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Lasers & Sources

Predictive semiconductor laser design free of fit parameters

Recent research developments have culminated in the first-ever closed-loop design of a semiconductor laser without employing fit parameters.
27 February 2007, SPIE Newsroom. DOI: 10.1117/2.1200702.0536

Semiconductor optical amplifiers (SOAs) and lasers (SLs) are ubiquitous critical components in modern-day commercial and military technologies. The systematic optimization of these systems and the potential cost savings of fast-tracking to a final optimized SOA or SL structure for a targeted wavelength in a single wafer growth (including calibration runs) promises to have a wide economic impact across all semiconductor laser technologies. Now the culmination of a series of basic research successes on the first-principles calculation of semiconductor optical properties has led to the first-ever prediction of end-packaged semiconductor multiple quantum well (MQW) laser device performance without resorting to the use of adjustable fit parameters.1

Semiconductor wafer growth can produce heterostructures of very high quality with stoichiometrically correct growth of individual monolayers. But despite significant advances in molecular beam epitaxy (MBE) and metal-organic chemical vapor deposition (MOCVD) growth technologies, a critical void remains in predicting the performance of final packaged functional amplifier and laser devices. The lack of predictive semiconductor device design and growth monitoring capability can be traced to the extreme complexity of calculating from first principles the semiconductor optical response and radiative/nonradiative recombination rates. Now, critical ingredients such as absorption/gain and refractive index (a-factor) as well as spontaneous and Auger recombination rates can be computed for a wide range of material systems (II-VIs, III-Vs), provided that the bulk bandstructure parameters are known. This dedicated approach to device construction by quantitative numerical modeling can dramatically reduce time and cost, fast tracking to truly optimized devices.

Figure 1. Input-output characteristic for a 1.3µm InGaAsP (indium gallium arsenide phosphide) ridge laser predicted without free-fit parameters (lines) at two temperatures. Corresponding experimental data for the same structure (points).

For example, in Figure 1, the L-I (output power vs. input current) characteristic (predicted, solid line) and measured (points) for a 4QW InGaAsP (indium gallium arsenide phosphide) ridge waveguide laser structure is shown at two temperatures. The remarkable feature here is that the calculation preceded the wafer growth and device packaging, so that there was no access to experimentally measured data. No parameters needed to be adjusted to get this agreement (with the cavity losses extracted from cutback experiments used to close the loop). Using known input bandstructure parameters such as band offsets and Luttinger parameters, photoluminescence (PL) spectra were calculated for different carrier densities and temperatures.

Figure 2 shows the measured PL spectra (points) for the aforementioned device grown according to the design prescription. A gain database, precomputed for the designed epitaxial structure, was used to establish the accuracy and quality of the actual wafer growth. The measured PL peaks show an offset of –23nm from the design, indicating that the actual growth was off by 1–2% in indium or arsenic concentration. The precomputed PL peaks were inhomogeneously broadened by 14meV to account for inevitable growth fluctuations from the ideal single-crystal spectra. Note the comparison between predicted and measured PL.

Once the PL spectra unambiguously established the reliability of device growth, the gain spectra were immediately accessible from the precomputed gain databases (see Figure 2). The next step in generating the numerical model was to compute both spontaneous and Auger recombination rates at the same level of sophistication.2 (Defect recombination is insignificant in determining the optical properties of these high-quality grown semiconductor crystals.) Figure 3 shows the precomputed spontaneous and Auger rates over a range of internal carrier densities ranging from below to above the transparency point at a fixed temperature: note the radical departure from the usual phenomenological spontaneous and Auger carrier density dependence at and above transparency density.

Figure 2. Experimental photoluminescence (PL) spectra (points) and computed PL (black curves). Red curves are gain spectra for the inverted semiconductor.

Combining the above inputs generated the L-I curves in Figure 1 at two different temperatures. Considering the critical role of the above recombination processes—not only in determining gain and slope efficiency but also in all dynamic properties (modulation rates, gain switching, injection locking, and so on) of SOAs and SLs—the impact of this work reaches well beyond the accurate prediction of an L-I characteristic. The application of these powerful results carries over to a broad class of semiconductor material systems generating light from the UV/visible (e.g., gallium nitride)3 to the far-infrared (indium gallium antimonide 2–10µm).

Figure 3. Log-log plots of the normalized spontaneous emission (left axis) and normalized Auger rates for the same structure as Figure 1. The straight lines represent the phenomenological rates.

Jerome V. Moloney, Joerg Hader
Mathematics, College of Optical Sciences, University of Arizona, Nonlinear Control Strategies
Tucson, AZ

Jerome V. Moloney is a professor of optical sciences and mathematics as well as director of the Arizona Center for Mathematical Sciences at the University of Arizona. He is also president of Nonlinear Control Strategies Inc. in Tucson. His research interests include semiconductor laser materials and modeling, ultraintense short-pulse propagation phenomena, computational nanophotonics, and plasmonics.

Joerg Hader is a senior scientist at Nonlinear Control Strategies Inc., and a research assistant professor in optical sciences at the University of Arizona. His research interests include the rigorous many-body microscopic calculation of the optical properties of semiconductor II-VI and III-V material systems for passive and active semiconductor systems.

Stephan W. Koch
Department of Physics, University of Marburg
Marburg, Germany
Mathematics, College of Optical Sciences, University of Arizona, Nonlinear Control Strategies
Tucson, AZ 

Stephan W. Koch is a professor of physics at the University of Marburg in Germany, and an adjunct professor of optical sciences at the University of Arizona. Research interests include microscopic calculation of optical properties of semiconductor passive and active media.