bristow_2007#

A. D. Bristow, N. Rotenberg and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm”, Appl. Phys. Lett. 90, 191104 (2007)

Source record · Catalogue · Review register

DOI: 10.1063/1.2737359

Source kind: measurement

Recorded technique: Single-beam Z-scan (open aperture for beta, closed aperture with S = 0.13 for n2; the text says ‘closed and open aperture ... respectively’, reversed, p. 191104-1) of bulk Si at 300 K. Source: an optical parametric amplifier, nominally 200 fs pulses at 1 kHz for 1100-2200 nm, frequency-doubled in BBO for 850-1100 nm; linearly polarized ~100 nJ pulses focused by a 10 cm lens, z0 = 5 mm, focal spot 75 um FWHM (knife edge); Ge or PbS detectors in reference and signal arms, lock-in detection. Sample: ‘125 um thick wafer of intrinsic, double sided polished crystalline Si, cut with the normal axis along the [001] crystal direction’. ‘Fresnel losses were incorporated in determining the peak intensity inside the sample’; peak intensity ~8 GW/cm2 (pp. 191104-1, -2).

Materials in structured entries: Si

Dataset quantities: band_gap, nonlinear_index, two_photon_absorption_coefficient

Contents: 6 datasets; 1 formula.

Curation notes#

Article pages 191104-1 to -3 = PDF pages 2-4 (PDF page 1 is the publisher’s cover page). Identity checked against the first page. No tables: every value here is a text value (inline points, with the page).

WHAT IS HERE. Text values at 1220 nm (p. 191104-2): ‘Fits to the data yield beta = 2.1 +- 0.4 cm/GW and n2 = (4.7 +- 2.0) x 10^-5 cm2/GW’ (Fig. 1, peak intensity 7.8 GW/cm2). Abstract (p. 191104-1): ‘With a broad peak near the indirect gap and maximum value of 2 +- 0.5 cm/GW, the dispersion of beta compares favorably with theoretical calculations of Garcia and Kalyanaraman ... Within our wavelength range, n2 varies by a factor of 4 with a peak value of 1.2 x 10^-13 cm2/W at lambda = 1800 nm.’ The maximum beta has no stated wavelength (‘a broad peak or plateau for lambda < 1200 nm’, p. 191104-2), so it is not a dataset. The spectra themselves (beta at ~24 wavelengths 850-2200 nm, Fig. 2; n2 at ~20 wavelengths, Fig. 3; squares with error bars) are figures only: not digitised. Fig. 2 also shows others’ beta (Refs. 7, 15, 9, 18) and the Garcia-Kalyanaraman fit; Fig. 3 Dinu et al.’s n2 [18], a guide to the eye and a Kramers-Kronig estimate from the fitted beta.

DEFINITIONS. Eq. (1), open aperture: T_open(z) = 1 - (1/(2 sqrt 2)) beta I0 L_eff / (1 + (z/z0)^2); Eq. (2), closed aperture: T_closed(z) = 1 - (8 pi / (lambda sqrt 2)) (z/z0) (1 - S)^0.25 L_eff n2 I0 / ((1 + (z/z0)^2)(9 + (z/z0)^2)) - (1/(2 sqrt 2)) L_eff beta I0 (3 - (z/z0)^2) / ((1 + (z/z0)^2)(9 + (z/z0)^2)); I0 the on-axis peak intensity inside the sample, L_eff = (1 - exp(-alpha L)) / alpha (p. 191104-1). So beta is that of dI/dz = -alpha I - beta I^2 and n2 that of n = n0 + n2 I, with reflection losses removed. 200-fs pulses: the Si Raman response (15.6 THz) is partly included; the paper does not discuss it: part unknown.

ERRORS AND CHECKS (pp. 191104-1, -2): ‘The experimental results are consistent within experimental error, which, in our case, is mainly related to obtaining values of peak laser intensity and small differences in beam shape with tuning.’ Free-carrier absorption estimated at ~3 % of the 2PA (for sigma = 5e-18 cm2 at 1060 nm), the Drude index change ~-1e-4, band filling and gap shrinkage negligible; I0^2 scaling verified at several wavelengths; three-photon absorption across the direct gap (lambda < 1070 nm) negligible (Wherrett’s scaling); for lambda > 1400 nm the variation of beta with the polarization direction was < 5 % ‘and within experimental error’. The level of the +- is not stated.

LITERATURE QUOTED (p. 191104-1): Reintjes and McGroddy [15], beta = 1.5 cm/GW at 100 K, 1060 nm, picosecond pulses (dataset beta_reintjes_1973, reproduced); ‘a similar value was obtained by Boggess et al. at 300 K’ [16] (no number); Reitze et al. [17] ‘5 < beta < 36 cm/GW for 90 fs pulses in the range 620 >= lambda >= 550 nm’ (across the direct gap, 3.4 eV); at 1300 or 1500 nm ‘values [9, 10, 18] of beta ~0.8 cm/GW’; n2 ‘values (~3 x 10^-14 cm2/W) reported for 1300 and 1550 nm’ [18] (Dinu et al., dataset n2_dinu_2003, reproduced); Sabbah and Riffe [25] beta ~5 cm/GW, ‘only an estimate’. The indirect gap E_gi = 1.12 eV (p. 191104-1) is the input of the fit (dataset eg_indirect). The text’s ‘measurements at 1300 and 1550 um by Dinu’ (p. 191104-2) means nm.

KRAMERS-KRONIG ESTIMATE (p. 191104-2, -3): n2(omega) = (c/pi) int beta(omega, omega’) / (omega^2 - omega’^2) domega’ with ‘the approximation [27] beta(omega, omega’) = beta([omega + omega’] / 2)’ (Ref. 27 = sheik_bahae_1991, its Eq. 4) gives values ‘well below the measured results’; direct-gap 2PA ‘shifts the estimate upward by only 1 x 10^-14 cm2/W’; the rest attributed to ‘the neglect of Raman and quadratic Stark contributions’.

REPRODUCTIONS OF THIS PAPER: jansonas_2022 (lit_eff_Si_bristow_2007: ‘~10.4 +- 2’ x 1e-14 cm2/W at 2.2 um, a reading of Fig. 3: not printed here); ensley_2019 notes ‘Bristow et al.’s ~0.4 cm/GW’ at 2 um (Fig. 2); poulvellarie_2018 computes its waveguide nonlinear coefficients ‘on the basis of the data from’ this paper.

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