Amplification of terahertz radiation on intersubband transitions has been analyzed by numerical Monte Carlo simulation for p-type delta-doped Ge films with in-plane transport configuration of applied electric and magnetic fields. A significant increase of the gain is found, compared to existing bulk p-Ge lasers, due to spatial separation of light and heavy hole streams, which reduces scattering of light holes on ionized impurities and heavy holes. The considered device has potential as a widely tunable (2-4 THz) laser with high duty cycle and operating temperatures up to 50 K

Dolguikh, M. V.

Muravjov, A. V.

Peale, R. E.

English

University of Central Florida (UCF): STARS (Showcase of Text, Archives, Research & Scholarship)

University of Central Florida STARS Faculty Bibliography 2000s Faculty Bibliography 1-1-2006 Terahertz amplification in delta-doped germanium films with in-plane transport M. V. Dolguikh University of Central Florida A. V. Muravjov University of Central Florida R. E. Peale University of Central Florida Find similar works at: https://stars.library.ucf.edu/facultybib2000 University of Central Florida Libraries http://library.ucf.edu This Article is brought to you for free and open access by the Faculty Bibliography at STARS. It has been accepted for inclusion in Faculty Bibliography 2000s by an authorized administrator of STARS. For more information, please contact STARS@ucf.edu. Recommended Citation Dolguikh, M. V.; Muravjov, A. V.; and Peale, R. E., "Terahertz amplification in delta-doped germanium films with in-plane transport" (2006). Faculty Bibliography 2000s. 6088. https://stars.library.ucf.edu/facultybib2000/6088 J. Appl. Phys. 99, 093106 (2006); https://doi.org/10.1063/1.2193067 99, 093106© 2006 American Institute of Physics.Terahertz amplification in delta-dopedgermanium films with in-plane transportCite as: J. Appl. Phys. 99, 093106 (2006); https://doi.org/10.1063/1.2193067Submitted: 13 October 2005 . Accepted: 09 March 2006 . Published Online: 12 May 2006M. V. Dolguikh, A. V. Muravjov, and R. E. PealeTerahertz amplification in delta-doped germanium filmswith in-plane transportM. V. Dolguikh, A. V. Muravjov, and R. E. PealeaDepartment of Physics, University of Central Florida, Orlando, Florida 32816 and College of Opticsand Photonics, University of Central Florida, Orlando, Florida 32816Received 13 October 2005; accepted 9 March 2006; published online 12 May 2006Amplification of terahertz radiation on intersubband transitions has been analyzed by numericalMonte Carlo simulation for p-type delta-doped Ge films with in-plane transport configuration ofapplied electric and magnetic fields. A significant increase of the gain is found, compared to existingbulk p-Ge lasers, due to spatial separation of light and heavy hole streams, which reduces scatteringof light holes on ionized impurities and heavy holes. The considered device has potential as a widelytunable 2–4 THz laser with high duty cycle and operating temperatures up to 50 K. © 2006American Institute of Physics. DOI: 10.1063/1.2193067INTRODUCTIONGeneration of terahertz stimulated emission on direct op-tical transitions between valence subbands for bulk p-Gecrystals in crossed electric E and magnetic B fields is wellknown.1,2 The lifetime of magnetized light holes, which de-fines the population inversion, depends on three major scat-tering processes. Acoustic phonon scattering, which in-creases with lattice temperature, tends to thermalize thedesired nonequilibrium hole distribution. Scattering of lightholes on ionized impurities limits the maximum acceptableconcentration of acceptors, and thus the concentration of ac-tive carriers, to the level of 1014 cm−3, so that the gain hasnot exceeded 0.1–0.2 cm−1 in homogeneously doped p-Gelasers. Carrier-carrier collisions also cause intersubband andintrasubband transitions.3 We recently presented4 a planarp-Ge laser concept with vertical transport, in which periodicdelta doping reduces scattering of light holes on impuritiesand heavy holes, thus increasing the upper laser-level life-time. The resulting increase in gain would allow operatingtemperatures up to 77 K and continuous duty cycle whilepreserving the feature in bulk p-Ge lasers of broad tunability2–4 THz. In this paper we present a different configurationof the intersubband terahertz laser on delta-doped multilayerGe thin films, in which the transport is predominantly inplane. Spatial separation of light and heavy hole streams isachieved, but with significantly larger carrier concentrationsthan possible for vertical transport, which allows muchhigher gain. Theoretical results for the considered device ob-tained by means of Monte Carlo simulation are presentedhere.A practical goal is development of a terahertz laser basedon thin germanium films with small signal gain coefficientsufficient to operate at liquid nitrogen temperatures. An ad-ditional motivating factor for pursuing this approach, whenterahertz quantum cascade lasers have already achieved thistemperature milestone,5,6 is the unique very wide gain spec-trum 2–4 THz for the transitions between valence sub-bands. This feature is potentially important for building aterahertz laser with wide tunability, which none of the otherknown terahertz semiconductor lasers possesses.7THEORETICAL METHODSHole dynamics, hole distribution functions, and the gainon direct optical light-to-heavy hole transitions are calculatedby the Monte Carlo simulation method using classical mo-tion equations and hole scattering probabilities.8,9 Two va-lence subbands light and heavy holes with isotropic andparabolic dispersion laws are considered. The isotropic ap-proach is justified by the small warping of the germaniumvalence band. We can neglect quantum confinement effectsbecause the considered structure has no heteroboundaries,only delta-doped layers. We also neglect Landau quantiza-tion, which is a good approximation for magnetic fields of2 T and below. Time or ensemble averaged momentum andposition yield the hole distribution functions f l,hk ,r sub-band l ,h, wave vector k, and coordinate r. The distribu-tion functions were considered uniform in the horizontalplanes according to the geometry of the problem. The stan-dard Rees rejection technique chooses among scatteringprocesses.8 The rate of each scattering process is given by atemperature-dependent analytic expression. Optical phononscattering is treated in a deformation potential approxima-tion.10,11 Acoustic phonon scattering is simplified accordingto Ref. 12. Inelasticity for acoustic phonon scattering isincluded.13 Brooks-Herring model14 with inverse Debyescreening length and Yukawa potential was used for ionizedimpurity scattering. Hole-hole scattering was calculated ac-cording to Ref. 3. Iteration determines the self-consistent so-lution of the Poisson equation and thereof the spatial carrierdistribution and potential profile.4 The small signal gain iscalculated as the difference between the gain on direct inter-subband light-to-heavy hole transitions and free carrier ab-sorption assisted by phonons and ionized impurities.13,15 Upto liquid nitrogen temperatures and impurity concentrationsof 1015–1016 cm−3, the main contribution to free carrierabsorption comes from optical phonon emission by heavyholes.15 Lattice absorption16 was not included in the calcula-tions and was considered separately see below.aElectronic mail: rep@physics.ucf.eduJOURNAL OF APPLIED PHYSICS 99, 093106 20060021-8979/2006/999/093106/4/$23.00 © 2006 American Institute of Physics99, 093106-1CALCULATION RESULTSThe mechanism of building up the population inversionin p-type germanium in crossed electric and magnetic fieldsis presented in Fig. 1. Due to different effective masses, theratio between the magnitudes of applied electric and mag-netic fields can be chosen typically E=1.5 kV/cm and B=1 T, so that light holes become confined on cyclotron tra-jectories below the optical phonon energy threshold, givingthem long lifetimes. For the same fields, heavy hole trajec-tories are only slightly perturbed, allowing frequent scatter-ing on optical phonons.The in-plane carrier transport configuration for activedelta-doped germanium structures is presented in Fig. 2. Themagnetic field is oriented along the layers. The orientation ofthe electric field is chosen to keep the heavy hole current Jhwithin the doped layers. Light holes move across the un-doped layers due to the drift in the direction perpendicular toboth applied electric and magnetic fields. The structure pe-riod is chosen to roughly equal the average light hole freepath at 10–20 K for the applied fields. The average carrierconcentration is chosen to be 1−21015 cm−3. This trans-port configuration achieves spatial separation of light holesfrom both impurity and heavy holes. Though some heavyholes remain in the undoped regions their negative effect onthe inversion population is less severe than that of ionizedimpurity centers.4Figure 3 presents the pattern of hole trajectories withinone period of the structure from the actual Monte Carlosimulation with parameters given in the caption. Heavy holesare depicted by thin black lines, which tend to flow down-ward along, and be concentrated within, the doped layers.Light holes thin white lines drift across the undoped region.On this scale, the cyclotron orbits of heavy holes are justvisible while those of light holes are smaller than the widthof the drift lines.The calculated electric potential surface is presented inFig. 4. In the given applied fields Figs. 2 and 3 and in thepresence of optical phonon scattering, heavy holes experi-ence streaming motion along the doped layers. Because lightholes are free from inelastic optical phonon scattering, theymore rapidly gain a significant vertical component of EBFIG. 2. Schematic of in-plane transport of carriers in periodically delta-doped p-type germanium structures in crossed electric and magnetic fields.The surface indicates the periodic doping profile. Currents Jh and Jl andelectric field E are coplanar and perpendicular to the applied B field. E is thesuperposition of the applied electric field and the Hall field. Electric2–3 kV/cm and magnetic 2 T fields, applied as shown, provide strongcurrent of heavy holes Jh along heavily doped layers with intense ionizedimpurity and phonon scattering indicated by open circles and stars, respec-tively. Light holes are pulled from the layers by the fields and have com-ponent of current Jl across the layers. These light holes have a long lifetimein the undoped regions, with their trajectories defined by the self-consistentbuilt-in electric field.FIG. 3. Monte Carlo simulated hole trajectories within one period of thedelta-doped structure in crossed electric and magnetic fields. E=3 kV/cm,B=2 T, period d=2000 nm, and average hole concentration is 1.51015 cm−3. The white trajectories represent light holes, while the blacktrajectories represent heavy holes.FIG. 4. Self-consistent potential profile calculated for the same parametersas Fig. 3, except E=2.5 kV/cm.FIG. 1. Mechanism of stimulated emission on direct optical transitions be-tween light and heavy hole subbands. The left graph shows light and heavyhole orbits in the plane perpendicular to the applied magnetic field. The rightfigure shows the allowed energies of light and heavy holes as a function ofthe magnitude of the momentum wave vector. Heavy holes scatter rapidlywith optical phonon emission. Light holes are magnetized, have muchsmaller scattering rates, and therefore have a long lifetime. Overpopulationof the light hole subband results in terahertz gain on direct optical light-to-heavy hole transitions.093106-2 Dolguikh, Muravjov, and Peale J. Appl. Phys. 99, 093106 2006drift velocity. Thus, light holes enter the undoped regions inhigher absolute numbers than heavy holes do.Resulting light and heavy hole concentration distribu-tions are shown in Fig. 5 together with the doping profile fora structure with average carrier concentration of 1.51015 cm−3 and d=2000 nm. In the center of the undopedregions, the concentration of light holes exceeds that ofheavy holes. Considering the much higher density of statesin the heavy hole band, this then represents a very highlyinverted population in such regions of the crystal. The heavyholes moving along the doped layers create strong negativeinversion in these regions. The concentration peak of lightholes inside the doped layers represents light holes that ex-perience transition to the heavy hole band before they havethe chance of escaping to the undoped regions. These lightholes partially compensate the negative inversion inside thedoped layers created by the heavy holes.Figure 6 presents the spatial-spectral gain distributioncalculated with the same parameters as Figs. 4 and 5. Gain isshown as a function of optical transition wave number andvertical distance in the structures. Heavy black contours in-dicate the intersection of the gain surface with the zero-gainlevel. The gain surface has strong broad amplification bandsin the undoped regions and narrow but strong absorptionregions near the doped layers. The gain surface follows thecarrier distribution in Fig. 5. Free carrier absorption has beenincluded in Fig. 6.The spatially averaged net gain in the structure is pre-sented in Fig. 7. Results with and without free carrier absorp-tion are presented. Even with free carrier absorption, the gainat 100 cm−1 of nearly 1 cm−1 exceeds that in usual bulk p-Gelasers by a factor of about 10.Figure 8 presents the dependence of the gain at 100 mwavelength on lattice temperature for two different structureperiods. Comparison of the gain is made with experimentalgermanium lattice absorption at the same wavelength.16 Netgain persists up to at least 40 K. Calculations of the gain fordifferent applied fields and structure periods confirm the ex-pectation that the optimal period of the structure for themaximum average gain should approximately equal themean free path of the light holes. For parameters as in Figs.3–5 this length is about 2 m, which can be seen in Fig. 5from the exponential decrease of the light hole concentrationwith the vertical distance from the doped layers. A smallerperiod would allow light holes to cross the undoped regionand scatter on impurities in the next layer. Moreover, asmaller period allows relatively more frequent interaction be-tween light and heavy holes. A larger period would increasethe relative thickness of the absorbing regions near the dopedlayers. At higher temperatures and higher doping concentra-tions, the mean free path decreases. This decreases the op-timal period of the structure, which can be seen in Fig. 8 asthe crossing of the 1 and 2 m curves near 40 K.DISCUSSION AND CONCLUSIONMeans of creating an inversion population on direct op-tical transitions between light and heavy hole subbands withFIG. 5. Distribution of light and heavy hole concentrations across the struc-ture. Most of the heavy holes are concentrated in the vicinity of the dopedlayers, whereas light holes have much higher concentration in the undopedregions than have heavy holes.FIG. 6. Spatial-spectral gain distribution across two structure Nav=1.51015 cm−3, d=2000 nm, E=2.5 kV/cm, B=2 T, T=10 K with free car-rier absorption included.FIG. 7. Calculated spatially averaged terahertz gain  in the structure withparameters as for Figs. 4–6. The net curve - includes the free carrierabsorption coefficient .FIG. 8. Spatially averaged gain at 100 m wavelength as a function oflattice temperature. The legend indicates the structure period. Experimentalgermanium lattice absorption Ref. 16 is presented for comparison.093106-3 Dolguikh, Muravjov, and Peale J. Appl. Phys. 99, 093106 2006in-plane transport in delta-doped structures have been pro-posed theoretically and demonstrated with Monte Carlosimulation. The spatial separation of light holes from ionizedimpurities and separation of currents for light and heavyholes eliminate light hole scattering on ionized impuritiesand on the majority of heavy holes. This allows an increaseof light hole concentration to the level of 1–31014 cm−3, which is ten times higher than the typical lighthole concentration in bulk p-Ge lasers.The desired separation of light and heavy hole streamsrequires the majority of heavy holes to flow along the dopedlayers, while light hole current has a vertical component. Asshown in Figs. 2 and 3, this requires that the internal electricfield have a vertical component in the growth direction. Incase of trivial contact configuration on the edges of the struc-ture, when net carrier transport is parallel to the doped layers,heavy hole current would point slightly into the undopedmaterial, in order to compensate the vertical component oflight hole current see Fig. 2. This in turn could lead tosmaller gain values than calculated. In order to achieve theoptimal gain one should arrange a slight drain of the currentin the vertical direction approximately 10% of the in-planecurrent value to adjust the direction of heavy hole current tolie within the doped layers. This can be achieved, in prin-ciple, by making an array of auxiliary contacts on the top andthe bottom of the structure.Due to the high gain estimates found for the considereddevice, higher temperature operation is possible than for bulkp-Ge lasers. The smaller active volume and planar geometryfacilitate heat extraction, which will allow higher duty. Thesimplicity and low growth precision requirements allowchemical vapor deposition CVD, which can produce struc-tures of remarkable active thickness. High quality structures,similar to those discussed here, with the thickness above30 m have been demonstrated.4 Due to the homoepitaxialnature of the structure and an absence of hetero interfaces,growth of 100–150 m thick structures without remarkabledefect concentrations appears feasible. Such structures wouldbe suitable for making low-loss confocal cavities for thespectral range of 2–4 THz.ACKNOWLEDGMENTSThis work was partially supported by AFOSR ContractNos. F49620-02-C-0025 and F49620-02-C-0027. One of theauthors R.E.P. acknowledges support from an ASEE/AFRLsummer faculty fellowship in 2005 and the encouragementof his host, Dr. Richard Soref.1V. N. Shastin, Opt. Quantum Electron. 23, S111 1991.2E. Bründermann, in Long Wavelength Infrared Semiconductor Lasers, ed-ited by H. K. Choi Wiley, New Jersey, 2004, pp. 279–343.3M. V. Dolguikh, A. V. Muravjov, and R. E. Peale, Phys. Rev. B 73,075327 2006.4M. V. Dolguikh, A. V. Muravjov, R. E. Peale, M. Klimov, O. A. Kuz-netsov, and E. A. Uskova, J. Appl. Phys. 98, 023107 2005.5B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, Appl.Phys. Lett. 82, 1015 2003.6B. S. Williams, S. Kumar, H. Callebaut, Q. Hu, and J. L. Reno, Appl.Phys. Lett. 83, 5142 2003.7A. V. Muravjov, M. V. Dolguikh, R. E. Peale, O. A. Kuznetsov, and E. A.Uskova, Proc. SPIE 5727, 44 2005.8C. Jacoboni and L. Reggiani, Rev. Mod. Phys. 55, 645 1983.9C. Jacoboni, R. Brunetti, and P. Bordone, in Theory of Transport Proper-ties of Semiconductor Nanostructures, edited by E. Scholl Chapman andHall, London, 1998, p. 59.10G. L. Bir and G. E. Pikus, Symmetry and Strain-induced Effects in Semi-conductors Wiley, New York, 1974.11P. Lawaetz, Phys. Rev. 174, 867 1968.12J. D. Wiley, Phys. Rev. B 4, 2485 1970.13E. V. Starikov and P. N. Shiktorov, Opt. Quantum Electron. 23, S1771991.14B. K. Ridley, Quantum Processes in Semiconductors Oxford UniversityPress, New York, 1999.15Yu. K. Pozhela, E. V. Starikov, and P. N. Shiktorov, Phys. Status Solidi B128, 653 1985.16R. Brazis and F. Keilmann, Solid State Commun. 70, 1109 1989.093106-4 Dolguikh, Muravjov, and Peale J. Appl. Phys. 99, 093106 2006

Terahertz amplification in delta-doped germanium films with in-plane transport

Crossref

https://stars.library.ucf.edu/cgi/viewcontent.cgi?article=7087&amp;context=facultybib2000

Terahertz amplification in delta-doped germanium films with in-plane transport

Abstract

Similar works

Full text

Available Versions

University of Central Florida (UCF): STARS (Showcase of Text, Archives, Research & Scholarship)

Crossref