We carry out a self-consistent analytical theory of unipolar current and noise properties of metal-semiconductor-metal structures made of highly resistive semiconductors in the presence of an applied bias of arbitrary strength. By including the effects of the diffusion current we succeed in studying the whole range of carrier injection conditions going from low level injection, where the structure behaves as a linear resistor, to high level injection, where the structure behaves as a space charge limited diode. We show that these structures display shot noise at the highest voltages. Remarkably the crossover from Nyquist noise to shot noise exhibits a complicated behavior with increasing current where an initial square root dependence (double thermal noise) is followed by a cubic power law.