Effects of Uniaxial Stress on the Indirect Exciton Spectrum of Silicon

Laude, L.D.; Pollak, Fred H.; Cardona, M.

doi:10.1103/physrevb.3.2623

Cited by 239 publications

(45 citation statements)

References 24 publications

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“…The susceptibility (only the imaginary part is required for absorption and is quoted after symmetry and selection rules have been used to reduce the form) is given by [12] b Reference [13] c Reference [14] d Reference [15] e Reference [16] f Reference [17] g Reference [18] h Reference [19] i Reference [20] j Reference [21] for a transition from state n to n ′ at wavenumber k with spin σ and polarization i or j. The variables above are as follows: e is the electronic charge, is Planck's constant divided by 2π, m is the effective mass, m 0 is the free electron mass, E p is the Kane matrix element defined in terms of the momentum Hamiltonian as 2 m0 | S ↓ |p x |X ↓ | 2 , S is the Kane parameter, a 0 is the Bohr radius, k max is the maximum k wavenumber, ε 0 is the permittivity of free space and Ω is the volume of the sample.…”

Section: Description Of Modeling Techniquementioning

confidence: 99%

8-bandk.pmodeling of the quantum confined Stark effect in Ge quantum wells on Si substrates

Paul

2008

Phys. Rev. B

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Recent work using compressively strained-Ge quantum wells grown on Si1−yGey virtual substrates has demonstrated efficient modulation on a silicon substrate through the quantum confined Stark effect with performance comparable to many direct bandgap III-V materials. The absorption of compressively strained-Ge quantum wells is calculated using an 8-band k.p solver within the envelope function technique. The calculated absorption spectra provide excellent agreement with experimental results, demonstrating that the absorption is dominated by the direct bandgap and allow a number of predictions of the absorption for different polarizations, quantum well widths, electric fields and strain to be calculated. It is also shown that some of the experimental results in the literature require tensile strained substrates to produce agreement with the theoretical calculations.

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Section: Description Of Modeling Techniquementioning

confidence: 99%

8-bandk.pmodeling of the quantum confined Stark effect in Ge quantum wells on Si substrates

Paul

2008

Phys. Rev. B

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“…In Eq. (12) we have used a single effective deformation potential Ξ i 8 eV [32] which absorbs the effect of the valleys' ellipsoidal energy dispersion. Substituting Eq.…”

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confidence: 99%

Spin-Orbit Symmetries of Conduction Electrons in Silicon

Dery

2011

Phys. Rev. Lett.

122

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We derive a spin-dependent Hamiltonian that captures the symmetry of the zone edge states in silicon. We present analytical expressions of the spin-dependent states and of spin relaxation due to electron-phonon interactions in the multivalley conduction band. We find excellent agreement with experimental results. Similar to the usage of the Kane Hamiltonian in direct band-gap semiconductors, the new Hamiltonian can be used to study spin properties of electrons in silicon.PACS numbers: 78.60.Fi, 71.70.Ej Silicon is an ideal material choice for spintronics due to its relatively long spin relaxation time and central role in semiconductor technology. These characteristics are the reason for the wide interest in recent spin injection experiments [1][2][3][4]. To date, however, modeling of basic spin properties in silicon required elaborate numerical methods [5]. Notably, the availability of transparent spin-dependent theories in direct gap semiconductors have spurred the field of semiconductor spintronics [6]. The importance of a lucid theory that accurately describes spin properties of conduction electrons in silicon with relatively simple means is thus clear.In the first part of this letter we derive a Hamiltonian that captures spin properties of conduction electrons in silicon. The Hamiltonian is constructed by its invariance to the symmetry operations of the space group, G 2 32 , which describes the symmetry of the X-point at the edge of the Brillouin zone [7,8]. In silicon the X-point is closer to the absolute conduction band minimum than all other high symmetry points. While k·p and tight-binding models have been available for many decades [9][10][11][12][13][14][15][16][17], spin has heretofore been ignored since spin-orbit coupling in Si is weak [18][19][20][21][22] and lattice inversion symmetry causes spin degeneracy. The present work is motivated by the emergence of experimental work on spin-polarized electron transport in silicon [1][2][3][4].In the second part, this Hamiltonian is used to elucidate the nature of intravalley and intervalley spin relaxation processes in silicon due to electron-phonon interactions. Our approach unravels the underlying physics, structure and symmetries of dominant spin-flip mechanisms. These insights cannot be shown by state-of-the art numerical studies in which only the magnitude and temperature dependence are calculated [5]. We derive analytical forms and selection rules of the dominant spin-flip matrix elements and explain the subtle distinction between spin and momentum scattering processes. Importantly, it is shown that spin relaxation due to intravalley scattering is caused by coupling of the lower and upper conduction bands (whereas intravalley momentum relaxation is governed by dilation and uniaxial deformation potentials of the lower conduction band). The accepted

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“…The numerical value of Ξ sh is not well known. The experimental data give Ξ u ≈ 7 − 8 eV [28,33] and the numerical data on the band splitting give ∆E ≈ 0.7 eV [34] so that Ξ sh is in the range of 280 − 360 eV; this is essentially an order of magnitude estimate.…”

Section: Discussionmentioning

confidence: 90%

“…The parameter of the electron coupling to shear strain in silicon is not easy to access in the experiment [28,33]. Measurements of the nonlinear frequency shift provide a direct means for determining this parameter.…”

Section: Discussionmentioning

confidence: 99%

Strong vibration nonlinearity in semiconductor-based nanomechanical systems

Moskovtsev

Dykman

2017

Phys. Rev. B

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We study the effect of the electron-phonon coupling on vibrational eigenmodes of nano-and micro-mechanical systems made of semiconductors with equivalent energy valleys. We show that the coupling can lead to a strong mode nonlinearity. The mechanism is the lifting of the valley degeneracy by the strain. The redistribution of the electrons between the valleys is controlled by a large ratio of the electron-phonon coupling constant to the electron chemical potential or temperature. We find the quartic in the strain terms in the electron free energy, which determine the amplitude dependence of the mode frequencies. This dependence is calculated for silicon microsystems. It is significantly different for different modes and the crystal orientation, and can vary nonmonotonously with the electron density and temperature.

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Effects of Uniaxial Stress on the Indirect Exciton Spectrum of Silicon

Cited by 239 publications

References 24 publications

8-bandk.pmodeling of the quantum confined Stark effect in Ge quantum wells on Si substrates

8-bandk.pmodeling of the quantum confined Stark effect in Ge quantum wells on Si substrates

Spin-Orbit Symmetries of Conduction Electrons in Silicon

Strong vibration nonlinearity in semiconductor-based nanomechanical systems

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