On the nature of point defect and its effect on electronic structure of rocksalt hafnium nitride films

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ScienceDirect Acta Materialia 81 (2014) 315–325 www.elsevier.com/locate/actamat

On the nature of point defect and its effect on electronic structure of rocksalt hafnium nitride films ⇑

Zhiqing Gu,a Chaoquan Hu,a, Xiaofeng Fan,a Le Xu,b Mao Wen,a Qingnan Meng,a Lei Zhao,a ⇑ Xianliang Zhenga and Weitao Zhenga, a

School of Materials Science and Engineering, Key Laboratory of Mobile Materials, MOE, and State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, People’s Republic of China b Central Iron and Steel Research Institute (CISRI), Beijing 100081, People’s Republic of China Received 15 May 2014; revised 30 July 2014; accepted 19 August 2014

Abstract—Although point defects are found to exist commonly in non-stoichiometric group-IVB transition metal nitrides, the identification of primary point defects still causes some disagreement. The formation mechanism and influence of primary point defects on electronic structures are not yet well explored. This study finds that the types and formation mechanism of primary point defects in rocksalt hafnium nitride (d-HfNx) films can be identified by a combination of first-principles calculations and grazing incidence X-ray diffraction, Raman and high-resolution transmission electron microscopy experiments. It is shown that the primary point defects in sub- and over-stoichiometric d-HfNx films are N and Hf vacancies, respectively, which arise preferentially because they are thermodynamically more stable than other types of point defects, such as interstitials and antisites, because they have much lower formation energy and equilibrium formation enthalpy. Furthermore, it is found that the formation of N and Hf vacancies have an important role in changing electronic structures. N vacancies act as donor-like defects and can add extra free electrons to the conduction band at a rate of an electron per N vacancy, while Hf vacancies serve as acceptor-like defects and efficiently reduce free electrons at a rate of two electrons per Hf vacancy. Additionally, the formation of N vacancies can induce two new interband absorption bands centered at 0.81 and 2.27 eV, while the incorporation of Hf vacancies create an additional interband absorption band at 3.75 eV. These new insights are demonstrated by good agreement between calculations and experiments. Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Transition metal nitrides; Formation mechanism; Stoichiometry; First-principles calculations; Interband absorption

1. Introduction The group-IVB transition metal nitrides crystallizing in rocksalt structure (d-TMNx, TM = Ti, Zr, Hf) are well known as a class of fascinating and technologically important film materials. Their excellent properties, including high hardness, thermal stability, IR reflectance, electrical conductivity, corrosion resistance and good diffusion barrier [1–5], make them very promising candidates for applications in wear-resistant coatings [2–4], solar control coatings on windows [6,7], decorative coatings [6,8], highly reflecting back contacts in solar cells [2,9] and LED devices [10], field effect transistor metal gates [1,11] and diffusion barriers in microelectronics [1,2,12]. In d-TMNx films, the point defects related to stoichiometry x commonly exist, because it is difficult to obtain the nominally stoichiometric films experimentally. Many studies have revealed that the

⇑ Corresponding authors. Present address: School of Materials Science and Engineering, Jilin University, Qianjin Street #2699, Changchun 130012, People’s Republic of China. Tel.: +86 431 85168246; e-mail addresses: [email protected]; [email protected]

point defects determine many important properties of d-TMNx films [13–16], including chemical bonding, optoelectronic properties [13,16–18], mechanical properties [19–23], thermal stability [13,24,25] and gold-like appearance [25–27]. To obtain the desired properties for tailorable applications, therefore, it is necessary to identify the nature of point defects and understand their influence on the electronic structures of non-stoichiometric d-TMNx films. To date, some research on point defects for d-TiNx [7,8,23,26,28–30], d-ZrNx [23,31] and d-HfNx [19,32] films, prepared by magnetron sputtering or pulsed laser deposition, have been performed, in which the researchers have consistently found that N vacancies are the primary point defects in sub-stoichiometric d-TMNx. However, for overstoichiometric d-TMNx films, certain disagreement exists in the assignment of primary point defects, in which most investigations have agreed that metal vacancies are primary point defects in both over-stoichiometric d-TiNx and d-ZrN films, whereas a few researchers have proved that nitrogen interstitials are dominant point defects in TiNx films. Although the observed differences may be attributed to different microstructures of the analyzed films as a result

http://dx.doi.org/10.1016/j.actamat.2014.08.040 1359-6462/Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

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of the various deposition and measurement techniques adopted, it is clear that further studies are needed on identifying the primary point defects for d-TMNx films, especially for d-HfNx films because of a lack of previously systematic investigation. Furthermore, the formation mechanism of primary point defects and their roles on changing electronic structures have not yet been well explored. This work identifies the types of primary point defects in sputtered d-HfNx films with different stoichiometry (0.809 6 x 6 1.165) and explores the effects of primary point defects on electronic structures by a combination of grazing incidence X-ray diffraction (GIXRD), Raman and highresolution transmission electron microscopy (HRTEM), optical reflectivity measurements and first-principles calculations. It is shown that N and Hf vacancies are preferentially formed in sub- and over-stoichiometric d-HfNx films, respectively, which is due to N and Hf vacancies having the lowest formation energy among all possible types of point defects. Furthermore, the consistency between experiments and calculations demonstrates that the formation of N vacancies can increase the concentration of free electrons at a rate of an electron per N vacancy and induce two additional interband transition absorptions at 0.81 eV and 2.27 eV, while the formation of Hf vacancies can efficiently reduce the concentration of free electrons at a rate of two electrons per Hf vacancy and produce a new interband transition absorption at 3.75 eV. 2. Experimental and computational details 2.1. Preparation and characterization of d-HfNx films d-HfNx films 600 nm thick were simultaneously deposited on both single-crystal Si (0 0 1) and optical glass substrates by radiofrequency (RF) reactive sputtering a pure Hf target in mixed discharge gases of Ar and N2. The distance between the target and substrate holder was fixed at 55 mm, and the chamber was evacuated by a turbomolecular pump to 4  104 Pa prior to film deposition. Before being introduced into the vacuum chamber, Si (0 0 1) and glass substrates were cleaned ultrasonically in acetone, alcohol and distilled water ether, consecutively. During the deposition, the flow rate of Ar and N2 was accurately controlled by independent mass flow controllers. The stoichiometry x of d-HfNx films was changed from 0.809 to 1.165 by increasing the nitrogen flow rate from 2.4 to 6.0 SCCM, while the argon flow rate, the RF power, work pressure, substrate negative bias and substrate temperature were kept at 80 SCCM, 150 W, 1.0 Pa, 80 V and 200 °C, respectively. X-ray diffraction (XRD) measurements were carried out in GIXRD mode by a Bruker D8tools X-ray diffractometer using Cu Ka as the incident radiation. The microstructure of the films was characterized using HRTEM (JEOL TEM-2010). The stoichiometry x of the films was determined by X-ray photoelectron spectroscopy (XPS) measurements (VG ESCA LAB MKII), in which a monochromatized Al Ka (1486.6 eV) X-ray source was used, and Ar+ cleaning procedure lasting 180 s was applied to all samples prior to XPS quantitative analysis in order to remove the adventitious carbon and absorbed oxygen from the sample surface. Raman measurements were obtained by using the 514.5nm line of an Ar+ laser with a Renishaw 1000 microspectrometer, providing 0.6 W of beam power irradiating under

the frequency range 1001600 cm1. The reflectivity spectrum in the range 2502500 nm was obtained by ultraviolet–visible-near infrared (UV–VIS-NIR) spectrometry, using a PerkinElmer Lambda 900 instrument. The complex dielectric function and plasma frequency xp were obtained by fitting the reflectance spectra using a Drude–Lorentz model [33]. The concentration of free electrons n was obtained by the equation n = e0m*x2p/e2, where permittivity of vacuum e0 = 8.85419  1012 F m1, effective electron mass m*  me = 9.109  1031 kg [34], electron charge e = 1.60218  1019 C, and xp is the plasma frequency. By fitting the measured reflectance spectra, the plasma frequency is found to be 10.75, 10.58, 10.22, 9.51, 9.10, 8.73, 8.11 and 7.66  1015 Hz, respectively, for HfNx films with x = 0.809, 0.851, 0.917, 0.989, 1.039, 1.071, 1.104 and 1.165. Substituting these data into the above equation, the concentration of free electrons of HfNx films was obtained. The film thickness was determined using a Dektak3 surface profile measuring system. 2.2. Computational method Density functional theory calculations were performed to explore the effect of point defects on the electronic structure of HfNx. The method of projector-augmented wave potentials were employed as implemented in the Vienna Ab initio Simulation Package code [35,36]. The generalized gradient approximation with the parameterization of PerdewBurkeErnzerhof was used to express the exchange–correlation energy of interacting electrons [37]. The kinetic energy cutoff of 550 eV was used for the plane wave expansion. The Monkhorst–Pack method was used to sample the k points. The Brillouin zones were sampled with the high-density C-centered k-point grid. The spin-polarization effect was considered in the calculations. The point defects considered in HfNx do not introduce the localized magnetic moment and result in the spin-polarization. The calculated lattice constant of pristine HfN with space group ˚ , which is similar to that from the experiFm–3m is 4.53 A ˚ ). The high- and low-concentration point ments (4.58 A defects are considered by the model of ideal 8-, 16-, 24-, 32- and 64-atom HfN cells with one vacancy or interstitial or anti-site. The band structure of HfN was calculated in a primitive cell with two atoms, wherein the k points of 21  21  21 were used. 3. Results and discussion 3.1. Identification of the primary point defects in sub- and over-stoichiometric d-HfNx films Fig. 1a shows the GIXRD spectra for three typical d-HfNx films with x = 0.809, 1.039 and 1.165, wherein the (1 1 1), (2 0 0), (2 2 0) and (3 1 1) diffraction peaks assigned to the rocksalt phase occur simultaneously, indicating that HfNx films remain crystallized in the rocksalt structure as x varies from 0.809 to 1.165. This fact can be further demonstrated by selected area electron diffraction (SAED) patterns (Fig. 1b–d), in which the diffraction rings from (1 1 1), (2 0 0), (2 2 0) and (3 1 1) are clearly observed. These results show that the rocksalt structure d-HfNx films can be retained for a wide range of stoichiometry x from 0.809 to 1.165, which is closely related to the existence of certain point defects in sub-stoichiometric (x < 1) or

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Fig. 1. Typical (a) GIXRD and (b–d) SAED patterns for d-HfNx films.

over-stoichiometric (x > 1) films. It is known that, in substoichiometric d-HfNx films, the primary point defects may be N vacancies (VN), Hf interstitials (IHf) or Hf antisites (AHf, Hf on a N site), whereas in over-stoichiometric films the possible dominant point defects are Hf vacancies (VHf), N interstitials (IN) or N antisites (AN). The present authors expect that introducing different types of defects will produce different changes in the microstructures and electronic structures, which can allow clear identification of the main types of point defects. To achieve direct correlations between the point defects and structural change, a series of experiments including GIXRD, Raman and HRTEM, along with first-principles calculations, were performed to analyze the primary point defects in sub-stoichiometric (0.809 6 x 6 0.989) and over-stoichiometric (1.039 6 x 6 1.165) d-HfNx films. It is well known that, if some point defects are introduced into a perfect HfN crystal, a certain degree of lattice contraction or expansion will take place, which will induce the change in lattice parameter of the HfN crystal. In order to identify the primary defects, the role of vacancy, interstitial and antisite defects on changing lattice parameter of HfN is studied by first-principles calculations, and the corresponding results are shown in Fig. 2a and b. For the sake of comparison, the experimentally measured lattice parameters for sub-stoichiometric (0.809 6 x 6 0.989) and over-stoichiometric HfNx films (1.039 6 x 6 1.165) are also shown in Fig. 2c. For sub-stoichiometric HfNx, the introduction of IHf and AHf causes a continuous increase in lattice parameter compared with stoichiometric HfN (Fig. 2a), which is completely opposite, with a decrease in measured

lattice parameter as x decreases from 0.989 to 0.809 (Fig. 2c). In contrast, the introduction of VN leads to a gradual decrease in lattice parameter (Fig. 2b), which agrees well with the experimentally observed trend (Fig. 2c), indicating that the primary point defects are VN rather than IHf and AHf in sub-stoichiometric HfNx films (0.809 6 x 6 0.989). In the case of over-stoichiometric HfNx films, introducing IN causes a continuous increase in lattice parameter, and incorporating AN has almost no effect on the lattice parameter (Fig. 2a), which is completely different from the experimentally observed trend (Fig. 2c). In contrast, when VHf are incorporated into stoichiometric HfN, the lattice parameter rapidly decreases (Fig. 2b), which is consistent with a decrease in measured lattice parameter on increasing x from 1.039 to 1.165, proving that the dominant point defects are VHf rather than IN and AN in over-stoichiometric HfNx films (1.039 6 x 6 1.165). Many investigation have revealed that, in perfect stoichiometric d-HfN crystals, first-order Raman scattering is forbidden by symmetry and only second-order scattering is allowed [32]. However, when point defects exist in dHfN crystals, first-order scattering will occur as a result of Oh symmetry being broken. Hence, the Raman spectrum is also an effective tool for identifying the point defects. The Raman spectra of d-HfNx films with x = 0.809, 1.039 and 1.165 are shown in Fig. 3a, in which the occurrence of first-order acoustic (TA, LA) and optical peaks (O) at 168, 189 and 532 cm1 reveals that both sub- and overstoichiometric d-HfNx films contain certain types of point defects. In the case of sub-stoichiometric HfNx films, both TA and LA peaks shift gradually to higher frequencies as x

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Fig. 2. (a, b) The change in lattice parameter of HfNx with different x induced by vacancies, interstitials and antisites relative to perfect stoichiometric HfN obtained by first-principles calculations, and (c) the change in measured lattice parameter of HfNx films with different x obtained from XRD spectra, in which the solid line is a guide for the eyes.

Fig. 3. (a) Typical Raman spectra over the frequency range 100–1600 cm1 for d-HfNx films, (b) the shift in the positions of first-order acoustic (TA, LA) and optical (O) peaks, and (c) the ratio (IO/IA) of integrated intensity of first-order optical peak to that of acoustical peak as a function of x.

decreases from 0.989 to 0.809 (Fig. 3b), and at the same time, the position of O peaks remain essentially constant, indicating that the phonon softening in the acoustic branches takes place, which is attributed to a decrease in the number of valence electrons induced by an increase in VN [28,32]. This phenomenon implies that the primary point defects are VN rather than IHf and AHf in substoichiometric HfNx films (0.809 6 x 6 0.989). For overstoichiometric HfNx films, the O peak shifts continuously towards a higher frequency as x increases from 1.039 to 1.165 (Fig. 3b), while the position of the A peak remain basically unchanged, which means that the degree of structural order around the N sites significantly decreases

[32,38]. This observation, combined with a linear decrease in lattice parameter with an increase in x from 1.039 to 1.165 (Fig. 2c), consistently demonstrates that the dominant point defects are VHf, rather than IN and AN, in over-stoichiometric HfNx films (1.039 6 x 6 1.165). Furthermore, the ratio (IO/IA) of the integrated intensity of the first-order optical peaks to that of acoustical peaks can be regarded as a measure of relative concentration of VN and VHf (CVN/CVHf) [39]. It can be seen from Fig. 3c that the IO/IA increases continually from 0.34 to 1.41 as x increases from 0.809 (sub-stoichiometry) to 1.165 (overstoichiometry), meaning that a gradual transition from VN to VHf takes place. These findings agrees well with

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XRD measurements, consistently proving that the types of point defects in HfNx films depend strongly on x: for 0.809 6 x 6 0.989, the primary defects are VN, whereas for 1.039 6 x 6 1.165 the dominant defects are VHf. Previous experimental and theoretical investigations have shown that, for sub-stoichiometric d-TiNx and d-ZrNx films, the primary defects are VN, which is in good agreement with the present findings in HfNx films. It is noted that in the case of over-stoichiometric films, two different assignments exist in the types of primary point defects. One is nitrogen interstitials (IN), which was only found in a few investigations on d-TiNx films. Another is metal vacancies (VTi and VZr), which were proved in most of investigations on d-TiNx and ZrNx films. The present findings (VHf) in d-HfNx films are consistent with the latter. In order to confirm further that the dominant point defects are VHf rather than IN in over-stoichiometric d-HfNx films, HRTEM measurements were performed. Fig. 4 shows the HRTEM lattice images for d-HfNx films with x = 1.039 and 1.165, in which well-crystallized nanograins are uniformly distributed on the film surface (Fig. 4a and b), and a highly ordered crystal lattice is observed from the enlarged images of nanograins (Fig. 4c and d). For nearly stoichiometric HfNx film (x = 1.039), the measured values of (1 1 1) and (2 0 0) interplanar spacing are d111 = 0.2688 nm and d200 = 0.2306 nm, whereas for overstoichiometric film (x = 1.165) they are d111 = 0.2643 nm and d200 = 0.2283 nm. Such a significant decrease in interplanar spacing agrees well with the results from GIXRD measurements, indicating that the primary point defects are VHf, rather than IN, in over-stoichiometric HfNx films, because the introduction of IN can lead to lattice expansion, while the incorporation of VHf promotes lattice contraction, which is confirmed by first-principles calculations (Fig. 2a). Additionally, it is noted that, for nearlystoichiometric HfNx film (x = 1.039), no apparent defects appear in the HRTEM image (Fig. 4c), while for overstoichiometric film (x = 1.165), some void spaces can be seen clearly, as shown in the region of white circles (Fig. 4d). The present authors find that the Burgers circuits drawn around these core of void spaces are completely closed, indicating that the observed void spaces do not originate from certain dislocation, but more possibly from VHf and their cluster [40,41]. These findings from HRTEM images agree well with GIXRD and Raman measurements, consistently proving that, in over-stoichiometric d-HfNx films, the dominant point defects are VHf. 3.2. Reason for preferential formation of VN and VHf in suband over-stoichiometric d-HfNx films In order to explore the possible reason why VN and VHf, rather than other point defects such as interstitials and antisites exist preferentially in sub-stoichiometric and over-stoichiometric HfNx films, the present authors calculated the equilibrium formation enthalpy of the compounds HfmNn with different defective structures and formation energy of a single point defect in a perfect HfN crystal by first-principles calculations. The equilibrium formation enthalpy of the compounds HfmNn is defined as [8,42,43]   DH ðHf m Nn Þ ¼ EðHf m Nn Þ  mEðHf hcp Þ  n=2EðN2 Þ =ðm þ nÞ ð1Þ

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where E(HfmNn), E(Hfhcp), E(N2) are the total energies of hafnium nitride (HfmNn), a bulk (hexagonal close packed) Hf atom, and a free N2 molecule, respectively; n and m are the number of Hf and N atoms in the supercell. The formation enthalpy of HfmNn with different defective structures is displayed in Fig. 5, in which for an arbitrary value of x (n/m) sub-stoichiometric HfmNn containing VN always has a much lower formation enthalpy than those containing IHf or AHf, suggesting that, for sub-stoichiometric HfmNn, the defective structures with VN are energetically most favorable and stable. Similar results are also found in the case of over-stoichiometric HfmNn, in which for an arbitrary value of x (n/m) the HfmNn structures with VHf exhibit a lowest formation enthalpy, meaning that, for over-stoichiometric HfmNn, the defective structures with VHf are energetically most favorable and stable. The study now turns to considering the formation energies (EF) of the single point defects in a 64-atom supercell. To check the convergence of the formation energies, a 96-atom supercell was also constructed. It was found that the formation energies of point defects calculated by the 64-atom supercell are well converged. For example, the difference between the formation energies of the interstitials calculated by the 64-atom and 96-atom supercells is not more than 0.1 eV. The formation energies (EF) of the single N-related point defects can be defined as [8,13,42] EF ¼ EðHf m Nn Þ þ x=2EðN2 Þ  ETMN

ð2Þ

where ETMN is the total energy of the defect-free d-HfN supercell, and x = 1,1, and 0 for VN, IN and AN defects, respectively. Analogously, the formation energies EF for the single Hf-related defects can be calculated using the formula EF ¼ EðHfm N n Þ þ xEðHfhcp Þ  ETMN

ð3Þ

where x = 1,1 and 0 for VHf, IHf and AHf defects, respectively. Table 1 shows the formation energy EF of various single defects and the rate of change in lattice parameter representing lattice distortion, n = d[a(x)/a0]/dx, where a(x) and a0 are lattice parameters of non-stoichiometric HfNx and stoichiometric HfN, respectively. Besides the interstitials located at tetrahedral sites, the interstitials as dumbbells are also considered, based on the previous investigations on other nitrides and carbides [15,42]. It can be seen that, for sub-stoichiometric HfNx samples, the formation energy of VN (3.12 eV) is much lower than that of IHf (11.01 eV) in the dumbbell along (1 1 1) or AHf (13.21 eV), which indicates that VN is more easily incorporated into a perfect HfN crystal than IHf or AHf. Similar results also appear in the case of over-stoichiometric HfNx samples, in which VHf is found to be more easily formed in a perfect HfN crystal because it has a relatively low formation energy (1.90 eV) compared with IN (2.66 eV) at a tetrahedral site or AN (11.38 eV). Additionally, the n of VN and VHf are equal to 0.011 and 0.052, respectively, indicating that the introduction of VN and VHf into a perfect HfN crystal will induce a very small lattice distortion. These results agree well with calculations on the formation enthalpy of the HfmNn compounds, consistently proving that the introduction of VN or VHf into a perfect HfN crystal is energetically most favorable and most stable, which is responsible for the preferential formation of VN or VHf in sub- or over-stoichiometric HfNx films.

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Fig. 4. (a, b) HRTEM lattice images of HfNx films with x = 1.039 and 1.165, and (c, d) enlarged images of the detailed atomic arrangement of the white square framed region in (a) and (b).

Fig. 5. Formation enthalpy of HfmNn with different defective structures as a function of x (n/m).

3.3. Changes in electronic structure of d-HfNx films induced by VN and VHf Having confirmed that VN and VHf are the primary point defects in sub-stoichiometric (x < 1) and overstoichiometric (x > 1) HfNx films, the study now investigates the effects of VN and VHf on the electronic structure by first-principles calculations combined with optical experiments. To compare with the experiments, two typical models of Hf8N7 and Hf7N8 containing a high concentration of

VN and VHf, respectively, are constructed with ideal stoichiometric (x = 1) structure. The total and partial density of states (TDOS and PDOS) of HfN, Hf8N7 and Hf7N8 are calculated, and the corresponding results are shown in Fig. 6a–c, respectively. Three energy regions can be clearly distinguished: (a) from 18 to 14 eV, (b) from 9 to 3 eV, and (c) from 2.3 to 2 eV. The first region is mainly due to N s-electron contributions. The second region is characterized by the strong hybridization of one d electrons orbital with eg symmetry of the metal Hf with the N 2p electrons orbital. The third region is filled mainly by the Hf d electrons. Therefore, the electronic properties of d-HfNx are controlled mainly by the hybridized states and freeelectron states near the Fermi level. In all TDOS (Fig. 6d) there are some states near the Fermi level, indicating that all d-HfNx samples contain some free electrons and exhibit metal-like behavior. In order to compare quantitatively the relative TDOS around the Fermi level for different HfNx structures, the ratio of the integrated TDOS from 0.15 eV up to 0.15 eV to that of the whole valence energy region up to Fermi energy is calculated [43]. It is found that Hf8N7 containing VN has a relative high TDOS (0.0398) at EF compared with stoichiometric HfN (0.0257). Hence, VN act as donor-like defects, which add extra free electrons to the conduction band. In contrast, Hf7N8 with VHf has a notably reduced TDOS at EF (0.0172) relative to stoichiometric HfN (0.0257). Accordingly, VHf serve as acceptor-like defects that spatially localize free carriers in the conduction band. In order to quantitatively investigate the effects of VN and VHf on the concentration of free electrons, the energy band structure of HfN in a primitive cell was calculated. It is known that there are nine valence electrons in a

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Table 1. Formation energy EF of various single defects in a perfect crystal and the rate of change in lattice parameter representing lattice distortion, n = d[a(x)/a0]/dx, where a(x) and a0 are lattice parameters of non-stoichiometric HfNx and stoichiometric HfN, respectively. Stoichiometry

Defect type

Geometry

EF (eV)

n

x<1

AHf VN IHf IHf IHf

Octahedral Octahedral Tetrahedral Dumbbell along (1 1 1) Dumbbell along (1 1 0)

13.21 3.12 12.26 11.01 12.09

0.140 0.011 0.417 0.360 0.360

x>1

AN VHf IN IN IN

Octahedral Octahedral Tetrahedral Dumbbell along (1 1 1) Dumbbell along (1 1 0)

11.38 1.90 2.66 4.25 3.49

0.029 0.052 0.181 0.245 0.170

Fig. 6. TDOS and PDOS for HfN, Hf8N7, and Hf7N8 obtained by first-principles calculations.

primitive cell of HfN, four from Hf and five from N. The ratio of the integrated TDOS of the hybridized states from 3 eV up to 9 eV to that of the whole valence energy region up to Fermi energy is 2/3, indicating that there are six electrons contributing to the covalent-like Hf–N bond. From the band structure of HfN in a primitive cell (Fig. 7a), two nitrogen 2p bands and one Hf band appear between 3 and 9 eV, and they are occupied by six electrons to form the Hf–N bond, in which two electrons fill one d band, and the remaining four electrons fill two N 2p bands. Compared with two N 2p bands occupied by three electrons in a single neutral N atom, this situation can be roughly regarded as one electron transferring from Hf to N and causing the formation of a nitrogen ion.

One expects that, when a nitrogen ion is removed from a stoichiometric HfN crystal to form a VN, the charge transfer of roughly one electron from Hf to N will not occur, and the corresponding electron from Hf contribution is returned to Fermi level, that is, the formation of a VN can add one extra free electron to the conduction band. In contrast, it is expected that the formation of a VHf will reduce two free electrons from the Fermi level. The first electron is lost because one free electron from Hf itself is now missing from the Fermi level. The second electron is deprived because an electron transfer from Hf to N is forbidden owing to the absence of a nearest-neighbor Hf atom. As a result, the N atom has to trap an electron from the Fermi level to form the nitrogen ion. According to these

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Fig. 7. (a) Energy band structure for HfN in a primitive cell along the different symmetry lines of the Brillouin zone, where energy is in eV, and the Fermi level is at zero, and (b) the ratio of rate of change in measured free-electron concentration to defect concentration (c), Dn/CVN = 2:1 for VN and Dn/CVHf = 4:1 for VHf.

predictions, the rate of change in the concentration of free electrons at the Fermi level can be expressed as Dn=(nn0)/ n0 = k(1x), where n0 is the concentration of free electrons in the stoichiometric HfN, and k is the change in the numbers of free electrons induced by a point defect in HfNx, k = 1 for VN and k = 2 for VHf. For a given x, the concentration of VN (CVN) and VHf (CVHf) can be defined as CVN=(1x)/2 and CVHf=(x1)/2 [14], respectively. Substituting the expression of CVN and CVHf into the above equation, Dn can be expressed as Dn = 2kCVN for VN and Dn=(2k)CVHf for VHf. Hence, the ratios of rate of change in the concentration of free electrons to the concentration of point defects are Dn/CVN = 2k:1 = 2:1 for VN and Dn/ CVHf = 2k:1 = 4:1 for VHf. In order to confirm the above predictions, the concentrations of free electrons in HfNx films with different concentrations of VN or VHf were measured, and the corresponding results are shown in Fig. 7b. It can be clearly seen that, as the concentration of VN increases, Dn increases, with Dn/CVN = 2:1. Additionally, Dn rapidly decreases, with Dn/CVHf = 4:1 as the concentration of VHf increases. These experimental findings are in good agreement with theoretical predictions, suggesting that N vacancies act as donor-like defects, which add extra free electrons to the conduction band at a rate of an electron per N vacancy, while Hf vacancies serve as acceptor-like defects, which promote the reduction of free electrons at a rate of two electrons per Hf vacancy. It is noted from TDOS (Fig. 6d) that, for the defect-free stoichiometric HfN, the only sharp peak is at 5.55 eV below the Fermi level, which arises mainly from N p electrons according to the partial density of states (Fig. 6a). However, as VN is introduced into stoichiometric HfN, an additional two states at 2.26 eV and 1.10 eV below the Fermi level occur (Fig. 6d), indicating the formation of new VN-induced localized states, which arise from the Hf atoms near the VN according to the partial density of states (Fig. 6b). The nearest-neighbor Hf d electrons cannot be effectively hybridized and are localized in the VN owing to the absence of N atoms. In the case of over-stoichiometric Hf7N8 containing VHf, several broad peaks at 3.85 eV below the Fermi level appear (Fig. 6d), meaning the formation of new VHf-induced localized states. PDOS results (Fig. 6c) show that these states are related to the N p states neighboring the VHf, and their occurrence is attributed to

the absence of Hf atoms, leading to the non-full hybridization of nearest-neighbor N atoms. The above results indicate that the formation of VN induces two defect energy levels at 1.10 eV and 2.26 eV, while the introduction of VHf produces a defect energy level at 3.85 eV. Therefore, it is expected that electrons trapped in these localized states can jump towards higher-energy free states around the Fermi level, which will produce three additional interband transition absorption bands located at the photon energy of 1.10, 2.26 and 3.85 eV. In order to prove the existence of these defect-induced absorption bands, the measured imaginary part of the dielectric function for HfNx films is displayed in Fig. 8. Each curve representing the imaginary part is composed of four absorption bands, one of which arises from the contribution of intraband transition absorption related to free electrons, and another three bands originating from the contribution of interband transition absorption corresponding to bound electrons. The interband transition absorption band centered at 4.90 eV appears in all HfNx films, which is attributed to the intrinsic interband transition from the N p electrons to unoccupied states around the Fermi level according to calculated DOS (Fig. 6a). For the sub-stoichiometric HfNx films containing VN, there are two new interband absorption bands located at 2.27 and 0.81 eV (Fig. 8a and b) in addition to intrinsic interband transition. For the over-stoichiometric HfNx films, a new interband transition absorption band at 3.75 eV (Fig. 8d and e) can be observed. Based on the calculated DOS, two interband absorption bands at 2.27 and 0.81 eV that appeared in sub-stoichiometric HfNx films are attributed to the interband transition from defect states of VN to the unoccupied states located around the Fermi level (calculated energy separations are 2.26 and 1.10 eV), while the interband transition absorption band at 3.75 eV only occurring in over-stoichiometric HfNx films is assigned to the interband transition from defect states of VHf to the unoccupied states located around the Fermi level (calculated energy separation is 3.85 eV). The consistency between the present calculations and experiments proves that defect-induced interband absorption bands really exist in non-stoichiometric HfNx films. Furthermore, it can be seen from Fig. 8c and f that the relative integrated intensity of these absorption bands depends strongly on the concentration of corresponding

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Fig. 8. (a–c) Typical imaginary parts (e2) of the dielectric function for sub-stoichiometric d-HfNx films containing VN, and the ratio of integrated intensity of VN-induced interband absorption bands to that of intrinsic interband absorption bands. (d–f) Typical imaginary parts (e2) of the dielectric function for over-stoichiometric d-HfNx films containing VHf, and the ratio of integrated intensity of VHf-induced interband absorption bands to that of intrinsic interband absorption bands.

vacancy defects. As x increases from 0.809 to 0.989, the concentration of VN gradually decreases and, as a result, two VN-induced interband absorption bands at 0.81 and 2.26 eV become weaker (Fig. 8c). However, as x increases further from 1.039 to 1.165, the concentration of VHf gradually increases, and the VHf-induced interband absorption band accordingly gets stronger (Fig. 8f).

4. Conclusions The types and formation mechanism of primary point defects in rocksalt hafnium nitride (d-HfNx) films (0.809 6 x 6 1.165) can be identified by a combination of first-principles calculations and GIXRD, Raman and HRTEM experiments. It is found that, for sub-stoichiometric d-HfNx films (0.809 6 x 6 0.989), the primary point defects are N vacancies, whereas for over-stoichiometric films (1.039 6 x 6 1.165), the dominant defects are Hf vacancies. The preferential formation of N or Hf vacancies is attributed to their having much lower formation energy and equilibrium formation enthalpy than other types of

point defects, including interstitials and antisites, which enables them to exist in non-stoichiometric d-HfNx films more thermodynamically favorable and more stable. Furthermore, the calculations and experiments consistently demonstrate that the formation of N or Hf vacancies plays important roles in changing the electronic structure and optoelectronic properties of d-HfNx films. It is found that a nitrogen vacancy can act as a donor-like defect, and its formation can promote an increase in the free-electron concentration at a rate of an electron per N vacancy, while the Hf vacancy shows acceptor-like behavior, and its creation causes a significant reduction in the free-electron concentration at a rate of two electrons per Hf vacancy. Additionally, one also finds that the formation of N or Hf vacancies in non-stoichiometric d-HfNx films can induce new interband absorption bands centered at 0.81, 2.27 or 3.75 eV. The intensity of these absorption bands depends strongly on the concentration of corresponding vacancy defects. This investigation discovers the nature of point defects in rocksalt hafnium nitride films and their role on controlling electronic structures and properties, which is of great significance for important technological applications.

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Acknowledgements The support from the National Natural Science Foundation of China (Grant Nos. 51102110, 51102111 and 51372095), the program for studying abroad of the China Scholarship Council (201306175022), the National Major Project for Research on Scientific Instruments of China (2012YQ240264), the special Ph.D. program (Grant No. 200801830025) from MOE, the Major science and technology project of Jilin Province (Grant No. 11ZDGG010), the NSF of China (Grant no. 51372095), the “211” and “985” project of Jilin University, China, and the program for Changjiang Scholars and Innovative Research Team in University is highly appreciated.

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