Ellipsometric spectra of polycrystalline thin film tantalum nitride (TaN) have been collected and analyzed to obtain the complex dielectric function (ɛ = ɛ1 + iɛ2) and complex refractive index (N = n + ik) spectra over the photon energy range of 0.059–8.500 eV. Complex optical properties are obtained for TaN in the as-deposited state and rapid thermal annealed at 750 °C for 30 s post deposition. A parametric expression including the contribution from intraband and interband transitions along with a structural model is used and fitted to experimental ellipsometric spectra using iterative least-square regression, which minimizes the unweighted error function or mean square error to extract complex optical properties. The parametric expression developed in this work is successful in describing and differentiating the optical response of measured as-deposited and annealed TaN films and can potentially be used to analyze the optical properties of similar TaN films regardless of their deposition techniques.

Tantalum nitride (TaN) is utilized by optical and electronic industries due to its high chemical and mechanical stability, high melting point, and good electrical and thermal conductivity (Ref. 1). Some applications of TaN thin films are as diffusion barriers in microelectronics, oxidation and corrosion resistant coatings in optical and mechanical equipment, stable thin film resistors, and biomedical material in artificial valves (Ref. 2). Additionally, properties of TaN are highly tunable by obtaining various stable and metastable phases that can be easily fabricated using a variety of deposition techniques (Refs. 1–4). Depending upon growth parameters such as temperature, argon to nitrogen gas flow ratio, and pressure, different phases including face-centered cubic (TaN), body-centered cubic (TaN0.05), orthorhombic (Ta4N, TaN, and Ta3N5), tetragonal (Ta4N5), and hexagonal (TaN, Ta5N6) phases can be obtained. These stoichiometry and crystal phase variations have been reported to result in different physical, chemical, and mechanical properties (Refs. 1 and 5–11). Though extensive studies have been made historically to explore the nature of TaN and its phases, a thorough evaluation of its complex optical spectra in an extended photon energy range from lower infrared (IR) to ultraviolet (UV) has not been reported.

In this work, spectroscopic ellipsometry is used to determine the complex dielectric function (ɛ = ɛ1 + iɛ2) and complex refractive index (N = n + ik) of cubic + hexagonal mixed phase polycrystalline TaN thin films deposited on (100)-oriented crystalline silicon (c-Si) wafers using pulsed DC magnetron sputtering (Ref. 12). The mixed cubic + hexagonal phase structure is confirmed with x-ray diffraction. Optical properties of TaN thin films in the as-deposited state and annealed at 750 °C for 30 s under atmospheric pressure argon are investigated in the photon energy range of 0.059–8.500 eV. Silicon substrates used to fabricate TaN thin films contain 1.5 nm of silicon dioxide (SiO2) native oxide layers and are considered in the model for data analysis.

  • Accession Nos.: 01829 and 01830

  • Optical Property Characterization Technique: SE

  • Host Material: TaN thin film on c-Si wafer

  • Instrument: J.A. Woollam FTIR-VASE, J.A. Woollam VUV-VASE

  • Published Spectra: 4

  • Spectral Category: Technical

Specimen Number: 01829

Sample Description: c-Si substrate/SiO2 native oxide/ as-deposited TaN thin film/air ambient

History & Significance N/A

Analyzed Region: Sample surface

Sample Conditions During Measurement: Air ambient

Ex Situ Preparation and Mounting: N/A

In Situ Preparation: N/A (Fig. 1)

Chemical Name: (100)-oriented c-Si

Layer Composition: Substrate c-Si/diamond cubic single crystal

Structural Formula: Single crystal substrate wafer

CAS Registry No: N/A

Layer Manufacturer/Supplier: N/A

As-received Condition: N/A

Host Material Characteristics: Homogenous, isotropic, crystalline, solid, semiconductor

Layer Form: N/A

Lot Number: N/A

Features Observed: N/A

Chemical Name: SiO2 native oxide

Layer Composition: SiO2

Structural Formula: N/A

CAS Registry No: N/A

Layer Manufacturer/Supplier: N/A

As-received Condition: N/A

Host Material Characteristics: Homogenous, amorphous, solid, dielectric

Layer Form: N/A

Lot Number: N/A

Features Observed: N/A

Chemical Name: TaN

Layer Composition: Polycrystalline, cubic and hexagonal mixed phase

Structural Formula: Polycrystalline

CAS Registry No: N/A

Layer Manufacturer/Supplier: N/A

As-received Condition: N/A

Host Material Characteristics: Homogenous, polycrystalline, solid, conductor

Layer Form: N/A

Lot Number: N/A

Features Observed: N/A

Specimen Number: 01830

Sample Description: c-Si substrate/SiO2 native oxide/annealed TaN thin film/air ambient

History and Significance: Sample annealed at 750 °C for 30 s post deposition of TaN thin film on c-Si substrate

Analyzed Region: Sample surface

Sample Conditions During Measurement: Air ambient

Ex Situ Preparation and Mounting: N/A

In Situ Preparation: N/A (Fig. 2)

Chemical Name: (100)-oriented c-Si

Layer Composition: Substrate c-Si/diamond cubic single crystal

Structural Formula: Single crystal substrate wafer

CAS Registry No: N/A

Layer Manufacturer/Supplier: N/A

As-received Condition: N/A

Host Material Characteristics: Homogenous, isotropic, crystalline, solid, semiconductor

Layer Form: N/A

Lot Number: N/A

Features Observed: N/A

Chemical Name: SiO2 native oxide

Layer Composition: SiO2

Structural Formula: N/A

CAS Registry No: N/A

Layer Manufacturer/Supplier: N/A

As-received Condition: N/A

Host Material Characteristics: Homogenous, amorphous, solid, dielectric

Layer Form: N/A

Lot Number: N/A

Features Observed: N/A

Chemical Name: TaN

Layer Composition: Polycrystalline, cubic and hexagonal mixed phase

Structural Formula: Polycrystalline

CAS Registry No: N/A

Layer Manufacturer/Supplier: N/A

As-received Condition: N/A

Host Material Characteristics: Homogenous, polycrystalline, solid, conductor

Layer Form: N/A

Lot Number: N/A

Features Observed: N/A

Instrument # 1 of 2

Instrument Manufacturer: J.A. Woollam Company

Manufacturer Model No: IR-VASE

Instrument Configuration: Fourier transform, rotating compensator spectroscopic ellipsometer

Spectral Range: 0.059–0.700 eV

Measurement Angle(s) of Incidence: 70°

Acquired Data Type: N = cos(2ψ),C = sin(2ψ)cosΔ, S = sin(2ψ)sinΔ

Instrument # 2 of 2

Instrument Manufacturer: J.A. Woollam Company

Manufacturer Model No: VUV-VASE

Instrument Configuration: Rotating analyzer N2 purged spectroscopic ellipsometer operated with adjustable retarder present in the beam path

Spectral Range: 0.7–8.5 eV

Measurement Angle(s) of Incidence: 70°

Acquired Data Type: N = cos(2ψ), C = sin(2ψ)cosΔ, S = sin(2ψ)sinΔ

Ellipsometric spectra in terms of N = cos(2ψ), C = sin(2ψ)cosΔ, and S = sin(2ψ)sinΔ are obtained from two ellipsometers and analyzed simultaneously for as-deposited and annealed TaN samples. Short wavelength IR to UV range (0.7–8.5 eV) ellipsometric spectra are obtained in a continuously nitrogen purged chamber to minimize the effect of ambient oxygen and water vapor absorption at high photon energies. In the IR extended range (0.059–0.700 eV), ellipsometric spectra are collected in normal air ambient where the probing light from the ellipsometer does not suffer from atmospheric absorption effects. Measured ellipsometric spectra collected with the two instruments are simultaneously fit using a single optical/structural model with a least-squares regression algorithm to minimize the unweighted error function σ (Ref. 13) that quantifies the difference between the measured and simulated spectra. The equation describing σ is
σ = 1000 × 1 3 n m i = 1 n [ ( N i m o d N i e x p ) 2 + ( C i m o d C i e x p ) 2 + ( S i m o d S i e x p ) 2 ] ,
where n and m represent the number of measured values and the number of fit parameters, respectively, and the model generated, and experimental ellipsometric spectra are denoted by mod and exp in their corresponding N, C, and S data. Bruggeman effective medium approximation (EMA) (Ref. 14) layers are initially considered below and above the TaN thin film to describe the optical spectra of any physically mixed layer. SiO2 + TaN and TaN + void EMA layers representing the underlying interface and the surface roughness, respectively, are considered with a 0.5 volume fraction of each constituent material in the respective layer. The model is not sensitive to the physically mixed layer lying underneath the TaN films, which is attributed to a high absorption of TaN throughout the measured photon energy range (Ref. 15). The final structural model of both as-deposited and annealed samples consists of semi-infinite c-Si wafer substrate/1.5 nm of native oxide SiO2/TaN thin films/surface roughness layers/air ambient as shown in Figs. 1 and 2. Fit parameters in the model include those within the parametric expression developed for ɛ and the bulk and surface roughness thicknesses describing TaN. Reference optical properties for c-Si and native oxide in separate energy ranges of 0.059–6.500 and 6.5–8.5 eV are obtained from previously reported spectra (Refs. 16–18) and simultaneously used in the respective photon energy ranges in the model to characterize TaN. The as-deposited and annealed films have bulk thicknesses of 80 ± 3 and 84 ± 13 nm and surface roughness thicknesses of 9 ± 1 and 3 ± 1 nm, respectively. Effective thicknesses of each are 84 ± 2 and 85 ± 7 nm as defined as the sum of the bulk layer and half the surface roughness thickness and show very close agreement with those obtained by x-ray reflectivity (XRR) of 83.8 ± 0.5 and 83.2 ± 0.7 nm, respectively. Slight deviations may be due to sampling different scanning locations in films, although the results are within error of each other. Fits of the experimental (symbol) and model generated (solid line) XRR spectra obtained using the GSAS-II fitting software are shown in Fig. 3.
FIG. 1.

Depiction of specimen layers.

FIG. 1.

Depiction of specimen layers.

Close modal
FIG. 2.

Depiction of specimen layers.

FIG. 2.

Depiction of specimen layers.

Close modal
FIG. 3.

Experimental (symbol) and model fit (solid line) of XRR spectra for (a) as-deposited and (b) annealed TaN thin films on single crystal silicon (c-Si) wafer substrates [Accession Nos. (a) 01829 and (b) 01830].

FIG. 3.

Experimental (symbol) and model fit (solid line) of XRR spectra for (a) as-deposited and (b) annealed TaN thin films on single crystal silicon (c-Si) wafer substrates [Accession Nos. (a) 01829 and (b) 01830].

Close modal

Spectral features of both as-deposited and annealed TaN thin films are described using a common parametric optical property model with contribution from both intraband and interband transitions. Spectra in ɛ and N are described by the sum of a constant additive term to the real part of ɛ (ɛ = 1), a single Drude expression (Ref. 19) describing the intraband absorption by free electrons along with three Lorentz oscillators (Ref. 20) and a Tauc–Lorentz oscillator (Refs. 21 and 22) accounting for interband transitions of bound electrons at different resonance energies. Resulting values and error margins of all fit parameters for as-deposited and annealed TaN thin films are shown in Table I. Figure 4 shows good agreement of the model and experimental ellipsometric spectra for both as-deposited and annealed TaN samples, with σ of 3.81 and 5.78 also indicating a good quality of fit. Spectra in ɛ and N obtained for both films are represented in Figs. 5 and 6, respectively.

FIG. 4.

Experimental (symbols) and model fit (lines) ellipsometric spectra [in N = cos(2ψ), C = sin(2ψ)cosΔ, S = sin(2ψ)sinΔ] of (a) as-deposited (Ref. 26) and (b) annealed (Ref. 26) TaN thin films on single crystal silicon (c-Si) wafer substrates over the 0.059–8.500 eV spectral range [Accession Nos. (a) 01829 and (b) 01830].

FIG. 4.

Experimental (symbols) and model fit (lines) ellipsometric spectra [in N = cos(2ψ), C = sin(2ψ)cosΔ, S = sin(2ψ)sinΔ] of (a) as-deposited (Ref. 26) and (b) annealed (Ref. 26) TaN thin films on single crystal silicon (c-Si) wafer substrates over the 0.059–8.500 eV spectral range [Accession Nos. (a) 01829 and (b) 01830].

Close modal
FIG. 5.

Complex dielectric function (ɛ = ɛ1 + iɛ2) spectra for (a) as-deposited (Ref. 26) and (b) annealed (Ref. 26) thin film polycrystalline TaN over the 0.059–8.500 eV spectral range [Accession Nos. (a) 01829 and (b) 01830].

FIG. 5.

Complex dielectric function (ɛ = ɛ1 + iɛ2) spectra for (a) as-deposited (Ref. 26) and (b) annealed (Ref. 26) thin film polycrystalline TaN over the 0.059–8.500 eV spectral range [Accession Nos. (a) 01829 and (b) 01830].

Close modal
FIG. 6.

Complex index of refraction (N = n + ik) spectra for (a) as-deposited (Ref. 26) and (b) annealed (Ref. 26) thin film polycrystalline TaN over the 0.059–8.500 eV spectral range [Accession Nos. (a) 01829 and (b) 01830].

FIG. 6.

Complex index of refraction (N = n + ik) spectra for (a) as-deposited (Ref. 26) and (b) annealed (Ref. 26) thin film polycrystalline TaN over the 0.059–8.500 eV spectral range [Accession Nos. (a) 01829 and (b) 01830].

Close modal
TABLE I.

Parameters describing ɛ for annealed and unannealed TaN thin films. ɛ = 1.

Contribution typeFit parametersAs-deposited TaNAnnealed TaN
Drude ρ (×10−4 Ω cm) 3.0 ± 0.1 3.0 ± 0.1 
τ (fs) 3 ± 1 4.0 ± 0.5 
Lorentz (1) A1 12 ± 3 11 ± 2 
Γ1 (eV) 8± 2 6.7± 0.2 
E1 (eV) 3.0 ± 0.7 2.7 ± 0.3 
Lorentz (2) A2 4.6 ± 0.9 2.7 ± 0.4 
Γ2 (eV) 7 ± 2 3 ± 1 
E2 (eV) 9.8 ± 0.5 10.5 ± 0.3 
Lorentz (3) A3 44 ± 6 44 ± 8 
Γ3 (eV) 1.2 ± 0.9 1.0 ± 0.6 
E3 (eV) 0.4 ± 0.1 0.4 ± 0.1 
Tauc–Lorentz A1 (eV) 436 ± 175 241 ± 63 
Γ1 (eV) 2.6 ± 0.2 2.9 ± 0.2 
E1 (eV) 5.3 ± 0.2 5.2 ± 0.1 
Eg1 (eV) 4.84 ± 0.04 4.51 ± 0.06 
Contribution typeFit parametersAs-deposited TaNAnnealed TaN
Drude ρ (×10−4 Ω cm) 3.0 ± 0.1 3.0 ± 0.1 
τ (fs) 3 ± 1 4.0 ± 0.5 
Lorentz (1) A1 12 ± 3 11 ± 2 
Γ1 (eV) 8± 2 6.7± 0.2 
E1 (eV) 3.0 ± 0.7 2.7 ± 0.3 
Lorentz (2) A2 4.6 ± 0.9 2.7 ± 0.4 
Γ2 (eV) 7 ± 2 3 ± 1 
E2 (eV) 9.8 ± 0.5 10.5 ± 0.3 
Lorentz (3) A3 44 ± 6 44 ± 8 
Γ3 (eV) 1.2 ± 0.9 1.0 ± 0.6 
E3 (eV) 0.4 ± 0.1 0.4 ± 0.1 
Tauc–Lorentz A1 (eV) 436 ± 175 241 ± 63 
Γ1 (eV) 2.6 ± 0.2 2.9 ± 0.2 
E1 (eV) 5.3 ± 0.2 5.2 ± 0.1 
Eg1 (eV) 4.84 ± 0.04 4.51 ± 0.06 

SPECTRAL FEATURES TABLE

Spectrum ID #IdentityCompositionFeature location in rangePhoton energy (eV)Wavelength (nm)nkε1 (real)ε2 (imaginary)
01829 Layer 1 As-deposited TaN  0.07 17 714 13.97 13.37 16.33 373.73 
 0.40 3100 6.66 5.37 15.53 71.58 
 1.95 633 3.77 2.74 6.70 20.74 
 2.10 589 3.65 2.67 6.19 19.56 
 3.05 405 3.08 2.26 4.33 13.95 
 4.85 256 2.79 1.54 5.39 8.62 
 8.00 155 2.48 2.28 0.94 11.35 
01830 Layer 1 Annealed TaN at 750 °C for 30 s  0.07 17 714 12.99 12.92 1.72 335.98 
 0.40 3100 5.89 5.29 6.71 62.37 
 1.95 633 3.18 2.63 3.23 16.73 
 2.10 589 3.06 2.57 2.76 15.74 
 3.05 405 2.44 2.20 1.09 10.74 
 4.85 256 2.12 1.39 2.59 5.90 
 8.00 155 1.74 1.67 0.25 5.83 
Spectrum ID #IdentityCompositionFeature location in rangePhoton energy (eV)Wavelength (nm)nkε1 (real)ε2 (imaginary)
01829 Layer 1 As-deposited TaN  0.07 17 714 13.97 13.37 16.33 373.73 
 0.40 3100 6.66 5.37 15.53 71.58 
 1.95 633 3.77 2.74 6.70 20.74 
 2.10 589 3.65 2.67 6.19 19.56 
 3.05 405 3.08 2.26 4.33 13.95 
 4.85 256 2.79 1.54 5.39 8.62 
 8.00 155 2.48 2.28 0.94 11.35 
01830 Layer 1 Annealed TaN at 750 °C for 30 s  0.07 17 714 12.99 12.92 1.72 335.98 
 0.40 3100 5.89 5.29 6.71 62.37 
 1.95 633 3.18 2.63 3.23 16.73 
 2.10 589 3.06 2.57 2.76 15.74 
 3.05 405 2.44 2.20 1.09 10.74 
 4.85 256 2.12 1.39 2.59 5.90 
 8.00 155 1.74 1.67 0.25 5.83 

Measured TaN thin films exhibit metallic characteristics as illustrated by the low resistivities (ρ) in the Drude expressions along with absorption due to interband electronic transitions at different resonance energies. For as-deposited TaN, absorption peaks in visible and UV photon energy ranges are observed at 3.0 ± 0.7, 4.84 ± 0.04, and 9.8 ± 0.5 eV as denoted by resonance energy (En) of Lorentz (1), Tauc–Lorentz, and Lorentz (2) oscillators, respectively. Additionally, an IR absorption feature, as described by a Lorentz (3) oscillator, is observed at 0.4 ± 0.1 eV. It should be noted that the optical properties of TaN over this spectral range have not been previously reported to our knowledge. While the physical explanation to the origin of this feature at 0.04 ± 0.1 eV is beyond the scope of our present work and would require further characterization of band structure and fermi surface of TaN films, similar IR absorption features have been studied for some transition metals (Ref. 23) and are attributed to low photon energy interband electronic transitions of bound electrons. For atomic layer deposited conductive thin film TaNx, (x ≤ 1), resonance features are observed at 2.2 and 6.5 eV (Ref. 24). Differences in the absorption peaks in our TaN thin films compared to Langereis et al. are attributed to the different fabrication method and stoichiometry. For the annealed films, the absorption peaks are observed at roughly similar resonance energies to that of the as-deposited TaN thin film with notable variations in their corresponding transition strengths and damping factors described by amplitudes (An) and broadening (Γn), respectively. The higher scattering time of 4.0 ± 0.5 fs obtained in the Drude expression for the annealed TaN film as compared to 3 ± 1 fs for as-deposited can be attributed to the formation of larger crystalline grains or improved ordering resulting in lower frequencies of conducting electrons scattering from grain boundaries or point defects (Ref. 25). Figures 7 and 8 clarify differences in ɛ and N spectra over the measurement ranges of the two ellipsometers. The developed optical and structural model in this work is successful to describe the optical properties of TaN thin films with physically realistic fit parameters and low σ and can be used to characterize conductive TaN thin films fabricated using different techniques.

FIG. 7.

Comparison of spectra in ɛ between as-deposited and annealed TaN from (a) 0.059–0.700 eV and (b) 0.7–8.5 eV.

FIG. 7.

Comparison of spectra in ɛ between as-deposited and annealed TaN from (a) 0.059–0.700 eV and (b) 0.7–8.5 eV.

Close modal
Fig. 8.

Comparison of spectra in N between as-deposited and annealed TaN from (a) 0.059–0.700 eV and (b) 0.7–8.5 eV.

Fig. 8.

Comparison of spectra in N between as-deposited and annealed TaN from (a) 0.059–0.700 eV and (b) 0.7–8.5 eV.

Close modal
The Drude expression (Ref. 19) is described by
ε ( E ) = 2 ε 0 ρ ( τ E 2 + i E ) ,
where is the reduced Planck’s constant, ε 0 represents the permittivity of free space, τ is the scattering time, and ρ is the resistivity.
Each Lorentz oscillator (Ref. 20) is described by
ε n ( E ) = A n Γ n E n E n 2 E 2 i Γ n E ,
where A n, Γ n, and E n are the amplitude, broadening, and resonance energy, respectively.
The equation for the imaginary and real parts of the Tauc–Lorentz oscillator (Refs. 21 and 22) are, respectively, expressed as
ε 2 n ( E ) = { [ A n E n Γ n ( E n E g n ) 2 E ( [ E 2 E n 2 ] 2 + Γ n 2 E 2 ) ] , E > E g n 0 , E E g n
and
ε 1 n ( E ) = 2 π P E g n E ε 2 n ( E ) E 2 E 2 d E ,
where A n, Γ n, E n, E g n, and P are the amplitude, broadening, resonance energy, Tauc-gap energy, and Cauchy principal value of the Kramers–Kronig integral, respectively.

Free Parameters in the Model: All parameters listed in Table I along with bulk film and surface roughness thicknesses are free fitting parameters.

Fixed Parameters in the Model: Constant additive term ɛ = 1 for as-deposited and annealed TaN thin films.

Reference Spectra and Sources: Spectra in ɛ for c-Si and native SiO2 from 0.059–6.500 and 6.5–8.5 eV are obtained from Refs. 16–18.

Information Gained from Other Techniques Used to Fix Parameters in the Analysis: None

This material is based on research sponsored by Air Force Research Laboratory under Agreement No. FA9453-21-C-0056. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views expressed are those of the authors and do not reflect the official guidance or position of the United States Government, the Department of Defense, or of the United States Air Force. The appearance of external hyperlinks does not constitute endorsement by the United States Department of Defense (DoD) of the linked websites, or the information, products, or services contained therein. The DoD does not exercise any editorial, security, or other control over the information you may find at these locations. Approved for public release; distribution is unlimited. Public Affairs release approval # AFRL-2022-5793.

The authors have no conflicts to disclose.

Bishal Shrestha: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). Samantha T. Jaszewski: Resources (equal); Writing – review & editing (equal). Jon F. Ihlefeld: Resources (equal); Writing – review & editing (equal). Steve L. Wolfley: Resources (supporting). M. David Henry: Resources (supporting). Nikolas J. Podraza: Conceptualization (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article and its supplementary material.

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Supplementary Material