LEDs are made up of compound semiconductor instead of elemental semiconductor. Why?

LEDs are basically p-n junction diodes which can emit electromagnetic waves depending upon the energy band gap of used semiconductor. 

This emission takes place only due to de-excitation of electrons. When electrons recombine the electron holes in the valence band, it releases energy (hv) in the form of photons. These photons form an electromagnetic wave. 

So, to produce visible light rays photons should have energy equivalent to energy of a visible light i.e., 1.8eV(Red light) - 3.1eV(Blue light).

So, the energy band gap should be such that the wavelength of wave lies in visible region. This band gap can only be obtained by using compound semiconductor (Eg: GaAs, InP). If we use elemental semiconductor (Eg: Ga, Si), then infrared rays will be emit instead of visible light rays.