Why is Terahertz radiation so hard to generate? This paper (and many others I've read) claim that searching for ways of producing THz radiation is a high-interest research topic.
However, something I've just never understood is why it's so hard compared to other frequency ranges: we seem to have no problem producing radio waves or visible light, so why is THz/IR so hard to produce? Basically, what's preventing us from using the same concepts that we use to produce other wavelengths to produce THz?
If I had to guess intuitively, it would be something having to do with the fact that it coincides with thermal excitations, so if you wanted to use the same concept as an LED but just use a material with a smaller band gap like HgCdTe, the fact that all the carriers are constantly excited at room temperature would be really inconvenient (which kind of meshes with my experience of having to use LN2 to cool FTIR machines).
 A: First, for clarification: As Jon Custer already mentioned, THz radiation is not difficult to generate. It's simply part of the black body radiation. What is in fact difficult is to generate coherent or at least narrow-band THz radiation.
Regarding emission from semiconductor material: There is not so many materials, which would offer a bandgap in the THz range. You're right, HgCdTe is one of the candidates, InAsSb would be another option. And there are probably more. What they have in common is simply the fact that you can't get/fabricate them with a good crystal quality. There are a lot of engineering issues like missing substrate materials for functional layers, defects causing intrinsic carriers or mid-gap states, which could provide recombination paths, ... Furthermore, even if one could fabricate these materials, they would not be very robust, simply due to their material parameters. High bond energies go hand in hand with high bandgap and vice versa.
Therefore, people try to circumvent this by doing all kind of bandgap engineering. One prominent example are quantum cascade lasers, where the radiation is created from transitions between conduction band states, though these devices don't reach room temperature yet. Actually not even close, they are still limited to < 200 K. Another option is frequency doubling or tripling of resonant tunneling diodes (which to my knowledge can produce THz radiation but no coherence).
Finally, the THz range is not only characterized by missing sources, but it's hard to find good (meaning narrow-band, fast) detectors as well! To my knowledge, bolometric detection, where you heat a small chip and measure the conductivity change, is still the most common way. Also the detector side requires cryogenic cooling to eliminate thermal background.
A: There are essentially two ways of generating coherent radiation from solid-state devices:


*

*Classical electronic oscillators, in which charge is made to oscillate back and forth within a device... the frequency of radiation corresponds to the frequency of charge oscillation.

*Solid-state lasers, in which charge-carriers undergo a transition between two quantum states... here, the frequency corresponds to the energy separation between the states.


The literature often refers to a "terahertz gap", because both of these approaches hit their limit around the ~0.1-10 THz band.  Classical oscillators stop working at high frequencies because the speed of oscillation is limited by capacitive effects, and the transit time for electrons to move around the device.  Conventional semiconductor lasers stop working at low frequencies because (as has been mentioned in the previous answer) the band gap of materials is much too large (1 THz = 4 meV), so even "narrow" band gap materials like InSb or HgCdTe are far too big (a few hundred meV).
Quantum cascade lasers (QCLs) can generate radiation in the 1-5 THz band, with output powers exceeding 1 W by exploiting transitions between pairs of quantum-confined states entirely within the conduction band of a semiconductor heterostructure.  Since the states in the valence band are unused, the bandgap of the material is (almost) irrelevant.  THz QCLs are still limited to cryogenic temperatures, however, since any thermal excitation can kill the laser action very easily by redistributing electrons between the very closely-spaced states.
Another very significant challenge for creating THz semiconductor lasers comes from the need to confine light within the laser medium.  At near-infrared/visible, the wavelength is a few microns or shorter, and so it is possible to create semiconductor lasers with dimensions much greater than this wavelength.  As such, optical dielectric waveguides can be created quite easily that confine light simply through a difference in the refractive index of the laser material and its cladding.  At THz frequencies, however, the wavelength is hundreds of microns, and this would require QCLs to be made much thicker than the practical (and financial!) limit of epitaxial growth technology.  As such, alternative waveguide approaches based on surface plasmons (i.e., the light field is tightly "pinned" to the interface between a metal and a semiconductor).
However, at these long wavelengths, a great proportion of the energy from the THz radiation is lost to free electrons in the metal.
Another limiting effect in semiconductors comes from Reststrahlen absorption (in which photons are absorbed by mechanical vibrations (phonons) in the crystal lattice).  In GaAs (the most common THz QCL material), the Reststrahlen absorption occurs around 36 meV (or ~9 THz), which effectively makes it impossible to generate THz radiation anywhere near that frequency in GaAs.
Altogether, these effects make the development of THz semiconductor lasers quite challenging!
