franta_2013b#
D. Franta, D. Nečas, L. Zajíčková, I. Ohlídal, J. Stuchlík and D. Chvostová, “Application of sum rule to the dispersion model of hydrogenated amorphous silicon”, Thin Solid Films 539, 233 (2013)
Source record · Catalogue · Review register
DOI: 10.1016/j.tsf.2013.04.012
Source kind: measurement
Recorded technique: Three a-Si:H films (#1654, #1655, #1656; 540, 53 and 212 nm) by plasma-enhanced CVD from pure silane (25 Pa, 30 sccm, 13.56 MHz, 0.06 W cm^-2, substrate at 220 C) on double-side polished c-Si (p. 237). Ellipsometry 0.6-8.9 eV (Jobin Yvon UVISEL, 0.6-6.5 eV, 55-75 degrees; Woollam VUV-VASE, 4-8.9 eV, 65 and 75 degrees), near-normal (6 degrees) reflectance 1.13-6.5 eV and transmittance 1.13-1.38 eV (Perkin Elmer Lambda 45), IR transmittance 0.046-0.93 eV (Bruker VERTEX 80v) (p. 237). All data fitted together (multi-sample) with six dispersion models built on the sum rule; structural model: c-Si substrate, homogeneous film with a rough overlayer (Rayleigh-Rice) on the front and a smooth one on the back; overlayers taken as fused silica from Palik’s handbook (philipp_1985); c-Si from the authors’ own unpublished model (p. 237).
Materials in structured entries: a-Si_H
Dataset quantities: atom_density, band_gap
Contents: 3 datasets; 7 formulas.
Curation notes#
Journal pages 233-244 = pdf pages 1-12. Identity (six authors) checked against the first page. The companion theory paper is franta_2013 (ref. [16], ‘Application of Thomas-Reiche-Kuhn sum rule to construction of advanced dispersion models’); this paper applies it to a-Si:H. All values refer to films (form = film).
EQUATION MAP, for the implementation (E photon energy in eV; each term is a normalised dielectric function of unit transition strength, Eq. (3), times N_t, Eq. (4)): - Eq. (6), p. 234: eps_r^0 by Kramers-Kronig from F^0; eps_i^0 = F^0/E. - Eq. (7), p. 234: the valence-to-conduction interband term with an asymmetric, Lorentz-modified JDOS, eps_i,vc^0 = sgn(E) (|E| - E_g)^2 (E_h - |E|)^2 / (C_N E^2 [(|E| - E_c)^2 + B_c^2]) on (E_g, E_h): franta_2013’s Eq. (59) with kappa = 2, nu = 1. It is NOT implemented in optmat.solid.udm (whose interband term is the symmetric one, Eq. (56) there). Appendix A (p. 242) gives its C_N and real part in closed form. Checked here (2026-09-26) with the PJDOS-EX parameters (E_g 1.723, E_h 22, E_c 3.455, B_c 1.180 eV): Appendix A’s C_N = 855.9099 equals the quadrature of Eq. (7)’s numerator times E to double precision, and its real part equals the numerical Kramers-Kronig transform to about 1e-12 at 0.5-30 eV. (An earlier reading had found the same.) - Eqs. (9)-(11), p. 234: the higher-energy valence term, E_xi = E_g/2 + E_x; the same as the implemented term (udm._higher). - Eq. (12), p. 235: the Urbach tail (four parts), with ‘E_m = E_g/2 + E_h/2’, the mean energy of the interband transitions, as SPIE 9628 (franta_2015b) Eq. (33) defines it. Appendix B (pp. 242-243): its real part and C_N. The functional form is udm._urbach’s; optmat calls it with E_h in place of E_m, following the authors’ later program (TC-321, finding 1). Which of the two this paper’s fits used is not stated. - Eqs. (13)-(15), p. 235: core (K, L) terms, replaced by the constant 2/(3 pi E_zeta^2), E_zeta = E_K + E_g/2 or E_L + E_g/2; E_K = 1842 eV, E_L = 103 eV; n_K = 1.55 and n_L = 8.33, Shiles et al.’s values for aluminium (p. 236). - Eqs. (16)-(19), p. 235: phonon Gaussians with the Dawson-integral real part; E_p = h c nu_p, B_p = h c beta_p / (2 sqrt(2 ln 2)) (beta_p the FWHM). The same as the implemented term (udm._gaussian). Hazard: the library’s LaTeX of Eq. (19) reads ‘2 sqrt(2) ln 2’; the page image has the root over ‘2 ln 2’. - Section 2.6, p. 235: localized-state transitions, one Gaussian (E_loc, B_loc, N_loc). - Eqs. (20)-(23), p. 236: the alternative interband forms (Tauc-Lorentz, Campi-Coriasso, Cody-Lorentz, and the two-exciton extension). Appendix C (Tauc-Lorentz real part and C_N, three branches) is scrambled in the library’s Markdown (its lines interleave with Appendix B’s): use the page image (pdf page 11, p. 243). - Eqs. (24)-(35), pp. 236-237: the total strength N = N_e + N_Si + N_H, N_e = (14 - 13 f_H) N_a, N_Si = 0.003829 (1 - f_H) N_a, N_H = 0.000545 f_H N_a; N_K = n_K (1 - f_H) N_a, N_L = n_L (1 - f_H) N_a; N_TO = alpha_TO N_Si, N_p = alpha_p N_H; N_ve = N - N_K - N_L - N_ph; N_vx = alpha_x N_ve, N_u = alpha_u N_ve, N_loc = alpha_loc N_ve; N_vc the rest. The library’s Markdown reads ‘F_a’ in the parameter list (p. 237); the PDF prints N_a.
DENSITY (not a vocabulary quantity for the mass density; notes only). With the PJDOS-2EX value N_a = 118.3 eV^2 and f_H = 0.11 (p. 237): atomic density 5.462e28 m^-3 (Eq. (36), the dataset atom_density), electron density 6.866e29 m^-3 (Eq. (37)), mass density 2277 kg m^-3 (Eq. (38)); Menna’s flotation value for similar films is 2300 kg m^-3, and 2200-2300 kg m^-3 is taken as the expected range, a criterion for the models (pp. 237-238). Table 2 gives rho per model (1898-2391). c-Si has N_e = 6.991e29 m^-3 (p. 241). f_H = 0.11 was fixed from earlier IR analysis of similar films (p. 237). franta_2013’s Table 1 gives a-Si:H N_a = 122.9 eV^2 and 5.674e28 m^-3 ‘determined from optical data’, not from this paper’s Table 2.
OTHER VALUES (notes only): Table 1 (p. 237), deposition time 40, 4, 16 min; film thickness 540, 53, 212 nm; overlayer thickness 2.38, 2.12, 2.52 nm; rms roughness 0.52, 0.47, 0.50 nm; autocorrelation length 2.18 nm (all three) for #1654, #1655, #1656. Eq. (42) alpha_H = 0.381, Eq. (43) alpha_Si = 2.8e-4, Eq. (45) effective charges e*_H/e = 0.617, e*_Si/e = 0.23 (p. 241); for c-Si (unpublished) alpha_Si = 3.14e-5, e*_Si/e = 0.0784 (Eq. (46), p. 241). Section 4.5 (pp. 241-242): eps_K(0) = 1.2e-5 and eps_L(0) = 0.0204, so a Tauc-Lorentz eps_inf should be fixed at 1.02 (Eq. (47)); Eqs. (48)-(49) give N_a from TL parameters with n_ve ~ 4.12. The Urbach tail and localized-state results ‘are not reliable because both effects are weak and the samples were composed of substrates and films optically similar in the transparent region’ (p. 240). Figures 3-6 (eps of the films, fits, DOS/JDOS comparison, n and k of a-Si:H and c-Si): not digitised.
refractiveindex.info has no page for this paper (checked in data/external).
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
franta_2013b/band_gap_pjdos_2ex#
{
"id": "band_gap_pjdos_2ex",
"material": "a-Si_H",
"file": "a-Si_H/franta_2013b__band_gap_pjdos_2ex.csv",
"table": "tbl_d0ad1c1043c4",
"quantity": "band_gap",
"unit": "eV",
"abscissa": "label",
"use": "primary",
"parameters": {
"kind": "effective",
"form": "film",
"technique": "ellipsometry and spectrophotometry (dispersion-model fit)"
}
}
Table 2, E_g of the PJDOS-2EX model, the authors’ most reliable (p. 240): the onset of the interband term of Eq. (23), a fitted model parameter, below which the Urbach tail (E_u = 0.029 eV) absorbs. Three films fitted together. ‘rounded according to their estimated statistical errors’ (caption); no uncertainty printed.
franta_2013b/band_gap_other_models#
{
"id": "band_gap_other_models",
"material": "a-Si_H",
"file": "a-Si_H/franta_2013b__band_gap_other_models.csv",
"table": "tbl_d0ad1c1043c4",
"quantity": "band_gap",
"unit": "eV",
"abscissa": "label",
"use": "check",
"parameters": {
"kind": "effective",
"form": "film",
"technique": "ellipsometry and spectrophotometry (dispersion-model fit)"
}
}
Table 2, E_g of the other five models fitted to the same data (PJDOS-EX, PDOS, PJDOS-TL, PJDOS-CC, PJDOS-CL; rows labelled by model): 1.562-1.939 eV, showing how far the fitted gap depends on the model’s form. Not independent of band_gap_pjdos_2ex.
franta_2013b/atom_density#
{
"id": "atom_density",
"material": "a-Si_H",
"table": "text",
"quantity": "atom_density",
"unit": "m-3",
"abscissa": "none",
"use": "check",
"parameters": {
"counts": "atoms",
"form": "film"
}
}
1 inline points in the source record.
Eq. (36), p. 237: the atomic density from the PJDOS-2EX density parameter N_a = 118.3 eV^2 (and f_H = 0.11 fixed), printed ‘5.462 x 10^28 m^-3’. A model-derived value (the model’s valence strength), not a direct measurement.
Formulas#
franta_2013b/udm_pjdos_ex#
{
"id": "udm_pjdos_ex",
"material": "a-Si_H",
"equation": "Eqs. (2)-(35), pp. 234-237; Table 2 (p. 238), PJDOS-EX column",
"printed": "epsilon(E) = 1 + sum_t N_t epsilon_t^0(E), N = N_vc + N_u + N_vx + N_K + N_L + N_ph + N_loc (Eqs. (4), (28)); valence-to-conduction term: Eq. (7) interband term (Lorentz-modified asymmetric JDOS, Appendix A) with the higher-energy term Eqs. (9)-(11)",
"variable": "E: photon energy (eV); N_a in eV^2; energies in eV; alpha_loc printed x 10^6",
"range": "0.046-8.9 eV (the data fitted); films #1654, #1655, #1656 on c-Si, fitted together",
"coefficients": {
"N_a": "122.0",
"f_H": "0.11",
"n_K": "1.55",
"E_K": "1842",
"n_L": "8.33",
"E_L": "103",
"E_g": "1.723",
"E_h": "22",
"E_c": "3.455",
"B_c": "1.180",
"alpha_x": "0.221",
"E_x": "8",
"alpha_u": "0.025",
"E_u": "0.05",
"alpha_loc_1e6": "13.2",
"E_loc": "0.597",
"B_loc": "0.353"
},
"fixed": [
"f_H",
"n_K",
"E_K",
"n_L",
"E_L",
"E_h",
"E_x",
"E_u"
],
"parameters": {
"form": "film"
},
"check": "Table 2 checked cell by cell against its image (2026-09-26); the extraction script checks these strings against the library cells. Not evaluated: no n, k table is printed, and the phonon parameters (formula phonons) are given for one model only."
}
PJDOS-EX: four free parameters for the valence excitations; E_h and E_x fixed at 22 and 8 eV from Kang’s tight-binding and Jochym’s DFT calculations (p. 238). Fit quality (Table 2): chi = 1.173 (all data), chi_E = 4.450, chi_R = 1.418, chi_T = 1.657, chi_IRT = 0.967; mass density rho = 2348 kg m^-3 (from N_a and f_H, Eq. (38)). A separate fit adding an offset eps_inf gave eps_inf = 1.012, chi = 1.173 (Table 2, last rows; eps_inf is incompatible with the sum rule and is used only as a diagnostic, p. 239). ‘The values are rounded according to their estimated statistical errors’ (caption). Fixed values (footnote a) are listed in fixed. Phonon terms: the formula phonons. The same Urbach tail (Eq. (12)), core terms (Eqs. (13)-(15)), phonon Gaussians (Eqs. (16)-(19)) and localized-state Gaussian in all six models (p. 237).
franta_2013b/udm_pdos#
{
"id": "udm_pdos",
"material": "a-Si_H",
"equation": "Eqs. (2)-(35), pp. 234-237; Table 2 (p. 238), PDOS column",
"printed": "epsilon(E) = 1 + sum_t N_t epsilon_t^0(E), N = N_vc + N_u + N_vx + N_K + N_L + N_ph + N_loc (Eqs. (4), (28)); valence-to-conduction term: the parametrised density of states of ref. [24] (Franta et al., Opt. Express 15, 16230 (2007)), no sigma -> xi* term; its Gaussian 1 and 2 are the rows A_c1 ... B_c2; N_vc replaces the old amplitude A",
"variable": "E: photon energy (eV); N_a in eV^2; energies in eV; alpha_loc printed x 10^6",
"range": "0.046-8.9 eV (the data fitted); films #1654, #1655, #1656 on c-Si, fitted together",
"coefficients": {
"N_a": "98.6",
"f_H": "0.11",
"n_K": "1.55",
"E_K": "1842",
"n_L": "8.33",
"E_L": "103",
"E_g": "1.939",
"E_h": "27.0",
"A_c1": "23.7",
"E_c1": "3.840",
"B_c1": "0.372",
"A_c2": "30.9",
"E_c2": "0.681",
"B_c2": "1.721",
"alpha_u": "0.292",
"E_u": "0.098",
"alpha_loc_1e6": "15.5",
"E_loc": "0.593",
"B_loc": "0.348"
},
"fixed": [
"f_H",
"n_K",
"E_K",
"n_L",
"E_L"
],
"parameters": {
"form": "film"
},
"check": "Table 2 checked cell by cell against its image (2026-09-26); the extraction script checks these strings against the library cells. Not evaluated: no n, k table is printed, and the phonon parameters (formula phonons) are given for one model only."
}
PDOS: ref. [24] is franta_2007, whose Eqs. (19)-(23) are this density-of-states parameterisation (C(S) with two Gaussians in |S|) and whose Table 2 fits it, without the sum rule, to another ‘typical’ a-Si:H film (E_g 1.822, E_h 27.8, A_1 11.7, E_1 3.648, B_1 0.429, A_2 11.2, E_2 0.812, B_2 1.945; the Urbach part there is a localized DOS, Eq. (23)). Eight free parameters; ‘the low value of mass density indicates that the model distribution of valence electron excitations is not correct’ (p. 239). Fit quality (Table 2): chi = 1.148 (all data), chi_E = 4.127, chi_R = 1.422, chi_T = 1.652, chi_IRT = 0.960; mass density rho = 1898 kg m^-3 (from N_a and f_H, Eq. (38)). A separate fit adding an offset eps_inf gave eps_inf = 1.056, chi = 1.148 (Table 2, last rows; eps_inf is incompatible with the sum rule and is used only as a diagnostic, p. 239). ‘The values are rounded according to their estimated statistical errors’ (caption). Fixed values (footnote a) are listed in fixed. Phonon terms: the formula phonons. The same Urbach tail (Eq. (12)), core terms (Eqs. (13)-(15)), phonon Gaussians (Eqs. (16)-(19)) and localized-state Gaussian in all six models (p. 237).
franta_2013b/udm_pjdos_tl#
{
"id": "udm_pjdos_tl",
"material": "a-Si_H",
"equation": "Eqs. (2)-(35), pp. 234-237; Table 2 (p. 238), PJDOS-TL column",
"printed": "epsilon(E) = 1 + sum_t N_t epsilon_t^0(E), N = N_vc + N_u + N_vx + N_K + N_L + N_ph + N_loc (Eqs. (4), (28)); valence-to-conduction term: the Tauc-Lorentz form Eq. (20) (Appendix C), sigma -> sigma* and sigma -> xi* not separated",
"variable": "E: photon energy (eV); N_a in eV^2; energies in eV; alpha_loc printed x 10^6",
"range": "0.046-8.9 eV (the data fitted); films #1654, #1655, #1656 on c-Si, fitted together",
"coefficients": {
"N_a": "124.2",
"f_H": "0.11",
"n_K": "1.55",
"E_K": "1842",
"n_L": "8.33",
"E_L": "103",
"E_g": "1.562",
"E_h": "22",
"E_c": "3.617",
"B_c": "2.197",
"alpha_u": "0",
"E_u": "0.05",
"alpha_loc_1e6": "14.9",
"E_loc": "0.572",
"B_loc": "0.423"
},
"fixed": [
"f_H",
"n_K",
"E_K",
"n_L",
"E_L",
"E_h",
"E_u"
],
"parameters": {
"form": "film"
},
"check": "Table 2 checked cell by cell against its image (2026-09-26); the extraction script checks these strings against the library cells. Not evaluated: no n, k table is printed, and the phonon parameters (formula phonons) are given for one model only."
}
PJDOS-TL: three parameters E_g, E_c, B; the highest chi_E and chi_R (p. 239). Fit quality (Table 2): chi = 1.374 (all data), chi_E = 6.715, chi_R = 1.899, chi_T = 1.589, chi_IRT = 0.958; mass density rho = 2391 kg m^-3 (from N_a and f_H, Eq. (38)). A separate fit adding an offset eps_inf gave eps_inf = 0.919, chi = 1.374 (Table 2, last rows; eps_inf is incompatible with the sum rule and is used only as a diagnostic, p. 239). ‘The values are rounded according to their estimated statistical errors’ (caption). Fixed values (footnote a) are listed in fixed. Phonon terms: the formula phonons. The same Urbach tail (Eq. (12)), core terms (Eqs. (13)-(15)), phonon Gaussians (Eqs. (16)-(19)) and localized-state Gaussian in all six models (p. 237).
franta_2013b/udm_pjdos_cc#
{
"id": "udm_pjdos_cc",
"material": "a-Si_H",
"equation": "Eqs. (2)-(35), pp. 234-237; Table 2 (p. 238), PJDOS-CC column",
"printed": "epsilon(E) = 1 + sum_t N_t epsilon_t^0(E), N = N_vc + N_u + N_vx + N_K + N_L + N_ph + N_loc (Eqs. (4), (28)); valence-to-conduction term: the Campi-Coriasso form Eq. (21)",
"variable": "E: photon energy (eV); N_a in eV^2; energies in eV; alpha_loc printed x 10^6",
"range": "0.046-8.9 eV (the data fitted); films #1654, #1655, #1656 on c-Si, fitted together",
"coefficients": {
"N_a": "107.4",
"f_H": "0.11",
"n_K": "1.55",
"E_K": "1842",
"n_L": "8.33",
"E_L": "103",
"E_g": "1.845",
"E_h": "22",
"E_c": "3.903",
"B_c": "2.375",
"alpha_u": "0.097",
"E_u": "0.071",
"alpha_loc_1e6": "14.7",
"E_loc": "0.597",
"B_loc": "0.346"
},
"fixed": [
"f_H",
"n_K",
"E_K",
"n_L",
"E_L",
"E_h"
],
"parameters": {
"form": "film"
},
"check": "Table 2 checked cell by cell against its image (2026-09-26); the extraction script checks these strings against the library cells. Not evaluated: no n, k table is printed, and the phonon parameters (formula phonons) are given for one model only."
}
PJDOS-CC: three parameters; the best fit among the three- and four-parameter models, density low (p. 239). Fit quality (Table 2): chi = 1.153 (all data), chi_E = 4.150, chi_R = 1.407, chi_T = 1.667, chi_IRT = 0.966; mass density rho = 2067 kg m^-3 (from N_a and f_H, Eq. (38)). A separate fit adding an offset eps_inf gave eps_inf = 1.033, chi = 1.153 (Table 2, last rows; eps_inf is incompatible with the sum rule and is used only as a diagnostic, p. 239). ‘The values are rounded according to their estimated statistical errors’ (caption). Fixed values (footnote a) are listed in fixed. Phonon terms: the formula phonons. The same Urbach tail (Eq. (12)), core terms (Eqs. (13)-(15)), phonon Gaussians (Eqs. (16)-(19)) and localized-state Gaussian in all six models (p. 237).
franta_2013b/udm_pjdos_cl#
{
"id": "udm_pjdos_cl",
"material": "a-Si_H",
"equation": "Eqs. (2)-(35), pp. 234-237; Table 2 (p. 238), PJDOS-CL column",
"printed": "epsilon(E) = 1 + sum_t N_t epsilon_t^0(E), N = N_vc + N_u + N_vx + N_K + N_L + N_ph + N_loc (Eqs. (4), (28)); valence-to-conduction term: the Cody-Lorentz form Eq. (22), with E_p, combined with the Urbach tail of Section 2.3",
"variable": "E: photon energy (eV); N_a in eV^2; energies in eV; alpha_loc printed x 10^6",
"range": "0.046-8.9 eV (the data fitted); films #1654, #1655, #1656 on c-Si, fitted together",
"coefficients": {
"N_a": "109.8",
"f_H": "0.11",
"n_K": "1.55",
"E_K": "1842",
"n_L": "8.33",
"E_L": "103",
"E_g": "1.803",
"E_p": "1.065",
"E_h": "22",
"E_c": "3.755",
"B_c": "2.410",
"alpha_u": "0.094",
"E_u": "0.040",
"alpha_loc_1e6": "14.7",
"E_loc": "0.596",
"B_loc": "0.353"
},
"fixed": [
"f_H",
"n_K",
"E_K",
"n_L",
"E_L",
"E_h"
],
"parameters": {
"form": "film"
},
"check": "Table 2 checked cell by cell against its image (2026-09-26); the extraction script checks these strings against the library cells. Not evaluated: no n, k table is printed, and the phonon parameters (formula phonons) are given for one model only."
}
PJDOS-CL: four parameters (p. 239). Fit quality (Table 2): chi = 1.159 (all data), chi_E = 4.207, chi_R = 1.408, chi_T = 1.659, chi_IRT = 0.965; mass density rho = 2114 kg m^-3 (from N_a and f_H, Eq. (38)). A separate fit adding an offset eps_inf gave eps_inf = 1.013, chi = 1.159 (Table 2, last rows; eps_inf is incompatible with the sum rule and is used only as a diagnostic, p. 239). ‘The values are rounded according to their estimated statistical errors’ (caption). Fixed values (footnote a) are listed in fixed. Phonon terms: the formula phonons. The same Urbach tail (Eq. (12)), core terms (Eqs. (13)-(15)), phonon Gaussians (Eqs. (16)-(19)) and localized-state Gaussian in all six models (p. 237).
franta_2013b/udm_pjdos_2ex#
{
"id": "udm_pjdos_2ex",
"material": "a-Si_H",
"equation": "Eqs. (2)-(35), pp. 234-237; Table 2 (p. 238), PJDOS-2EX column",
"printed": "epsilon(E) = 1 + sum_t N_t epsilon_t^0(E), N = N_vc + N_u + N_vx + N_K + N_L + N_ph + N_loc (Eqs. (4), (28)); valence-to-conduction term: Eq. (23): the interband term without excitons (franta_2013 Eq. (56)) plus two excitonic terms of amplitudes A_c1, A_c2, with the higher-energy term Eqs. (9)-(11)",
"variable": "E: photon energy (eV); N_a in eV^2; energies in eV; alpha_loc printed x 10^6",
"range": "0.046-8.9 eV (the data fitted); films #1654, #1655, #1656 on c-Si, fitted together",
"coefficients": {
"N_a": "118.3",
"f_H": "0.11",
"n_K": "1.55",
"E_K": "1842",
"n_L": "8.33",
"E_L": "103",
"E_g": "1.745",
"E_h": "22",
"A_c1": "26.9",
"E_c1": "3.492",
"B_c1": "1.136",
"A_c2": "0.523",
"E_c2": "2.564",
"B_c2": "0.553",
"alpha_x": "0.184",
"E_x": "8",
"alpha_u": "0.035",
"E_u": "0.029",
"alpha_loc_1e6": "13.7",
"E_loc": "0.596",
"B_loc": "0.356"
},
"fixed": [
"f_H",
"n_K",
"E_K",
"n_L",
"E_L",
"E_h",
"E_x"
],
"parameters": {
"form": "film"
},
"check": "Table 2 checked cell by cell against its image (2026-09-26); the extraction script checks these strings against the library cells. Not evaluated: no n, k table is printed, and the phonon parameters (formula phonons) are given for one model only."
}
PJDOS-2EX: eight parameters for the valence-to-conduction transitions plus alpha_x; ‘the most reliable from the points of view of the optical constants as well as mass density determination’ (p. 240). Fit quality (Table 2): chi = 1.149 (all data), chi_E = 4.113, chi_R = 1.333, chi_T = 1.660, chi_IRT = 0.965; mass density rho = 2277 kg m^-3 (from N_a and f_H, Eq. (38)). A separate fit adding an offset eps_inf gave eps_inf = 0.992, chi = 1.149 (Table 2, last rows; eps_inf is incompatible with the sum rule and is used only as a diagnostic, p. 239). ‘The values are rounded according to their estimated statistical errors’ (caption). Fixed values (footnote a) are listed in fixed. Phonon terms: the formula phonons. The same Urbach tail (Eq. (12)), core terms (Eqs. (13)-(15)), phonon Gaussians (Eqs. (16)-(19)) and localized-state Gaussian in all six models (p. 237).
franta_2013b/phonons#
{
"id": "phonons",
"material": "a-Si_H",
"equation": "Eqs. (16)-(19), (30)-(31), p. 235 and p. 237; Table 3 (p. 238)",
"printed": "epsilon_i,p^0 = [exp(-(E - E_p)^2/(2 B_p^2)) - exp(-(E + E_p)^2/(2 B_p^2))]/(sqrt(2 pi) B_p E_p); E_p = h c nu_p, B_p = h c beta_p/(2 sqrt(2 ln 2)); N_TO = alpha_TO N_Si, N_p = alpha_p N_H",
"variable": "nu_p, beta_p (FWHM) in cm^-1; alpha_p relative strengths (of N_H for the seven hydrogen modes, of N_Si for TO)",
"range": "0.046-0.93 eV (360-7500 cm^-1, the IR transmittance)",
"coefficients": {
"nu_S1_ref21": "2000",
"nu_S1": "1996.6",
"beta_S1": "87.8",
"alpha_S1": "0.114",
"nu_S2_ref21": "2090",
"nu_S2": "2073.6",
"beta_S2": "87.8",
"alpha_S2": "0.019",
"nu_S3_ref21": "2120",
"nu_S3": "2120",
"beta_S3": "87.8",
"alpha_S3": "0",
"nu_B2_ref21": "890",
"nu_B2": "890",
"beta_B2": "121.0",
"alpha_B2": "0.0092",
"nu_B3_ref21": "850",
"nu_B3": "850",
"beta_B3": "121.0",
"alpha_B3": "0.0050",
"nu_W_ref21": "640",
"nu_W": "644.1",
"beta_W": "121.0",
"alpha_W": "0.234",
"nu_R_ref21": "590",
"nu_R": "590",
"beta_R": "121.0",
"alpha_R": "0",
"nu_TO_ref21": "470",
"nu_TO": "470",
"beta_TO": "63.9",
"alpha_TO": "0.00028"
},
"fixed": [
"nu_S3",
"nu_B2",
"nu_B3",
"nu_R",
"nu_TO"
],
"parameters": {
"form": "film"
},
"check": "Table 3 checked cell by cell against its image (2026-09-26). Eq. (42): the sum of the seven hydrogen alpha_p, 0.114 + 0.019 + 0 + 0.0092 + 0.0050 + 0.234 + 0 = 0.3812, printed 0.381; Eq. (43) alpha_Si = alpha_TO = 2.8e-4 (printed 0.00028); Eq. (45) sqrt(0.381) = 0.617 and 14 sqrt(2.8e-4) = 0.234, printed 0.617 and 0.23."
}
The phonon terms of Table 3, ‘listed ... only for the PJDOS model’ because the IR dielectric function ‘was practically identical for all the models’ (p. 240); the paper does not say which PJDOS model. Modes after Brodsky et al. (ref. [21]): stretching S1, S2, S3, bending B2, B3, wagging W, rocking R, and the Si TO mode; nu_*_ref21 are Brodsky’s positions, printed beside this work’s. Fixed values (footnote a) are listed in fixed. Peak S3 (SiH3) ‘was not observed’ (alpha 0); SiH:SiH2:SiH3 about 10:1:0 (p. 240).
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.