Why do LEDs continue to emit light?

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The electrons need energy to cross the potential barrier between the N and P types. So apply a voltage and they get over and recombine with the "holes" and emit a certain wavelength of light. Then what happens? Does the voltage have to be great enough to then knock them out of the holes and send them down the conducting wire so a new electron can fill the same hole? How do they continue to emit light after all the holes are initially filled?
 
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Jd0g33 said:
The electrons need energy to cross the potential barrier between the N and P types. So apply a voltage and they get over and recombine with the "holes" and emit a certain wavelength of light. Then what happens?
Density of holes decreased at that point where the hole disappeared. Random motion of holes tends to keep the density of holes homogeneous. So eventually some hole will drift to that position.

Holes are constantly being destroyed at one end of the p-type semiconductor, while at the other end holes are being created. The holes diffuse from high hole density area to low hole density area.

To get electric fields mentioned, I add that a hole reacts to density of holes and other charges at a distance, in other words hole reacts to electric fields.