- Q: What Did the Scientist Say to the LED? A: Don’t Be Square
Conventional quadrangular (square) LEDs are less efficient than triangular ones.
A major issue with gallium-nitride LEDs is that, although they efficiently generate short-wavelength photons, the high refractive index of GaN (n = 2.5) traps much of the light inside the semiconductor chip as a result of total internal reflection. Scientists at many laboratories have addressed this problem, developing several techniques to reduce it. Texturing the LED surface, for example, has enhanced the optical output by as much as 100 percent in the vertical direction.
Figure 1. Scientists fabricated GaN LEDs in the shape of a square (left) and a triangle (right). Each diode consisted of a 2-μm-thick silicon-doped n-GaN layer, a multiquantum-well (MQW) active region consisting of InGaN wells and undoped Un-GaN barriers between them, and a 150-nm-thick magnesium-doped p-GaN layer. The total surface areas of the two diodes were very nearly the same. Images reprinted with permission of IEEE Photonics Technology Letters.
However, all these experiments have been carried out with traditionally shaped quadrangular LEDs. Now, investigators at Gwangju Institute of Science and Technology and at Korea Photonics Technology Institute, both in Gwangju, have fabricated triangular-shaped LEDs and have shown that the optical extraction efficiency can be boosted by as much as another 48 percent beyond that of quadrangular LEDs.
Figure 2. Consider a light source, P, in a quadrangular block of GaN surrounded by air (left). A photon emitted from the source hits the first wall at an angle of incidence θi. It follows directly from Snell’s law and plane geometry that the photon will be trapped inside the block by total internal reflection if 23.5° <θi <66.5°. On the other hand, in a triangular block of GaN, the corresponding condition is 23.5° <θi <36.5°. Clearly, more light escapes from the triangular LED than from the quadrangular one. And although the numbers change, this general conclusion is valid regardless of the refractive index of the material surrounding the GaN.
They fabricated LEDs in both shapes (Figure 1). From purely geometrical considerations, they expected that total internal reflection would trap less of the light in the triangular LED (Figure 2).
Figure 3. Measurements with an integrating sphere showed that the triangular LED emitted more light than the quadrangular one at all drive currents. TRA LED = triangular LED; QDA LED = quadrangular LED.
To determine the total number of photons emitted by each LED, the scientists placed each one in an integrating sphere and measured the total flux as a function of the drive current (Figure 3). In this case, the LEDs were encapsulated in epoxy (n = 1.5), and an analysis such as the one outlined in the caption of Figure 2 indicates that no light is trapped inside the triangular LED but that a significant amount is trapped inside the quadrangular one.
Figure 4. An angular measurement of the light emitted from the two diodes at 20-mA drive current showed that the intensities were nearly identical in the vertical direction but that the triangular LED emitted more strongly in the horizontal direction.
The triangular shape increased the total light-extraction efficiency by 48 percent at a drive current of 20 mA, and by 24 percent at 100 mA.
The scientists also measured the angular distribution of the light emitted by the two LEDs (Figure 4). Although both emitted about the same intensity in a direction straight out from the diode, the sideways intensity of the triangular LED was significantly greater.
IEEE Photonics Technology Letters, Dec. 1, 2007, pp. 1865-1867.
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