Influence of lattice heating time on femtosecond laser-induced strain waves in InSb

Physical Review B - Condensed Matter and Materials Physics

Volumn 78, Issue 17, 2008, Pages

  Krasniqi, F S ^a,b   Johnson, S L ^a   Beaud, P ^a   Kaiser, M ^a   Grolimund, D ^a   Ingold, G ^a  

^a PAUL SCHERRER INSTITUTE   (Switzerland)

^b DESY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 56349091992     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.174302     Document Type: Article

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50. In the case of parabolic band approximation, Δ Ee = (ℏω - Eg) / (1+ me / mh) and Δ Eh = (me / mh) Δ Ee, where me and mh are the effective masses for electrons and holes.
51. In the case of InSb, a laser pulse (ℏω ≈ 1.55 eV) of fluence just below the melting threshold (∼10 mJ cm-2) creates an electron density on the order of 1021 cm-3. Because of the limited states in the Γ valley (≲ 1020 cm-3), an intervalley scattering time τΓ→' L (or τΓ→ X) smaller than (or comparable to) the laser-pulse duration is needed to clear out the phase space for further transitions.
52. Energy and momentum conservations impose constrains on the maximum wave vector qmax of the LO phonons that interact with the electrons. Conservation of energy states that Ec (ki) ∼ Ec (kf) =∼., I LO whereas conservation of momentum, qmax = ki ∼ kf, with ki and kf standing for initial and final states of the electron in the k space. For InSb, with Ec (ki) ∼ 1.33 eV and ∼., I LO ∼ 0.024 eV, qmax ∼ 3Ã- 107 cm∼1.
53. For parabolic bands Ce can be calculated following chapter 2 in Ref., with He = F3/2 (νe) / F1/2 (νe), where νe = (μ e ∼ ECB) / (kB Te), μ e is the quasi-Fermi level for the electrons, and Fj (ν) is the Fermi-Dirac integral of the order j.
54. Chapter 23, Eq. (23.29) of Ref..
55. For parabolic bands, kB Te ∼1 eV and Ne on the order of 1021 cm∼3, He ∼ 1.2.
56. The resulting differential equation for the displacement u (z,t) is of the form ∼ 2 u/∼ t2 = c1 ∼ 2 u/∼ z2 +g (c2, z,t), where g is an arbitrary function that does not depend on u, and c1 and c2 ∼ { c2a, c2b, } are constants. An analytical solution of this type of equation can be found in Ref..
57. A possible surface damage has been ruled out by comparing the unperturbed rocking curves before and after laser excitation. Visible sample damage (very faint mark) was first observed at a laser fluence of about 11 mJ/ cm2 but there was no measurable loss in diffraction efficiency. The surface damage was considerable at about 14 mJ/ cm2 with about 10% unpumped diffraction loss over 30 min.
58. The optimal τ, and its uncertainty Δτ are determined by minimizing the chi square with respect to τ and ΔθB (Ref.45).