Evans, CA

Ikonic, Z

Kelsall, RW

Lever, LJM

Valavanis, A

White Rose Research Online

This is a repository copy of Theory and design of (111) oriented Si/SiGe quantum cascade lasers.White Rose Research Online URL for this paper:http://eprints.whiterose.ac.uk/110097/Version: Published VersionConference or Workshop Item:Valavanis, A orcid.org/0000-0001-5565-0463, Lever, LJM, Evans, CA et al. (2 more authors) Theory and design of (111) oriented Si/SiGe quantum cascade lasers. In: Photon 08, 26-29 Aug 2008, Edinburgh, UK. (Unpublished) eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. Institute of Microwaves and PhotonicsSCHOOL OF ELECTRONIC AND ELECTRICAL ENGINEERING,FACULTY OF ENGINEERINGTheory and design of (111) oriented Si/SiGe quantum cascade lasersA. Valavanis*, L. Lever, C. A. Evans, Z. Ikonić and R. W. Kelsall* a.valavanis05@leeds.ac.ukOverview• Conduction band structure• QCL design• Transport calculations• Waveguide modelling and gain(001) conduction bandQCL design complicated due to:• Strain → different energies for valley sets (perpendicular & in-plane) • Anisotropy → different effective masses for valley sets• Perp. effective mass ≈ 0.92 me → small oscillator strengthBulk Si/SiGe band edge in 6 valleys (for Ge < 85%)Conduction band offsetsUsable (001) band offset limited [2]:• Deep quantum wells for perp. valleys. (ΔV ≈ 400 meV)→ Strongly bound states• But, shallow wells for in-plane valleys overlap→ Strong optical absorption→ Leakage currents• QCL design limited to energies below in-plane valleys[2] A. Valavanis et. al., Phys. Rev. B 78, 035420 (2008)(111) conduction bandMany problems solved by moving to (111) orientation:• Identical valley cross-sections→ All valleys at same energy→ All effective masses identical• Smaller quantisation effective mass ≈ 0.26 me [1]→ larger oscillator strength[1] S. Smirnov & H. Kosina, Solid-State Electron. 48, 1325 (2004)Conduction band offsets• (001) energy range limited by  strain splitting between valley sets→ Large substrate Ge content desirable• But ~10% Ge needed for mechanical stability→ Usable energy range ~ 50 meV• No strain splitting between valleys in (111) orientation→ Band offset increases with barrier Ge fraction→ 50% Ge barriers give 150 meV band offsetBound to continuum QCL design5.2 THz, seven well design• Optical transition between bound state and continuum states• Si wells/Si0.6Ge0.4 barriers• n-type doping of 5×1016 cm-3 throughout (modulation doping may be poor)• Designed for 7.4 kV/cm applied electric field• 10% Ge virtual substrate for strain balanceTransport modellingScattering rates used to determine populations:• Time independent perturbation model of scattering• Self-consistent solution of rate equations gives populationsPopulation inversion achieved:• Fast Coulombic scattering depopulates miniband• Long upper laser level lifetime:• Si wells minimise alloy disorder scattering• Low Ge barriers reduce interface roughness• Optical transition (20 meV) below phonon energy (43 meV)Current density• Current density peaks at design field due to band alignment• Low temperature peak of 2 kA/cm2• Current increases with temperature due to faster scattering10-120KWaveguide modellingSurface plasmon waveguide:• Poor confinement, Γ=17%• Low waveguide losses aw=10 cm-1• High threshold gain:2D finite element modelling of modal overlap:Double-metal waveguide:• Γ=100%• Threshold gain of 31 cm-11-mwTH cm 68=Γ+= aagGain spectrum• Calculated at 7.4 kV/cm applied electric field• Peak at 5.2 THz• Other peaks due to transitions to lower energy subbands•Gain decreases with temperature due to• Linewidth broadening• Reduced population inversion• Gain exceeds losses up to 105 KConclusions(111) oriented Si/SiGe is a good candidate for THz QCLs• Low effective mass: mq = 0.26 me• Large usable band offset: ΔV ~ 150 meVNet gain predicted for bound-to-continuum laser• 5.2 THz emission• Double metal waveguide has gain threshold of 31 cm-1• Gain predicted up to 105 KAcknowledgmentsThis work is supported by• EPSRC doctoral training allowance funding• DTI-MNT contract 491: “Fast THz Cameras”

Theory and design of (111) oriented Si/SiGe quantum cascade lasers

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Theory and design of (111) oriented Si/SiGe quantum cascade lasers

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