Absorbed Light Output GaAs Transparent Encapsulation GaAs FIGURE 83.4 Effect of(a)opaque substrate, (b)transparent substrate, and(c)encapsulation on photons emitted at the pn Junction and where t, and t, are the minority carrier lifetimes associated with the radiative and nonradiative recombi nation processes, and t is the effective lifetime. The radiative efficiency is defined as n=R/(R1+Rm)=t/τ (83.10) and the internal quantum efficiency is ni= ny 83.11) (c) It is clear from Fig. 83. 4 that many of the photons generated on either side of the junction will pass through sufficient bulk semiconductor to be reabsorbed. In fact the photon energy may be ideally suited to reabsorption if it exceeds the semiconductor direct bandgap. It is obvious, then, why GaAs is opaque and Gap transparent to photons from Ga(As: P) junctions. Clearly, a greater efficiency might be expected from the transparent substrate with reflecting contact [Fig. 83. 4(b) The photon must strike the LED surface at an angle less than the critical angle for total internal reflection, 1/n (83.12) and next, nLED are the external and internal refractive indices, respectively. For air, next=1, but critical angle loss be reduced by encapsulating the device in an epoxy lens cap[ Fig 83. 4(c)] to increase both nat >1 and the angle of incidence at the air interface. Even within angles less than 0, there is Fresnel loss, with transmission ratio T=4n/(1+n)2 (83.13) The total external quantum efficiency is then the fraction of photons emitted [Neamen, 1992], given by n。=1/(1+v/AT e 2000 by CRC Press LLC© 2000 by CRC Press LLC and where tr and tnr are the minority carrier lifetimes associated with the radiative and nonradiative recombi￾nation processes, and t is the effective lifetime. The radiative efficiency is defined as h = Rr/(Rr + Rnr) = t/tr (83.10) and the internal quantum efficiency is hi = hg (83.11) (c) It is clear from Fig. 83.4 that many of the photons generated on either side of the junction will pass through sufficient bulk semiconductor to be reabsorbed. In fact the photon energy may be ideally suited to reabsorption if it exceeds the semiconductor direct bandgap. It is obvious, then, why GaAs is opaque and GaP transparent to photons from Ga(As:P) junctions. Clearly, a greater efficiency might be expected from the transparent substrate with reflecting contact [Fig. 83.4(b)]. The photon must strike the LED surface at an angle less than the critical angle for total internal reflection, qc, where sin qc = next /nLED = 1/n (83.12) and next, nLED are the external and internal refractive indices, respectively. For air, next = 1, but critical angle loss can be reduced by encapsulating the device in an epoxy lens cap [Fig. 83.4(c)] to increase both next > 1 and the angle of incidence at the air interface. Even within angles less than qc, there is Fresnel loss, with transmission ratio T = 4n/(1 + n)2 (83.13) The total external quantum efficiency is then the fraction of photons emitted [Neamen, 1992], given by [Yang, 1988] he = 1/(1 + avo/AT) (83.14) FIGURE 83.4 Effect of (a) opaque substrate, (b) transparent substrate, and (c) encapsulation on photons emitted at the pn junction. A Absorbed Photons Graded Alloy GaAs1-y Py (y=0 0.4) Graded Alloy GaAs1-y Py Reflective Contact Emitted Photons Emitted Photons Predominantly Electron Injection Transparent Plastic Encapsulation Al Top Contact Light Output Insulating Layer Al Back Contact GaAs GaAs P GaAs1-yPy Ga P B n p n n p (a) (b) (c) qc p