Handbook of Modern Coating Technologies
Extracting information of coatings
SE offers sensitive, nondestructive, fast and precise measurements for films, so it has been widely used in characterization of coatings by extracting diverse valuable information, such
as the thickness, roughness, optical indices, energy band gap, anisotropy, and compositions. If in situ SE is used, the growth kinetics of coating is even could be investigated.
- Ex situ measurements
- Thickness/roughness characterization
Thickness characterization is the most important and common usage of ellipsometry. After a reliable stratified model is constructed based on the structure and composition information of the sample, and the optical constants of the layers are known, the thickness of each layer can be extracted accurately and facilely.
Walsh et al. [55] used two-wavelength ellipsometry with a simple two-layer model (shown in Fig. 2—3) for characterizing the thickness of spin—coated poly(methyl methacrylate) (PMMA) films. The results showed that the PMMA film thicknesses (ranging from 0.08 to 2.0 pm) were linear related to c1'33^-0'50, where c is the initial polymer concentration in solution (1.0—7.5 wt.%) and w is the spin speed (1000—4000 rev/min) for preparing the films.
SE has been a well-known characterization tool to evaluate the surface quality of coatings. Bhattacharyya et al. [56] prepared metallic films with sputter deposition method and determined the surface roughness with SE. They treated the surface layer as the mixture of bulk material and air so that Bruggeman EMA was introduced. It was found that the increase in surface roughness of the films followed the increase in thickness. The same conclusion was also drawn based on AFM and grazing-incidence X-ray reflectivity (GIXR) measurements. Mendoza-Galvan et al. [57] also used SE to determine simultaneously the roughness and thicknesses of CuCdTeO thin films prepared by using reactive cosputtering technique.
| n0
n0,d1 n2,d2 |
| N3 = П3 - ікз |
| FIGURE 2-3 Schematic of an idealized two-layer system used for the ellipsometric analysis of thin, spin—coated polymer films on thermal oxides of silicon [55]. |
SE can also be used to determine the thicknesses of an interface layer. As shown in Fig. 2—4, a two-layer optical model (ambient-bulk layer-interface layer-substrate) was built to fit the SE data and extract the thickness of the fois-1,2-(triethoxysilyl)ethane (BTSE) films [58], which were prepared by dipping the Al substrates into BTSE solutions. The results shown in Table 2—3 indicates that the thickness of the films increased with the BTSE bath concentration and the curing condition had significant influence on the film quality. The SE results were consistent with these of Auger electron spectroscopy and transmission electron microscopy (TEM) measurements.
| Cauchy dispersion | ||
| Silane coating | relation Thickness (nm) Non uniformity (%) | |
| EMA (cauchy + x% Al) | ||
| AloOo | Thickness (nm) | |
| Al (pseudo constantants | ||
| Л, | n and k |
| Presumed structure Optical model
FIGURE 2-4 Two-layer optical model used for deconvoluting the SE data to determine the silane layer optical constants, film thickness, and nonuniformity [58]. SE, Spectroscopic ellipsometry.
|
Table 2-3 Comparable thickness of silane films determined by SE [58].
BTSE, b/s-1,2-(triethoxysilyl)ethane; SE, spectroscopic ellipsometry.
|
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Surface roughness
W -Ti-O film
SiO2(interface)
Si substrate
FIGURE 2-5 Stack model of the Ti-doped WO3 constructed for ellipsometry data analysis [59].
SE can be applied to extract the thickness information about the interface layer and surface roughness simultaneously. Ramana et al. [59] reported the SE results on the radio frequency (RF) magnetron sputtered Ti-doped WO3 films. As shown in Fig. 2-5, a three-layer optical model was built, in which the surface roughness and interface layer were considered simultaneously to accurately deconvolute the experimental data. Both the surface roughness and interface thickness determined were very thin, and the growth temperature almost had no influence on the film thickness. As shown in Fig. 2-6, the film thicknesses obtained from SE and observed by SEM were in good agreement with each other.
120
Deposition temperature (°C)
|
|||||||||||||||||||||||||||||||
100
80
60 я M
І 40 20 0
FIGURE 2-6 Thickness of Ti-doped WO3 films grown at various temperatures. Insert shows the variation in surface roughness of the films with growth temperature [59].
| Glue | Layer 2 Layer 3 | |
| a - Si | Layer 4 | |
| S i N | Layer 5 | |
| Layer 6 | ||
| 10 nm |
FIGURE 2-7 TEM image of the a-Si/SiN multilayer sample [60]. TEM, Transmission electron microscopy.
Moreover, SE can measure the thicknesses (including the total thickness and the thickness of each layer) of a multilayer sample based on a complex optical model. As a typical example, the structure of an amorphous silicon—silicon nitride multilayer sample is shown in Fig. 2-7 [60].
Table 2-4 Thickness values for the a-Si/SiN multilayer sample determined by SE and TEM [60].
SE, Spectroscopic ellipsometry; TEM, transmission electron microscopy.
|
SE provided detailed quantitative information about that system. Both the Tauc-Lorentz oscillator and Cauchy dispersion models were used to describe the dielectric functions of amorphous silicon and silicon nitride, respectively. The thickness values were obtained by analyzing SE data, which were in accord with those measured results by TEM, as shown in Table 2—4.
These typical applications of SE to measure the thickness or roughness of coatings are listed in Table 2—5.
- Optical and electric properties characterization
By using SE, the complex optical constants N (or dielectric functions є) of layers can be determined, then their optical and electric properties such as the energy band gap, free carriers concentration, can be derived. Therefore SE has been developed as an important method to measure the optical and electric properties of coatings.
Shaaban et al. [61] used SE to study the changes of the optical properties with the thickness for ZnSe films. They found that the refractive index of ZnSe film increases when the thickness increases within the used wavelength range. Fig. 2—8 shows this change tendency of the optical constants (including both refractive indices and extinction coefficients) with thicknesses.
Optical anisotropic materials have special properties and are very important in the field of optics. This kind of material has two sets optical indices No (no and ko) and Ne (ne and ke), here the subscripts o (means ordinary) and e (means extraordinary) express the directions are parallel or perpendicular to the substrate, respectively. SE also could be applied to study the optical anisotropic materials. Yokoyama et al. [62,63] demonstrated the application of VASE for characterization of the optical anisotropy organic amorphous films. To deconvolute SE data, uniaxial anisotropic models were introduced. Results showed the molecular structure affects significantly the optical properties of the films, the longer the molecular length was, the larger the differences of ordinary and extraordinary optical constants became, which was shown in Fig. 2—9.
| characterization. | ||||||
| Ellipsometric
experimental |
N- A relation | Parameters | ||||
| No. | Systems | conditions | Optical model | used | extracted by SE | Refs. |
| 1 | PMMA on Si | VASE, wavelengths | Two-layer model | Cauchy dispersion | Thickness and refractive | [55] |
| at 4050 and | equation | index | ||||
| 6328 | ||||||
| 2 | Mo/Si/Mo or | Phase-modulated, | Two-layer model | Bruggeman EMA | Thicknesses of total film, | [56] |
| W/Si/W | wavelength | compact layer, surface | ||||
| on c-Si | range | layers, and volume | ||||
| 300-1200 nm | fraction | |||||
| 3 | CdTeOx and | Photon energy | Two-layer model | Lorentz harmonic | Film thickness, | [57] |
| CuCdTeO | range of | oscillator and | roughness, dielectric | |||
| on glass | 1.5-5 eV | Bruggeman | functions, and volume | |||
| EMA | fractions | |||||
| 4 | BTSE on Al | VASE, wavelength | Single-layer model | Cauchy dispersion | Thickness, optical | [58] |
| range | and two-layer | equation and | constants, and | |||
| 250-1700 nm | model with | Bruggeman | nonuniformity | |||
| nonuniform top layer | EMA | |||||
| 5 | Ti-doped | Wavelength range | Three-layer model | Tauc-Lorentz | Thickness, optical | [59] |
| WO3 on | 250-1350 nm | model | constants, and relative | |||
| Si | density | |||||
| 6 | a-Si and SiN | VASE, wavelength | Multilayer model | Tauc-Lorentz and | Thicknesses of total film | [60] |
| on Si | range | Cauchy models | and each layer and | |||
| 250-820 nm | and Bruggeman EMA | refractive index | ||||
| Table 2-5 Brief summary of SE applications for the thickness/roughness |
| BTSE, b/s-1,2-(Triethoxysilyl)ethane; EMA, effective medium approximation; PMMA, poly(methyl methacrylate); SE, spectroscopic ellipsometry; VASE, variable angle spectroscopic ellipsometry. |
| FIGURE 2-8 The spectral dependence of refractive index n and extinction coefficient k of ZnSe films with different thicknesses [61]. |
| Wavelenght (nm) |
| FIGURE 2-9 Dependence of ordinary and extraordinary refractive indices and extinction coefficients on molecular length (a) 4,4'-bis(N-carbazole)biphenyl; (b), (c) The derivatives of (a); (d) 4,4'-bis[(N-carbazole)styryl]biphenyl [62]. |
The related optical properties, such as the complex refractive index (optical constants, N), absorption coefficient (a), normal incidence reflectivity (R), and dielectric constant (e) can also be detected by the following formulas [64—66]:
| 4nk |
| a — |
| A |
| (2.16) |
N — n 1 ik (2.15)
[n-1]21 k2
11]21 k2
| (2.18) |
| (2.19) |
e — (n1ik)2 — e1 1 ie2
where
e1 — n2 - k2
| Thickness (nm) | Eg ellipso (eV) | Eg UV—vis (eV) |
| 153.5 | 3.0984 | 3.18 |
| 156.5 | 3.0966 | 3.10 |
| 167.2 | 3.0031 | 3.08 |
| 177.9 | 2.8241 | 2.90 |
| 186.9 | 2.7758 | 2.71 |
| 204.9 | 2.5627 | 2.54 |
| Table 2-6 The bandgap with different thickness from SE and UV-vis [68]. |
| SE, Spectroscopic ellipsometry. |
e2 = 2nk (2.20)
| n(E) — пх 1 —- |
| Qj 5 2(4Cj-B2)1/2 |
| where |
| (2.21)
(2.22) (2.23) (2.24) (2.25) |
| k(E — Aj(E Eg)
( ) E2 - BjE 1 C |
| Bq-E 1 Co- |
| E2 - BjE 1 Ci |
| A- B2
Bqі — q- (- -2 1 EgBj - E^ 1 Cj) |
| Aj B2
Cq, — - (E 1 Ci) - 2EgCj) |
After the N—A or e— A relationship is obtained, the other physical properties of the material which is relevant to the absorption of the light, such as their energy band gap of semiconductors, could be calculated further with Forouhi—Bloomer (FB) dispersion relations. FB dispersion relations are expressed as follows [67,68]:
in which A,, B,, Ci, Eg, and nN are fitting parameters. Das et al. [68] used FB relations to obtained the optical gap of the nanocrystalline CdS thin films successfully. The energy band gap of CdS thin films with different thicknesses is listed in Table 2—6, and the values extracted by SE are in accordance with those from UV—vis measurements.
| a — |
| 4nk |
| A |
| (2.16) |
The optical band gap also can be calculated from the optical absorption coefficient (a), which could be determined experimentally by using Eq. (2.16) [69,70] and the values of the known wavelength (A) as well as the extinction coefficient (k) measured by SE:
| FIGURE 2-10 Plot of (ahu)1/2 versus hu for MoS2 thin films. (a) Thickness of the MoS2 thin film is 1.99 nm. (b) Thickness of the MoS2 thin film is 9.83 nm [69]. |
| a = |
| K (hv -Eg )m hv |
| (2.26) |
At the same time, the relationship of the absorption coefficient and the photon energy can be described as:
where K is a constant, hu is the incident photon energy, Eg is the optical band gap, and m is a number characterizing the transition process, respectively. It should be noted that the value of m is determined by the band gap transition type, m equals 1/2 for a direct transition, and m equals 2 for an indirect transition. Based on these equations, the value of Eg could be calculated easily by fitting the linear part of the plot and then extrapolating to (ahu)1/m = 0, where hu = Eg. Fig. 2—10 demonstrates the calculation procedure with a typical example, which involves the measurement of optical band gap of MoS2 thin films [69]. Chung et al. [71] also studied the direct optical band gap, electronic structure and lattice dynamics of Li2Ni(WO4)2 with SE and Raman scattering measurements.
| £1(u) = £n |
| ш |
| 2 2 |
| Є2(ш) |
| 2
ШрШт ш(ш2 - ш2) |
| (2.27) |
| (2.28) |
SE could be used to extract the information about charge carriers in metals or semiconductors (such as the carrier concentration). Usually the light energy could be absorbed by the free carriers in metals and semiconductors and the dielectric functions of the materials would be changed, which could be described by Drude model very well. The Drude model is expressed as [49,72]:
where єю, шр, and шт are the permittivity, plasma frequency, and scattering frequency, respectively. Then, the charge carrier concentration Nc and the mobility p can be calculated with the relations [73]:
| (2.30) |
| Nc 5 |
| (2.29) |
| e2 |
e
uT m*
where e0 is the free-space permittivity, e is the electronic charge, and m* is the effective mass of the carriers. Using this approach, Jing et al. [74] found that in Ga—doped ZnO (GZO) thin films, the accurate electron effective mass (me*) is more impactful than the optical band gap shift for analyzing the electrical transport behavior.
IRSE was used by Nakano et al. [75] to determine the carrier concentration of n-type GaAs epitaxial layers. The results derived from the IR ellipsometry and from the electrochemical capacitance—voltage (C—V) measurements were consistent very well, as shown in Table 2—7. The difference of the carrier concentrations obtained by these two methods was no more than 19%. Morino et al. [76] used terahertz time-domain spectroscopic ellipsometry to study the electric properties of an InN epilayer and found that the electric properties of the films were improved with the increase in the film thickness.
Table 2—8 summarizes the main applications of SE to measure optical and electric properties mentioned above.
- Other properties characterization
As we introduced above, when a layer is the mixture of two or more components, EMA model is a good approach to obtain the average optical constants or dielectric functions based on equations [27] such as Eq. (2.14). In those equations, the volume fractions (V) of each component of the layer are involved and can be calculated, then the density and porosity could be derived.
Schubert et al. [77] used IRSE to characterize a mixed-phase BN thin film, which was the mixture of isotropically h-BN and c-BN. By using the Bruggeman EMA [54] to describe the
Table 2-7 Comparison of Nc extracted by SE and C— V methods [75].
C—V, Capacitance—voltage; SE, spectroscopic ellipsometry.
|
Table 2-8 Brief summary of SE applications for optical and electric properties
EMA, Effective medium approximation; GZO, Ga—doped ZnO; SE, spectroscopic ellipsometry; VASE, variable angle spectroscopic ellipsometry.
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dielectric functions of the mixed-phase BN thin film, the volume fraction of c-BN in the film was estimated. Vargas et al. [78] reported the relative density (which is the ratio of film density to that of the bulk material) of films can be determined according to the following Lorentz—Lorentz relation:
Pf _ (■nf -1)2. (пь +1)2 Pb (nf + 1)2 (nb -1)2
where pf pb, Uj and nb are the density of the film and the bulk material, the refractive index of the film, and the bulk material, respectively. SE was used to determine the "n" values in Eq. (2.31) and the relative density was calculated further.
- In situ measurement
It is well known that the ellipsometry measurement is fast and nondistractive, so many processes can be monitored by in situ SE in real-time. Not only the growth rates were obtained, but also the growth kinetics and mechanisms were elucidated. An important application of in situ SE is to study the initial growth stages of films because of the high sensitivity of SE. Fig. 2—11 shows the deposition process of RF magnetron sputtered molybdenum thin film which was obtained by using in situ RTSE [79]. The variations of the Mo bulk layer thickness and surface roughness thickness under three Ar pressures were obvious different, which revealed the mechanisms of the Ar pressure affects the nucleation and growth for the molybdenum thin film.
Lyon et al. [80] prepared Hgx_xCdxTe alloys with x > 0.5 by using molecular beam epitaxy method and determined its real-time composition with SE. SE possesses sufficient sensitivity (can distinguish the tiny composition different about A x~ 0.0002) as well as very good run- to-run stability (Ax~ 0.0012), so it could be applied in the feedback-control system.
| 0
Я M О '-Я <3 м 3 PQ |
| 14
12 10 8 6 4 2 0 |
| о
я м о я S |
| Time (min) |
| FIGURE 2-11 Surface roughness and bulk layer thicknesses versus deposition time obtained by RTSE for Mo depositions at three Ar pressures [79]. RTSE, Real-time spectroscopic ellipsometry. |
In situ SE could be employed to track and measure the film growth process not only in the vacuum environment, but also in the solution environment. Therefore in situ SE has been applied widely in chemical studies in which solutions are involved. Dardona et al. [81] prepared trivalent Cr process (TCP) conversion coatings on Al substrates and studied the formation process by using in situ SE within the spectral region of 1.3—4.3 eV. They used Cauchy dispersion relation to describe the film optical constant and then calculated the film thickness. The results showed that the film thickness is related to the immersion time, and
the initial stages of film formation included three stages, that is, the chemical thinning of the native oxide layer, formation of a very thin initiation layer, and the subsequent rapid formation of the TCP film.
SE is a typical optical technique so that it does not disturb the electric measurements. Therefore SE has been a powerful tool in the field of electrochemistry to study the formation or dissolution of the films on the electrode surface. Li et al. [82] employed in situ SE to obtain detailed insights into the growth of anodic ZrO2 films in an inorganic electrolyte contained F_ ion. Three different models were constructed for the dynamic SE data analysis. Four distinguished phases were found during the initial growth stage of anodic ZrO2 film, namely, formation of compact barrier layer, formation of pores, pore evolution to nanotubes and the nanotube steady-growth. Moreover, in those different phases, the thickness of porous layer increased linearly with the anodization time and the rate was 25.6 nm/s. Similarly Lei et al. [83] studied the initial stages of anodization of aluminum in H2SO4.
In Table 2—9, the typical applications of in situ SE in several environments (vacuum, solution, and electrochemical cell) are summarized.
