Ab initio thermodynamics of deposition growth: Surface terminations of TiC(111) and TiN(111) grown by chemical vapor deposition

Jochen Rohrer and Per Hyldgaard

Phys. Rev. B 82, 045415 – Published 20 July 2010

Abstract

We present a calculational method to predict terminations of growing or as-deposited surfaces as a function of the deposition conditions. Such characterizations are valuable for understanding catalysis and growth phenomena. The method combines ab initio density-functional-theory calculations and experimental thermodynamical data with a rate-equations description of partial pressures in the reaction chamber. The use of rate equations enables a complete description of a complex gas environment in terms of a few, (experimentally accessible) parameters. The predictions are based on comparisons between free energies of reaction associated with the formation of surfaces with different terminations. The method has an intrinsic nonequilibrium character. In the limit of dynamic equilibrium (with equal chemical potential in the surface and the gas phase) we find that the predictions of the method coincide with those of standard ab initio based equilibrium thermodynamics. We illustrate the method for chemical vapor deposition of TiC(111) and TiN(111), and find that the emerging termination can be controlled both by the environment and the growth rate.

Received 19 March 2010

DOI:https://doi.org/10.1103/PhysRevB.82.045415

Authors & Affiliations

Jochen Rohrer^* and Per Hyldgaard

BioNano Systems Laboratory, Department of Microtechnology, MC2, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden

^*rohrer@chalmers.se

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Vol. 82, Iss. 4 — 15 July 2010

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Images

Figure 1
Different surface terminations for a film deposited on a substrate. The schematics shows the case for a binary material AB formed of alternating A and B layers, represented by differently colored balls. While the interfacial composition largely is determined by the substrate properties, the composition of the surface layer strongly depends on the deposition environment, possibly leading to an AB film that slightly deviates from full stoichiometry.Reuse & Permissions
Figure 2
Schematics of CVD of $Ti X$ and of the kinetics in the formation of excess layers. The upper panel gives a principle sketch of a CVD apparatus. A supply gas mixture that contains several different gases with different concentrations $c_{i}$ is injected into the CVD chamber via valve 1 at a rate $R_{sup}$ . The chamber is kept at a constant temperature $T$ and pressure $p$ . Inside the chamber the gases react and form $Ti X$ . Reaction products and unused supply gas are exhausted at a rate $R_{exh}$ via valve 2. The set of lower panels illustrates kinetic effects that specify the surface termination. A Ti $(X)$ surface layer can be deposited from a Ti $(X)$ carrying gas, here shown for ${TiCl}_{4}$ . As indicated, the process involves a set of unknown complex transition states.Reuse & Permissions
Figure 3
Formation of excess layers and associated free energies of reaction $G_{r}$ . The top panel illustrates the formation of a C excess layer from ${CH}_{4}$ on a Ti-terminated surface. The bottom panel shows the formation of a Ti excess layer from ${TiCl}_{4}$ and $H_{2}$ on a C-terminated surface. From a kinetic perspective, formation of specific clusters and presence of $H_{2}$ may catalyze the process shown in the upper panel; thermodynamically, such catalytic processes do not, however, affect the free energy of reaction.Reuse & Permissions
Figure 4
(Color online) Critical values of the scaled reaction rate $r_{TiN}^{crit}$ as functions of temperature at different pressures and HCl concentrations. Red (dark) lines correspond to a deposition pressure of $p_{1} = 50 mbar$ and green (light) lines to $p_{2} = 500 mbar$ . Solid lines correspond to no HCl content $c_{HCl, 1} = 0$ in the supply gas, dashed lines to a content of 1% HCl $c_{HCl, 1} = 0.01$ . The insert shows the corresponding analysis for TiC.Reuse & Permissions
Figure 5
(Color online) Free energies of reaction $G_{r}$ of CVD bulk TiC (solid), excess Ti (dashed), and C excess layers (dashed-dotted) at the $Ti X (111)$ surface as a function of the scaled reaction rate $r_{TiC}$ . We assume a total pressure of $p = 50 mbar$ and a deposition temperature of $T = 980 ° C$ inside the CVD chamber. Red (dark) lines correspond to experimental values (Ref. 34) for the supply gas compositions, see also main text. In particular, the supply gas contains 1% HCl. The green (light) lines correspond to the case where no HCl is supplied.Reuse & Permissions
Figure 6
(Color online) Free energies of reaction $G_{r}$ of CVD bulk TiN, excess Ti and excess N layers at the $Ti X (111)$ surface as a function of the scaled reaction rate $r_{TiN}$ . In the top panel, experimental values (Ref. 37) for the supply gas compositions from are used, see also main text. Temperature and pressure are chosen as in Fig. 5. The termination critically depends on the scaled deposition rate. The bottom panel illustrates the effect of varying deposition parameters. For bulk, excess Ti, and excess N, the same line style as in the upper panel applies. Blue (dark) lines correspond to an HCl concentration of 2% in the supply gas. Green (light) lines correspond to the case where the $N_{2}$ concentration is decreased to 1% and the temperature is raised to $T = 1200 ° C$ . In both cases, the changes are assumed to be balanced by the $H_{2}$ concentration. An increased HCl concentration leads to a N-terminated surface, independently the value of $r_{TiN}$ . A decreased $N_{2}$ concentration favors Ti termination.Reuse & Permissions

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