IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 44, NO. 6, JUNE 2008
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Measurement of Semiconductor Laser Gain by the Segmented Contact Method Under Strong Current Spreading Conditions Sergey Suchalkin, David Westerfeld, Member, IEEE, Gregory Belenky, Fellow, IEEE, John D. Bruno, John Pham, Fred Towner, and Richard L. Tober
Abstract—A segmented contact method for the measurement of optical gain is developed for the case of strong current spreading. A simple model of current spreading in a ridge laser with a segmented contact is proposed and analyzed. We show that current spreading effects should be taken into account in lasers with low threshold current densities and high “opening” voltages. When applied to interband cascade lasers, the method gives an internal optical loss of 10–17 cm 1 and a differential gain of 2.9 cm/A at 80 K, which agrees well with previously reported Hakki–Paoli data. The limitations of the technique are discussed. Index Terms—Interband cascade lasers (ICL), Mid-infrared (IR) lasers, optical gain.
I. INTRODUCTION PTICAL gain measurements are one of the most important characterization procedures for semiconductor lasers. There are several techniques that allow one to measure the optical gain in absolute units. These include the analysis of the longitudinal mode contrast (Hakki–Paoli [1] and Cassidy [2] approaches), the “reciprocal efficiency versus cavity length” approach, [3] and “single pass” techniques [4]–[8]. The latter method allows a direct measurement of the net gain and internal optical loss of the laser structure and is not limited to subthreshold pumping as the Hakki–Paoli technique is. “Single pass” measurements on a diode laser can be done using a segmented upper contact, which allows for varying the length of the pumped section of the device [7], [9]. By measuring the amplified spontaneous emission spectra corresponding to different pumped lengths, one can obtain the net optical gain spectra of the structure. The technique requires the measurement of the length of the pumped segments, which can be a problem under conditions of strong current spreading since the
O
Fig. 1. Distribution of optical gain along the device under conditions of low and high current spreading.
Manuscript received October 3, 2007; revised December 12, 2007. This work was supported in part by NYSTAR under Contract C020000, in part by the Army Research Office (ARO) under Grant W911NF0610399, and in part by the National Science Foundation (NSF) under Grant DMR0710154. S. Suchalkin and G. L. Belenky are with the State University of New York (SUNY) at Stony Brook, StonyBrook, NY 11794-2350 USA e-mail:
[email protected];
[email protected]). D. Westerfeld is with the Power Photonic Corporation, Stony Brook, NY 11790 USA (e-mail:
[email protected]). J. D. Bruno, F. J. Towner, and J. T. Pham are with Maxion Technologies, Inc., College Park, MD 20740 USA (e-mail:
[email protected]; ftowner@maxion. com;
[email protected]). R. L. Tober is with the U.S. Army Research Laboratory, Adelphi, MD 207831197 USA (e-mail:
[email protected]). Digital Object Identifier 10.1109/JQE.2008.917972
pumped region is then not precisely delineated. The efficacy of current spreading depends on the laser structure design and on the bias current range. For lasers characterized by low threshold current densities and relatively high “opening” voltages such as interband cascade lasers (ICLs) the current spreading is efficient and must be taken into account. We can identify two major problems with the segmented contact method when it is used under strong current spreading conditions. • Maintaining the same current density at all of the pumped segments If current spreading cannot be ignored, simple scaling of the total bias current with the number of segments in the pumped area does not provide for a fixed pumping condition. A possible way to control the current density is obtained by monitoring the spontaneous emission intensity through the special windows in the segment contacts [9]. This requires precise intensity measurements with high spatial resolution of the light collection. • Accurately determining the effective length of the pumped section As illustrated in the Fig. 1, the actual length of the pumped stripe can exceed the total length of the pumped segments, and the optical gain may vary with the coordinate along the stripe. In this paper, we suggest a way to avoid these difficulties, and we present a “single pass” method developed for the case of strong current spreading.
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Fig. 2. Equivalent electrical scheme for current spreading. The arrows represent the current flow.
(though we still have current spreading outside the pumped region). Assuming that the segments are uniform, electrical connection of zeroth and first segments at the condition of constant voltage will not change the total current flowing through the unpumped segments. The current profile will not change but just shift towards the unpumped side of the stripe. As the additional segments are connected to the pumped stripe, the total current will increase with constant increment. The bias current density can then be found as a ratio of the current increment and segment area. B. Experimental Determination of Current Spreading Parameters
II. CURRENT SPREADING A. Theoretical Model In the simplest model, the structure can be presented as a one dimensional semi-infinite chain of resistors (Fig. 2), where is the lateral resistance, which does not depend on the bias is the effective transverse resistance of the segvoltage, and is high at ment, which depends on the transverse current . low transverse currents reflecting the fact that transverse voltage cannot be less than the “opening” voltage of the device. The gain is proportional to the effective transverse current . In the case of strong current spreading, the effective transverse is not equal to the total curcurrent under the th segment which is fed into this segment. To obtain a simple anrent alytical expression connecting and , we assume that is independent of current and voltage. This assumption is only good for the analysis of the limiting cases. The segment number is counted from the left (light emitting) edge of the stripe. If is fed into the zeroth segment (Fig. 3), the total current the transverse current under the th segment can be expressed through the total bias current as
where (1) The dimensionless parameter is between 0 and 1 and depends and the effective on the ratio between the lateral resistance . If , the current transverse resistance spreading is strong and the effective length of the pumped region exceeds the total length of the pumped stripes. Another . At this condition, is small and limiting case is most of the bias current flows through the pumped zeroth seg. In a real device, changes from ment: segment to segment and depends on the bias current, so the current spreading profile changes with the bias. If we electrically connect the zeroth and first segments and , then in the limit of weak current spreading, the double transverse current density stays the same whereas in the limit of strong current spreading, the same procedure will lead up to a twofold increase in the bias current density under the pumped segments. This problem can be eliminated by replacing the current source with a voltage source. By maintaining the same voltage on all the segments in the pumped region we ensure a uniform transverse current density in the pumped sections
To study the effects of current spreading we used an interband cascade laser (ICL) [10] with a segmented upper contact. These lasers operated in the spectral range 2–5 m and are characterized by a low threshold current density K) [11], [12] and relatively high ( 5–15 A/cm opening voltages V K), so in the bias current range of interest, the current spreading is strong. The 3-mm-long upper contact of the deeply etched stripe was divided into 14 segments separated by 20- m-wide trenches. The trench depth should be sufficient to reduce current spreading between the adjacent segments but not so deep that additional optical losses are introduced. A trench depth of 0.08 m was chosen to cut through the highly conductive cap layer of our sample without producing significant damage to the upper optical cladding layer. Light propagating along the waveguide was collected from the uncoated facet at the end of the 3-mm-long sample. Additionally, each segment of the device had a separate windowed electrical contact allowing observation of the intensity of light emitted in the direction normal to the sample surface. The first step of the experiment was to measure the dependence of the electroluminescence (EL) intensity observed through the contact windows on the segment voltage. This measurement was made with uniform pumping of all segments, and was used as a reference for experiments where the segments were not all pumped. This was accomplished by recording the average emission from the windows while pumping with all segments connected in parallel. This uniform-pumping – characteristic was recorded at numerous discrete voltages; cubic spline interpolation was then used to allow the prediction of light emission at arbitrary voltages within the experimental range. The reference – dependence was measured in a similar way: all segments were electrically connected and transverse bias current under a segment was recorded as a function of bias voltage. We found that EL intensity distribution along the stripe correlates with the current distribution, so the contribution of the scattered light is small and we can use EL as a tool to monitor the current spreading. Mid-infrared (mid-IR) images of pumped sections consisting of different numbers of segments are presented in Fig. 3. The spots between the segments look brighter possibly due to slightly increased light scattering at the intersegment trenches. The current spreading makes it very difficult to determine the absolute length of the pumped section as well as the pumping current. The low variation of EL intensity within the pumped
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SUCHALKIN et al.: MEASUREMENT OF SEMICONDUCTOR LASER GAIN
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Fig. 4. Total current through the device versus number of pumped segments.
Fig. 3. Mid-IR images of with 1 (top), 2, 3, 4, 5, and 6 (bottom) segments pumped. U = 6:684 V.
segments indicates that the current density within the pumped region is reasonably constant and the material is uniform. The EL intensity distribution along the stripe changes with the bias current. The dependencies of the total current through the structure on the number of pumped segments at different pumping voltages are presented in Fig. 4. The functions show a deviation from a linear dependence with longer pumped sections. At low pumping voltages and longer pumped lengths, the dependences become sublinear while at higher pumping voltages superlinear deviations were observed. The sublinear dependence can be explained as an effect of the finite length of the device. At low pumping voltages current spreading is very effective and as the end of the pumped section shifts closer to the right end of the device (i.e., more segments are pumped) the “current spreading tail” is interrupted by the sample edge and the current increment is reduced. In the linear regime, the total current scales with the area of the pumped section: increasing the pumped length by one segment increases the total current by a constant increment. This increment corresponds to the transverse current through each segment of the pumped section. The ratio of the current increment to the segment area gives the pumping current density. At higher voltages and longer excited sections, the total current increases superlinearly with the pumped section length. Below we will show that this may indicate the effect of high intensity emission on the lifetime of the injected carriers. In the framework of the semi-infinite resistor chain model presented above, it is possible to determine the values of the intersegment impedances. With two segments (13 and 14) on the end of the sample pumped, we measure the voltages at all of the other segments. Using a reference – characteristic it is possible to determine the transverse current under th contact from the measured segment contact voltage. The measured segment voltages and interpolated segment currents are presented in Fig. 5.
Fig. 5. Segment voltages and currents.
The in-plane resistances can be computed from the data in Fig. 5 as the voltage differences between neighboring segments divided by the sum of the currents in all of the lower-numbered segments. The results are shown in Fig. 6. Two of the resistor values (11 and 13) are zero due to the fact that segments 13 and 14 are electrically connected in this experiment, as are segments 11 and 12. The average value for the other resistances is 23.5 , and is fairly constant between segments. The intersegment resistance 1 is somewhat higher than the others, possibly due to inaccuracies in determining the current of the end segcan be calculated ment. An in-plane resistance of 117.5 from the 100- m stripe width and 20- m trench width. The effective transverse resistance Re can be calculated from the data in Fig. 5 as the ratio between segment voltage and transverse current. III. GAIN MEASUREMENTS A. Method Description In the case of high current spreading, the effective length of the “gain stripe” may be considerably greater than the length of the pumped section. Moreover, outside the pumped section, the gain becomes a function of the coordinate along the stripe. Let us consider the optical gain as a function of the current density , wavelength and the coordinate along the stripe . Under the assumption that the emission
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Fig. 6. Intersegment resistances.
Fig. 7. ASE spectra taken at different pumped section lengths.
intensity is low enough that we can neglect the effect light intensity could have on the optical gain (i.e., ignoring gain saturation resulting from a reduction of carrier concentration through stimulated emission), we can express the spectral intensity of light emitted by a stripe of the length (5) is the current density in the pumped segments, is a function proportional to the local spectral radiance of the active area material at the current density , and taken at the left edge of the stripe (Fig. 1). This integral can be presented as a sum of two parts: an integral over the and are constant, pumped section of the length , where and and an integral over the rest of the stripe where both vary as a result of current spreading where
(6) It should be stressed that here is the total length of the pumped segments. Resolving the first integral and denoting the second , we obtain integral as (7) By measuring spectra corresponding to three different lengths, , and we obtain a system of three independent equations and . Since all the pumped segthat can be solved for ments have the same potential, there is no lateral current between them and, for a long enough sample, does not depend on the length of the pumped section. The simplest form of the solution can be obtained if (8) In this case, the optical gain can be expressed as (9)
Fig. 8. Optical gain at different pumping current densities.
where are the spectra of amplified spontaneous emission, measured at three different pumped section lengths which fulfill (8). Same formula was used by Xin et al. [13] to eliminate the effect of unguided spontaneous emission. B. Experiment Amplified spontaneous emission spectra taken at different pumped section lengths are presented in Fig. 7. The back facet of the device was destroyed to avoid generation. One can see that the light intensity increases superlinearly with pumped length near the spectrum maxima, which, according to (9), indicates optical amplification. The slight modulation of the spectra is probably due to onset of the substrate modes [14], [15]. Gain curves obtained using amplified spontanteous emission (ASE) spectra from three pumped sections of different length are presented in Fig. 8. An internal optical loss of approximately 10–17 cm and a differential gain of 2.9 cm/A agree well with previously reported Hakki–Paoli data [14]. The gain spectrum calculated using ASE spectra from two pumped sections is shown in Fig. 9 (hollow circles). To obtain this gain curve we used emission spectra from one- and two segment pumped sections. One can see a strong deviation from the calculated gain spectrum when the current spreading is accounted for (solid squares). At higher bias voltages, the peak gain measured by the single path method decreases and the shape of the gain curve changes.
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SUCHALKIN et al.: MEASUREMENT OF SEMICONDUCTOR LASER GAIN
Fig. 9. Single pass gain spectra obtained with and without considering the current spreading effect.
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accuracy of the single pass technique under these high field conditions. Accurate measurements require that the segments be small enough so that the carrier concentration under maximum pumping is not significantly depleted over the length of three segments. While the length of the individual segments is determined by the highest gain that is to be measured; the overall length of the sample is determined by the lowest gain that is anticipated and the current spreading distance. The overall length must be sufficient to observe a significant change in ASE over the available pumped length. Also, the sample must be long enough that the unpumped region at the back of the sample is larger than the current spreading distance so that the current spreading “tail” does not reach the facet. The sample under consideration used segments of uniform length. This simplifies the mathematical analysis, but is not required to use the single pass technique. An exponentially increasing segment size would permit a single mask set to be used for samples having very different maximum gains. IV. SUMMARY
Fig. 10. Amplified spontaneous emission spectra for different pumped section lengths.
This result can be explained in terms of gain reduction due to a high optical field. This process is similar to the optical gain pinning in a semiconductor laser. If the pumped section is long and bias current is high, the intense ASE depletes the concentration of injected carriers in the wells and reduces the optical gain even without a laser cavity. This process is clearly seen in the transformation of the ASE spectrum as the pumped section length increases (Fig. 10). The crossing points in Fig. 10 indicate where the intensity in the high-energy wing of the ASE spectrum starts to decrease with increased pumped section length. This indicates carrier concentration depletion induced by the high intensity optical field [16]. The effect of carrier concentration depletion under conditions of long pumped lengths and high injection is also revealed in the superlinear increase of total current with increased pumped section length (Fig. 4, highest two voltages). In this case, the high optical field results in a decreased injected carrier lifetime due to stimulated emission. At low temperatures the leakage in ICLs is small and recombination in the optical quantum wells gives the major contribution to the total current through the device. At this condition the decreased carrier lifetime results in increased current since the pump voltage is maintained constant. Operation in the long-pumped-length and high-injection regime where the optical field affects the carrier concentration invalidates the assumptions which underlie (9), and limits the
Current spreading in ICL structures depends on the bias voltage, and the current may spread for very considerable distances under low bias voltages. The effective current spreading distance decreases with increased bias. The 2-D in-plane spe. cific resistance of this ICL structure is 117 A single pass optical gain measurement technique was developed that can be applied under conditions of strong current spreading, i.e., when the typical current spreading distance is not much less than the pumped length. The applicability conditions for this method have been discussed. The single pass technique was used to measure the internal optical loss of 10–17 cm and differential gain of 2.9 cm/A at 80 K of an ICL structure. These measurements agree well with previous Hakki–Paoli results. The effect of optical depletion of carrier concentration was observed at high bias current and longer pumped sections. The effect manifests itself as a decrease in the EL intensity in the short wavelength part of the EL spectrum and a superlinear increase of the total current with the pumped section length ACKNOWLEDGMENT The authors would like to thank G. Meissner for help with device mounting. REFERENCES [1] B. W. Hakki and T. L. Paoli, “Gain spectra in gaas double-heterostructure injection lasers,” J. Appl. Phys., vol. 46, pp. 1299–1306. [2] D. T. Cassidy, “Technique for measurement of the gain spectra of semiconductor diode-lasers,” J. Appl. Phys., vol. 56, pp. 3096–3099, 1984. [3] G. H. B. Thompson, G. D. Henshall, J. E. A. Whiteaway, and P. A. Kirkby, “Narrow-beam 5-layer (GaAl)As/GaAs heterostructure lasers with low threshold and high peak power,” J. Appl. Phys., vol. 47, pp. 1501–1514, 1976. [4] K. L. Shaklee and R. F. Leheny, “Direct Determination of Optical Gain in Semiconductor Crystals,” Appl. Phys. Lett., vol. 18, p. 475, 1971. [5] P. S. Cross and W. G. Oldham, “Monolithic Measurement of Optical Gain and Absorption in PbTe,” J. Appl. Phys., vol. 46, pp. 952–954, 1975. [6] E. O. Goebel, G. Luz, and E. Schlosser, “Optical gain spectra of InGaAsP-InP Double heterostructures,” IEEE J. Quantum Electron., vol. QE-15, no. 8, pp. 697–700, Aug. 1979.
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[7] P. Blood, G. M. Lewis, P. M. Smowton, H. Summers, J. Thomson, and J. Lutti, “Characterization of semiconductor laser gain media by the segmented contact method,” IEEE J. Sel. Topics Quantum Electron., vol. 9, no. 5, pp. 1275–1282, Sep./Oct. 2003. [8] D. Westerfeld, S. Suchalkin, R. Kaspi, A. P. Ongstad, and G. L. Belenky, “Absorption and single-pass gain measurements in optically pumped type-II midinfrared laser structures,” IEEE J. Quantum Electron., vol. 40, no. 12, pp. 1657–1662, Dec. 2004. [9] J. D. Thomson, H. D. Summers, P. J. Hulyer, P. M. Smowton, and P. Blood, “Determination of single-pass optical gain and internal loss using a multisection device,” Appl. Phys. Lett., vol. 75, pp. 2527–2529, Oct. 1999. [10] R. Q. Yang, J. L. Bradshaw, J. D. Bruno, J. T. Pham, and D. E. Wortman, “Mid-infrared type-II interband cascade lasers,” IEEE J. Quantum Electron., vol. 38, no. 6, pp. 559–568, Jun. 2002. [11] C. L. Canedy, W. W. Bewley, M. Kim, C. S. Kim, J. A. Nolde, D. C. Larrabee, J. R. Lindle, I. Vurgaftman, and J. R. Meyer, “High-tempera: – : m,” Appl. Phys. ture interband cascade lasers emitting at Lett., vol. 90, Apr. 2007. [12] J. L. Bradshaw, N. P. Breznay, J. D. Bruno, J. M. Gomes, J. T. Pham, F. J. Towner, D. E. Wortman, R. L. Tober, C. J. Monroy, and K. A. Olver, “Recent progress in the development of type II interband cascade lasers,” Physica E, vol. 20, pp. 479–485, Jan. 2004. [13] Y. C. Xin, Y. Li, A. Martinez, T. J. Rotter, H. Su, L. Zhang, A. L. Gray, S. Luong, K. Sun, Z. Zou, J. Zilko, P. M. Varangis, and L. F. Lester, “Optical gain and absorption of quantum dots measured using an alternative segmented contact method,” IEEE J. Quantum Electron., vol. 42, no. 7, pp. 725–732, Jul. 2006. [14] S. Suchalkin, J. Bruno, R. Tober, D. Westerfeld, M. Kisin, and G. Belenky, “Experimental study of the optical gain and loss in InAs/GaInSb interband cascade lasers,” Appl. Phys. Lett., vol. 83, pp. 1500–1502, Aug. 2003. [15] D. Westerfeld, S. Suchalkin, M. Kisin, G. Belenky, J. Bruno, and R. Tober, “Experimental study of optical gain and loss in 3.4–3.6 m interband cascade lasers,” in Proc. IEEE Optoelectron., Aug. 2003, vol. 150, pp. 293–297. [16] E. O. Goebel, O. Hildebrand, and K. Lohnert, “Wavelength Dependence of Gain Saturation in GaAs Lasers,” IEEE J. Quantum Electron., vol. 13, no. 10, pp. 848–854, Oct. 1977.
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Sergey Suchalkin graduated from St. Petersburg Electrical Engineering University, St. Petersburg, Russia, in 1989 and received the Ph.D. degree in physics and mathematics from the Ioffe Physical Technical Institute, St. Petersburg, Russia, in 1998. His thesis research was focused on far-infrared spectroscopy of semiconductor structures in a strong magnetic field. After graduation, he worked at the Ioffe Physical Technical Institute and the Max Planck Institute, Stuttgart, Germany. Since 2000, he has been with the department of Electrical and Computer Engineering, State University of New York at Stony Brook. He is a coauthor of more than 40 scientific papers in refereed journals, one review and one book chapter. His research interests include physics of low-dimensional semiconductor structures as well as design and characterization of semiconductor lasers.
David Westerfeld (M’00) received the A.S. degree in engineering science from the State University of New York at Farmingdale in 1996. He received the B.S., M.S., and Ph.D. degrees in electrical engineering from Stony Brook University, Stony Brook, NY, in 1999, 2001, and 2005, respectively. He is with the Power Photonic Corporation where he works on GaSb based high power mid-IR laser and LED projects. He is also an adjunct faculty member at Stony Brook University. Before joining Power Photonic, he worked for Northrop Grumman on airborne electronic and optical systems. Mr. Westerfeld is a member of the IEEE Laser and Electro-Optics Society, the IEEE Education Society, and the Optical Society of America.
Gregory L. Belenky (F’05) received the Ph.D. degree in physics and mathematics from the Institute of Semiconductors, Kiev, Ukraine (formerly U.S.S.R.), in 1969 and the Doctor of Physical and Mathematical Sciences degree from the Institute of Physics, Baku, Azerbaijan (formerly U.S.S.R.). In 1991, he joined the AT&T Bell Laboratories, Murray Hill, NJ and, in 1995 he joined the State University of New York at Stony Brook, where he is currently a Distinguished Professor in the Department of Electrical and Computer Engineering. His ideas have found application in the development of continuous wave midinfrared lasers and laser array with record room temperature characteristics in the 2.3–2.7 spectral range. He is an author of more than 130 papers, principal author of four reviews and several patents. His former Ph.D. students are successfully working in the USA, Russia, Japan and Azerbaijan.
John D. Bruno received the B.S. degree in physics from The Cooper Union at New York in 1974 and the Ph.D. degree in condensed matter theory from Rutgers University, New Brunswick, NJ, in 1980. His thesis research employed renormalization group methods to study the critical behavior of compressible magnetic systems. After a postdoctoral position in the Physics Department at The University of Utah and a Faculty position in the Physics Department at Villanova University, he joined the technical staff of The Army Research Laboratory (formally Harry Diamond Laboratories), Adelphi, MD, where he worked primarily in the area of III–V semiconductor optoelectronic device physics and MBE growth. In 2000, he co-founded Maxion Technologies, Inc., College Park, MD, where he presently serves as President and CTO. He has co-authore more than 60 publications in peer-reviewed journals along with a number of technical reports, presentations, and patents.
Fred J. Towner received the B.S. degree in physics from the Pennsylvania State University, University Park, in 1986 and the M.S. degree in electrical engineering from the University of Maryland, Baltimore County, in 1992. In 1986, he joined Martin Marietta Laboratories, Baltimore, MD, where he worked in the areas of optoelectronics and crystal growth. In 1997, he joined Quantum Epitaxial Designs, Bethlehem, PA, and worked with the large scale production of epi wafers. In 2002, he joined Maxion Technologies, Inc., College Park, MD, to head crystal growth efforts in support of the companies IR laser programs. He has co-authored more than 20 publications in peer-reviewed journals.
John T. Pham received the B.S. degree in electrical engineering from University of Maryland, College Park, in 1989. In 1989, he joined the Army Research Laboratory, Adelphi, MD, where he worked in the area optoelectronic device fabrication and packaging. In 2000, he co-founded Maxion Technologies, Inc., College Park, MD, and worked in the area of device fabrication and packaging. He has co-authored more than 20 publications in peer-reviewed journals.
Richard L. Tober received the Ph.D. degree in solid-state physics from the University of Texas at Dallas. He then held a post-doctoral position at the Center for Applied Quantum Electronics, North Texas State University, under Prof. A. Smirl, studying optical properties of MBE grown quantum well structures. He then accepted a position as Research Physicist at the Army Research Laboratory, Adelphi, MD. Since then, he has investigated fundamental properties of MBE grown III–V materials for optoelectronic devices and has published on topics ranging from a symmetry forbidden pyroelectric effect in strained-layer quantum wells grown on [111] substrates to the optical properties of type-II superlattice IR detector structures. Recently, he became the program leader for the Army’s mid-IR laser development program and is responsible for coordinating the MBE growth, laser fabrication and packaging, and experimental research efforts. He spent three months in Iraq during 2007 in order to help transition technology to the war fighter.
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