Control of Electron-State Coupling in Asymmetric $\mathrm{Ge}/\mathrm{Si}\text{\ensuremath{-}}\mathrm{Ge}$ Quantum Wells

Control of Electron-State Coupling in Asymmetric $Ge / Si − Ge$ Quantum Wells

C. Ciano, M. Virgilio, M. Montanari, L. Persichetti, L. Di Gaspare, M. Ortolani, L. Baldassarre, M.H. Zoellner, O. Skibitzki, G. Scalari, J. Faist, D.J. Paul, M. Scuderi, G. Nicotra, T. Grange, S. Birner, G. Capellini, and M. De Seta

Phys. Rev. Applied 11, 014003 – Published 2 January 2019

Abstract

Theoretical predictions indicate that the n-type $Ge / Si − Ge$ multi-quantum-well system is the most promising material for the realization of a $Si$ -compatible THz quantum cascade laser operating at room temperature. To advance in this direction, we study, both experimentally and theoretically, asymmetric coupled multi-quantum-well samples based on this material system, that can be considered as the basic building block of a cascade architecture. Extensive structural characterization shows the high material quality of strain-symmetrized structures grown by chemical vapor deposition, down to the ultrathin barrier limit. Moreover, THz absorption spectroscopy measurements supported by theoretical modeling unambiguously demonstrate inter-well coupling and wavefunction tunneling. The agreement between experimental data and simulations allows us to characterize the tunneling barrier parameters and, in turn, achieve highly controlled engineering of the electronic structure in forthcoming unipolar cascade systems based on n-type $Ge / Si − Ge$ multi-quantum-wells.

Received 24 September 2018
Revised 2 December 2018

DOI:https://doi.org/10.1103/PhysRevApplied.11.014003

Physics Subject Headings (PhySH)

Electronic structure Integrated optics Optoelectronics Photonics

Quantum cascade lasers Quantum wells Semiconductor compounds

Chemical vapor deposition

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

C. Ciano¹, M. Virgilio^2,*, M. Montanari¹, L. Persichetti¹, L. Di Gaspare¹, M. Ortolani³, L. Baldassarre³, M.H. Zoellner⁴, O. Skibitzki⁴, G. Scalari⁵, J. Faist⁵, D.J. Paul⁶, M. Scuderi⁷, G. Nicotra⁷, T. Grange⁸, S. Birner⁸, G. Capellini^1,4, and M. De Seta¹

¹Dipartimento di Scienze, Università Roma Tre, V.le G. Marconi 446, I-00146 Rome, Italy
²Dipartimento di Fisica “E. Fermi, “Università di Pisa, Largo Pontecorvo 3, I-56127 Pisa, Italy
³Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale A. Moro 2, I-00185 Rome, Italy
⁴IHP – Leibniz-Institut für innovative Mikroelektronik, Im Technologiepark 25, D-15236 Frankfurt (Oder), Germany
⁵Institute for Quantum Electronics, ETH Zürich, Zürich, Switzerland
⁶School of Engineering, University of Glasgow, Rankine Building, Oakfield Avenue, Glasgow G12 8LT, United Kingdom
⁷Istituto per la Microelettronica e Microsistemi (CNR-IMM), VIII strada 5, I-95121 Catania, Italy
⁸nextnano GmbH, Südmährenstr. 21, D-85586 Poing, Germany

^*michele.virgilio@unipi.it

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 11, Iss. 1 — January 2019

Subject Areas

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(Top) A schematic diagram of an ACQW module with definition of the relevant thicknesses (see Table 1). (a) Z-contrast STEM micrograph of a $Ge / {Si}_{0.2} {Ge}_{0.8}$ calibration sample (alloy material appears darker); in the inset, the thickness of the $Ge$ well (red) and $Si − Ge$ barrier (blue) measured by STEM vs nominal thickness. The narrowest $Si − Ge$ barrier is 1.6 nm thick. (b) Z-contrast STEM image of sample S4. (c) XRD RSM around the (224) reflections of $Si − Ge$ for sample S3. Scale bars are 10 nm in panels (a) and (b).
Reuse & Permissions
Figure 2
Energy of the fundamental, first-excited, and second-excited electron states (E₀, E₁, and E₂, respectively) calculated for (a) uncoupled, b_t = 10 nm and x_Ge = 0.81, and (d) coupled, b_t = 2.3 nm and x_Ge = 0.87, ACQWs as a function of w_L. Electron energy and squared wavefunction at w_L= 8 and w_L = 22 nm for uncoupled (b),(c) and coupled (e),(f) ACQWs (solid and dotted black curves represent the L and Δ₂ band profiles, respectively). The potential drop across the ACQW period in plot (b) is related to static charge effects associated with the presence of a dopant tail in the tunneling barrier and in the thin well.
Reuse & Permissions
Figure 3
Transition energy and oscillator strength as a function of w_L, calculated (a),(b) for b_t = 10 nm and x_Ge= 0.81 and (c),(d) for b_t= 2.3 nm and x_Ge= 0.87. Solid red (green) curve refers to the E₀₁ (E₀₂) transition. In panels (a),(c), the energy of the calculated E₀₁ and E₀₂ absorption resonances are represented by dotted curves. In panel (d), the ratio between the two oscillator strengths is also reported. The oscillator strength of each transition varies between 0 and 1/m* where m* = 0.135 in electron-mass units is the electron effective mass along the confinement direction, resulting from the values for the L inverse mass tensor reported in Ref. [27].
Reuse & Permissions
Figure 4
(a) Dots: experimental ISB absorption spectra measured by FTIR of samples S5 (top), S4 (middle), and S1 (bottom), with Lorentzian fits of the peaks centered at $E_{01}^{abs}$ and $E_{02}^{abs}$ (red and green curves, respectively). (b) Corresponding calculated spectra for w_L= 12 nm and variable thin-barrier width b_t. (c) Energy difference $E_{02}^{abs} - E_{01}^{abs}$ and (d) ratio of the integrated spectral weight of the two ISB absorption peaks, plotted vs b_t. Closed (open) symbols are used for experimental (numerical) data. (e) Calculated squared wavefunctions for sample S5.
Reuse & Permissions
Figure 5
(a) Dots: experimental ISB absorption spectra measured by FTIR of samples S3 (top), S1 (middle), and S2 (bottom), with Lorentzian fits of the peaks centered at $E_{01}^{abs} and E_{02}^{abs}$ (red and green curves, respectively). (b) Corresponding calculated spectra at fixed b_t= 2.3 nm for different w_L. (c) $E_{01}^{abs}$ (red symbols) and $E_{02}^{abs}$ (green symbols) and (d) ratio of the integrated spectral weight of the two ISB absorption peaks vs w_L. Closed (open) symbols are used for experimental (numerical) data. (e) Calculated squared wavefunctions for sample S2.
Reuse & Permissions

Physical Review Applied

Control of Electron-State Coupling in Asymmetric Ge/Si−Ge Quantum Wells

C. Ciano, M. Virgilio, M. Montanari, L. Persichetti, L. Di Gaspare, M. Ortolani, L. Baldassarre, M.H. Zoellner, O. Skibitzki, G. Scalari, J. Faist, D.J. Paul, M. Scuderi, G. Nicotra, T. Grange, S. Birner, G. Capellini, and M. De Seta

Phys. Rev. Applied 11, 014003 – Published 2 January 2019

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Subject Areas

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Control of Electron-State Coupling in Asymmetric $Ge / Si − Ge$ Quantum Wells