At T>0 the Fermi-Dirac distribution determines the occupation of states above the Fermi level. The number of occupied states depends on both the density of states and the probability of occupation of an available state as controlled by the Fermi Dirac distribution function. For semiconductors it is often a good approximation to expand the Fermi Dirac distribution function into the Boltzmann distribution. 

It is not determined. DOS gives informacion about the number of states per unit energy and  carrier concentration n is given in different units