The e¤ectiveness of Light Emitting Diode (LED) depends on several inherent factors.which contribute.to their overall e¢ ciency. Here we explore the Light Extraction E¢ ciency (LEE) extraction ; in the LED semiconductor substrate, which can be de…ned as the number of photons emitted into free space per second divided by the number of photons emitted from the active semiconductor region per second. The generally large di¤erence in index of refraction n sc between the semiconductor substrate and the surrounding media(air) n air creates the total internal re ‡ection (TIR) that is responsible for the limiting factor in light extraction of the material. LEEs di¤er depending on the semiconductor material used for the pn junction as well as the surface treatment of the material. It has been shown that rough surface treatments create more favorable conditions for light extraction. To better understand what takes place at the surface of the semiconductor, we adress the derivation of blackbody radiation and how it is related to our model. We then introduce a triangle-like geometry into the rough surface treatment and demonstrate using monte-carlo ray-trace (Light Tools Software), that close to 100% LEE can be obtained for surface treatments of this design.
1: IntroductionThe Light Extraction E¢ ciency (LEE) inside Light Emitting Diodes (LEDs) is a key limiting factor in overall function and e¢ ciency of today's LEDs. To improve the e¢ ciency of LEDs, we must address improvements that can be made to the semiconductor substrates to increase the LEE. Here, we will focus on geometric improvements that can be made to the LEE of semiconductor substrates using ray-trace software -Light Tools.For an ideal LED, the active region of the semiconductor would emit one photon for every electron injected, and thus have an external quantum e¢ ciency of unity. The external quantum e¢ ciency, EQE , can be de…ned as, EQE = Number of photons emitted into free space per second Number of electrons injected into the LED per second = IQE extr (1) where we de…ne IQE , to be the internal quantum e¢ ciency, and extr , as the light extraction e¢ cency (LEE)[1]. The IQE can be de…nied as follows, IQE = Number of photons emitted from the active region per second Number of electrons emitted into the LED per secondThe photons emitted into the LED from the active region should escape the LED substrate to create the light we see. In an ideal LED, all photons escape and we would see an LEE, extr ; of 100%. However, realistically we see many photons trapped inside of the semiconductor substrate yielding < 100% for extr . extr = Number of photons emitted into free space per second Number of photons emitted into the active region per second (3)The amount of light we see emitted from the LED depends on each of these e¢ ciencies including the electrical current delivered to the system, and can be represented by the power converstion e¢ ciency ( ) also known as the wall plug e¢ ciency[1].