johnson_1972#
P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals”, Phys. Rev. B 6, 4370-4379 (1972)
Source record · Catalogue · Review register
Source kind: measurement
Recorded technique: Normal-incidence reflectance R_0 and transmittance T_0 and the p-polarised transmittance at 60 deg incidence, T_60^p, of vacuum-evaporated films on fused quartz, measured at room temperature with a Unicam SP700 double-beam recording spectrophotometer, 0.5-6.5 eV (the p polarisation by a pair of Glan prisms, one in each beam). The three measurements were inverted together (an approximate Newton-Raphson search for the intersection of the three contours in n-k-d space; Nestell and Christy) for n, k and the film thickness d where the contours cross steeply; with d so fixed (to about +-2 A), n and k over the whole range from two of the three measurements (usually R_0 and T_0; T_60^p sometimes combined with one of them). T corrected for the back-surface reflection of the substrate (whose index was taken from the AIP Handbook). R_0 by a double reflection at about 12 deg from two simultaneously evaporated films, the beam-path loss (about 6 %) calibrated with fresh aluminium mirrors (pp. 4371-4373).
Materials in structured entries: Ag, Au, Cu
Dataset quantities: effective_mass, electron_collision_time, extinction_coefficient, refractive_index
Contents: 12 datasets; 0 formulas.
Curation notes#
Journal pages 4370-4379 = PDF pages 1-10 (PDF page 1 opens with the end of the previous paper’s references). Identity checked against the first page (the library flags warnings on the bibliographic record only: a PDF date hint of 2011).
WHAT IS TABULATED. Table I (‘Optical constants for copper, silver, and gold as well as the approximate errors in n and k’, p. 4374, tbl_c125cb44d750): n and k of Cu, Ag and Au against the photon energy, 0.64-6.60 eV (49 rows, steps of 0.12-0.13 eV), and one pair of error columns, Delta n and Delta k, printed ‘+-0.18’ ..., which apply to all three metals: Delta n = 0.18 at 0.64 eV, falling to 0.02 from 1.26 eV; Delta k = 0.65 at 0.64 eV, falling to 0.007 from 1.88 eV. No wavelength column is printed: the abscissa is the energy as printed. These are ‘average values’ over the films of each metal (pp. 4373-4374). The analysis was done in n and k (‘All of our data analysis was done in terms of the complex index of refraction’, p. 4373): n and k are the primary results, and epsilon is presented only in figures (Figs. 2-4, epsilon_1 and epsilon_2 against energy with bands for the instrumental error; epsilon = (n + ik)^2).
UNCERTAINTY. The errors of Table I are the stated per-row errors (sigma column, level not stated): estimates from the instrumental accuracy of the reflection and transmission measurements, ‘calculated by assuming that the accuracy of our transmission and reflection measurements was +-0.5% of full scale’ (scales 0-10 %, 0-20 %, 0-100 %; p. 4373); the spectrophotometer’s accuracy ‘about +-0.005 for measurements above 0.2 and about +-0.0005 for measurements from 0 to 0.1’ (p. 4373). Abstract: the error in d was +-2 A, ‘that in n, k was less than 0.02 over most of the spectral range’. In the infrared n is least certain: for silver ‘an uncertainty in n of about +-40% of its value’ (p. 4375); epsilon_2 = 2nk ‘contains a large percentage error’ there, epsilon_1 ~ -k^2 is accurate (p. 4379).
SAMPLES (films; parameters.form = film). 99.99 % pure metals evaporated at about 60 A/s (for smooth surfaces) at below 4e-6 Torr in an oil-pumped bell jar onto fused-quartz substrates at room temperature (cleaned ultrasonically in Lakeseal Laboratory Glass Cleaner, rinsed in distilled water, dried with a hot-air gun); gold from a conical tungsten basket, silver and copper from tantalum-foil boats; the substrate masked until the source was at temperature (p. 4372). Measured within 5 min of exposure to air, reproducible for days after. Thicknesses (p. 4373): Cu, two films of 297 and 305 A (the table’s average; a 486 A film agreed within the error); Ag, 304 and 375 A; Au, 343 and 456 A (a 186 A film did not converge as evaporated and after annealing gave values ‘not representative of bulk gold’; bulk values need films of about 300 A or more). Several gold films were annealed at 150 C for 9-12 h in vacuum or nitrogen, with no measurable change beyond a small one at 4.5-5.5 eV (pp. 4373-4375). Results independent of thickness over 250-500 A (p. 4378; the abstract’s film range is 185-500 A).
TABLE II (p. 4376, tbl_d5e8fa5d3264): the free-electron optical mass m_0 (electron masses) and the relaxation time tau (s) of each metal, from the Drude model fitted to the infrared: m_0 from the slope of -epsilon_1 against lambda^2 (Fig. 5; epsilon_1^f = 1 - lambda^2/lambda_p^2, lambda_p^-2 = N e^2/(pi m_0 c^2)), ‘assumed that all the noble metals have one conduction electron per atom’ (N, the conduction-electron density, is not printed); tau from the slope of epsilon_2/lambda against lambda^2 (Fig. 6; epsilon_2^f = lambda^3/(lambda_p^2 tau’), tau’ = 2 pi c tau). The Drude form is printed (p. 4375): epsilon^f(omega) = 1 - omega_p^2/(omega(omega + i/tau)), omega_p^2 = 4 pi N e^2/m_0 (Gaussian units). Recorded as effective_mass (carrier electron) and electron_collision_time, with the printed errors as sigma. For copper the text uses m_0 = 1.49 m and tau = 6.87e-15 s (p. 4376), tau to one more digit than Table II’s 6.9. The paper does ‘not wish to stress the reliability of our values for the relaxation times’ (p. 4377). CHECK (2026-09-28, scratch): straight-line fits to Table I’s rows at 0.64-1.26 eV give tau = 6.7e-15 (Cu), 2.7e-14 (Ag) and 7.9e-15 s (Au), against Table II’s (6.9 +- 0.7)e-15, (31 +- 12)e-15 and (9.3 +- 0.9)e-15; the slope of -epsilon_1 gives hbar omega_p = 8.73 (Cu), 9.10 (Ag) and 9.07 eV (Au), i.e. with Table II’s m_0 a conduction-electron density of 8.24e28, 5.77e28 and 5.90e28 m^-3 (the atomic density the paper assumed is not printed; the fitted energy range is not stated).
TEXT VALUES (notes only). Silver’s plasma resonance, observed as the minimum of the p-polarised transmission, is at 3.78 +- 0.02 eV (p. 4377), in agreement with McAlister and Stern; epsilon_1 = n^2 - k^2 from Table I crosses zero between 3.74 and 3.87 eV (3.81 eV by linear interpolation). Interband epsilon_2^b (Figs. 7-9: Cu against the theories of Williams et al. and Fong et al. and the data of Nilsson and of Pells and Shiga; Au against Christensen and Seraphin’s theory and Theye’s and Pells and Shiga’s data) is in figures only. Earlier optical masses quoted: Cu 1.42-1.45, Ag 0.96-1.03, Au 0.94-1.04 m (p. 4377).
FIGURES (not digitised). Fig. 1: the R, T and T_60^p contours in the n-k plane. Figs. 2-4: epsilon_1, epsilon_2 of Cu, Ag, Au against energy. Fig. 5: -epsilon_1 against lambda^2; Fig. 6: epsilon_2/lambda against lambda^2 (infrared). Figs. 7-9: epsilon_2^b.
REPRODUCTIONS. Babar and Weaver (babar_2015) compare with these values (‘JC’), and their website file (optical-constantsCuAgAu.xlsx) has a ‘JC’ sheet; Hagemann, Gudat and Kunz’s composites reproduce them for Cu, Ag and Au (babar_2015’s notes; DESY report SR-74/7). No curated record reprints them.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
johnson_1972/n_Cu#
{
"id": "n_Cu",
"material": "Cu",
"file": "Cu/johnson_1972__n_Cu.csv",
"table": "tbl_c125cb44d750",
"quantity": "refractive_index",
"abscissa_unit": "eV",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"form": "film",
"technique": "normal-incidence reflectance and transmittance and 60 deg p-polarised transmittance of films, inverted for n, k and thickness"
}
}
Table I, p. 4374: n of copper, 0.64-6.60 eV, 49 rows; the average of two films of 297 and 305 A on fused quartz. sigma is the table’s Delta n (common to the three metals).
johnson_1972/k_Cu#
{
"id": "k_Cu",
"material": "Cu",
"file": "Cu/johnson_1972__k_Cu.csv",
"table": "tbl_c125cb44d750",
"quantity": "extinction_coefficient",
"abscissa_unit": "eV",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"form": "film",
"technique": "normal-incidence reflectance and transmittance and 60 deg p-polarised transmittance of films, inverted for n, k and thickness"
}
}
Table I, p. 4374: k of copper, 0.64-6.60 eV, 49 rows (films as n_Cu). sigma is the table’s Delta k.
johnson_1972/n_Ag#
{
"id": "n_Ag",
"material": "Ag",
"file": "Ag/johnson_1972__n_Ag.csv",
"table": "tbl_c125cb44d750",
"quantity": "refractive_index",
"abscissa_unit": "eV",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"form": "film",
"technique": "normal-incidence reflectance and transmittance and 60 deg p-polarised transmittance of films, inverted for n, k and thickness"
}
}
Table I, p. 4374: n of silver, 0.64-6.60 eV, 49 rows; films of 304 and 375 A on fused quartz. sigma is the table’s Delta n; in the infrared the paper puts silver’s n at about +-40 % (p. 4375), more than the table’s 0.02-0.18 at small n.
johnson_1972/k_Ag#
{
"id": "k_Ag",
"material": "Ag",
"file": "Ag/johnson_1972__k_Ag.csv",
"table": "tbl_c125cb44d750",
"quantity": "extinction_coefficient",
"abscissa_unit": "eV",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"form": "film",
"technique": "normal-incidence reflectance and transmittance and 60 deg p-polarised transmittance of films, inverted for n, k and thickness"
}
}
Table I, p. 4374: k of silver, 0.64-6.60 eV, 49 rows (films as n_Ag). sigma is the table’s Delta k.
johnson_1972/n_Au#
{
"id": "n_Au",
"material": "Au",
"file": "Au/johnson_1972__n_Au.csv",
"table": "tbl_c125cb44d750",
"quantity": "refractive_index",
"abscissa_unit": "eV",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"form": "film",
"technique": "normal-incidence reflectance and transmittance and 60 deg p-polarised transmittance of films, inverted for n, k and thickness"
}
}
Table I, p. 4374: n of gold, 0.64-6.60 eV, 49 rows; the average of films of 343 and 456 A on fused quartz. sigma is the table’s Delta n.
johnson_1972/k_Au#
{
"id": "k_Au",
"material": "Au",
"file": "Au/johnson_1972__k_Au.csv",
"table": "tbl_c125cb44d750",
"quantity": "extinction_coefficient",
"abscissa_unit": "eV",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"form": "film",
"technique": "normal-incidence reflectance and transmittance and 60 deg p-polarised transmittance of films, inverted for n, k and thickness"
}
}
Table I, p. 4374: k of gold, 0.64-6.60 eV, 49 rows (films as n_Au). sigma is the table’s Delta k.
johnson_1972/m0_Cu#
{
"id": "m0_Cu",
"material": "Cu",
"file": "Cu/johnson_1972__m0_Cu.csv",
"table": "tbl_d5e8fa5d3264",
"quantity": "effective_mass",
"unit": "m_e",
"abscissa": "none",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"carrier": "electron",
"form": "film"
}
}
Table II, p. 4376: the free-electron optical mass of copper, 1.49 +- 0.06 electron masses, from the infrared slope of -epsilon_1 against lambda^2 (Fig. 5), assuming one conduction electron per atom. A Drude-model parameter of the film data, not a band mass.
johnson_1972/m0_Ag#
{
"id": "m0_Ag",
"material": "Ag",
"file": "Ag/johnson_1972__m0_Ag.csv",
"table": "tbl_d5e8fa5d3264",
"quantity": "effective_mass",
"unit": "m_e",
"abscissa": "none",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"carrier": "electron",
"form": "film"
}
}
Table II, p. 4376: the free-electron optical mass of silver, 0.96 +- 0.04 electron masses (as m0_Cu).
johnson_1972/m0_Au#
{
"id": "m0_Au",
"material": "Au",
"file": "Au/johnson_1972__m0_Au.csv",
"table": "tbl_d5e8fa5d3264",
"quantity": "effective_mass",
"unit": "m_e",
"abscissa": "none",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"carrier": "electron",
"form": "film"
}
}
Table II, p. 4376: the free-electron optical mass of gold, 0.99 +- 0.04 electron masses (as m0_Cu).
johnson_1972/tau_Cu#
{
"id": "tau_Cu",
"material": "Cu",
"file": "Cu/johnson_1972__tau_Cu.csv",
"table": "tbl_d5e8fa5d3264",
"quantity": "electron_collision_time",
"unit": "s",
"scale": 1e-15,
"abscissa": "none",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"form": "film"
}
}
Table II, p. 4376: the Drude relaxation time of copper, (6.9 +- 0.7) x 10^-15 s, printed with the column factor 10^-15 (the scale), from the infrared slope of epsilon_2/lambda against lambda^2 (Fig. 6). The text uses 6.87e-15 s for copper (p. 4376). The paper does not stress the relaxation times’ reliability (p. 4377).
johnson_1972/tau_Ag#
{
"id": "tau_Ag",
"material": "Ag",
"file": "Ag/johnson_1972__tau_Ag.csv",
"table": "tbl_d5e8fa5d3264",
"quantity": "electron_collision_time",
"unit": "s",
"scale": 1e-15,
"abscissa": "none",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"form": "film"
}
}
Table II, p. 4376: the Drude relaxation time of silver, (31 +- 12) x 10^-15 s (as tau_Cu); ‘Results for silver are the least accurate’ (p. 4375).
johnson_1972/tau_Au#
{
"id": "tau_Au",
"material": "Au",
"file": "Au/johnson_1972__tau_Au.csv",
"table": "tbl_d5e8fa5d3264",
"quantity": "electron_collision_time",
"unit": "s",
"scale": 1e-15,
"abscissa": "none",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"form": "film"
}
}
Table II, p. 4376: the Drude relaxation time of gold, (9.3 +- 0.9) x 10^-15 s (as tau_Cu).
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.