Relation between carrier temperature and lattice temperature, under injections When we are learning the semiconductor physics, we always encounter a key concept, which is the carrier temperature. However, there is not any detailed definition of such carrier temperature. Do we resemble the carrier in the semiconductor to the atoms in the atmosphere, and this carrier temperature a measure of kinetic energy of all the carriers? How does it relate to the lattice temperature? 
 A: You can think of carriers in a semiconductor device as a gas (look at the statistical physics of the electron gas for more details).
Carriers/electron gas in a III-V semiconductor reach thermal equilibrium with the atoms in the lattice by exchanging longitudinal optical (LO) phonon (phonon gas). Similar logic applies to other materials, but I know about the III-Vs.
In most devices operating in steady state the electron temperature is equal to the lattice temperature.
However, if you inject electrons (and holes) into the semiconductor at a high energy then you have made a hot-carrier. For example, you can do this by illuminating a sample with a laser of much higher energy than the band gap, the carriers are photo generated with excess kinetic energy which is essentially the same as them having an elevated temperature. Another way to do this would be to inject carriers over a barrier.
In certain devices it's possible for the electronic temperature to be greater than the lattice temperature in steady state operation. For example the hot-electron transistor.
In these devices energy is added to the electronic system faster than it can be removed via the emission of LO phonons.
Conversely it is possible to refrigerate the electron gas if you withdraw energy from it faster than it is added. Confusingly you can also do this with a laser in a process called radiative cooling.
