We report analysis of the carrier distribution during terahertz emission process with carrier–phonon interaction based on p-doped strained SiGe/Si single quantum-well. The results of this analysis show that a considerable number of carriers can penetrate the phonon wall to become “hot” carriers on an approximately picosecond timescale. These hot carriers relax after the removal of the applied voltage, generating a “second” emission in the measurement. This investigation provides an understanding of the carrier dynamics of terahertz emission and has an implication for the design of semiconductor terahertz emitters

Hong, C. C.

Hung, K. M.

Kuo, J.-Y.

Soref, R. A.

Sun, Greg

English

University of Massachusetts Boston: ScholarWorks at UMass

University of Massachusetts BostonScholarWorks at UMass BostonPhysics Faculty Publications Physics5-24-2010Carrier dynamics of terahertz emission based onstrained SiGe/Si single quantum wellK. M. HungNational Kaohsiung University of Applied SciencesJ.-Y. KuoNational Kaohsiung University of Applied SciencesC. C. HongNational Taiwan UniversityGreg SunUniversity of Massachusetts Boston, greg.sun@umb.eduR. A. SorefAir Force Research Laboratory, Hanscom Air Force BaseFollow this and additional works at: http://scholarworks.umb.edu/physics_faculty_pubsPart of the Physics CommonsThis Article is brought to you for free and open access by the Physics at ScholarWorks at UMass Boston. It has been accepted for inclusion in PhysicsFaculty Publications by an authorized administrator of ScholarWorks at UMass Boston. For more information, please contact library.uasc@umb.edu.Recommended CitationHung, K. M.; Kuo, J.-Y.; Hong, C. C.; Sun, Greg; and Soref, R. A., "Carrier dynamics of terahertz emission based on strained SiGe/Sisingle quantum well" (2010). Physics Faculty Publications. Paper 9.http://scholarworks.umb.edu/physics_faculty_pubs/9Carrier dynamics of terahertz emission based on strained SiGe/Si singlequantum wellK. M. Hung, J.-Y. Kuo, C. C. Hong, H. H. Cheng, G. Sun et al.  Citation: Appl. Phys. Lett. 96, 213502 (2010); doi: 10.1063/1.3432075 View online: http://dx.doi.org/10.1063/1.3432075 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v96/i21 Published by the American Institute of Physics.  Related ArticlesVertical nonpolar growth templates for light emitting diodes formed with GaN nanosheets Appl. Phys. Lett. 100, 033119 (2012) Irregular spectral position of E || c component of polarized photoluminescence from m-plane InGaN/GaN multiplequantum wells grown on LiAlO2 Appl. Phys. Lett. 99, 232114 (2011) Improvement in spontaneous emission rates for InGaN quantum wells on ternary InGaN substrate for light-emitting diodes J. Appl. Phys. 110, 113110 (2011) Influence of high temperature AlN buffer on optical gain in AlGaN/AlGaN multiple quantum well structures Appl. Phys. Lett. 99, 171912 (2011) Two-color InGaN/GaN microfacet multiple-quantum well structures grown on Si substrate J. Appl. Phys. 110, 083518 (2011)  Additional information on Appl. Phys. Lett.Journal Homepage: http://apl.aip.org/ Journal Information: http://apl.aip.org/about/about_the_journal Top downloads: http://apl.aip.org/features/most_downloaded Information for Authors: http://apl.aip.org/authors Downloaded 29 Mar 2012 to 158.121.194.143. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionsCarrier dynamics of terahertz emission based on strained SiGe/Si singlequantum wellK. M. Hung,1 J.-Y. Kuo,1 C. C. Hong,2 H. H. Cheng,2,a G. Sun,3 and R. A. Soref41Department of Electronics Engineering, National Kaohsiung University of Applied Sciences,Kaohsiung 807, Taiwan2Center for Condensed Matter Sciences and Graduate Institute of Electronics Engineering,National Taiwan University, Taipei 106, Taiwan3Department of Physics, University of Massachusetts–Boston, Boston, Massachusetts 02125, USA4Sensors Directorate, Air Force Research Laboratory, Hanscom AFB, Massachusetts 01731, USAReceived 12 November 2009; accepted 26 April 2010; published online 24 May 2010We report analysis of the carrier distribution during terahertz emission process with carrier–phononinteraction based on p-doped strained SiGe/Si single quantum-well. The results of this analysis showthat a considerable number of carriers can penetrate the phonon wall to become “hot” carriers on anapproximately picosecond timescale. These hot carriers relax after the removal of the appliedvoltage, generating a “second” emission in the measurement. This investigation provides anunderstanding of the carrier dynamics of terahertz emission and has an implication for the design ofsemiconductor terahertz emitters. © 2010 American Institute of Physics. doi:10.1063/1.3432075The development of semiconductor light sources in theenergy range of terahertz THz has attracted a great deal ofattention in recent years.1–10 In group-IV p-type doped struc-tures, THz emission has been reported in both bulk Ge andstrained SiGe single quantum well SQW structures.1–6 Inboth these cases, the energy band of the valence band is splitinto heavy-hole HH and light-hole LH bands. Emissionhas been attributed to the optical transition of electricallyexcited carriers between the impurity levels associated withthe HH and LH bands. The dynamics of these carriers hasbeen characterized by a streaming motion under the consid-eration that the energy of the excited carriers can only in-crease up to that of optical phonons before being scattered,because of the presence of a “hard” phonon wall. A previoustheoretical analysis of the carrier distribution under an ap-plied electric field indicated the occurrence of populationinversion;5,6 this led to investigations for obtaining a betterunderstanding of the emission mechanism and for improvingthe emission efficiency.We report analysis of the carrier dynamics of the THzemission with carrier–phonon interaction on the p-dopedstrained SiGe/Si SQW structure. The results show that theelectrically excited carriers attain the LO-phonon energywithin the timescale of picosecond and a considerable num-ber of carriers move beyond the LO-phonon energy level tobecome “hot” carriers. These hot carriers relax after the re-moval of the applied voltage, generating a “second” emissionas demonstrated in the measurement.The sample used in this study was grown by MolecularBeam Epitaxy MBE on n-type Si 100 substrate104  cm. It comprises a a 100-nm-thick undoped Sibuffer layer, b a 20-nm-thick Si0.85Ge0.15 layer with boron-doped at the center, and c a 20-nm-thick Si capping layerwith boron -doped at the center. The doping concentrationsfor layers b and c are determined to be 51011 cm−2 bythe technique of secondary ion mass spectrometry. Thesample was cut into 1 cm2 squares with four polished sides.Aluminum contact electrodes, separated by 6 mm, were de-posited on top of the sample. This was followed by rapidthermal annealing to allow Al to diffuse into the SiGe middlelayer to form Ohmic contacts. The resistivity of the sample is7.5 k cm at 4.2 K. The SiGe SQW is under in-plane com-pressive strain and the HH band lie below the LH band. Aschematic of the flat valence band profile along the growthdirection is plotted in Fig. 1. Quantum confinement results inthe formation of confined subband levels. For the HH andLH subbands, the ground state is denoted by EHH and ELH,respectively. The associated ground-state acceptor levels forthe two ground states are denoted as EHH1S and ELH1S, respec-tively. The energy splitting between EHH and ELH is 32 meV,and the LO-phonon energy is LO=59.1 meV3 for thestructure described above.Under an electrical field applied along the SQW plane,the free carriers located at the bottom of HH subband gainenergy following the in-plane dispersion relationship of theHH subband. A schematic diagram of the in-plane dispersionaAuthor to whom correspondence should be addressed. Electronic mail:hhcheng@ntu.edu.tw.EnergyE 1sHHHH bandedgeEHHELHSi SiGe SiLH bandedgeLHE 1sHHE 1sLHHHopticalphononenergyE 1sLHFIG. 1. Color online Left: Schematic diagram of SiGe SQW valence bandprofile along the growth direction. The confined levels of HH and LH bandsare denoted as EHH and ELH and their associated acceptor levels are denotedas EHH1S and ELH1S , respectively. Right: in-plane dispersion curve of the twobands. Carrier dynamics showing the three processes of 1 resonant tunnel-ing, dashed arrow line, 2 THz optical transition dotted arrow line, and3 LO-phonon scattering dashed-dotted arrow line.APPLIED PHYSICS LETTERS 96, 213502 20100003-6951/2010/9621/213502/3/$30.00 © 2010 American Institute of Physics96, 213502-1Downloaded 29 Mar 2012 to 158.121.194.143. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionscurve for both the HH and the LH subbands is plotted inFig. 1. As carriers accelerate toward high energy levels, thefollowing two processes occur: a as the carrier energy ap-proaches that of ELH1S, some of the carriers undergo resonanttunneling to occupy the acceptor level ELH1S indicated by thedashed arrow line while the rest continue to accelerate to-ward higher energy levels. Those carriers that have tunneledto the ELH1S state can then fall to the lower-energy acceptorstates of EHH1S, yielding THz emission indicated by the dottedarrow line. The remaining carriers continue to accelerate,passing the energy level ELH1S. b Upon reaching the energylevel of the LO-phonon, a “hard” phonon wall is imposedwhere all the carriers are scattered by the emission of opticalphonons and relax toward the top of the HH subband indi-cated by the dashed-dotted arrow line. These relaxed carri-ers repeatedly undergo the two processes described above;this process is referred to as “streaming motion.”The time-dependent carrier distribution function fk canbe expressed as follows:5,6 fkt+eF fkkx=   fkttunnel+   fktelastic, 1where k=kxiˆ+kyjˆ is the in-plane carrier-momentum vectorand F is the strength of the electric field. The terms on theright-hand side of Eq. 1 represent the rate of change in fkassociated with the tunneling process first term and carrier-impurity elastic scattering second term. It is observed thatpopulation inversion occurs between the energy level of theexcited state of ELH1S and several impurity levels of the HHsubband; this population inversion is attributed to the slowrecombination rate for the ELH1S to EHH1S transition as comparedto the timescale of the carriers reaching the energy level ofELH1S.5,6Here, we have “softened” the phonon wall by includingthe carrier–phonon interaction in the modeling. The rateequation of LO-phonon scattering is given by11,12  fktLO-phonon= qDq2q2Ek − Ek+q − LOfk+q − fk ,2where Dq is the carrier–LO-phonon coupling constant and isdefined as Dq2= 1 /−1 /0e2LO /2Ad, where 0 isthe dielectric constants at highzero frequencies. A is thesample area and d is the thickness of the SQW. Using theparameters from references5,6 for Eq. 1 and a free carrierconcentration of Ef =1 meV, fk is calculated for a range ofelectric fields from 100 to 1500 V/cm applied along thex-direction. A color contour profile for an electric field of1200 V/cm and the spectra recorded at ky =0 are plotted inFig. 2. At t=0 Fig. 2a, fk is centered at the zone center ofthe HH subband with kx2+ky2=0. As t increases, fk elongatesalong the field direction and the peak amplitude of fk reducesas the carrier energy increases, as shown in the spectra Figs.2b–2d. This decrease in the peak amplitude of fk is at-tributed to various scattering processes. At t=1 ps Fig.2b, as the energy of the carriers approaches the acceptorlevel of ELH1S, which is denoted by the red dashed line, thefollowing two processes occur. First, a few carriers are scat-tered back to the energy region of the HH zone center, asshown by the weak feature in the spectrum indicated by thesolid arrow line; this scattering is attributed to the elasticscattering described above. Second, carriers undergo reso-nant tunneling to occupy the ELH1S state and subsequently fallto the EHH1S state, leading to THz emission. At aroundt=3 ps Fig. 2c, most of the carriers cross the resonantstate of ELH1S and acquire energies that are approximatelyequal to the LO-phonon energy denoted by the green dashedline. The distribution function broadens because of LO-phonon scattering. At this point, the energy levels of somecarriers become higher than the LO-phonon energy level,while very few carriers appear in the energy region of theHH zone center, as indicated by the weak amplitude in thespectrum plotted in the inset; this is attributed to the lowcoupling strength of the carrier–LO-phonon interaction. Att=5 ps Fig. 2d, fk broadens further as more carriers aresubjected to phonon scattering. However, a considerablenumber of carriers are distributed beyond the LO-phononenergy level. A similar behavior is also observed under otherelectric fields. Under low electric fields, carriers penetrate thephonon wall with a longer time; the opposite behavior isobserved for large voltages.The measurement of the THz emission from our samplewas conducted as follows. A voltage pulse generator wasused for electrical excitation; this generator produces asquare pulse voltage with a pulse magnitude up to 1000 Vand a pulse duration of 1–14 	s AVTEC. A resistor with aresistance of 1  was placed in series with the sample inorder to measure the current. For THz detection, a Ga-dopedGe detector was used. The detector was first calibrated byboth electrical and optical measurements at a temperature of	6 K. Electrical measurement revealed that the detector ex-hibited an electrical characteristic similar to that of a conven-1SLHELOKx (109m-1)Ky(108m-1)FIG. 2. Color Contour diagram of time evolution of carrier distributionfunction plotted as a function of kx and ky. Spectra for ky =0 are also shown.Electric field of 1200 V/cm is applied along the kx-direction. The coloredmark on the left-hand side indicates the intensity of the distribution function.213502-2 Hung et al. Appl. Phys. Lett. 96, 213502 2010Downloaded 29 Mar 2012 to 158.121.194.143. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionstional PN junction, wherein at an applied voltage of 	2 V,the current increases rapidly. Optical characterization wasperformed using Fourier transform infrared spectroscopyequipped with a helium-cooled Si bolometer. The spectrumshowed that the detector responded to an energy range from	50 to 150 cm−1 with two sharp transitions with peak posi-tions at 68 and 74 cm−1 and a reasonably sharp transitionwith a peak position at 137 cm−1 The absorption spectrumof the detector is shown as insert of Fig. 3. THz emissionwithin this range will induce a photocurrent in the detectorwhich was biased at the onset of 2 V. Measurements of theemission from the sample were performed at a low tempera-ture of 4.2 K, with both the sample and the detector im-mersed in liquid helium. The detector was placed near thesample at a distance of about 5 mm.A family of recorded signals with different pulsed volt-ages of a duration of 4 	s is shown in Fig. 3. Two distinctsignals are clearly resolved; one labeled S1 appeared withinthe pulse duration t4 	s and another labeled S2 afterthe applied pulsed voltage was switched off. Signal S1 isassociated with the optical transition of ELH1S →EHH1S as dis-cussed above. For signal S2, the emission is associated withthose carriers that exhibit energies greater than the phononenergy. These hot carriers relax after the removal of the ap-plied voltage. As the carriers pass through the energy level inresonance with the ELH1S state, they can once again tunnel tothe ELH1S state and undergo a transition to the EHH1S state, yield-ing a second THz emission.In summary, we have presented the analysis of the car-rier dynamics of THz emission by taking into account thecarrier–phonon interaction. The results show that most of thecarriers cross the LO-phonon energy level. This suggests thatthe mechanism of streaming motion employed previously isnot supported. These findings provide a practical understand-ing of the carrier dynamic during THz emission process andcan assist the design of semiconductor THz emitters.The authors would like to thank the National ScienceCouncil of the Republic of China for its financial supportunder Grant No. 98–2112–M-002–014–MY3.1I. V. Altukhov, E. G. Chirkova, M. S. Kagan, K. A. Korolev, V. P. Sinis,M. A. Odnoblyudov, and I. N. Yassievich, Sov. Phys. JETP 88, 51 1999.2Yu. P. Gousev, I. V. Altukhov, K. A. Korolev, V. P. Sinis, M. S. Kagan, E.E. Haller, M. A. Odnoblyudov, I. N. Yassievich, and K. A. Chao, Appl.Phys. Lett. 75, 757 1999.3A. Blom, M. A. Odnoblyudov, H. H. Cheng, and K. A. Chao, Appl. Phys.Lett. 79, 713 2001.4I. V. Altukhov, E. G. Chirkova, V. P. Sinis, M. S. Kagan, Yu. P. Gousev, S.G. Thomas, K. L. Wang, M. A. Odnoblyudov, and I. N. Yassievich, Appl.Phys. Lett. 79, 3909 2001.5M. A. Odnoblyudov, I. N. Yassievich, M. S. kagan, Y. M. Galperin, and K.A. Chao, Phys. Rev. Lett. 83, 644 1999.6M. A. Odnoblyudov, I. N. Yassievich, V. M. Chistyakov, and K. A. Chao,Phys. Rev. B 62, 2486 2000.7A. Borak, S. Tsujino, C. Falub, M. Scheinert, L. Diehl, E. Müller, H. Sigg,D. Grützmacher, U. Gennser, I. Sagnes, S. Blunier, T. Fromherz, Y. Cam-pidelli, O. Kermarrec, D. Bensahel, and J. Faist, Mater. Res. Soc. Symp.Proc. 832, p. F4.2.1 2005.8S. Tsujino, H. Sigg, M. Scheinert, D. Grützmacher, and J. Faist, IEEE J.Sel. Top. Quantum Electron. 12, 1642 2006.9S. A. Lynch, P. Townsend, G. Matmon, D. J. Paul, M. Bain, H. S. Gamble,J. Zhang, Z. Ikonic, R. W. Kelsall, and P. Harrison, Appl. Phys. Lett. 87,101114 2005.10S. G. Pavlov, H.-W. Hübers, J. N. Hovenier, T. O. Klaassen, D. A. Carder,P. J. Phillips, B. Redlich, H. Riemann, R. K. Zhukavin, and V. N. Shastin,Phys. Rev. Lett. 96, 037404 2006.11K. Hess, Advanced Theory of Semiconductor Devices Prentice-Hall, NewJersey, 1988.12P. Lawaetz, Phys. Rev. B 4, 3460 1971.0 2 4 6 8 10 1202040608010012040 80 120 160 200Absorption(arbunit)Wavenumber (cm-1)S2330V/cmSignallevel(meV)Time (s)1300V/cm670V/cm1000V/cmS1FIG. 3. Measured signal level at different applied voltages with a pulsedduration of 4 	s. Dashed line marks the removal of applied pulsed voltage.Inset: absorption spectrum of the photodetector.213502-3 Hung et al. Appl. Phys. Lett. 96, 213502 2010Downloaded 29 Mar 2012 to 158.121.194.143. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions

Carrier dynamics of terahertz emission based on strained SiGe/Si single quantum well

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Carrier dynamics of terahertz emission based on strained SiGe/Si single quantum well

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