Academic and industry research progress in germanium nanodevices
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...Similar to silicon, Ge is an excellent semiconductor, and it is widely used in rectifiers and transistors (Ravi 2011; Coteli et al. 2017)....
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...This can be overcome by implementing lowdimensional structures, such as quantum wells (QWs) for FET (QW-FET) where enhanced carrier mobility at high carrier density can be obtained [20, 21]....
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...Two dimensional systems are introduced in Section 2.2 where MOSFET and QW-FET are presented together with the description, by means of the effective mass approximation, of the quantum confinement....
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...Contributed talk: “Split cyclotron resonances in strained Ge quantum well probed by THz time-domain spectroscopy”, ICOOPMA 2014, Leeds, UK (July 2014) vii List of abbreviations 2DEG/2DHG Two dimensional electron/hole gas AFM atomic force microscopy BIA bulk inversion asymmetry CB conduction band CES constant energy surface CMOS complementary metal oxide semiconductor CR cyclotron resonance CRA/CRI cyclotron active/inactive modes CVD chemical vapour deposition DOS density of states DP Dyakonov-Perel mechanism EFA envelope function approximation EMA effective mass approximation EOS electro-optic sampling EPP empirical pseudopotential method EY Elliott-Yafet mechanism FET field effect transistor FB Fabry-Perot HH heavy hole HWP half wave plate iPCE interdigitated photoconductive emitter IQHE integer quantum Hall effect ITRS International Technology Roadmap for Semiconductors JDOS joint density of states LL Landau level MOD modulation doping MOS metal-oxide-semiconductor MOSFET metal-oxide-semiconductor field effect transistor MT magnetotransport NPP nonlocal pseudopotential method OQHE optical quantum Hall effect PC photoconductive PD photodiode PP pseudopotential method viii PR-THz-TDMS polarisation-resolved THz-TDMS QHE quantum Hall effect QW quantum well QW-FET quantum well field effect transistor QWP quarter wave plate RMS root mean square RP-CVD reduced-pressure chemical vapour deposition RP-THz-TDS rotatable polarisation THz-TDS SC semiconductor SdH Shubnikov-de Haas sGe-QWs strained germanium quantum wells SIA structural inversion asymmetry SOI spin-orbit interaction THz-TDS THz time-domain spectroscopy THz-TDMS THz time-domain magneto-spectroscopy VB valence band WAL weak anti-localisation WL weak localisation XTEM cross-sectional transmission electron microscopy ix List of symbols a lattice constant a‖ in-plane lattice constant a0 unstrained lattice constant a†, a creation and annihilation operators A = A(r) vector potential α Rashba coefficient for electrons α(ω) absorption coefficient bij BIA coefficient B applied magnetic field Beff effective magnetic field BBIA(k‖) effective magnetic field from BIA BSIA(k‖) effective magnetic field from SIA β Rashba coefficient for HHs and LHs βMT Rashba coefficient for HHs and LHs from MT measurements βp Rashba coefficient from the spin-split density obtained from THz-TDMS c speed of light ∆ Rashba splitting energy ∆p Rashba splitting energy obtained from THz-TDMS ∆MT Rashba splitting energy from MT measurements ∆− momentum matrix element ∆0,∆ ′ 0 SO-energies Γ Landau level linewidth (broadening) g density of states gB density of states for Landau levels at B g0 electron g-factor g∗ effective g-factor x E energy Eg energy gap E(k↓), E(k↑) energy for spin-down and spin-up states E±(k‖) energy for spin-down and spin-up states in 2D-systems Emn energy for the n-th subband and m bulk band (see m) E±mnN (B) spin-split energy for the band m, n-th subband and Landau level index N E± = √ 1/2(Ex ± iEy) cyclotron resonance active and inactive mode E±CR = E ↑↓ CR = ~ωc,↑↓ cyclotron resonance energies: transition energies from spin-up to spin-up states and from spin-down to spin-down states η ellipticity E0, E ′ 0 energy gaps E(k) energy dispersion EF Fermi energy ETHz THz-pulse Et(ω) THz-pulse transmitted through the sample Er(ω) reference THz-pulse E electric field ‖ in-plane element of the strain tensor (ω) complex dielectric function L lattice dielectric function f(E,µF, T ) Fermi-Dirac distribution f occupation factor γ1, γ2, γ3 Luttinger parameters γ′1, γ ′ 2, γ ′ 3 reduced Luttinger parameters H Hamiltonian H ′ij perturbed component of the Hamiltonian HSO spin-orbit Hamiltonian I ijl invariants j total angular momentum J current density k wavevector k‖ in-plane wavevector kF Fermi wavevector k± = kx ± iky κ′ reduced Luttinger paramater L quantum well thickness l orbital angular momentum λ spin-orbit coupling factor xi λc magnetic length m index for conduction, light hole or heavy hole band m0 electron mass m∗b effective mass at the band-edge (i.e. k = 0) m∗THz effective mass obtained from magnetic field dependence of the cyclotron frequency mj projection of total angular momentum m∗HH effective mass for heavy holse m∗LH effective mass for light holes mij matrix tensor element of the effective mass m∗MT effective mass obtained from MT experiments µB = e~/(2m0) Bohr magneton µF chemical potential µ mobility n subband index in quantum wells nB number of states (per unit area) for Landau levels ñ = n(ω) + iκ(ω) complex refractive index N volume carrier density N± spin-split density (+: up, −: down) Ns sheet carrier density N Landau level index ωc cyclotron frequency Ωdir volume of the primitive cell in real space Ωrec volume of the primitive cell in reciprocal space P, P ′ momentum matrix element p = −i~∇ momentum operator p = ~k kinetic momentum pMT↑,↓ spin-split sheet density from MT measurements pTHz↑,↓ spin-split sheet density from THz-TDMS pTHz2D total sheet density from fits of THz-TDMS psum2D total sheet density from sum rule pHall2D total sheet density from classical Hall conductivity ψ wavefunction Ψ(r) wavefunction expansion in terms of band-edge Bloch functions Q momentum matrix element rij SIA coefficient ρ resistivity tensor σ conductivity tensor σ(ω) optical conductivity σ0 DC sheet conductivity σ vector of Pauli spin matrices s spin angular momentum τ lifetime xii τs spin lifetime τtr transport lifetime τTHz cyclotron resonance lifetime from THz-TDMS τq quantum lifetime θF Faraday angle ΘF (ω,B) complex Faraday angle v speed, drift velocity ν Landau levels filling factor V0(r) periodic crystal potential Vg pseudopotential form factor VG gate voltage x element content χ2 residual xiii Abstract Terahertz time-domain spectroscopy (THz-TDS) allows the investigation, in a noncontact fashion and in the meV range (1 THz = 4.14 meV), of the coherent motion of particles close to their equilibrium position....
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...In Section 1.1.1 the quantum well FET (QW-FET)[21] has been introduced as an alternative device to maintain Moore’s law....
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...22 Moreover, characterising QWs gives an estimation of their intrinsic mobility, i.e. not affected by other mechanisms related to the realisation of the QW-FET....
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