jing_2012#

X. Jing, Y. Tian, J. Zhang, S. Chen, Y. Jin, J. Shao and Z. Fan, “Modeling validity of femtosecond laser breakdown in wide bandgap dielectrics”, Appl. Surf. Sci. 258, 4741 (2012)

Source record · Catalogue · Review register

DOI: 10.1016/j.apsusc.2012.01.070

Source kind: theory

Recorded technique: Rate-equation calculations of the femtosecond breakdown threshold of a 9-eV dielectric (fused silica): Keldysh photoionization (Eqs. 3-5) combined in turn with four avalanche models (Stuart, Sparks-Duthler, Thornber, Drude; Eqs. 6-9), a density-dependent collision time (Starke, Eq. 10) and a 100-fs relaxation (Eq. 11), with the critical density as the damage criterion; compared with published surface thresholds against pulse duration and wavelength (Figs. 7-8).

Materials in structured entries: SiO2

Dataset quantities: avalanche_coefficient, band_gap, damage_threshold_fluence, effective_mass, electron_collision_time, electron_trapping_time, ionization_rate, multiphoton_ionization_cross_section, refractive_index

Contents: 21 datasets; 3 formulas.

Curation notes#

Journal pages 4741-4749 = PDF pages 1-9. Identity validated.

MODEL INPUTS (datasets assumed): E_g = 9 eV; m_e* = 0.635 m_e, ‘a measured value accepted generally to be accurate for fused silica’ [1] (Sudrie et al., Phys. Rev. Lett. 89, 186601 (2002)), the reduced mass m_e m_h/(m_e + m_h) (p. 4742-4743); n0 = 1.46 (Fig. 4 caption); tau_r = 100 fs (p. 4744: ‘Li et al. had indicated that the plasma energy in dielectrics experienced ultra-fast decay which lasted only ~100 fs ... In our calculation, the relaxation time tau_r = 100 fs was applied’); the Starke collision time Eq. (10); the critical density n_cr = eps0 m_e* omega^2/e^2 = 1.1e21 cm^-3 (Fig. 4; 1.106e21 with m_e* = 0.635 m_e at 800 nm, checked); e = 1.6e-19 C, eps0 = 8.854e-12 F/m.

LITERATURE (datasets reproduced), p. 4742: ‘The effective electron mass of m_e [24], 0.86 m_e [20], 0.635 m_e [1], 0.64 m_e [2], and 0.5 m_e [4,13] ... were often used in theoretical calculation of photoionization rate and avalanche ionization rate for fused silica’ (refs. 24 Kaiser et al. 2000, 20 Wu et al. 2005, 1 Sudrie et al. 2002, 2 couairon_2005, 4 Vaidyanathan et al. 1980, 13 Yuan et al. 2007); the relaxation time ‘between 150 and 250 fs for fused silica was found [41-43]’ and 150 fs ‘often used’ [1,2,20] (a range: not extracted); tau_c ‘in the range from 10^-16 s to 10^-14 s [1,8,19,20,35-37]’ (range, not extracted); sigma_6 of Lenzner et al. [11] 6.0e-52 and of Li et al. [10] 3.0e-56 cm^-3 s^-1 (cm2/W)^6 (p. 4743); Stuart’s alpha ~ 0.01 cm2 ps^-1/GW (stuart_1996); the Sparks model’s tau_c = 1.36e-15 s ‘In Refs. [4,13]’; the measured collision time 1.7 fs near 5e19 cm^-3 [39] (Sun et al., Opt. Lett. 30, 320 (2005)); surface thresholds 2.8 J/cm2 (‘a typical surface damage threshold ... measured in the experiment with parameters similar to our calculation [11,16,27]’), 1.5 J/cm2 (Li et al. [10], 25 fs single pulse) and 2.3 J/cm2 (Jia et al. [3], 800 nm, 150 fs, three shots) (pp. 4745, 4747).

CHECKS (2026-09-26): the fluence 2.74 J/cm2 = (pi/ln 2)^(1/2) I0 tau_p/2 with I0 = 25.74 TW/cm2 (a lost glyph in the library text, ‘TW/cm2’ in the pdf text layer) and tau_p = 100 fs (2.7399); sigma_6 I^6 at 3.5e13 W/cm2 = 4.04e34 cm^-3 s^-1 (printed 4.1e34); the Starke tau_c at 5e19 cm^-3 with m_e* = 0.635 m_e, E_g = 9 eV: 3.52 fs (printed ‘about 3.5 fs’; 4.42 fs with m_e); gamma = 1 at 3.5e13 W/cm2 (0.999 with gamma = omega sqrt(m_e* E_g)/(eE), I = c n0 eps0 E^2/2, n0 = 1.46). The Keldysh-limit sigma_6 = 2.2e-47 per volume is couairon_2005’s 9.6e-70 per atom times 2.1e22 cm^-3 (2.0e-47), and the paper’s W_MPI (4.1e34) and W_PI (1.6e32) at 3.5e13 W/cm2, gamma = 1, are couairon_2005’s (3.7e34, 1.6e32): the paper says ‘we calculated’ Fig. 1; the agreement of W_PI suggests the same implementation or a reproduction (not cited as such). The Lenzner and Li sigma_6 here disagree by ~1e7 with couairon_2005’s per-atom values (see couairon_2005’s notes).

EFFECTIVE GAP: Eq. (4) prints E’_g = E_g[1 + 1/(2 gamma^2)]; hamam_2018 prints eps_eff = eps_g[1 + 1/(4 gamma^2)]: the factor differs (and so do the gamma conventions); not resolvable here. Eq. (4)’s <E’_g/hbar omega + 1> is typeset as <E’_g/(hbar omega + 1)> in the library text; as printed in the rendering.

FIGURES ONLY: Fig. 1 (Keldysh, multiphoton and tunnel rates for 9 eV silica at 800 nm, with the two literature sigma_6), Fig. 2 (Eq. 10), Fig. 3 (avalanche rates against field), Figs. 4-9 (electron density; calculated thresholds against duration, wavelength and collision time; comparison with Lenzner, Jia, Varel, Li).

Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.