you must give us the definition of the transmission coefficient at Fermi level.

Best wishes

Yes. In general more energy states or energy bands gives a higher transmission probability. But based on your question, the relation is not "equal" - it is better to say "positively correlated".

Thank you so much for the responses :)