johnson_1972 ============ P\. B\. Johnson and R\. W\. Christy, "Optical Constants of the Noble Metals", Phys\. Rev\. B 6, 4370\-4379 \(1972\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/PhysRevB\.6\.4370 `__ **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 ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 :doc:`review register ` for the checks and decisions.