None of the answers get the most important feature of semiconductor LEDs: It's their energy bandgap. In metals, the electrons fill up energies up to a certain level, the Fermi level. In order to travel through the material, the electrons have to get into an empty state above that. In metals, the empty states start directly above the Fermi level (actually, that's the definition of a metal).
In semiconductors, there's a forbidden zone above the filled levels. The width of this gap is specific to the material used and defines both the color of the LED and its forward voltage. You have to 'lift' the electrons above the band gap to transport them into the LED and get light out. So your applied voltage has to be higher than the band gap. The band gap is given in eV, and if you just add the "e" to the forward voltage, you'll get the band gap of the used semiconductor in eV. If you calculate 1242/E (band gap in eV), you'll get the wavelength of the emitted light in nm.
The band gap has nothing to do with the doping, or the characteristics of the pn junction (though both are important to make the LED work). If you want emission of a certain wavelength of light, that defines the set of materials you have to use to make the LED, which has this specific band gap. (I'm a physicist, and for me the wavelength and energy (and voltage) are one and the same.) That's why it took so long to make blue and with this white LEDs: There simply was no usable material with the right band gap.
The price you have to pay for a high energy/low wavelength LED (blue/UV) is the high band gap/forward voltage.
"Nifty is the Lord" - A. Einstein