green_2008#
M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients”, Sol. Energy Mater. Sol. Cells 92, 1305-1310 (2008)
Source record · Catalogue · Review register
DOI: 10.1016/j.solmat.2008.06.009
Source kind: compilation
Recorded technique: A self-consistent evaluation, not a new measurement. A curve of the reflectance R of silicon against photon energy, from below 0.005 eV to above 29 keV, was assembled from the literature (Section 3, p. 1307), its phase found by the Kramers-Kronig relation (Eq. 1) and n and k computed from R and the phase (Eqs. 2-3). The reflectance: 1-6 eV, the ellipsometric tabulation of Herzinger et al. (J. Appl. Phys. 83, 3323 (1998)) as the baseline, adjusted (multiplier within 0.2 % of unity over most of the range) for Jellison (Optical Materials 1, 41 (1992)), Philipp (J. Appl. Phys. 43, 2835 (1972)) and Aspnes and Studna (Phys. Rev. B 27, 985 (1983)); below 1 eV, R from Eq. 4, n = 3.4164 + 0.085818 E^2 + 0.010149 E^4 (E in eV), fitted to the indices of Salzberg and Villa (1957), Lukes (1959), Primak (1971) and Icenogle et al. (1976) corrected to 300 K and assumed valid to zero energy, merged with the 1-6 eV baseline over 0.8-1.5 eV; 6-20 eV, Philipp’s reflectance as recalculated from Aspnes’s tabulated n, k (Hunter’s also considered); 20-29 eV, Hunter’s; 29 eV-30 keV, Henke et al. (updated by Soufli and Gullikson); above 30 keV a power law. A multiplier of 0.945 on R above 29 eV brought the phase at 0.85-1.16 eV to 0 +- 0.00008 rad (p. 1307). Above 0.5 um (below 2.5 eV) k was instead computed from measured absorption coefficients and n from that k and the fitted R (p. 1308); the alpha measurements of Weakliem and Redfield (J. Appl. Phys. 50, 1491 (1979)), MacFarlane et al. (Phys. Rev. 111, 1245 (1958)), Keevers and Green (Appl. Phys. Lett. 66, 174 (1995)), Trupke et al. (J. Appl. Phys. 94, 4930 (2003)) and Reece et al. (unpublished, 2001) ‘were given highest weighting from 0.47 to 1.45 um’. The two routes agreed from 0.46 to 0.6 um. The temperature coefficients were ‘calculated from cited and additional data sets [32]’ (Jellison and Modine, elevated temperatures) (p. 1308). Values at 300 K (27 C); intrinsic silicon.
Materials in structured entries: Si
Dataset quantities: absorption_coefficient, extinction_coefficient, refractive_index
Contents: 3 datasets; 0 formulas.
Curation notes#
Journal pages 1305-1310 = PDF pages 1-6; Table 1 is on pp. 1306-1307 (PDF pp. 2-4, three library tables). Identity checked against the first page.
WHAT IS TABULATED. Table 1 (‘Optical properties of intrinsic silicon at 300 K including normalised temperature coefficients’): against the free-space wavelength lambda, 0.25-1.45 um at 0.01 um steps (121 rows), the absorption coefficient alpha (/cm, three significant figures), n (three decimals), k (three decimals, printed only to 1.00 um; an en dash from 1.01 um), and the normalised temperature coefficients C_n = (1/n)(dn/dT) and C_k,alpha = (1/k)(dk/dT) in 10^-4/K (‘alpha has an identical coefficient to k’). alpha = 4 pi k / lambda (p. 1305); lambda (um) = 1.23984190 / E (eV), ‘for standard dry air, wavelengths will be about 0.03% shorter’ (p. 1305): the wavelengths are vacuum wavelengths. Checked (2026-10-14): k agrees with alpha lambda / (4 pi) in every row within the rounding of the two printed columns. epsilon_2 = 2nk at 0.29 um is 46.05, the paper’s 46.1 +- 0.9 at 290 nm (p. 1308).
ACCURACY (p. 1308, Section 5, quoted): ‘Error limits on tabulated k and alpha are estimated to increase from +-0.3% at 0.25 um to +-4% beyond 0.46 um, +-10% beyond 1.2 um and to become even larger beyond 1.4 um. For n, estimated accuracy is better than +-0.1% beyond 1.0 um, increasing to about +-0.5% at shorter lambda except below 0.3 um where it increases to +-1%.’ Recorded as relative_rows, level ‘bound’ (the paper’s ‘error limits’): alpha and k 0.3 % at 0.25 um, 4 % at 0.47-1.20 um, 10 % at 1.21-1.40 um; n 1 % at 0.25-0.29 um, 0.5 % at 0.30-1.00 um, 0.1 % at 1.01-1.45 um. The paper states no number for alpha and k at 0.26-0.46 um (where the limit rises from 0.3 to 4 %) or beyond 1.40 um (‘even larger’): those rows carry no uncertainty. k’s printed resolution (0.001) exceeds the 4 % limit wherever k <= 0.012 (lambda >= 0.68 um), and at 0.94-1.00 um k = 0.001 is alpha rounded by up to a factor of two. Comparisons at two laser lines (p. 1308): Taft’s (4.088 +- 0.003) - i(0.0314 +- 0.0016) at 546.1 nm, Geist’s 3.874 - i(0.0159 +- 0.0004) at 633.0 nm (both extrapolated to 300 K), against the table’s (4.090 +- 0.003) - i(0.0289 +- 0.0012) and (3.874 +- 0.002) - i(0.0162 +- 0.0006); and Gatesman’s n = 3.4170 +- 0.0001 at 236.6 um, 0.04 % above Eq. 4 at 22 C.
TEMPERATURE COEFFICIENTS (p. 1308, Eqs. 6-10). c_p = (1/p) dp/dT = d(ln p)/dT, for p = n, k or alpha, at 300 K; the paper’s preferred use is the power law p(T) = p(T0) (T/T0)^b with b = C_p(T0) T0 (Eqs. 9-10), shown for alpha against Weakliem and Redfield, MacFarlane et al. and Trupke et al. at 249, 363 and 473 K (Fig. 2). They are normalised coefficients, not dn/dT, and are not recorded as thermo_optic_coefficient: they stay in each row’s printed cells. dn/dT = n C_n, from 2.9e-4 n at 0.25 um to 0.6e-4 n (2.1e-4 /K) at 1.04-1.45 um, printed to one or two significant figures.
WHAT IT IS BUILT FROM. Every value is the paper’s own Kramers-Kronig evaluation of a reflectance curve it assembled from others’ measurements (above), with k above 0.5 um from others’ alpha weighted together: no column reproduces one source’s values, but n depends mostly on Herzinger et al. (1-6 eV) and on Eq. 4’s prism indices below 1 eV, and alpha above 0.47 um on Weakliem and Redfield, MacFarlane et al., Keevers and Green, Trupke et al. and Reece et al. The datasets are therefore checks, never fitted beside those measurements. Schinke et al. (2015, schinke_2015) find good agreement in alpha except beyond 1200 nm (their Fig. 16).
REFRACTIVEINDEX.INFO. main/Si/nk/Green-2008.yml (data/external/refractiveindex_info) holds n and k from this table, with k from 0.45 um recomputed from alpha; see the register entry for the comparison.
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
green_2008/alpha_300K#
{
"id": "alpha_300K",
"material": "Si",
"file": "Si/green_2008__alpha_300K.csv",
"table": "tbl_85bbdac968fa",
"quantity": "absorption_coefficient",
"unit": "cm-1",
"abscissa_unit": "um",
"use": "check",
"parameters": {
"base": "e",
"temperature_k": 300,
"form": "bulk",
"technique": "Kramers-Kronig evaluation of compiled reflectance and absorption data"
},
"uncertainty": {
"level": "bound",
"relative_rows": {
"0.25": 0.003,
"0.47": 0.04,
"0.48": 0.04,
"0.49": 0.04,
"0.5": 0.04,
"0.51": 0.04,
"0.52": 0.04,
"0.53": 0.04,
"0.54": 0.04,
"0.55": 0.04,
"0.56": 0.04,
"0.57": 0.04,
"0.58": 0.04,
"0.59": 0.04,
"0.6": 0.04,
"0.61": 0.04,
"0.62": 0.04,
"0.63": 0.04,
"0.64": 0.04,
"0.65": 0.04,
"0.66": 0.04,
"0.67": 0.04,
"0.68": 0.04,
"0.69": 0.04,
"0.7": 0.04,
"0.71": 0.04,
"0.72": 0.04,
"0.73": 0.04,
"0.74": 0.04,
"0.75": 0.04,
"0.76": 0.04,
"0.77": 0.04,
"0.78": 0.04,
"0.79": 0.04,
"0.8": 0.04,
"0.81": 0.04,
"0.82": 0.04,
"0.83": 0.04,
"0.84": 0.04,
"0.85": 0.04,
"0.86": 0.04,
"0.87": 0.04,
"0.88": 0.04,
"0.89": 0.04,
"0.9": 0.04,
"0.91": 0.04,
"0.92": 0.04,
"0.93": 0.04,
"0.94": 0.04,
"0.95": 0.04,
"0.96": 0.04,
"0.97": 0.04,
"0.98": 0.04,
"0.99": 0.04,
"1": 0.04,
"1.01": 0.04,
"1.02": 0.04,
"1.03": 0.04,
"1.04": 0.04,
"1.05": 0.04,
"1.06": 0.04,
"1.07": 0.04,
"1.08": 0.04,
"1.09": 0.04,
"1.1": 0.04,
"1.11": 0.04,
"1.12": 0.04,
"1.13": 0.04,
"1.14": 0.04,
"1.15": 0.04,
"1.16": 0.04,
"1.17": 0.04,
"1.18": 0.04,
"1.19": 0.04,
"1.2": 0.04,
"1.21": 0.1,
"1.22": 0.1,
"1.23": 0.1,
"1.24": 0.1,
"1.25": 0.1,
"1.26": 0.1,
"1.27": 0.1,
"1.28": 0.1,
"1.29": 0.1,
"1.3": 0.1,
"1.31": 0.1,
"1.32": 0.1,
"1.33": 0.1,
"1.34": 0.1,
"1.35": 0.1,
"1.36": 0.1,
"1.37": 0.1,
"1.38": 0.1,
"1.39": 0.1,
"1.4": 0.1
}
}
}
Table 1, pp. 1306-1307 (tbl_85bbdac968fa, tbl_282abc185c1f, tbl_76272313742f): alpha of intrinsic silicon at 300 K, 0.25-1.45 um, 121 rows, as printed (1.84E6 to 1.2E-8 /cm). A check: an evaluation weighted on others’ alpha measurements above 0.47 um (source notes).
green_2008/n_300K#
{
"id": "n_300K",
"material": "Si",
"file": "Si/green_2008__n_300K.csv",
"table": "tbl_85bbdac968fa",
"quantity": "refractive_index",
"abscissa_unit": "um",
"use": "check",
"parameters": {
"temperature_k": 300,
"form": "bulk",
"technique": "Kramers-Kronig evaluation of compiled reflectance and absorption data"
},
"uncertainty": {
"relative": 0.005,
"level": "bound",
"relative_rows": {
"0.25": 0.01,
"0.26": 0.01,
"0.27": 0.01,
"0.28": 0.01,
"0.29": 0.01,
"1.01": 0.001,
"1.02": 0.001,
"1.03": 0.001,
"1.04": 0.001,
"1.05": 0.001,
"1.06": 0.001,
"1.07": 0.001,
"1.08": 0.001,
"1.09": 0.001,
"1.1": 0.001,
"1.11": 0.001,
"1.12": 0.001,
"1.13": 0.001,
"1.14": 0.001,
"1.15": 0.001,
"1.16": 0.001,
"1.17": 0.001,
"1.18": 0.001,
"1.19": 0.001,
"1.2": 0.001,
"1.21": 0.001,
"1.22": 0.001,
"1.23": 0.001,
"1.24": 0.001,
"1.25": 0.001,
"1.26": 0.001,
"1.27": 0.001,
"1.28": 0.001,
"1.29": 0.001,
"1.3": 0.001,
"1.31": 0.001,
"1.32": 0.001,
"1.33": 0.001,
"1.34": 0.001,
"1.35": 0.001,
"1.36": 0.001,
"1.37": 0.001,
"1.38": 0.001,
"1.39": 0.001,
"1.4": 0.001,
"1.41": 0.001,
"1.42": 0.001,
"1.43": 0.001,
"1.44": 0.001,
"1.45": 0.001
}
}
}
Table 1, pp. 1306-1307 (three parts): n of intrinsic silicon at 300 K, 0.25-1.45 um, 121 rows, as printed. A check: from Kramers-Kronig of a reflectance built on Herzinger et al. (1-6 eV) and on Eq. 4’s fit of prism indices (below 1 eV) (source notes).
green_2008/k_300K#
{
"id": "k_300K",
"material": "Si",
"file": "Si/green_2008__k_300K.csv",
"table": "tbl_85bbdac968fa",
"quantity": "extinction_coefficient",
"abscissa_unit": "um",
"use": "check",
"parameters": {
"temperature_k": 300,
"form": "bulk",
"technique": "Kramers-Kronig evaluation of compiled reflectance and absorption data"
},
"uncertainty": {
"level": "bound",
"relative_rows": {
"0.25": 0.003,
"0.47": 0.04,
"0.48": 0.04,
"0.49": 0.04,
"0.5": 0.04,
"0.51": 0.04,
"0.52": 0.04,
"0.53": 0.04,
"0.54": 0.04,
"0.55": 0.04,
"0.56": 0.04,
"0.57": 0.04,
"0.58": 0.04,
"0.59": 0.04,
"0.6": 0.04,
"0.61": 0.04,
"0.62": 0.04,
"0.63": 0.04,
"0.64": 0.04,
"0.65": 0.04,
"0.66": 0.04,
"0.67": 0.04,
"0.68": 0.04,
"0.69": 0.04,
"0.7": 0.04,
"0.71": 0.04,
"0.72": 0.04,
"0.73": 0.04,
"0.74": 0.04,
"0.75": 0.04,
"0.76": 0.04,
"0.77": 0.04,
"0.78": 0.04,
"0.79": 0.04,
"0.8": 0.04,
"0.81": 0.04,
"0.82": 0.04,
"0.83": 0.04,
"0.84": 0.04,
"0.85": 0.04,
"0.86": 0.04,
"0.87": 0.04,
"0.88": 0.04,
"0.89": 0.04,
"0.9": 0.04,
"0.91": 0.04,
"0.92": 0.04,
"0.93": 0.04,
"0.94": 0.04,
"0.95": 0.04,
"0.96": 0.04,
"0.97": 0.04,
"0.98": 0.04,
"0.99": 0.04,
"1": 0.04
}
}
}
Table 1, pp. 1306-1307 (first two parts): k of intrinsic silicon at 300 K, 0.25-1.00 um, 76 rows, as printed to three decimals; the table prints a dash from 1.01 um, and those rows are not in the file. Equal to alpha lambda / (4 pi) within rounding: the same information as alpha_300K, at lower resolution from 0.5 um; not to be used beside it.
Formulas#
No formulas are recorded.
Corrections#
No dataset errata are recorded in this source record.
Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.