Optical losses in "close-confinement" epitaxial p-n junction lasers - Theory and experiment (1970)

The optical losses of "close-confinement" (single heterojunction) epitaxial injection lasers fabricated by liquid-phase epitaxy (LPE) have been described in terms of a simple waveguide model. Experimental and theoretical comparisons were made of LPE lasers with identical impurity profiles except for the addition of the Al <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> Ga <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> As p+-p heterojunction ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\DeltaE_{g}\sim 0.1</tex> eV) within <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-2 \mu</tex> of the p-n junction. This reduces the room-temperature absorption loss and hence the laser threshold-current density. The values of the internal laser loss α at 300°K range from 20 to 40 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> , while in the homojunction LPE lasers α is typically close to 100 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> . The laser gain coefficient β in the close-confinement lasers ranges from 3 to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6 \times 10^{-3}</tex> cm/A; values of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sim3 \times 10^{-3}</tex> cm/A. are estimated in similarly doped homojunction LPE lasers. However, β in diffused lasers is known to be substantially lower, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sim \leq 10^{-3}</tex> cm/A. We believe that substantial electron confinement exists in the homo-junction LPE laser because of the doping discontinuity at the p+p interface, which is absent in the diffused lasers. Thus, the β values are correspondingly lower in the diffused lasers. The addition of the (AlGa)As heterojunction does not, apparently, increase the electron confinement greatly as compared to homojunction LPE lasers when the active region width is about 2 μ (the optimum value for overall laser performance) for a given doping level. Values of the exterior differential quantum efficiency of 43 percent are obtained at 300°K in close-confinement lasers, which means that most of the light internally generated is emitted. Because of the reduced internal loss, the spontaneous exterior efficiency is also greatly increased by the addition of the heterojunction (a factor of 2-3). State-of-the-art values of the threshold current density of the optimum structures are 10 000 A/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> for a cavity length of 20 mils, with values of 8000 A/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> in exceptional units. A power conversion efficiency at 300°K of 10 percent has been measured, which agrees with the theoretically predicted value. It is noteworthy that the diode series resistance is unaffected by the addition of the heterojunction. The laser characteristics have been studied as a function of varying acceptor concentration, donor concentration, and bandgap energy discontinuity at the p+-p interface. Semiquantitative agreement for the laser loss between theory and experiment at 300°K and 77°K is obtained for an active region width of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sim 2 \mu</tex> , using reasonable values of the index of refraction differences between the various laser regions and free carrier losses. The major difference between simple waveguide theory and experiment is in the dependence on the width of the active region. Instead of a decrease in α with increasing width, the opposite occurs in the range investigated because the theory is not applicable when the width of the active region substanfially exceeds the minority carrier diffusion length. Furthermore, higher order mode propagation has been neglected. Such modes have been experimentally observed when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d \cong 5 \mu</tex> . The addition of the heterojunction greatly reduces the laser loss due to light leakage from the active region into the p+ region. The contribution to the laser loss resulting from leakage into the n-type side of the junction is small. It is unaffected, of course, by the addition of the heterojunction. This loss could be further reduced by use of a double heterojunction structure. Based on the theoretical results and comparison with experiment in which the Zn concentration is changed,it is concluded that the dominant loss is due to free carrier absorption (holes mainly) in the active region of the close-confinement lasers. Thus, it is not expected that the laser-loss coefficient will substantially vary with the cavity length. However, in the homojunction LPE (or diffused) laser this may not be the case. There the refractive index difference <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Deltan</tex> between the p+ and active p region is relatively small; hence, small variations in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Deltan</tex> due to increasing the laser photon energy by decreasing the cavity length may substantially reduce the optical waveguiding effect. Finally, we note that work in progress indicates that close-confinement lasers are capable of long-term operation (2000 hours) with power reductions of 20 percent or less when operating at a current density of 50 000 A/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (0.04 percent duty cycle). However, it is known that the laser life depends on the imperfection density in the active region. Hence, the metallurgy of the device is a key factor that must be carefully controlled in laser fabrication. In particular, dislocations can be introduced as a result of the slight lattice mismatch at the (AlGa)As-GaAs interface.