What is the theoretical limit of lumen/watt for lighting systems?
Nowadays we see LEDs with 300 lumen per watt luminous efficacy.


Maybe in the laboratory. Right now commercially available white LEDs are about 200 lm/w. 400 lm/w is the practical upper theoretical limit. US DOE estimated over 250 lm/w by 2025.

 


Commercial Blue LEDs have up to about 80% efficacy (Cree XP-3G and OSRAM Oslon SSL).
White LEDs use blue LEDs covered with a yellow phosphor.
Theoretically phosphors could produce better than 100% efficacy. 

If the cost of manufacturing a UV LED dropped dramatically, efficacy could skyrocket.  LEDs emitting near 400 nm with remarkably high efficiencies have been reported (Morita et al., 2004)


  What is the theoretical roof we would hit in distant future?


1 photon per electron is the ideal quantum efficiency of unity. 

Internal, extraction, external, and power are the four basic LED efficiencies. 

Internal: number of photons emitted from the active region per electron crossing the band gap.  Dependent on materials and temperature 

Extraction: Photons emitted by the active region that escape from the LED die. If all photons emitted by the active region are also emitted into free space, the extraction efficiency is unity. 

External:  the ratio of the number of useful light particles emitted to the 
number of electrons crossing the band gap. 

Power efficiency is the "wall plug" efficiency. The number of photons emitted per watt used. 

If the technology reached the theoretical maximum of one photon per electron 
The theoretical lm/w efficacy is based solely on the spectral output. 

There are three common units of measure for LED flux.  Luminous (lumens), radiometric (watts), and quantum (number of photons, SI unit = Moles).

Visible spectrum is 380 nm (770 THz) to 770 nm (390 THz) 
A 380 nm violet photon carries the most radiometric power. 
You will get most lumens from a watt of 555 nm (540 THz) green photons. 

602,214,085,700,000,000 electrons in 1 watt.
624,200,000,000,000,000 photons in 1 µMole.
which gives 1.036508469 µmol/w



Converting Photon Energy to Photon Flux

A photon has an energy quanta Ep which is defined by:

Ep= h•f 


where h = Plancks constant 6.63 x 10^-34, and

f = Frequency = c/λ
where c = speed of light = 299,800,000 m/s and &lt;br&gt;
λ = wavelength in meters&lt;br&gt;


Therefore 

Ep = h•(c/λ)


The number of photons, Np, can be calculated by 

Np = E/Ep
   = E•((λ•10^-9)/h•c)     
   = E [W/m2]•λ•10^-9[m]•/ (1.988•10^-25) 
   = E•λ•5.03•10^15 [1/(m²•s)]   (with Irradiance[W/m²])  


NOTE: above λ is in nm

The photon flux can be determined by:

Ef = Np/NA 


where NA = Avogadro number 6,022•10^23 / mol)



Together gives 
the equation for converting irradiance [W/m2] to quantum flux [µE]:

Ef = Np/NA = (E•λ•5.03•1015[1/(m2•s)])/(6.02•1017[1/µmol])
   = E•λ•0.836•10-2 [µmol/(m2•s)]




1 µMole of 555 nm photons = 0.2234 watts
Photopic Luminous Efficacy @ 555 nm = 147.2

147.2 x 1.036508469 µmol/w = 152.574 lm
152.574 lm / 0.2234 w = 683 lm/w

REFERENCES:

Light Emitting Diodes, 2nd Edition, E. Fred Schubert 


  candela (cd): The candela is the luminous intensity, in a given
  direction, of a source that emits monochromatic radiation of frequency
  540 THz hertz (555 nm) and that has a radiant intensity in that
  direction of 1/683 watt per steradian.
  source The International System of Measuring Units


candela to lumen calculator
Photopic Luminous Efficacy, Relative Sensitivity Curve for the C.I.E. Standard Observer
Irradiance Conversion Factors