Deposition processing and surface metrology of MoNx thin films by design of experiment and single variable (nitrogen flow rate) methods

In this study, the Taguchi design of experiment (DOE) was performed to optimize the deposition process of MoNx thin films using unbalanced magnetron sputtering (UBMS). Further single-variable experiments based on the sensitive parameter derived from the Taguchi experiments were conducted to investigate the effect of the parameter on the phase evolution, structure, and properties of the MoNx thin films. The MoNx thin films were deposited using DC-UBMS. Four controlling factors: N2 flow rate, substrate bias voltage, substrate temperature, and substrate rotational speed were selected in the Taguchi L9 matrix experiment. Electrical resistivity and hardness were chosen as the quality characteristics for the optimization. Analysis of variance (ANOVA) and analysis of mean (ANOM) were performed to identify the sensitive parameters and the optimum conditions. The confirmation test results for the optimizations of hardness (SH) and electrical resistivity (SR) were within the predicted ranges, and therefore the feasibility and reliability of the Taguchi optimization were verified. The results of ANOVA showed that nitrogen flow rate was the most sensitive factor. The optimum condition for the electrical resistivity was chosen to be the reference for the single-variable experiments, and nitrogen flow rate was selected as the controlling variable. The MoNx specimens in the single-variable experiment showed prevailing (200) texture that could be attributed to the lowest surface energy associated with (200) plane and the base metal steering effect by Mo (110). The results of single-variable experiments indicated that the retained Mo metal phase played an important role in hardness, electrical resistivity, and residual stress.


Introduction
Due to the excellent mechanical properties, high thermal stability, chemical inertness, high electric conductivity, transition metal nitrides (TMeNs) thin films have been widely applied in semiconductors for diffusion barriers and contact electrodes during the past decades. Molybdenum nitride (MoN x ) system is one of the TMeNs representing a class of versatile materials with remarkable mechanical, physical and chemical properties [1], which has a wide range of applications including superconducting material [2,3], active catalysts for a variety of reactions [4][5][6][7], and protective coatings [8][9][10][11]. Mo 2 N is a promising candidate for protective coating because of low wear rate and low friction coefficient combined with high hardness and good adhesion [9]. Especially, Mo and Mo 2 N possess a positive effect of tribo-oxidation in self-lubrication during wear due to the formation of orthorhombic Me n O 3n−1 Magnéli phase oxides, a well-known solid lubricant layer with structure containing easy moveable crystallographic shear planes [8,12]. This makes MoN x an ideal candidate for a wide range of tribological applications.
The Taguchi design of experiment (DOE) method offers a simple, economical and systematic way to optimize the design for performance, quality, and cost. In contrast to DOE, the most common method for the investigation of material properties is single-variable experiments, where only one factor is studied at a time. The process of choosing a single factor may be statistically passive in a way that may result in either a time-consuming process or deliver a product of inferior quality at a high cost. On the other hand, the matrix experiments give a more reliable assessment of factors with fewer experiments. To have the advantages of both methods, the feasible and practical approach is first to identify the sensitive factors and optimum conditions in the process by DOE method, and then, to refine the process window by choosing the most sensitive parameter to conduct the single-variable experiments. In our previous work, the Taguchi DOE method was successfully applied for the deposition process optimization on TiN [13], ZrN [13], and VN [14]. Since the approach of Taguchi method is only based on statistics to optimize deposition process, traditional single-variable experiments are essential to explore the effect of sensitive deposition parameters.
Therefore, this study aimed to find the optimum conditions for the deposition of MoN x thin films in an unbalanced magnetron sputtering (UBMS) system using the Taguchi DOE method. Further single-variable experiments based on the sensitive parameter were conducted to investigate the effect of the parameter on the phase evolution, structure, and properties of the MoN x thin films.

Taguchi methodology
Taguchi method is an experiment design based on statistics for promoting the product quality by minimizing but not eliminating the effect of the causes of variation such that the performance is minimally sensitive to the process parameters [15]. In general, two major tools are required in the Taguchi method, namely an orthogonal array (OA) to simultaneously accommodate several experimental design factors (parameters), and the signal to noise ratio (S/N) to serve as the quality characteristics to be optimized within experimental limits. The OA allows the effect of several parameters to be efficiently evaluated and is an important technique in matrix experiments. Further, an analysis of mean (ANOM) is adopted to estimate the factor effect, and a statistical analysis of variance (ANOVA) is employed to identify the effect of the deposition parameters within the experimental range. Finally, conformation experiments are implemented to determine the reliability of the optimum conditions obtained from the matrix experiment.
The partial factorial experiment design 3 4−2 , Taguchi L9, is extensively used in academia and industry due to the efficiency and reliability. Using a 9-run experiment derived from the statistical method, instead of 81-run full factorial experiments, one can predict the optimum conditions corresponding to some specific properties for a process in the experimental range. The Taguchi L9 consists of nine individual experiments corresponding to nine rows in the matrix. The four columns of the matrix represent the four factors in the process and each factor consists of three levels. The alternate levels for the factors define the experimental region. The difference of each level should be sufficiently large to cover a wide experimental region by these three levels. Furthermore, good regions and bad regions can be verified in an extensive experimental region for process factors.
In the Taguchi method, the summary statistic η (signal-to-noise ratio, S/N ratio) is an effective index to evaluate the effect of process parameters on a specific property. Two different types, the larger-the-better and the smaller-the-better, are applied to evaluate the summary statistic η in this study. The S/N ratio (η) is defined as where the mean square quality of characteristic for the larger-the-better type is (1/property) 2 , and for the smaller the better type is (property) 2 .
The effects of four process parameters could be estimated from the observed values of η in the nine experiments. For example, the evaluation of the effect of factor A at level 1 is The overall mean of the static η could be determined by After executing the AMOM and ANOVA, the sensitive factors for the quality characteristics and optimum conditions can be determined. Consequently, the predicted value of summary static η at optimum conditions can be obtained as follows where m is the average value of η for the matrix experiments, and m x and m y are the mean effects of two sensitive factors at the optimum level, which provide the highest value of η. The prediction of optimum quality characteristics can be derived as Predicted optimum quality characteristics 10 5 20 opt Finally, confirmation experiments with the optimum conditions must be conducted and the observed results should be compared with the prediction. This is a crucial step to verify the validity of the optimization. If the observed responses are within the uncertainty of the respective predictions, then the additive model is an adequate approximation of reality. Accordingly, the resultant optimum conditions suggested by DOE can be adopted. On the other hand, if the observations significantly deviate from the respective predictions, implying a strong interaction among the parameters, then the additive model is inappropriate.

Experimental details
The MoN x thin films were deposited using a reactive dc-UBMS system. A 2-in target of Mo (99.99% in purity) was utilized for sputtering deposition. The substrates with dimensions of 15 × 15 × 0.525 mm 3 were prepared from P-type (100) Si wafers. The chamber was evacuated down to a base pressure of 6.7 × 10 −4 Pa (5 × 10 −6 Torr). Meanwhile, the substrates were heated up to the desired deposition temperatures 300, 400, and 500°C. Before the sputtering process, the substrates were pre-sputtered by Ar ion to remove the surface oxide layer and increased the nucleation sites at −800 V for 5 min with Ar gas (99.9995% in purity) flow rate of 30 sccm. The working pressure was kept at 0.21 Pa (1.6 mTorr). After substrate cleaning, the Mo target was pre-sputtered by Ar ion to remove the nitride and/or oxide layer on the surface with Ar gas flow rate of 16 sccm at 0.25 Pa (1.9 mTorr). The Mo target current was fixed at 0.35 A and the deposition time was 90 min The deposition parameters based on the standard orthogonal array L9 are listed in table 1. Three alternative levels of four control factors were chosen, including N 2 flow rate, substrate bias voltage, substrate temperature, and the substrate rotational speed. The difference of each level should be large enough to contain a wide experimental region, which can also increase the probability to explore the nonlinearity of the relationship between the control factors and the noise factors. Thus, good regions and bad regions can be verified in an extensive experimental region for the process factors. In this study, the substrate bias was selected to be ranged from −30 to −90 V, because a bias <−30 V may produce a loose-packed film structure while that > −90 V will cause severe resputtering. For the range of N 2 flow rate, when the flow rate is <3 sccm, the sample contains too much retained Mo metal phase; in contrast, as the flow rate >7 sccm, the high nitrogen content atmosphere may initiate the target poisoning effect. For the substrate temperature, the maximum deposition temperature in the UBMS system is 500°C, and when the temperature is <300°C, low adatom mobility may develop a porous microstructure associated with numerous defects. The substrate rotational speed was chosen ranging from 6 to 18 rpm, which is based on the previous operating conditions on depositing other TMeN thin films.
The crystal structure and preferred orientation of the specimens were identified using an x-ray diffractometer (XRD) with Cu Kα1 x-ray source (λ = 1.5406 Å). The grain size of the MoN x thin films was estimated from the θ/2θ diffraction patterns using the Scherrer equation [16]. Grazing incidence x-Ray Diffraction (GIXRD) was utilized for phase identification and measuring the lattice constants of the thin films. The phase identification was performed by comparing the GIXRD patterns with the International Centre for Diffraction Data (ICDD) [17,18].
The topography and cross-sectional microstructure of the thin films were observed using a fieldemission gun scanning electron microscope (FEG-SEM). The thickness of the specimens was measured from the cross-sectional SEM images. The surface roughness and morphology were observed using an atomic force microscope (AFM).
The chemical compositions and chemical bonding states of the thin films were determined using x-ray photoelectron spectroscopy (XPS). The x-ray source was Al Kα (λ =1486.6 eV). The analysis of the constituent elements included Mo-3d, N-2s, O-1s, and C-1s. The deconvolution and the peak fitting of XPS spectra were carried out using the software XPSPEAK4.1 [19] with Lorentzian-Gaussian function. The Shirley method [20] was applied to subtract the background of the spectra. The relative atomic percentages of Mo, N, and O were acquired from the integrated intensity of the corresponding peaks, and calculated by the equation, = + +Ć where i represents Mo, N, or O, C i is the atomic percentage of the element I, and I i is the integrated intensity of the specific element i divided by the corresponding relative sensitivity factor (RSF) of each element. Laser curvature method was utilized to measure the residual stress of the thin films. The curvatures of the substrate were measured before and after the deposition, and the residual stress was calculated by the Stoney's equation [21]. The hardness of the thin films was determined by nanoindentation using a nanoindenter with a Berkovich indenter head. The Young's modulus of the thin film was measured following the Oliver-Pharr method [22]. The electrical resistivity of the thin films was measured using a four point probe. 4. Results

Optimization of the deposition process of MoN x thin films
Four deposition parameters in the sputtering system were set as the controlled factors for the DOE including nitrogen flow rate, substrate temperature, substrate bias, and substrate rotational speed. The designation of the specimens in the orthogonal matrix experiment is followed the Taguchi L9 table, as shown  in table 1. Table 2 summarizes all the experimental results, including chemical composition, structure, film thickness, mechanical properties, electrical resistivity, and roughness. Since the MoN x thin film is a promising material for diffusion barrier in microelectronics and for protective coatings in tribological applications, electrical resistivity and hardness were chosen as the quality characteristics for the optimization. SR and SH denote the confirmation experiments of the optimization for the electrical resistivity and hardness, respectively. Taguchi method is a statistical analysis, the ANOM and ANOVA are used to determine the sensitive factors on the quality characteristics and predict the optimum conditions. The cross-sectional morphology of the thin films was observed by SEM, and the images are shown in figure 1. Most specimens, except S7 and SR, exhibit a dense Zone T columnar structure, while specimens S7 and SR show loose-packed Zone I columnar structure. The film thickness tabulated in table 2 is nearly constant at a fixed deposition duration of 90 min. Figure 2 presents the θ/2θ XRD and GIXRD patterns for MoN x thin films in the Taguchi experiments. The results of GIXRD reveal the thin films containing Mo, γ-Mo 2 N, and β-Mo 2 N phases. The grain size and lattice constant of the MoN x films were calculated from the diffraction patterns and tabulated in table 3. The signal-to-noise ratios (S/N) of each parameter level for hardness and electrical resistivity calculated from table 2 are presented in table 4. Both statistical analyses, ANOM and ANOVA, were executed according to the data in table 4. Two types of statistical models, the larger-the-better and the smaller-the-better, were applied to hardness and electrical resistivity, respectively. The results of ANOVA for hardness and electrical resistivity are listed in table 5. Figure 3 illustrates the factor effect diagram from ANOM for the hardness of MoN x films, where T, N, B, and R accompanying with three alternative levels in the abscissa denote the substrate temperature, nitrogen flow rate, substrate bias, and substrate rotational speed, respectively. The solid square displays the average S/N ratio for each parameter level and the horizontal dash line represents the overall mean of the S/ N ratios. The perpendicular bar for each factor indicates the 95% confidence interval. In this case, a 95% confidence interval (   Figure 4 gives the 2D projection contour diagram of response surface for hardness with respect to substrate temperature and nitrogen flow rate. Therefore, the optimum conditions for the maximum hardness of MoN x thin films are T 1 N 3 B 2 R 1 : substrate temperature = 300°C, nitrogen flow rate = 7 sccm, substrate bias = −60 V, and substrate rotational speed = 6 rpm. Similar statistical analyses (figure 5) were performed for electrical resistivity in accordance with the smaller-the-better type. The results of ANOM and ANOVA summarized in tables 4 and 5, indicate that substrate temperature and nitrogen flow rate are the sensitive factors for electrical resistivity. Figure 6 presents the 2D projection contour diagram of response surface for electrical resistivity with respect to nitrogen flow rate and substrate temperature. Accordingly, the optimum conditions for the minimum electrical resistivity of MoN x thin films are T 3 N 1 B 3 R 2 : substrate temperature = 500°C, nitrogen flow rate = 3 sccm, substrate bias = −90 V, and substrate rotational speed = 12 rpm, which is different from the optimum conditions for hardness.
The final step of the Taguchi DOE method is to verify the predicted optimum conditions from the matrix experiments. The S/N ratios at the optimum conditions (η opt ) with predicted error are 29.57 ± 3.64 dB and −26.33 ± 13.32 dB for electrical resistivity and hardness, respectively. The predicted values for hardness and electrical resistivity are in the ranges of 19.8 ∼ 45.8 GPa and 4.5 ∼ 96.1 μΩ cm, respectively. Two confirmation experiments were conducted and the results were compared with the prediction values. The confirmation test values for hardness (SH) and electrical resistivity (SR) are 27 GPa and 8.6 μΩ cm, respectively, as listed in table 2, which are within the predicted ranges, and therefore the Taguchi experiments are valid.
Although Taguchi experiments were successfully conducted and the optimum conditions for hardness and electrical resistivity were obtained, the resultant parameters were only a reference window for the deposition of MoN x thin films. Further single-variable experiments should be conducted to refine the parameter window and thereby improving the quality of the MoN x thin films. The ANOVA results show that nitrogen flow rate possesses the largest 'F value' in the optimization for electrical resistivity, suggesting that  Noted that specimen N1 is the same as the SR specimen in the previous optimization experiments. Figure 7 shows the N/Mo ratio of the thin films significantly increases from 0.02 to 0.46 with increasing nitrogen flow rate. A MoN x thin film with a nearlystoichiometric composition (N/Mo = 0.46) of γ-Mo 2 N phase was obtained at nitrogen flow rate of 9 sccm.
The θ/2θ XRD patterns ( figure 8(a)) depict that the MoN x thin film deposited at 3 sccm N 2 flow rate displays a bcc α-Mo phase (ICDD #42-1120) with a highly (110) preferred orientation. As the N 2 flow rate increases from 3 to 9 sccm, the phase transforms from Mo metal phase to γ-Mo 2 N, and a mixture of the two phases can be observed for nitrogen flow rate at 4.5, 6.0 and 7.5 sccm. When the nitrogen flow rate increases from 3.0 to 6.0 sccm, the thin films reveal a broadening Mo (110) peak, indicating the decrease in crystallinity of Mo phase. Mo metal phase persists until N 2 flow rate reaches 6.0 sccm, whereas the γ-Mo 2 N phase becomes dominant when N 2 flow rate exceeds 6.0 sccm. The fcc γ-Mo 2 N is the only phase presented in specimens deposited at 7.5 sccm (N4) and 9 sccm (N5). As listed in Table 7, the grain size of Mo (110) decreases significantly from 27.3 to 4.1 nm, while that of γ-Mo 2 N (200) increases gradually from 8.1 to 17.8 nm with increasing N 2 flow rate. Though the N 2 flow rate ranged from 3 to 9 sccm shows little effect on the deposition rate of MoN x films, it strongly affects the chemical compositions (N/Mo Ratio), which is detailed in section '5.2.2 Composition.' The surface and cross-sectional morphology of the MoN x thin films observed by SEM are presented in figure 9. The cross-sectional morphology of all MoN x thin films in figure 9(b) shows columnar structure. A typical zone I structure with open-boundary columnar structure is observed in specimen N1. Other samples reveal zone T structure with fibrous grains separated by columnar structure without porous boundaries. The thickness of the MoN x thin films is ranged from 1064 to 1109 nm at a fixed deposition duration of 90 min (table 6). It is found that the deposition rate is nearly constant with nitrogen flow  rate, as shown in figure 7, indicating that the target poisoning is not pronounced in the deposition of MoN x thin films. The surface morphology of MoN x thin films is presented in in figure 9(a), where nanograins were observed on the sample surface. It is noteworthy that the topography of sample N1 reveals clear nanotwinned structure. The surface roughness of MoN x films was measured using AFM and the results are reported in table 6. All samples display similar roughness <3.0 nm, suggesting that the variation of N 2 flow rate does not have a strong influence on the surface roughness. Figure 10 depicts the variation of electrical resistivity of MoN x films with respect to N 2 flow rate. The electrical resistivity of the specimens rapidly increases from 8.6 to 109.7 μΩ cm with an increasing N 2 flow rate from 3.0 to 6.0 sccm. Then, the resistivity increases gradually from 109.7 to 144.2 μΩ cm with further increasing N 2 flow rate up to 9 sccm. The results indicate that the electrical resistivity of the MoN x thin films is sensitive to the N 2 flow rate. The formation of γ-Mo 2 N, as well as the incorporation of nitrogen into the Mo metal phase may cause the increase in electrical resistivity. Figure 11 shows the variation of residual stress of the MoN x thin films with N 2 flow rate. The residual stress ranges from −0.62 to 0.85 GPa. The compressive residual stress in specimen N1 may be due to the incorporation of interstitial nitrogen in the Mo lattice by ion peening effect during deposition. The residual      Previous studies [11,23] reported that the phase transformation occurs from α-Mo through β-Mo 2 N, γ-Mo 2 N to B1-MoN or δ-MoN with increasing nitrogen content. The various phases in Mo-N system characterize unique physical and chemical properties. Thus, the phases and microstructure are strongly correlated to the properties and the performance of molybdenum nitride thin films. The phase formation is a complex process of energy exchange between the energetic particles in PVD system. From the energetic point of view, the energy flux delivering onto the substrate controls the reactions of phase formation. The energy flux during the reactive sputtering deposition depends on several factors, such as sputtered atoms, kinetic and potential energies (heats of condensation and reactions), plasma radiation, energy transfer from gas ions, etc. The sensitive parameters are correlated to the primary mechanism of phase evolution associated with the energy transfer, indicating that substrate temperature and nitrogen flow rate significantly affect the kinetics and/or thermodynamics of the reaction.
Thermodynamics addresses the reaction feasibility, the extent of the reaction, and an upper limit of the specified reaction. When a reaction is feasible, thermodynamics can give information on the equilibrium partial pressure and the direction in the reaction. The standard Gibbs free energy δG°of the reaction 4Mo+N 2 = Mo 2 N is equal to −34400 − 9.2Tlog(T)+57.9T (in cal) [24]. The standard enthalpy of formation of Mo 2 N is H°f .298 = −16.8 kcal mol −1 (∼−70.3 kJ mol −1 ) [25]. From thermodynamics, the reaction has a relatively low driving force (the change of the standard Gibbs free energy) compared with other transition metal nitrides. For a thermally activated (Arrhenius-type) reaction, the reaction rate increases with temperature. However, for an  exothermic reaction, although the rate of individual forward and reverse reactions will increase with temperature. The net reaction rate will reach a maximum and then decrease with temperature [26]. The final reaction rate will be a compromise between thermodynamic and the kinetic factors. δG°of the reaction 4Mo+N 2 = Mo 2 N gives the equilibrium N 2 partial pressure, following the equation δG T°= RT ln(P N2 ). Accordingly, the equilibrium N 2 partial pressure for the three deposition temperatures 300, 400, and 500°C corresponds to 0.10 Pa (7.32 × 10 −4 Torr), 6.30 Pa Therefore, all partial pressures of the reactive gas are less than the corresponding equilibrium N 2 pressures, implying that there must be another mechanism that controls the formation of the Mo 2 N phase. Also, the reason for samples S7 and SR mainly containing Mo metal phase could be due to the thermal stability of the Mo 2 N phase. Stöber et al [27] reported a similar result that the dissociation of Mo 2 N thin film would be initiated at post-annealing temperature above 500°C.

5.2.
Effect of N 2 flow rate on structure and properties of the MoN x thin films 5.2.1. Crystal structure and texture Figure 8(a) shows a bcc α-Mo phase with a highly (110) preferred orientation at low N 2 flow rate, while γ-Mo 2 N with (200) texture prevails at a high N 2 flow rate. There are two possible mechanisms for the formation of thin film texture. The preferred orientation may be due to the lowest surface energy associated with thermodynamics. In the B1 or NaCl-type structure (space group Fm3m), (200) is the plane with the lowest surface energy [28], compared to (111) and (220) planes. Also, (110) plane is a relatively closepacked plane in BCC structure, implying that the Mo (110) plane possesses low surface energy. The other mechanism for MoN x thin film texture is the steering effect [29]. Wu et al [14] reported that the VN thin films tend to display a (200) preferred orientation at high deposition temperature and substrate bias voltage. This may be explained by the fact that the configuration of base-metal V (110) in BCC structure is similar to that of VN (200) plane in B1 structure. Thus, the transformation from V (110) to VN (200) is favored by both thermodynamic factor and the steering effect [29]. The θ/2θ XRD results in this study ( figure 8(a)) also agree with the steering effect.
The results of GIXRD in figure 8(b) show only Mo and γ-Mo 2 N phases, instead of MoN, which could be due to the limitation of the target power in our UBMS  system. Even though the N 2 flow rate is reached 9 sccm, the MoN phase is not formed in the thin film. β-Mo 2 N is expected to be obtained in experiments because β-Mo 2 N is a low-temperature stable phase in the phase diagram [30]. β-Mo 2 N is characterized by the diffraction peak at 2θ = 45.305°(β-Mo 2 N (004)). However, the possibility of the presence of β-Mo 2 N is ruled out by examining the θ/2θ XRD and GIXRD patterns. Thin film materials contain high density of defects compared to their bulk counterparts. The low target power limits the energy of the sputtered atoms, and thereby decreasing the mobility of adatoms to the equilibrium lattice sites. The lattice sites of nitrogen atoms in β-Mo 2 N are more ordered in comparison to those in the γ-Mo 2 N, where N atoms randomly distribute in 50% of the octahedral sites. Thus, β-Mo 2 N phase need more energy to establish the ordered structure. Figure 7 shows the N/Mo ratios of the MoN x thin films with respect to different nitrogen flow rates. It is important to examine the increase of N/ Mo ratio is due to increasing N atoms or decreasing Mo atoms. The deposition rate is nearly constant with nitrogen flow rate, implying that the target poisoning effect does not occur. In our previous study [31], the variation of N/Ti ratio in TiN thin film with nitrogen flow rate is mainly from the decrease of Ti content, which is related to the target poisoning effect. To estimate the transport of Mo atoms, the mean free path in the sputtering process should be considered. The mean free path of the particles in the chamber is estimated to be about 24 cm which is larger than the target-substrate distance, indicating that the sputtered Mo atoms can be  directly deposited on the substrate without collisions. All specimens were deposited under the constant current mode, the target power can be evaluated from the product of gun current (0.35 A) and the corresponding voltage provided in figure 7. Therefore, the same number of Mo atoms is deposited on the substrate. Thus, the variation N/Mo ratios is not governed by the Mo atoms but depends on the nitrogen content.

Composition
The results of Taguchi experiments in table 5 indicate that N 2 flow rate is the most sensitive factor. This suggests that nitridation of Mo is the major reaction affecting the structure and properties. In general, two types of mechanisms, diffusion-control and interfacecontrol, may involve in the kinetics of phase evolution. Assuming that the sticking coefficient is 1, deposition rate (  d) = 0.197 nm s −1 (the deposition rate of N5), the density of γ-Mo 2 N = 9.474 g cm −3 , the minimum nitrogen pressure can be estimated as follows. The atomic deposition rate can be obtained by the equation given as where r is the density of γ-Mo 2 N, N A is Avogadro number,  d is deposition rate, and M is the molecular weight of γ-Mo 2 N (= 205.89 g mol) −1 . Accordingly, the atomic deposition rate is 5.46 × 10 14 cm −2 · s −1 . The gas impingement rate can be calculated by the Hertz-Knudsen equation 10 7 22 where P is the partial pressure of N 2 gas, M is molecular weight of N 2 , and T is the chamber temperature. Since the atomic nitrogen fraction is 1/3 in Mo 2 N and a molecule contains two nitrogen atoms, the minimum nitrogen pressure determined by the relationship, (1/3) atomic deposition rate = 2Φ, is 3.76 × 10 −5 Pa (2.82 × 10 −7 Torr). The nitrogen partial pressure with different nitrogen flow rates ranges from 0.04 Pa (3.00 × 10 −4 Torr) to 0.09 Pa (6.84 × 10 −4 Torr). This indicates that the nitrogen partial pressure of all samples exceeds several orders of magnitude than the minimum value. Therefore, the phase evolution of MoN x thin films is a surfacereaction control process.
Thermodynamic calculation indicates that the driving force for the reaction 4Mo+N 2 = Mo 2 N is quite small. In addition, all nitrogen partial pressures during deposition are lower than the equilibrium value, about 133.33 Pa (1 Torr) at 500°C. Therefore, other reaction paths should exist for the phase evolution. The driving force of the nitridation of Mo can be increased and the activation barrier can be lowered by increasing the energy state of reactant. Sputtered Mo atoms and small fraction of N 2 + ions are the main reactive species in the sputtering deposition process. The fact that specimen N1 (at 3.0 sccm N 2 flow rate) contains mainly bcc Mo phase suggests that the hyperthermal sputtered Mo atoms react with nitrogen gas may not be the primary mechanism for nitridation. Baldwin et al [32] proposed that nitrogen ion is a major factor for Mo nitridation by ion implantation technique. They found that the amount of N 2 + ions is associated with the collisional dissociation probability of the impinging molecules. They also pointed out that the reactive nitrogen ions instead of nitrogen molecules could react with Mo. Therefore, N 2 + ions seem to play an important role in the UBMS processing. The ionization energy of N 2 + (15.59 eV [33]) is slightly lower than that of Ar + (15.76 eV [33]), and thus plasma discharge can ionize N 2 in the UBMS system. The amount of N 2 + ions can be increased by the collisional dissociation in the plasma discharge. When nitrogen atmosphere increases, the pronounced phase evolution could be due to the increase of N 2 + ions.
Consequently, the formation of N 2 + ions is the limiting step in the nitride formation. Therefore, high energy deposition technique, such as high power impulse magnetron sputtering (HiPIMS) is suggested to produce the nitrides with low free energy of formation, where high degree of ionization of sputtered metal and molecular gas may assist the reaction with low driving force.

Nanocomposites
The N/Mo ratios of most specimens are lower than the stoichiometric composition of Mo 2 N, where N = 27 ∼ 33 at%. The MoN x thin films prepared with different nitrogen flow rates are the nanocomposites consisting of Mo + γ-Mo 2 N. It is essential to understand the correlation between the phase fraction and the properties of the composites. Assuming specimen N5 is the reference of γ-Mo 2 N, the volume fraction of γ-Mo 2 N can be estimated as follows where V is the volume fraction, ρ is the density, M is the molecular weight. Figure 13 presents the volume fraction of γ-Mo 2 N with different N 2 flow rates. It can be seen that the volume fraction of γ-Mo 2 N increases with N 2 flow rate. Figure 12 indicates that all samples, except N1, have relatively high hardness. This can be explained by the nanograin structure of the MoN x thin films. Our previous study [34] proposed that the grain boundarymediated mechanisms instead of dislocation-slip mechanism is active for plastic deformation in nanocrystalline materials (grain size <20 nm). Note that sample N1 is Mo with N in solid solution, which has much higher hardness compared with pure Mo thin films. Figure 14 reveals the correlation between hardness and the volume fraction of γ-Mo 2 N (0 Vol% denotes the pure Mo metal thin film deposited without nitrogen gas). Two regions can be distinguished from the hardening rate in figure 14. In region I, the improvement of hardness is mainly from the solution hardening, nanotwinned structure, and precipitation strengthening. The effect of solution hardening and precipitation strengthening can be promoted with increasing nitrogen content. It is found that the hardening rate slows down in the region of high volume fraction of γ-Mo 2 N. The precipitation strengthening might become less significant as the volume fraction of γ-Mo 2 N 20% (region II). Figure 13 shows that the volume fraction of Mo decreases whereas that of γ-Mo 2 N increases with N 2 flow rate. The variation of hardness can be attributed to the volume fraction of retained Mo in the region II.

Hardness
Since the retained Mo may assist the grain rotation in  the MoN x thin film, the slight increase of hardness in region II may be due to the decreasing volume fraction of retained Mo. Figure 15(a) depicts the correlation between electrical resistivity and the volume fraction of γ-Mo 2 N. Unlike Mo metal thin film (N1) with an extremely low electrical resistivity, the γ-Mo 2 N thin film (N5) has a relatively high electrical resistivity. Because of the substantial difference in electrical resistivity between these two phases, the electrical resistivity is an appropriate index for the estimation of phase fraction. A nearly linear relationship is found in the region below 55 Vol.% of γ-Mo 2 N. Figure 15(b) shows the variation of residual stress with volume fraction of γ-Mo 2 N. The residual stress turns to the compressive stress state with increasing volume fraction of γ-Mo 2 N, suggesting that the retained Mo phase in MoN x thin films could relieve the compressive stress. The results indicate that electrical resistivity and residual stress are closely related to the retained Mo. Figure 15(c) shows the correlation between electrical resistivity and residual stress. The residual moves to the compressive stress state with increasing electrical resistivity. This implies that the retained Mo not only relieves the compressive stress but also reduces the resistivity of the thin films.

Conclusions
1. The Taguchi design of experiment was applied to optimize the deposition process of MoN x thin films using a DC unbalanced magnetron sputtering system. The confirmation test results for the optimizations of hardness (SH) and electrical resistivity (SR) are 27 GPa and 8.6 μΩ cm, respectively, which are within the predicted ranges, and therefore the feasibility and reliability of the Taguchi optimization were successfully verified. The results of analysis of variance (ANOVA) show that nitrogen flow rate possesses the largest 'F value' in the optimization for electrical resistivity, suggesting that nitrogen flow rate is the most sensitive factor.
2. According to the Taguchi matrix experiments, the optimum conditions for the minimum electrical resistivity of MoN x thin films are: substrate temperature = 500°C, nitrogen flow rate = 3 sccm, substrate bias = −90 V, and substrate rotational speed = 12 rpm.
3. Nitrogen flow rate was chosen to be the variable in the single-variable experiment for further refining the process parameters in the MoN x deposition process.
The MoN x specimens in the single-variable experiment show prevailing (200) texture that can be due to the lowest surface energy associated with (200) plane and the base metal steering effect by Mo (110).

The results of single-variable experiments indicate
that the retained Mo metal phase in the MoN x thin films plays an important role in hardness, electrical resistivity, and residual stress.
5. The process window of hardness is quite large for the Mo 2 N thin films even with large fraction of metal phase. The hardness of the Mo 2 N thin films only varies in a narrow range from 24.1 to 26.0 GPa.