Note the continuous transition from the direct gaas to the indirect gaP. The materials have an indirect bandgap for x>0.4 and have the same problems as light emitters as silicon. The efficiency of an indirect-gap emitter can be greatly enhanced by the introduction of appropriate impurity recombination centers, as shown in Fig. 83. 3(c). In the process shown, an injected minority carrier electron(in p-type material) is first trapped by the localized impurity(which is itself electrically neutral but which introduces a local potential to the lattice which attracts electrons). The center is then negatively charged and attracts a hole to complete the recombination process, which produces the photon. The recombination center solves the momentum transfer problem, because the trapped electron is localized to the impurity lattice site and has a momentum range according to the Heisenberg Uncertainty Principle of △p~h/2πa (83.5) that is, sufficient to include the processes shown in the diagram at p-O. In the cases used as examples,a nitrogen atom substitutes for a phosphorus, or a zinc-oxygen pair substitutes for adjacent gallium-phosphorus atoms in the GaAs P, lattice. The GaAs -P, system is well established, but can only produce wavelengths defined by the range of energy p widths, i.e., down to green. Blue LEDs require higher band-gap materials (a)SiC technology is well developed for high temperature semiconductor applications, but it has an indirect band gap, so its emission efficiency is very poor [Pierret, 1996 (b) Gan (and In/Al GaN alloys)is a direct band gap material system producing successful blue and blue green devices [iles, 1994; Nakamura, 1995; Pierret, 1996 (c)II-IV compounds such as ZnS and ZnSe possess direct band gaps in the 1.5-3.6eV range, offering the possibility of full spectrum LEDs within the single materials system iles, 1994] Device Efficiency In considering LED efficiencies, it is convenient to consider the emission process to consist of three distinct steps: (a)excitation,(b)recombination, and(c)extraction. These will be discussed with reference to Fig 83.4 (a) Photons created by minority electron recombination on the p-type side of the junction are more likely be successfully emitted from the surface of the device, for the structure shown in Fig. 83. 4(a)and(b)if the p-type region is a thin surface layer. For a given total LED current, I, made up of electron, hole, and space charge region recombination components, In,Ip and I, respectively, the electron injection efficiency( which provides the excitation)is Yn=I(I++1) (83.6) In principle, all the physical processes described above apply equally to both electrons and holes. However, the electron mobility, H,, is greater than that of a hole, Hp, and since p=Naμn/Nap (83.7) (where No N are n-type donor and p-type acceptor doping densities, respectively) greater Y, is attainable for a given doping ratio than hole injection efficiency, Yp Consequently, LEDs are usually p-n' diodes constructed (b)Some of the recombinations undergone by the excess electron distribution, An, in the p-type region will ad to radiation of the photon desired, but others will not, because of the existence of doping and various impurity levels in the bandgap. The total recombination rate, R, can be written in terms of the radiative and R + r (838) where n/t 83.9) e 2000 by CRC Press LLC© 2000 by CRC Press LLC Note the continuous transition from the direct GaAs to the indirect GaP. The materials have an indirect bandgap for x > 0.4 and have the same problems as light emitters as silicon. The efficiency of an indirect-gap emitter can be greatly enhanced by the introduction of appropriate impurity recombination centers, as shown in Fig. 83.3(c). In the process shown, an injected minority carrier electron (in p-type material) is first trapped by the localized impurity (which is itself electrically neutral but which introduces a local potential to the lattice which attracts electrons). The center is then negatively charged and attracts a hole to complete the recombination process, which produces the photon. The recombination center solves the momentum transfer problem, because the trapped electron is localized to the impurity lattice site and has a momentum range according to the Heisenberg Uncertainty Principle of Dp ~ h/2pa (83.5) that is, sufficient to include the processes shown in the diagram at p ~ 0. In the cases used as examples, a nitrogen atom substitutes for a phosphorus, or a zinc–oxygen pair substitutes for adjacent gallium–phosphorus atoms in the GaAs1–xPx lattice. The GaAs1-xPx system is well established, but can only produce wavelengths defined by the range of energy gap widths, i.e., down to green. Blue LEDs require higher band-gap materials: (a) SiC technology is well developed for high temperature semiconductor applications, but it has an indirect band gap, so its emission efficiency is very poor [Pierret, 1996]. (b) GaN (and In/Al GaN alloys) is a direct band gap material system producing successful blue and blue￾green devices [Jiles, 1994; Nakamura, 1995; Pierret, 1996]. (c) II-IV compounds such as ZnS and ZnSe possess direct band gaps in the 1.5–3.6eV range, offering the possibility of full spectrum LEDs within the single materials system [Jiles, 1994]. Device Efficiency In considering LED efficiencies, it is convenient to consider the emission process to consist of three distinct steps: (a) excitation, (b) recombination, and (c) extraction. These will be discussed with reference to Fig. 83.4. (a) Photons created by minority electron recombination on the p-type side of the junction are more likely to be successfully emitted from the surface of the device, for the structure shown in Fig. 83.4(a) and (b) if the p-type region is a thin surface layer. For a given total LED current, I, made up of electron, hole, and space￾charge region recombination components, In, Ip, and Ir , respectively, the electron injection efficiency (which provides the excitation) is gn = In/(In + Ip + Ir) (83.6) In principle, all the physical processes described above apply equally to both electrons and holes. However, the electron mobility, mn, is greater than that of a hole, mp, and since In/Ip = Nd mn/Na mp (83.7) (where Nd, Na are n-type donor and p-type acceptor doping densities, respectively) greater gn is attainable for a given doping ratio than hole injection efficiency, gp. Consequently, LEDs are usually p-n+ diodes constructed as in Fig. 83.4, with the p-layer at the surface. (b) Some of the recombinations undergone by the excess electron distribution, Dn, in the p-type region will lead to radiation of the photon desired, but others will not, because of the existence of doping and various impurity levels in the bandgap. The total recombination rate, R, can be written in terms of the radiative and nonradiative rates, Rr and Rnr, as R = Rr + Rnr (83.8) where Rr = Dn/tr , Rnr = Dn/tnr, R = Dn/t (83.9)