Contains reports on six research projects.Defense Advanced Research Projects Agency Universities Research Initiative (Contract N00014-46-K-0760)Strategic Defense Initiative/Innovative Science & Technology, managed by the U.S. Naval Research Laboratory (Contract N00014-87-K-2031)National Science Foundation (Grant EET-87-18417

Auyang, Sunny Y. C.

Becla, Piotr

Foner, Simon

Ram-Mohan, L. Ramdas

Sohn, Richard B.

Stark, Jason

Walrod, David B.

Wolff, Peter A.

Wong, Stephen

Xie, Hui

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Chapter 2. Infrared Nonlinear OpticsChapter 2. Infrared Nonlinear OpticsAcademic and Research StaffProfessor Peter A. Wolff, Dr. Sunny Y.C. Auyang, Dr. Piotra Becla, Professor L. Ramdas Ram-Mohan1Graduate StudentsAdy Levy, Cynthia Mcintyre, Jason Stark, David B. Walrod, Stephen Wong2.1 Magnetoresistance ofHgMnTeSponsorDefense Advanced Research Projects AgencyUniversities Research Initiative(Contract N00014-46-K-0760)Project StaffDr. Piotr Becla, Simon Foner, Professor PeterA. Wolff, Stephen WongAt low temperatures, p-type HgMnTe has anenormous negative magnetoresistance.2 Insome cases, magnetic fields of 6T decreaseits resistivity by factors as large as 106 to 106.To determine the mechanism of the largeconductivity change, we have performedpulsed, high electric field measurements ofcurrent-voltage characteristics in p-HgMnTe.The form of the i-v curves suggests that thelarge conductivity change results from amagnetic field induced, insulator-metal tran-sition. This conclusion is also consistentwith very low temperature transport measure-ments. 3Previous theoretical calculations4 have shownthat modest magnetic fields (B-5T) reorderthe valence band states in p-HgMnTe,causing a pancake-shaped acceptor wavefunction with a large radius in the transversedirection. The insulator-metal transition isthen caused by the increased spread of theacceptor state. The theory also implies thatthe magnetic pressure recompresses theacceptor to a spherical form at much higherfields. This conclusion has been confirmedwith magnetoresistance measurements in theFrancis Bitter National Magnet Laboratorypulsed field facility.5  Above 20T, theresistivity of cold p-HgMnTe increasessteadily - suggesting an ultimate return tothe insulator state - with dramatic changesin the ratio of parallel to perpendicular con-ductivity.2.2 Mode Mixing inGap SemiconductorsNarrowSponsorStrategic Defense Initiative/InnovativeScience & Technology, managed by theU.S. Naval Research Laboratory(Contract N00014-87-K-2031)Project StaffProfessor L. Ramdas Ram-Mohan, Richard B.Sohn, Hui Xie, Professor Peter A. Wolff1 Worcester Polytechnic Institute, Worcester, Massachusetts.2 A. Mycielski and J. Mycielski, J. Phys. Soc. Japan 49: Suppl. A807 (1980).3 T. Wojtowicz, T. Dietl, A. Sawicki, W. Plesiewicz, and J. Jaroszynski, Phys. Rev. Lett. 56:2419 (1986).4 A. Mycielski and J. Mycielski, J. Phys. Soc. Japan 49: Suppl. A807 (1980).5 S.B. Wong, P.A. Wolff, S. Foner, and P. Becla, Bull APS 34:7333 (1989), Abstract J15 2; S.B. Wong,Magnetotransport Studies of the Magnetic Field Induced, Metal-Insulator Transition in Hg1 -xMnxTe. Ph.D. diss.,Dept. of Phys., MIT, 1988.Chapter 2. Infrared Nonlinear OpticsThe effects of interband transitions inducedby resonant longitudinal-optic (LO) phononshave been studied theoretically in narrow gapPbl-xSnxTe 6 and Hgl-xCdxTe.7  With thebandgap, Eg, close to the LO phonon energy,hCL, we: 1) evaluate the dielectric functioncontaining contributions from interband tran-sitions induced by the LO phonons and bythe Coulomb potential interacting with car-riers, 2) show that the LO phonon-intrabandplasmon mixing is strongly influenced by theinterband transitions, leading to a downward"renormalization" in energy of the mixedmode, and 3) calculate the threshold forstimulated emission of LO phonons when acrystal with EG-hOL is optically pumped.These theoretical predictions could be testedwith infrared reflectivity experiments. Thecalculated reflectivity spectra are substantiallychanged by interband processes. Moreover,the threshold for stimulated phonon emission(Ithreshold-lkW/cm 2) is well within reach ofCO 2 laser technology.2.3 Plasma InstabilitiesQuasi-Two- Dimensional IElectron GasesSponsorNational Science Foundation(Grant EET-87-18417)Project StaffJason Stark, Professor Peter A. WolffRecent pulsed optical experiments inn-doped GaAs quantum wells8 suggest thathot carriers relax in times as short as 10 fsec,while p-type or undoped quantum wells haverelaxation times on the order of 50 fsec. Thisdiscrepancy is surprisingly large. WhileMonte Carlo calculations9 can account forsome of the trends in hot carrier relaxationexperiments, times as short as 10 fsec aredifficult to understand in terms of single-particle relaxation mechanisms.As an alternative, we have theoreticallystudied'o the possibility of collective modeinstabilities in these 2D systems. Thedielectric function of a quasi-two-dimensional electron gas is calculated, in therandom phase approximation, for a plasmawith a non-thermal, excited component.From this function, the plasma eigenfrequen-cies are determined for the case of a degen-erate electron plasma in the presence ofelectrons excited to energy, E0, above theFermi energy. Under such excitation,intrasubband plasma modes experience gainby inverse Landau damping, via coupling tothe energetic electrons. This behavior con-trasts with that of a three-dimensionalplasma, which is stable to the production ofplasmons for any spherically symmetricexcited distribution." The instability of two-dimensional plasmons is caused bysingularities in the one-dimensional densityof states for electrons travelling parallel tothe plasma mode. The unstable modes expe-rience amplification at rates on the order ofthe plasma frequency, relaxing energy fromthe excited distribution. While these growthrates are not fast enough to account for theobserved relaxation rates in n-dopedquantum wells, the calculations indicate analternative relaxation path, and imply thattwo-dimensional plasmas are less stable thanthose in three dimensions.To date, theserestricted to thecalculations havecase of a strictlybeentwo-6 L.R. Ram-Mohan, R.B. Sohn, and P.A. Wolff (to be published).7 H. Xie, L.R. Ram-Mohan, and P.A. Wolff (to be published).8 W.H. Knox, D.S. Chemla, G. Livescu, J.E. Cunningham, and J.E. Henry, Phys. Rev. Lett. 61:1290 (1988).9 S.M. Goodnick and P. Lugli, Phys. Rev. B 37:2578 (1988).10 J.B. Stark and P.A. Wolff (to be published).11 A.I. Akhiezer, I.A. Akhiezer, R.V. Polovin, A.G. Sitenko, and K.N. Stepanov, Collective Oscillations in a Plasma,Cambridge, Massachusetts: MIT Press, 1967.86 RLE Progress Report Number 131Chapter 2. Infrared Nonlinear Opticsdimensional plasma, without intersubbandtransitions. We are now investigating thestability of intersubband modes that areknown to have large oscillator strengths.Experiments to test these ideas will be per-formed by Jason Stark in collaboration withDaniel Chemla and Wayne Knox of AT&TBell Laboratories.2.4 Nonlinear Optics of ZeroGap SemiconductorsSponsorDefense Advanced Research Projects AgencyUniversities Research Initiative(Contract N00014-46-K-0760)Strategic Defense Initiative/InnovativeScience & Technology, managed by theU.S. Naval Research Laboratory(Contract N00014-87-K-2031)Project StaffDr. Sunny Y.C. Auyang, Professor Peter A.WolffIn previous work, we have demonstrated thatzero gap semiconductors, including HgTe, 12HgCdTe, and HgMnTel 3 have large thirdorder optical susceptibilities at 10.6y. Forexample, in Hg0.84Cd0.16Te with small bandgap at 80 K, X(3) = 1.5x10 -3 esu was meas-ured with CO2 laser, four-wave mixing exper-iments. Optical non-linearity in these zerogap materials is attributed to interband popu-lation modulation, caused by laser-inducedcarrier temperature fluctuations. Since thecarrier temperature relaxes rapidly (5 psec) tothat of the lattice, this process has a farhigher saturation power than the conven-tional band filling non-linearity in wider gapmaterials.To confirm this hypothesis, we calculatedl4the non-linear coefficient versus intensity inHg0.84Cd0.16Te. At low intensities, the the-oretical value, X(3) = 2x10 - 3 esu, is in reason-able agreement with the measuredX(3) = 1.5x10 - 3 esu. When the laser intensityexceeds I=10 kW/cm 2, X(3) falls because ofthe increase in Auger recombination ratecaused by the increase in dynamic carrierdensity. For instance, at 1=1 MW/cm 2, thedynamical carrier density is approximately3x1016/cc, with a corresponding electronFermi energy of 60 meV. The large Fermienergy pushes electrons to states of heaviermass, thereby reducing their mass. Thiseffect is quite pronounced in Hg0.84Cdo.16Te,which has nearly zero (F8 - F6) splitting, butless severe in HgMnTe whose (F8 - F6) split-ting is about 0.2 eV. These calculationspredict the saturation behavior observed inour four-wave mixing experiments.2.5 Optical Nonlinearity Dueto Resonant ImpurityScattering in HgCdSe:FeSponsorDefense Advanced Research Projects AgencyUniversities Research Initiative(Contract N00014-46-K-0760)Project StaffDr. Sunny Y.C. Auyang, Professor Peter A.WolffYears ago, Kaw' 5 suggested that large opticalnon-linearities could be caused by energy-dependent scattering rates of free carriers insemiconductors. It has since been recog-nizedl 6 that this mechanism is not effective inthe case of "soft" collisions, such as those12 P.A. Wolff, S.Y. Yuen, K.A. Harris, J.W. Cook, Jr., and J.F. Schetzina, Appl. Phys. Lett. 50:1858 (1987).13 S.Y. Auyang, P.A. Wolff, K.A. Harris, J.W. Cook, Jr., and J.F. Schetzina, J. Vac. Sci. Technol A6:2693 (1988).14 S.Y. Auyang and P.A. Wolff, JOSA, in press; P.A. Wolff, S.Y. Yuen, K.A. Harris, J.W. Cook, Jr., and J.F. Schetzina,to be published in Proceedings SPIE Meeting, Los Angeles, 1988.15 P. Kaw, Phys. Rev. Lett. 21:239 (1968).16 P.A. Wolff, S.Y. Yuen, and G.A. Thomas, Solid State Commun. 60:645 (1986).Chapter 2. Infrared Nonlinear Opticsdue to ionized impurities, but remains validfor abrupt, energy-dependent scatterings.n-HgCdFeSe provides an excellent exampleof such a scattering system, since Mycielskiet al.17 have shown that the Fe3+ level formsa sharp scattering resonance in the con-duction band. Thus, large optical non-linearities due to the Kaw mechanism areanticipated. To test this hypothesis, wehave performed 18 four-wave mixing exper-iments on HglxCdxSe:Fe samples withx=0.23 and x=0.30. In the former, wherethe Fe (3d) 6 level is resonant with the con-duction band, the measured X(3) is 20 timeslarger than in the x=0.30 sample with thed-level in the gap. These measurements sub-stantiate the Kaw mechanism; moreover, ourtheoretical calculations predict a X(3) in agree-ment with the measured value.2.6 Four-Wave Mixing inHeavily Doped n-GaAs EpilayersSponsorNational Science Foundation(Grant EET-87-18417)Project StaffDr. Sunny Y.C. Auyang, David B. Walrod,Professor Peter A. WolffRecent four-wave mixing experiments19 haveshown that the X(3) 's of heavily dopedn-GaAs epilayers are 100 times larger thanthose of bulk samples with the same dopinglevel. The effect has been observed in anumber of n-GaAs epilayers and also inn-lnSb epilayers. Since the electron plasmafrequencies in these highly doped samplesare approaching the 10.6 y laser frequency,we tentatively attribute the enhancement toplasma resonance effects. Calculations andfurther experiments to test this hypothesis arein progress.PublicationsMIT ThesisWong, S.B., Magnetotransport Studies of theMagnetic Field Induced, Metal-InsulatorTransition in Hg-xMnxTe. Ph.D. diss.,Dept. of Physics, MIT, 1988.17 A. Mycielski, P. Dzwonkowski, B. Kowalski, B.A. Orlowski, M. Dobrowolski, and J.M. Baranowski, J. Phys.C1 9:3605 (1986).18 P.A. Wolff, S.Y. Auyang, R.R. Galazka, and A. Mycielski, J. Vac. Sci. Technol. A6:2696 (1988).19 D.B. Walrod, S.Y. Auyang, P.A. Wolff, and R. Nahory, Bull. APS 34:460 (1989), Abstract B147.88 RLE Progress Report Number 131

Infrared Nonlinear Optics

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Infrared Nonlinear Optics

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