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 `__ · :doc:`Catalogue ` · :doc:`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one on the back; overlayers taken as fused silica from Palik's handbook \(philipp\_1985\); c\-Si from the authors' own unpublished model \(p\. 237\)\.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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 :doc:`review register ` for the checks and decisions.