Controlling the TiN electrode work function at the atomistic level: a first principles investigation

The paper reports on a theoretical description of work function of TiN, which is one of the most used materials for the realization of electrodes and gates in CMOS devices. Indeed, although the work function is a fundamental quantity in quantum mechanics and also in device physics, as it allows the understanding of band alignment at heterostructures and gap states formation at the metal/semiconductor interface, the role of defects and contaminants is rarely taken into account. Here, by using first principles simulations, we present an extensive study of the work function dependence on nitrogen vacancies and surface oxidation for different TiN surface orientations. The results complement and explain a number of existent experimental data, and provide a useful tool to tailoring transport properties of TiN electrodes in device simulations.

The paper reports on a theoretical description of work function of TiN, which is one of the most used materials for the realization of electrodes and gates in CMOS devices. Indeed, although the work function is a fundamental quantity in quantum mechanics and also in device physics, as it allows the understanding of band alignment at heterostructures and gap states formation at the metal/semiconductor interface, the role of defects and contaminants is rarely taken into account. Here, by using first principles simulations, we present an extensive study of the work function dependence on nitrogen vacancies and surface oxidation for different TiN surface orientations. The results complement and explain a number of existent experimental data, and provide a useful tool to tailoring transport properties of TiN electrodes in device simulations.

I. INTRODUCTION
The metal-insulator-metal (MIM) integrated capacitors are key device structures for modern analog and radio frequency integrated circuits 1 . This includes both twoterminal devices such as in ovonic selectors 2,3 , and layered gates in connection with high-κ metal-oxide dielectrics, such as, HfO 2 4 , TiO 2 5 , SiO 2 6,7 , and Al 2 O 3 8 . In this scenario, TiN recently become the reference metal for CMOS compatible gates and MIM devices 9 . The key feature in the realization of these devices is the alignment between the work function (WF) of the metal contact and the semiconductor band edges. It is generally assumed that TiN has a WF≈ 4.7 eV, even though this value can be modulated over a large energy range 4.1-5.3 eV, depending on the growth characteristic of the sample, the coupling with semiconductor (e.g. doped Si) or metal-oxide substrates or temperature treatments [10][11][12][13] .
TiN crystallizes in a cubic rocksalt structure, and can be easily cleaved along several low-index faces, such as (100), (110), and (111) surfaces. Previous works indicated a net trend in the surface formation energy of the cleavage surfaces, where TiN(100) is the most and TiN(111) is the least stable one 14 . Nonetheless, the growth of single crystal films is unusual and too expensive for any realistic technological application. Almost all TiN-based electrodes and gate contacts are made of polycrystalline films, whose constituting grains have different sizes and expose multiple faces, depending on the conditions and techniques used to grow the samples. In particular, the crystallinity of the substrate strongly affects the morphology, orientation, and resistivity of the films 15 . Different sets of XRD characterizations 9,10 indicate that in polycrystalline TiN films grown on SiO 2 and HfO 2 substrates, crystalline grains preferentially expose the (111) face, with minor contribution from the (200) one. Furthermore, in standard growth conditions (i.e. N-poor) TiN forms stable non-stoichiometric crystals (namely TiN x ) over a broad composition range x∈ [0.3 − 1.0] 16,17 . A large variety of multi-technique experiments [18][19][20][21] indicate that in substoichiometric TiN x materials the most recurrent defects are the nitrogen vacancies (V N ), and that high V N concentrations remarkably affect the optoelectronic 22,23 and the transport properties of the system, including its WF 11 . Finally, TiN easily undergoes surface oxidation 24,25 : this happens both when as-grown films or fresh cleavage surfaces are exposed to air 26,27 , and when TiN is in contact with other metal oxides.
While the role of interfaces with dielectric layers has been thoroughly studied 4,6,28 , the intrinsic structural and chemical origins of the WF variability have been rarely taken into account 10 . In this paper, we present a first principles investigation of the effects of surface termination, substoichiometry and oxidation on TiN WF. Our results indicate that the experimental measured WF values are the results of the average combination of all these structural and composition factors. In particular, the control of defect distribution and crystalline grains during growth can be engineered to tailor the transport properties of TiN for specific MIM characteristics.

II. COMPUTATIONAL DETAILS
DFT calculations for TiN thin films are performed using the Quantum ESPRESSO package 29 . Ab initio ultrasoft pseudopotentials 30 are used to describe the electronion interactions and the Perdew-Burke-Ernzerhof (PBE) functional 31 , within the generalized gradient approximation (GGA), is used to treat the exchange-correlation electron interaction. In the pseudopotential description, the following valence electron configurations are considered: N:2s 2 2p 3 , O:2s 2 2p 4 , and Ti:2s 2 2p 6 3s 2 3d 2 . Single particle wavefunction and charge are expanded in a plane wave basis set up to an kinetic energy cutoff of 30Ry, and 300 Ry, respectively. Geometry optimizations are carried out with convergence thresholds of 0.03eV/Å for the the forces on each atom. Extensive accuracy tests can be found in previous publications 22,26,32,33 .
TiN films are simulated by periodic supercells, where we included a thick vacuum layer (∼ 15Å) in the directions perpendicular to the surface. Each slab contains a variable Oxide and defective films are obtained starting from a 2 nm-thick TiN reference model, with (2×2) and (3×3) lateral periodicity for (100) and (111) surface, respectively. Oxide surfaces are prepared by adding oxygen on both outermost layers of TiN slabs (symmetric configuration), as N-substitutional atoms and O 2 adsorbed molecules. Defective TiN x systems are simulated including an increasing number of N vacancies (V N ) in the reference slabs.

A. Surface termination
TiN crystalizes in the NaCl lattice structure within the Fm 3 m space group; the most favored cleavage surfaces are the TiN(100), TiN(110) and Ti-terminated TiN(111) faces. We studied all these surfaces with different thicknesses from 1nm to 4 nm, as shown in Figure 1. After full atomic optimization, all structures undergo only minor relaxations of the outermost layers, in agreement with previous theoretical calculations 14,36 . Surface relaxation is sufficient to redistribute charge at the surface and to stabilize the structure. The analysis of the projected bandstructures (discussed e.g. in Ref. 32 ) indicates the presence of surface states in restricted regions (lenses) across the edges of the 2D Brillouin zone at high binding energies, while no surface states are present in the proximity of the Fermi level, for any considered surfaces.
The work function for all systems is calculated as the difference between the Fermi energy resulting from DFT calculations and the vacuum level, extracted from the double averaged electrostatic potentialV es 37 . The results ( Figure  2) clearly indicate the effect of the surface termination on the WF of TiN. The calculated WF are 2.96 eV, 3.17 eV and 4.67 eV for (100), (110) and (111) faces, respectively. The WF variability is related to the charge accumulation at surface: (100) and (110) have the same number of Ti and N atoms per layer, while (111) has alternative layer of Ti or N atoms, with a large charge accumulation on the Ti outermost layer. Thickness hardly affects the WF that, for all surface orientations, remains almost identical with respect to the number of layers (∆WF=30 meV). This is due to the the high electron density of TiN (n el ≈ 10 22 e/cm −3 ) 32 , which easily reaches the bulk-like behavior, in agreement with transport and optical measurements on thin TiN films 38,39 . These results are well representative of polycrystalline films, where the typical grain size is of the order of ∼2-3 nm 10 as well as of thicker single crystal surfaces 26 . In particular, the predominance of (111) exposed surfaces in polycrystalline systems 10 explains the close agreement of the average experimental WF values (∼ 4.6 eV) with the calculated results for the (111) surface.

B. Nitrogen vacancies
We investigated the effects of V N in the TiN x (100) and TiN x (111) surface, by considering an increasing number of N vacancies, from 0 to 50% of the total nitrogen amount, in a reference 2nm-thick TiN(100) and TiN(111) surface, respectively. In all cases, the removal of N atoms from TiN surfaces (i.e. inclusion of N vacancies) does not remarkably change the atomic structure, which maintains the characteristic of the ideal (undefective) cubic system. We do not observe any relevant atomic displacement, clusterization, or sub-phase formation in any system, even for extremely high sub-stoichiometric condition (e.g. removal of 50% of nitrogen). This is in agreement with the analysis of N-vacancies in sub-stoichiometric TiN x bulk, reported in Ref. 22 . The metallic character of TiN prevents the formation of charged defects and charge accumulation around the defects site, which might be responsible for polaronic distortion.
In order to gain insight on the stability of defective surface systems, we studied the formation energy of a single N vacancy as a function of the layer position. As shown in Figure 3a, we considered the first five layers (1L-5L), where 1L identifies the outermost N-layer, while 5L is representative of an inner (i.e. bulk like) layer. The formation energy of nitrogen vacancies is defined as 40 : where E tot (V N ) L is the total energy of the optimized TiN x defective surface including V N at layer L, E tot (surf ) is the total energy of the ideal TiN surface (i.e. no vacancies); n is the number of N-atoms being removed from a defect-free cell to its respective reservoir with chemical potential µ N , to form the defective cell. In the case of a single vacancy, n = 1. Growth conditions determine the bounds limits for the element chemical potential. In the Ti-rich/N-poor conditions N chemical potential in TiN can be obtained as where the chemical potential µ T iN = E tot (T iN ) is equal the total energy of TiN bulk (2 atoms per fcc cell) and µ T i = 1/2E tot (T i hcp ) is the Ti chemical potential extracted from the Ti hcp metal bulk (2 atoms per cell). The simulated formation energy of TiN and substoichiometric TiN x bulk systems have been calculated from first principles in Ref. 22 in very good agreement with previous results 41 .
For TiN(100) the defect formation energy is always negative (Figure 3b), with a damped even-odd oscillation which converge in the bulk to the value E f or =-1.1 eV 22 , where even layers have the lowest negative formation energies. TiN(111) also exhibits a damped even-odd trend, but in this case odd layers are energetically favored and the first layer has a small but positive formation energy. This behavior can be ascribed to the fact that (111) surface is Ti-terminated, and N atoms lay in subsurface layers (Figure 3a). This general trend confirms that defective TiN x surfaces are stable, and energetically favored, with tiny energy differences in the spatial distribution of N-vacancies, which can be considered uniformly distributed over the entire structure.
The calculated WFs are shown in Figure 4a, where the corresponding values of undefective TiN surfaces (dashed lines) are superimposed for comparison. In both cases, the inclusion of a single (i.e. very diluted) N-vacancy does not impart any relevant change in the WF of the system. However, when the Ti/N ratio increases as in the experimental systems, WF deviates from the stoichiometric value, as displayed in Figure 4b. The work function of TiN x (100) increases while WF of (111) decreases by hundreds of meV, in agreement with the experimental findings 42 . As the amount of N content is reduced, the WF of both TiN x surfaces approaches the value WF=4.2 eV, which is a fingerprint also of the hcp Ti metal.
This analysis indicates that single WF values, deriving from experiments and used in transport models, are instead results averaged over the full sample, where the surface terminations and the chemical composition play a combined role. The statistical predominance of the (111)  surface pins the WF final value close to 4.6 eV. TiN(100) has lower WF, but the presence of N-vacancies shifts WF to higher energy values closer to the (111) surface. The final overall value of a polycrystalline electrode depends on the specific percentage of exposed grain faces and on their composition, and thus on the specific growth conditions. This explains the large variability of the measured WFs. The formation of interfaces with doped semiconductors, of high-κ metal-oxides may further modify these values 10,43 .  26 . The one presented here best reproduced the transport and optical experimental properties of oxidized ultrathin TiN films 38 . The initial O:TiN(111) structure has been prepared along the same line, keeping the same oxygen percentage per TiN atoms of the (100) surface case, and including a mix of N-substitutional and on-surface adsorbed oxygen. After atomic optimization, both systems present a strong surface rearrangement and the formation of a mixed oxynitride layer, as shown in Figure 5a. Oxygen interacts with TiN surfaces, saturating exposed N-vacancies and bonding to outermost Ti atoms. In particular, O 2 molecules dissociate to best coordinate with Ti atoms. This leads the formation of TiN  Figure 5. Surface oxidation causes a blue-shift of WF in both systems, but while the difference with respect to the clean surface is ∆WF=0.75 eV for TiN(111), it is ∆WF=6.30 eV in the case of TiN(100). In the latter case oxygen acts as a capping layer that stabilizes the entire system, in agreement with previous theoretical calculations on MgO layers on TiN (100) surface 12 . The further growth of thick metal-oxide layers may mitigate this effect resulting in WF closer to range 4-5 eV, typically assumed for TiN/oxide gate interfaces [10][11][12] . Thus, the total or partial oxidation of crystal grains constitutes another degree of freedom in the overall WF value of TiN electrodes. Vertical dashed lines in DOS plots indicate the Fermi level, assumed as zero energy reference. In the WF plots (right panels) the zero energy reference is fixed to the vacuum level and the corresponding Fermi levels are shifted accordingly.

IV. CONCLUSION
We presented a detailed study of the structural, stoichiometric and chemical effects on the work function of intrinsic TiN films, as used in electrode contacts. Our results show that face orientation, N-vacancies and surface oxidations are different causes of modulation of TiN WF, whose final value depends on the details of the growth conditions. The typical predominance of TiN x grains with (111) terminations, is the main origin of the average WF measured in polycrystalline electrodes. The control of the growth conditions can be engineered to obtain a fine tuning of the electrode WF so to optimize the band alignment with the semiconductor elements of the devices.

V. ACKNOWLEDGMENTS
This work was supported in part by EC through H2020-NMBP-TO-IND project GA n. 814487 (INTERSECT).