Why do we need diffusion currents to explain semiconductor current flow? Why do we need the idea of carrier concentrations to explain current flow? Can we simply not associate the disparity in carrier concentrations between two samples to a disparity in relative charge thus leading to a formation of an electric field that causes a drift current?
 A: Diffusion currents play a significant role in the operation of semiconductors.  Circuit analysis would give incorrect results if they were ignored.  The reverse-bias current in a diode is diffusion current; ignoring it means getting the wrong answer in detailed analysis.  The electron current from emitter to base in an active npn transistor is also diffusion current, and is an essential ingredient to its operation.  Ignoring it here leads to the conclusion that transistors don't work!
A: The concept of drift and diffusion currents comes up when discussing the semi-classical model of the charge carrier flow in a semiconductor. In the model, the charge carriers (electrons and holes) are 'relatively free' to move about in random motion in the lattice formed by the semiconductor. However, they are scattered by the various atoms of the semiconductor and donor/acceptor ions in a lattice.
Speaking of the disparity of charge, the various regions of the semiconductor are always neutral during normal operation. However, since the behavior of the holes and electrons can be described as classical particles, with reduced masses (and hence the label semi-classical), they also follow motion similar to classical particles, like atoms of a gas, etc., and hence, diffusion currents should be expected.
It must be understood that diffusion currents are not due to the lattice 'pushing around' the electrons and holes because of the difference in concentration; it is purely a result of the random motion of the particles. If the concentration of the particles varies across the crystal, you would expect that, due to the random motion, they spread around evenly (although potential may be generated, causing drift of the charge carriers; but that is not what we are talking about).
