Surface Reaction Kinetics of Titanium Isopropoxide and Water in

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Surface Reaction Kinetics of Titanium Isopropoxide and Water in Atomic Layer Deposition Michael Reinke, Yury Kuzminykh, and Patrik Hoffmann J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b10529 • Publication Date (Web): 09 Feb 2016 Downloaded from http://pubs.acs.org on February 10, 2016

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The Journal of Physical Chemistry

Surface Reaction Kinetics of Titanium Isopropoxide and Water in Atomic Layer Deposition Michael Reinke, Yury Kuzminykh, and Patrik Hoffmann* Laboratory for Advanced Materials Processing, Empa, Swiss Federal Laboratories for Materials Science and Technology, Feuerwerkerstrasse 39, CH-3602 Thun, Switzerland Laboratory for Photonic Materials and Characterization, Ecole Polytechnique Fédérale de Lausanne, Station 17, CH-1015 Lausanne, Switzerland

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Abstract

In atomic layer deposition processes (ALD), surface reactions of adsorbed precursor species lead to the formation of thin films. In order to achieve a well-controlled, self-limiting process, the substrate is sequentially exposed to different precursor molecules, each one until the surface is completely saturated. The necessary time of exposure depends on precursor transport and on surface kinetics, of which the latter are determined by the respective activation energies for the surface reactions. In this contribution, we apply a surface kinetic model and surface reaction rates to describe the ALD process for the deposition of titanium dioxide utilizing titanium isopropoxide and water as reactive precursor combination. We examine in detail precursor surface coverages and investigate the influence of substrate temperature and exposure time on the hydrolytic decomposition of the adsorbed titanium precursor. In this way, we can quantify the deposition rate in each deposition cycle and examine the contribution of desired hydrolytic surface reactions and undesired pyrolytic decomposition reactions which limits the substrate temperature in ALD processes. We identify ALD threshold temperatures and discuss the influence of pulse durations on the so-called ALD window. Finally, we examine the influence of precursor and water residual pressure remaining in the reactor after their respective exposure pulses on the thin film growth behavior, which can arise either from limited pumping capacities in an ALD vacuum system or insufficient purging times, in particular for high complex geometries.


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Introduction

Atomic layer deposition (ALD) is a thin film deposition technique that relies on the sequential exposure of a heated substrate surface to reactive precursors. Within each individual precursor pulse, the substrate is exposed to precursor molecules until all active surface sites have reacted and the substrate surface is saturated with adsorbed precursor species. An important aspect of the design of each ALD process is the precise exposure duration, i.e. the respective pulse times. The duration of these pulses is dependent on the mass transport of precursors to the surface or the reactions kinetics on the surfaces. In order to describe the kinetics of an ALD process, precise information about surface reaction rates is necessary. Most efforts have been focused on the characterization of the prominent aluminum oxide process utilizing trimethylaluminum (TMA) and water as precursors. For this process, Elliot and Greer calculated the activation energies by density functional theory (DFT).1 Using these activation energies, Travis and Adomaitis2 modelled and described the surface species dynamics during the TMA half pulse. The same authors presented also a more comprehensive image of surface coverages, reaction rates using absolute rate reaction theory; in particular they calculated the temperature dependence of the growth per cycle.3 Another contribution by Xie et al. recently addressed also the influence of reactor geometries and flow dynamics.4 Other well investigated materials include zirconium oxide5, hafnium oxide5 and zinc oxide.6 In particular for the last one, the authors presented a comprehensive modelling not only of the chemistry, but of the entire process, i.e. including the flow dynamics within the reactor. ALD of titanium dioxide using titanium tetraisopropoxide (TTIP) and water was first reported by Ritala et. al.7 Since then, numerous publications have focused on the growth process itself 8-9,


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on the selective area growth10-12 and on potential applications.13, 14 Recently, we showed that this typical ALD precursor chemistry can be used to grow films in a CVD like fashion by simultaneous precursor exposure in high vacuum chemical vapor deposition (HV-CVD) conditions even within the ALD temperature window.15 The results of this study and depositions at higher temperatures allowed us to develop a surface kinetic model for the chemical vapor deposition of titanium dioxide with these precursors over a large temperature range (175°C-610°C).16 By solving the surface rate equations in continuous steady state conditions, we could fit the model to experimental results and derive the activation energies for pyrolysis and hydrolysis, and precursor desorption. In this contribution, we demonstrate how the same model can be applied for the atomic layer deposition of titanium dioxide using TTIP and water by solving the time dependent rate equations individually for each pulse and purge time. We use the model to investigate the transition conditions between ALD and CVD regime, i.e. we specify at what substrate temperatures and pulse times the CVD component of the growth rate is below a certain threshold and discuss the temporal evolution of the surface coverage. With thess data, the dynamics of surface occupations and precursor reactions, we derive the temperature dependent titania growth per cycle (GPC).Furthermore, we apply the model to a system where due to limited pumping efficiency, the precursor fluxes do not abruptly stop after their respective pulses. This situation either arises due to limited pumping capabilities or due to slow diffusion of precursor or water molecules out of complex geometries. In the final section, we compare the calculations based on the kinetic model to available literature and outline its limitations. Surface Kinetic Model


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In this section, we present the application of a surface kinetic model for the chemical vapor deposition of titania using TTIP and water in an HV-CVD process to describe the dynamics of an ALD process.. We have developed and described the model in detail recently, including derivation of the activation energies and pre-exponential factors for the respective reactions by fitting the surface kinetic model to experimental data.16 The experimental data was obtained for low temperature HV-CVD experiments within the ALD window (175- 225°C substrate temperature)15 as well as for experiments in typical CVD conditions (310- 620°C).17 The rate equations describing the model are presented in scheme 1, the corresponding activation energies and pre-exponential factors are summarized in table 1. The surface site densities are taken as in our previous publication: for TTIP Γ = 1.5×1014 cm-2, for water Γ = 1.5 ×1015 cm-2.16

Scheme 1. Time dependent rate equations employed as model for ALD of titanium dioxide. Γ

(x={TTIP;H2O}) designate surface occupations, Γ the total available surface sites. J and J are the TTIP and water impinging rates, s and s the sticking coefficients of

precursor and water and k - the respective reaction rates (des = desorption).

Table 1. Surface kinetic parameters for the surface kinetic model16: all reaction rates are

expressed by an Arrhenius law: exp , where υ is the pre-exponential factor (in s-1 -1 2 for k and k , in s cm for k

!"

$%&

and k #

!" )

and E the apparent activation energy


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(in kJ mol-1). The sticking coefficients s are temperature independent. s 0.30

s 0.91

k

k

υ

2.0×1010

5.0×109

4.7×10-7

1.3×103

E

114

81

86

185

k

!"

$%&

k #

!"

The formation of thin films in HV-CVD is driven by surface reactions with very limited gas phase interactions - comparable to ALD. Therefore we believe that the same model can be applied to HV-CVD and ALD processes. However, in order to ensure the applicability of the surface kinetic model to ALD conditions, it is important to verify that HV-CVD surface reactions are not determined but short-living surface species and are therefore the same as ALD surface reactions. Therefore, we calculate the surface residence time of an adsorbed TTIP molecule via τ

)

$& *./0 ++,- 1*23.4563070 89 : 1*;34563070 8++,-

. At ALD typical deposition temperatures

(225°C) and HV-CVD typical precursor impinging rates (1015 TTIP cm-2 s-1 and 5×1016 H2O cm2

s-1) the resulting surface residence time is 2.3s - at this temperature, the residence time is

determined mainly by the time until the hydrolytic surface reaction occurs, because desorption rates and pyrolytic reaction rates are comparatively low. Therefore, we conclude that HV-CVD reactions are mainly driven by long-living surface species and that the surface kinetic parameters are applicable for ALD processes as well. Figure 1 illustrates the principal features of the ALD process of titanium dioxide as modeled here. Initially, the surface is empty and all surface sites are available for precursor adsorption. Within a full ALD cycle composed of one exposure pulse of TTIP, one purging of TTIP, one


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exposure to water vapor and one purging of unreacted water, two contributions can lead to the formation of a thin film: hydrolytic (desired) reactions between adsorbed TTIP precursor and water as well as (undesired) pyrolytic decomposition of the precursor molecule. While the hydrolytic reaction is predominantly occurring during the water pulse, pyrolytic decomposition might appear during the entire cycle.

Figure 1. Schematic representation of the surface kinetic model. During the TTIP pulse, the surface is occupied by adsorbed TTIP species, which can either desorb or pyrolytically decompose on the substrate. During the water pulse, hydrolytic reaction leads to the desired atomic layer deposition like growth. Both pulses are separated by a purging time to evacuate non-reacted precursor molecules from the reactor.

The ALD process was simulated by solving the time dependent rate equations (given in scheme 1) of the kinetic model numerically using the MATHEMATICA software package. Each exposure and purge pulse was solved individually by choosing the fluxes accordingly, i.e. JH2O = 0 during the TTIP pulse, JTTIP = 0 during the water pulse and JTTIP = JH2O = 0 during the purging time. For the first TTIP pulse, we set the boundary conditions ΓTTIP = ΓH2O = 0. For each subsequent pulse, the surface occupations were chosen to match the final surface occupations of the previous pulse.


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To estimate the precursor impinging rate on the substrate, we calculate the diffusion mass flow through the so-called boundary or Prandtl layer in a viscous flow reactor according to Krumdieck.18 We assume a typical Reynolds number of Re = 500 and calculate the thickness δ of the diffusion layer at the center of a 100mm (x = 50 mm) silicon substrate with δ

√>

as 2.2

mm. The precursor flux to the substrate can be calculated via J ≈ $D ⋅ p&/$δ ⋅ R ⋅ T& where T is the absolute temperature, p the partial pressure of the precursor and D its diffusion coefficient. %

The diffusion coefficient can be approximated via E ⋅ F

)

G⋅H

I

JK

LM N

, where O

P

JK

is the

density of the molecules, d its diameter and M is mass.19 For TTIP, we calculate a diffusion coefficient of 4.9 cm2 s-1 at 200°C taking ps = 3hPa and d=7.9Å11 which leads to a precursor impinging rate of 1.0×1018 cm-2 s-1. By analogy, we calculate D=39.0 cm2 s-1 for water with ps = 12hPa and d=2.5Å 20, which results in an impinging rate of 4.0×1019 cm-2 s-1. These impinging rates were used for all simulations. An important aspect in our calculations is the quantification of the so-called growth per cycle (GPC) which is directly related to the mass uptake per cycle, which is frequently measured by a quartz crystal microbalance (QCM). We calculate the mass uptake assuming the reaction pathway described by Rathu et. al.9, i.e. the TTIP precursor molecule adsorbs dissociatively while losing two isopropyl ligands and the subsequent water exposure leads to the formation of two hydroxyl groups. The GPC is dependent on the number of adsorbed precursor molecules with the ALD cycle and we quantify this value by evaluating the absolute number of hydrolytic and pyrolytic reactions during each cycle. This number of incorporated titanium atoms can be converted into an equivalent thickness, assuming stoichiometric titanium dioxide films and a film density of 4 g/cm3.17 Results and Discussion


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In this section, we apply the surface kinetic model to investigate the surface kinetics during a complete cycle and evaluate the growth per cycle as function of precursor pulse durations and substrate temperature and estimate the upper temperature limit for the titanium dioxide formation by ALD. In the first part, we discuss the application of the kinetic model in an idealized environment, which means we assume that we instantaneously stop the precursor or water exposure at the end of pulse. Later, we take the slow decrease of precursor impinging rates according to the limited pumping capacities of the vacuum pump or purging system into consideration. In this situation, the hydrolysis reactions may as well take place during the subsequent purge or even within the subsequent TTIP pulse if the purge time is not sufficiently long. Surface Coverages In this section, we review the surface coverage dynamics during an ALD cycle consisting of a 4 second TTIP pulse, a 4 second purge, a 12 second water pulse and another 4 second purging pulse and a substrate temperature of 200°C. Here, we consider the situation, where the substrate is only exposed to precursor or water during their respective pulses, e.g. we assume the rapid and complete evacuation of the chamber during the purge phase to the pulse. Figure 2 illustrates the surface coverage of TTIP and water throughout an ALD cycle. During the initial TTIP pulse, the surface is entirely filled with chemisorbed TTIP molecules (within 0.005 s). In the purge time between TTIP and water pulse, the surface occupation slightly decreases due to desorption of precursor molecules and (undesired) pyrolytic decomposition. During the water pulse, the surface is then covered entirely with adsorbed water, which leads to the hydrolytic reaction of adsorbed TTIP molecules. Therefore their surface coverage continuously decreases during the water pulse.


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Figure 2. Relative surface densities of chemisorbed TTIP molecules and adsorbed water molecules. It is visible that the surface reaction for the population with adsorbed TTIP molecules is considerably quicker than the hydrolytic reaction between water and adsorbed TTIP.

It seems that the reaction kinetics during the TTIP pulse are considerably faster compared to the water pulse. We describe, however, the adsorption of TTIP on the surface with a temperature independent effective sticking coefficient s . In consequence, within our model the TTIP adsorption is barrier-free and therefore always limited by the mass transport through the diffusion layer and not by the chemical reaction rate. Therefore, the necessary TTIP pulse duration to entirely occupy the surface is dependent on the specific reactor geometry and precursor partial pressure. In an earlier version of the kinetic model, we have also tried to include a two stage TTIP adsorption process to the model and to investigate the kinetics of physisorption and chemisorption reaction as well. However, analysis showed that the experimental data does not allow determining the activation energies.16 However, the kinetics of the hydrolysis reaction is known. In the present case, the reaction is limited by the chemical reaction rate and therefore relatively independent on the reactor geometry during the water pulse. In the depicted case a small amount of TTIP stays unreacted


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after the water pulse; an indication that the water pulses have to be prolonged in order to promote complete reaction of the surface. Growth per Cycle Important information for every thin film growth process is the quantification of the growth rate. As ALD is a sequential process, commonly the growth per cycle acts as measure for the rate of thin film formation. Each hydrolytic reaction of TTIP leads to the formation of a new surface site, which can be occupied during the subsequent TTIP pulse by a chemisorbing TTIP molecule. Hence, we can evaluate the number of reacted TTIP molecules (either by hydrolysis or pyrolysis) as measure for the growth per cycle. As mentioned above, this number of incorporated titanium atoms can be converted into an equivalent film thickness (for this, we assume stoichiometric titanium dioxide films and a film density of 4 g/cm3). Before discussing the influence of process parameters on the growth per cycle, we consider the reactions during three individual cycles. Figure 3 summarizes precursor impinging rates, surface occupations, mass uptake and the number of reacted titanium precursor molecules (either by hydrolysis or pyrolysis) during three consecutive cycles of the above given exposure conditions (4 s TTIP, 4 s purge, 12 s H2O, 4 s Purge, see also Fig. 2) at different substrate temperatures (160°C, 200°C, 260°C).


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Figure 3. Number of impinging TTIP and water molecules, relative surface coverage, total mass uptake and number of reacted TTIP surface species during three ALD cycles at different substrate temperatures. At 160°C the hydrolysis rate is too slow to fully hydrolyze the adsorbed TTIP molecules during the water pulse, at 260°C the major faction of adsorbed TTIP molecules decompose pyrolytically which is detrimental to the ALD process as the growing film thickness on the substrate will be function of the precursor flow and therefore inhomogeneous and not conformal.

At 160°C, the hydrolysis reaction rate is insufficient to entirely hydrolyze the adsorbed TTIP molecules during the water pulse: only about 25% of the surface reacts to form new adsorption sites. In consequence, only a small amount of additional TTIP precursors can adsorb in the subsequent pulse and the growth per cycle is relatively small (0.16 Å). At this low temperature, pyrolytic decomposition of the precursor is negligible. Raising the substrate temperature to 200°C increases the hydrolytic reaction rate during the water pulse, which leads to the reaction of a large fraction of adsorbed TTIP molecules. The total


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growth per cycle in this condition sums up to 0.46Å/cycle. This value is comparable to reports in literature for the deposition of ALD with this precursor pair combination.9 As a comparison, for a complete reaction the growth per cycle would be 0.50Å/cycle, which is a consequence of the chosen total surface site density of 1.5 1014 cm-2. At 260°C substrate temperature, the contribution of pyrolytic decomposition of adsorbed TTIP precursors becomes dominant. During the initial TTIP pulse and purging time, adsorbed precursors constantly decompose and liberate new surface adsorption sites. This increases the total amount of deposited precursor molecules per cycle compared to the previous cases. During the purging time, precursors continue to decompose or to desorb which results in a less than 100% TTIP coverage at the beginning of water exposure. Then - due to the higher substrate temperature - also the hydrolytic reaction rate is increased. The total growth rate is 0.63Å/cycle, which can be separated in a hydrolytic contribution of 0.18 Å and a pyrolytic contribution of 0.45 Å. Exposure times are important parameters to optimize in ALD. So-called saturation curves are measured by changing the pulse durations over different deposition experiments. Due to the chemical reaction rate limitation during the water pulse, it is more instructive to examine the influence of the water pulse duration on the growth per cycle for four different temperatures (150°C, 175°C, 200°C and 225°C) as illustrated in figure 4 compared to the similar case for TTIP exposure. Generally, the growth per cycle is dependent on temperature and pulse duration. As the hydrolysis rate increases with temperature the pulse duration necessary to hydrolyze all adsorbed precursor molecules decreases. For elevated substrate temperatures (225°C) the influence of enhanced TTIP desorption during the purging pulse slightly decreases the achievable growth per cycle as compared to situation with a substrate temperature of 200°C.


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Figure 4. The influence of the water pulse duration on the growth per cycle is illustrated. The chemical reaction rate is higher at higher temperature; hence the saturation value of 0.5Å/cycle is reached after shorter exposure time.

The temperature dependent growth per cycle for this ALD process (4s TTIP – 4s purge – 12s H2O – 4s purge) is illustrated in figure 5a. At low temperatures, the film is mainly formed due to hydrolysis, while at high temperature pyrolysis is dominant. Between around 190°C and 240°C the growth rate for TTIP and water combination is relatively independent of the substrate temperature, a region that is usually referred to as “ALD-window”. It is important to notice, that already within this temperature range pyrolytic decomposition contributes significantly to the films growth, and therefore the conformality of ALD layers will suffer. In fact, for this chemistry, the apparent ALD window is a consequence of the mutual compensation of the hydrolysis and the pyrolysis reaction rates.Figures 5b and 5c give a comprehensive overview about the influence of different TTIP and water pulse durations on the growth per cycle and demonstrate that the precise position of the ALD-window is pulse duration dependent. It is emphasized, that the duration of both, TTIP and water pulses, have important consequences for the deposition process.


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Figure 5. Growth per cycle as function of temperature and precursors pulse durations. The ALD window, e.g. the temperature range where the growth rate is nearly independent of the substrate temperature is given in the upper graph. It is visible that even within the ALD window already a considerable amount of film can be formed due to pyrolytic decomposition; furthermore the influence of different lengths for TTIP pulse and water pulse are illustrated. While the length of the TTIP pulse shifts the high temperature limit (middle), the length of the water pulse shifts the low temperature limit of the ALD window (lower).

In order to suppress the pyrolytic decomposition as much as possible, a short TTIP pulse and subsequent short purging time is necessary. A long TTIP pulse increases the number of pyrolytic decompositions, which limits the upper temperature for a clean ALD process. In fact, the kinetics


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of the TTIP pulse is sufficiently fast to allow shortening TTIP pulse durations on flat, homogeneously precursor exposed substrates. For very short TTIP pulses at high deposition temperatures the growth per pulse becomes limited by precursor desorption. The extension of the ALD window into the higher temperature range is not a result of constant hydrolysis rate. But at higher temperatures the lower surface occupation due to increased desorption is compensated by the increased pyrolysis rate. Additionally this balance depends on the timing of the precursor supply and purging as well as precursor evacuation efficiency. A long water pulse favors self-saturated growth even at lower substrate temperatures. Therefore the lower temperature limit of the ALD window is shifted towards lower temperatures. Here, the lower hydrolysis reaction rate resulting from low temperatures can be compensated by the prolongation of the reaction time. Generally, due to slow surface kinetics of the hydrolytic reaction, long water pulses are beneficial to ensure a complete surface reaction.


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ALD Window – Upper Temperature Limit In an ideal ALD process, only surface reactions due to the interaction of the two utilized precursors contribute to the thin film formation. The substrate temperature is purposely kept low to minimize the so-called CVD component of the process. The definition of an upper temperature limit where this pyrolytic decomposition of adsorbed precursor molecules starts to interfere with the self-limiting ALD process, however, is not straightforward. As we describe the pyrolytic decomposition rate in our model by an Arrhenius law, there is no condition when the rate becomes zero and hence pyrolysis occurs even at relatively low temperatures. In consequence, we also can always identify a small pyrolytic contribution during the ALD process. Therefore, we will determine experimental conditions, where the contribution due to pyrolytic decomposition remains below a threshold value. The surface kinetic model allows calculation of the number of pyrolytic decomposition reaction of adsorbed precursor as function of time and substrate temperature. For this calculation we assume a surface that is fully occupied with adsorbed TTIP species and examine at what time and substrate temperature 1%, 5% or 10% of them have decomposed pyrolytically.

Figure 6. Upper temperature limit as function of TTIP pulse (solid line) or TTIP purge duration


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(dashed line) to ensure that less than 1%, 5% or 10% of adsorbed TTIP surface species have decomposed pyrolytically during the respective process steps. Additionally the upper ALD temperature limit according to Rahtu et. al (240°C) is indicated. 9

Figure 6 depicts the maximum substrate temperature that leads to 1%, 5% or 10% of CVD contribution either during the TTIP pulse (solid line) or during the subsequent purge time (dashed line). The differentiation between these two cases is important, as only the pyrolytic decomposition during TTIP exposure will limit the conformality of an ALD process. It is evident that for the strictest criteria of 1% the upper temperature limit is generally lower than for less stringent criteria. Additionally, the relation depends on the duration of pulse and purge, i.e. on how long adsorbed TTIP molecules wait for the arrival of their reactive partner (water). For instance, within 2 seconds 5% of the adsorbed precursor is reacted pyrolytically at a substrate temperature of 240°C, this corresponds to the experimentally found value by Rathu et. al. where the pulse length was chosen to be 2s.9 For a duration of 10 seconds the temperature must be kept below 225°C to meet the same criterion. In general, the longer waiting time needs to be compensated by the lower reaction rate at lower substrate temperatures in order to keep the CVD contribution at the same level. For an estimation of the total number of pyrolytically decomposed precursor molecules the total reactions during exposure and purge have to be summed up. Effect of Limited Pumping Capacity So far, we have analyzed the kinetics of atomic layer deposition in a rather idealized environment. We assumed that the precursor flux of TTIP and water abruptly stops during the purge. In order to describe the process closer to actual experimental conditions, it is mandatory to consider a slow decrease of the precursor impinging rate during the purge pulse and – if the


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purge time is short – even a mixed impingement during the subsequent exposure by the other precursor. The slow decrease is a consequence of the limited pumping performance of the vacuum pump with respect to the reactor volume and, or diffusion limited precursor flow through the diffusion layer or out of high aspect ratio holes. The importance of diffusion transport for the purging pulse has been discussed by Mousa et. al. for the deposition of Al2O3 and ZnO.21 For our calculations, we consider a reaction chamber with volume V of 30×30×15 cm3 which is purged by an inert gas. We assume a stationary pressure (ps) of 1 hPa at a flow rate Jpurge of 150 sccm. In a simplified calculation, the precursor partial pressure is continuously decreased by the purge gas which leads to a linear decrease of the initial precursor impinging rate (QR ,

x={TTIP,

J $t& J T1

H2O}) V

[\\\ 2-] W^X;Y4Z/ ;0

during

the

purge

_ for t > V^J#bc

which

) d #0

can

be

quantified

by:

and 0 otherwise.

Figure 7 shows the precursor impinging rates, surface occupations, mass uptake and number of reacted precursor molecules on the surface analogue to the previously discussed process in figure 2 – including, however, the residual background pressure due to the slow evacuation rate. It can be seen, that due to the relatively short purging time of 4 seconds after the water pulse, the water impinging rate is still higher than the TTIP impinging rate in the initial phase of the TTIP pulse. In consequence, the surface is rapidly filled not only with chemisorbed TTIP species, but is still occupied with water, which is visible in the corresponding surface occupation. This leads to a hydrolysis even during the TTIP pulse and to the formation of new adsorption sites. Thus, the principle of self-limitation is not preserved and the growth per cycle exceeds in this case the maximum growth per cycle for the purely self-limiting case. Furthermore, conformality of the thin films will be decreased due to less efficient water removal for high aspect surfaces.


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Figure 7. Number of impinging TTIP and water molecules, relative surface coverage, total mass uptake and number of reacted TTIP surface species during three ALD cycles at 200°C substrate temperature in case of non-ideal purging (0,0135 m3 chamber volume). The background impinging rate due to the background pressure leads to a modification of the relative surface densities of chemisorbed TTIP that were shown in figure 2. Due to the unwanted water exposure during the TTIP pulse, hydrolytic reactions are no longer restricted to the water pulse, but also lead to the generation of adsorption sites in the TTIP pulse and thereby increase the growth per cycle.

The influence of residual precursor is also slightly visible during the water pulse. Due to the non-negligible background pressure of TTIP, new surface sites can be readily re-occupied with impinging TTIP precursors, leading to a continuous growth within the water pulse as long as the TTIP impinging rate is still non-negligible. Due to these additional reactions the total growth per cycle is 0.79 Å which is higher as compared to the idealized case discussed above (0.46 Å). This enhancement is mainly due to


20

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


additional (not self-limited) hydrolysis during the TTIP pulse (0.17 Å). Other contributions are enhancements of 0.1 Å due to adsorbed TTIP precursors during the water pulse and hydrolytic reaction during the subsequent purge time (0.06 Å). In consequence, particularly the purge period after the water pulse should be extended. In figure 8, we demonstrate the influence of purging time on the growth per cycle. It is visible that for very short purge durations, there is a significant influence of water background pressure on the subsequent TTIP pulse leading to substantial hydrolytic reaction during the TTIP pulse. For the discussed pumping rate, 5.5 seconds of purging is necessary to remove water and to decrease the amount of hydrolytic reactions within the TTIP pulse.

Figure 8. The purging time after the water and TTIP pulse is optimized by plotting the growth per cycle as function of the purge duration. If water purging time is too short, the residual water pressure causes TTIP hydrolysis within the TTIP pulse and the subsequent purge. Only sufficiently long purging, here 5.5s, leads to a well-defined ALD process.

Comparison with Experimental Results and Limitations of the Kinetic ModelIn this section, we will compare the surface kinetic model to experimental data that we take from literature. Generally, a suitable set of data is hardy available from literature, since commonly


21


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Page 22 of 40

precise precursor impinging rates are not included in scientific publications and that in many experiments the nominal substrate exposure underestimates the actual exposure time. As outlined in this manuscript, the position of the so-called “ALD window” is highly dependent on precursor pulsing times; in consequence different values are published in literature. In the report of Rathu et al. the growth per cycle is temperature independent at substrate temperatures between (250°C – 325°C) – this is surprising as the authors observe the onset of thermal decomposition of the precursor at 240°C.9 The “ALD window” that can be identified by the surface kinetic model corresponds better to the values published by Xie et al. (175°C – 225°C).22 However, the reported growth per cycle (0.2 Å cycle-1) does not correspond to the values calculated by us. Generally, the growth-per-cycle within the ALD window drastically differs from publication to publication – Xie et al. report 0.2 Å cycle-1 22, Rahtu et al. 0.3 Å cycle19

and Kim et. al 0.55 Å cycle-1.23. It is therefore difficult to compare the growth per cycle to

experimental results from literature. Another approach is the comparison of mass uptake per cycle. Several groups have investigated the mass uptake during the titanium dioxide formation in atomic layer deposition using TTIP and water. Kim et al. determined a mass uptake of 13 ng cm-2 cycle-1 by X-ray fluorescence spectroscopy (and a corresponding growth rate of 0.55 Å cycle-1 by X-ray reflectivity measurements) for an ALD process constituting of a 3 second TTIP exposure followed by a 2s water exposure at 235°C substrate temperature23. Using the same parameters, a mass up-take of 12.2 ng cm-2 cycle-1 and a growth per cycle of 0.52 Å cycle-1 are predicted by the surface kinetic model. Aarik et al. used a quartz crystal microbalance (QCM) to investigate the time dependent mass uptake in an ALD process consisting of 20 seconds TTIP exposure, followed by a 10 second purge and 10 seconds of water exposure.8 Figure 9 compares their


22

Page 23 of 40

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experimental results with predictions of the surface kinetic model for different substrate temperatures (200°C and 275°C) and illustrates that the model is capable of describing the experimental results.

Figure 9. Comparison of predicted mass-uptake (red) and experimentally measured QCM signal as taken from literature8 for a single ALD cycle (exposure times are indicated). The correspondence between the two signals confirms the viability of the surface kinetic model. The surface kinetic model was fitted to experimental results over a wide temperature range (175° - 610°); applying the surface kinetic model to temperatures below this range are extrapolated and the accuracy decreases. The surface kinetic model generally resembles the experimental findings reported in literature well for temperatures above 150°C. Decreasing the temperature in the model leads to a drastic decrease of deposition rate, which is not coherent with reported data, for example by Xie et. al.22 Furthermore, the surface kinetic model is not capable of explaining the increase of the growth rate during the process as reported by Kim et al.23 This enhancement was attributed to a


23


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Page 24 of 40

crystallization process that occurs during film formation which effectively changes the number of hydroxyl groups. The comparison between their experimental results and our modelling indicates that the surface kinetic model describes the deposition process prior to the crystallization of the film.Conclusions We have presented the application of a surface kinetic model for analysis of an atomic layer deposition process for the deposition of titanium dioxide using titanium tetraisopropoxide (TTIP) and water as reactive partners. The model was used to illustrate the kinetics of the ALD process by analyzing surface coverages, surface reaction rates for hydrolytic and pyrolytic reactions, mass uptake and growth per cycle. We found that during the water pulse the growth is not limited by mass flow of precursor molecules to the substrate, but by the hydrolytic reaction rate. Accordingly, the pulse length of water has to be sufficiently long in order to favor self-saturated surface reactions, i.e. ideal ALD. Using the developed kinetic model, we have proposed a method to estimate the temperature dependent growth per cycle and the ALD temperature window, which are the key parameters for designing a true ALD process. For TTIP and water in typical ALD conditions it lies between 180°C and 240°C. The lower temperature limit is dependent on the duration of the water pulse: using longer pulses extend the ALD window towards lower temperatures as it promotes more hydrolytic reactions. The upper temperature limit, however, is defined by the duration of the TTIP pulse; here, longer pulses narrow the temperature range of the ALD window as more pyrolytic reactions can occur. We analyzed and differentiated the influence of undesired pyrolytic decomposition to the growth process. We showed that even within the ALD window a considerable amount of pyrolytic decomposition reactions contribute to the film growth. In fact, for TTIP and water, the


24

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ALD window is consequence of the mutual compensation of hydrolytic and pyrolytic surface reactions. Furthermore, evaluating the pyrolytic decomposition rate allows a correlation of the TTIP exposure duration and purge times to the amount of undesired CVD reactions occurring during an ALD process and to quantify temperature and exposure limits for ALD processes. It was illustrated that insufficient purge times (in particular for complex surface geometries) can lead to simultaneous exposure of TTIP and water: too short TTIP purge times lead to a quick repopulation of liberated sites by TTIP molecules during the water pulse and too short water purge durations lead to undesired hydrolytic reactions during the TTIP pulse. In both cases, the self-limiting nature of the ALD process is violated.

AUTHOR INFORMATION Corresponding Author * E-mail: [email protected], Phone: +41 58 765 62 62 Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding Sources The authors gratefully acknowledge the partial financial support of the Swiss National Science Foundation under contract 200021_13504. ABBREVIATIONS CVD, chemical vapor deposition; ALD, atomic layer deposition; HV-CVD, high vacuum chemical vapor deposition; GPC, Growth per Cycle; TTIP, titanium tetra isopropoxide.


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REFERENCES 1.

Elliott, S. D.; Greer, J. C., Simulating the Atomic Layer Deposition of Alumina from

First Principles. J. Mater. Chem. 2004, 14, 3246-3250. 2.

Travis, C.; Adomaitis, R., Modeling Alumina Atomic Layer Deposition Reaction

Kinetics during the Trimethylaluminum Exposure. Theor. Chem. Acc. 2013, 133, 1-11. 3.

Travis, C. D.; Adomaitis, R. A., Modeling ALD Surface Reaction and Process Dynamics

using Absolute Reaction Rate Theory. Chem. Vap. Deposition 2013, 19, 4-14. 4.

Xie, Y.; Ma, L.; Pan, D.; Yuan, C., Mechanistic Modeling of Atomic Layer Deposition of

Alumina Process with Detailed Surface Chemical Kinetics. Chem. Eng. J. 2015, 259, 213-220. 5.

Deminsky, M.; Knizhnik, A.; Belov, I.; Umanskii, S.; Rykova, E.; Bagatur’yants, A.;

Potapkin, B.; Stoker, M.; Korkin, A., Mechanism and Kinetics of Thin Zirconium and Hafnium Oxide Film Growth in an ALD Reactor. Surf. Sci. 2004, 549, 67-86. 6.

Holmqvist, A.; Törndahl, T.; Magnusson, F.; Zimmermann, U.; Stenström, S., Dynamic

Parameter Estimation of Atomic Layer Deposition Kinetics Applied to In-Situ Quartz Crystal Microbalance Diagnostics. Chem. Eng. Sci. 2014, 111, 15-33. 7.

Ritala, M.; Leskela, M.; Niinisto, L.; Haussalo, P., Titanium Isopropoxide as a Precursor

in Atomic Layer Epitaxy of Titanium Dioxide Thin Films. Chem. Mater. 1993, 5, 1174-1181. 8.

Aarik, J.; Aidla, A.; Uustare, T.; Ritala, M.; Leskelä, M., Titanium Isopropoxide as a

Precursor for Atomic Layer Deposition: Characterization of Titanium Dioxide Growth Process. Appl. Surf. Sci. 2000, 161, 385-395.


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9.

Rahtu, A.; Ritala, M., Reaction Mechanism Studies on Titanium Isopropoxide–Water

Atomic Layer Deposition Process. Chem. Vap. Deposition 2002, 8, 21-28. 10. Park, M. H.; Jang, Y. J.; Sung-Suh, H. M.; Sung, M. M., Selective Atomic Layer Deposition of Titanium Oxide on Patterned Self-Assembled Monolayers Formed by Microcontact Printing. Langmuir 2004, 20, 2257-2260. 11. Sinha, A.; Hess, D. W.; Henderson, C. L., Area-Selective ALD of Titanium Dioxide Using Lithographically Defined Poly(methyl methacrylate) Films. J. Electrochem. Soc. 2006, 153, G465-G469. 12. Reinke, M.; Kuzminykh, Y.; Hoffmann, P., Selective Growth of Titanium Dioxide by Low-Temperature Chemical Vapor Deposition. ACS Appl. Mater. Interfaces 2015, 7, 9736-9743. 13. Chen, X.; Mao, S. S., Titanium Dioxide Nanomaterials: Synthesis, Properties, Modifications, and Applications. Chem. Rev. 2007, 107, 2891-2959. 14. Paz, Y., Self-Assembled Monolayers and Titanium Dioxide: From Surface Patterning to Potential Applications. Beilstein J. Nanotechnol. 2011, 2, 845-861. 15. Reinke, M.; Kuzminykh, Y.; Hoffmann, P., Low Temperature Chemical Vapor Deposition Using Atomic Layer Deposition Chemistry. Chem. Mater. 2015, 27, 1604-1611. 16. Reinke, M.; Kuzminykh, Y.; Hoffmann, P., Surface Kinetics of Titanium Isopropoxide in High Vacuum Chemical Vapor Deposition. J. Phys. Chem., 2015, 119 (50), 27965-27971. 17. Reinke,

M.;

Ponomarev,

E.;

Kuzminykh,

Y.;

Hoffmann,

P.,

Combinatorial

Characterization of TiO2 Chemical Vapor Deposition Utilizing Titanium Isopropoxide. ACS. Comb. Sci., 2015, 17, 413-420.


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18. Krumdieck, S. P., Chapter 2 CVD Reactors and Delivery System Technology. In Chemical Vapour Deposition: Precursors, Processes and Applications, The Royal Society of Chemistry: 2009; pp 37-92. 19. Durst, F., Grundlagen der Strömungsmechanik: eine Einführung in die Theorie der Strömung von Fluiden. Springer-Verlag: 2007. 20. Schatzberg, P., Molecular Diameter of Water from Solubility and Diffusion Measurements. J. Phys. Chem., 1967, 71, 4569-4570. 21. Mousa, M. B. M.; Oldham, C. J.; Jur, J. S.; Parsons, G. N., Effect of Temperature and Gas Velocity on Growth per Cycle during Al2O3 and ZnO Atomic Layer Deposition at Atmospheric Pressure. J. Vac. Sci. Technol., A, 2012, 30, 01A155. 22. Xie, Q.; Musschoot, J.; Deduytsche, D.; Van Meirhaeghe, R. L.; Detavernier, C.; Van den Berghe, S.; Jiang, Y.-L.; Ru, G.-P.; Li, B.-Z.; Qu, X.-P., Growth Kinetics and Crystallization Behavior of TiO2 Films Prepared by Plasma Enhanced Atomic Layer Deposition. J. Electrochem. Soc. 2008, 155, H688-H692. 23. Kim, S. K.; Hoffmann-Eifert, S.; Reiners, M.; Waser, R., Relation Between Enhancement in Growth and Thickness-Dependent Crystallization in ALD TiO2 Thin Films. J. Electrochem. Soc. 2011, 158, D6-D9.

Table of Content Graphic


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Page 29 of 40


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment

29

Y

Y

Y

Y

Y

Y

Y

TiO2 GPC in ALD due to... he Journal of Physical Page 30Chemist of 40 Y

Y

Y

1 ...hydrolysis ... pyrolysis GPC [Å] 2 3 TTIP 0.5 4 water 5 ACS 6 Paragon Plus Environmen 1 50 200 250 7 8 substrate temperature [°C] Y

Y

Titanium (IV) Page 31 of 40 Isopropoxide (TTIP) Y

Y

Y

TTIP purge

Y

Y

Y

Y

Y

Y

Y

Y

H2O pulse

kdes TTIP des k H2 O

khydrolysis kpyrolysis

Y

ACS Paragon Plus Environment Y

Y

Y

Y

Y

Y

Y

Y

Y Y

TTIP pulse

Y

kdes TTIP

khydrolysis kpyrolysis

kpyrolysis

kpyrolysis Y

kdes H2 O

sH2 O

Y

Y

Y

sTTIP

Y

kdes TTIP

kdes TTIP

JH2O

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

1 2 3 JTTIP 4 5 6 7 8

The Journal of Water Physical Chemistry

Y

Y Y

Y

Y

H2O purge

Y

S u r f a c e O c c u p a t io n [ r e l.]

1 2 3 4 5 6 7 8

1 .0 0 .5 1 .0

T T IP

P u rg e

W a te r

2 0 0 °C

a d s o rb e d T T IP

a d s o rb e d

0 .5 0 .0

P u rg e

The Journal of4 sPhysical1 2Chemistry Page 32 4 s s 4 s of 40

w a te r

ACS Paragon Plus Environment 0 .0 0 5

4

8

T im e [s ]

1 2

1 6

2 0

2 4

Page 33 of 40 p r e c u r s o r flu x

1[c m s ] 2 s u rfa c e c o v e ra g e 3 [r e la t iv e ] 4 5 6m a s s u p t - a 2 k e 7[n g c m ] 8 9 r e a c t e d s p e c ie s 10 1 4 [1 0 c m -2 ] 11 12 13 14 15 -2

-1

1 0 1 0

H

1 8

1 .0 0 .5

1 6 0 °C

2 0 0 °C

2 6 0 °C


2 0

2

O

T T IP

0 .0 8 0 4 0

0

0 .1 6 Å / c y c le 4 0

2

0 .4 6 Å / c y c le

G P C 2 4

4 8

h y d r o ly s is

0 .6 3 Å / c y c le

G P C 7 2

2 4

4 8

h y d r o ly s is


p r o c e s s t im e [s ]


G P C

7 2

2 4

4 8


p y r o ly s is

7 2

4 s T T IP - 4 s p u rg e - x s H 2O The Journal of Physical Chemistry Page 34 of 40

0 .6

g r o w t h p e r c y c le [Å ]

1 2 0 3 4 5 6 0 7 8 9 0 10 11

1 5 0 °C

1 7 5 °C

2 0 0 °C

2 2 5 °C

.4 .2 .0 0

ACS Paragon Plus Environment 5

H 2

O

1 0 1 5 p u ls e d u r a t io n [s ]

2 0

a )

4 s T T IP - 4 s p u rg e - 1 2 s H


Page1 . 0 35 The ofJournal 40 of Physical Chemistry



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

0 .8

G P C c o n t r ib u t io n h y d r o ly s is

0 .6

p y r o ly s is

0 .4 0 .2 0 .0 1 .0 0 .8

1 0 0

b )

1 .0 0 .8

1 0 0

c )

1 5 0 3 s w a t e r p u ls e

2 0 0

O 2

2 5 0

4 s T T IP - 4 s p u rg e - x s H

6 s

1 2 s

0 .4 0 .0

2 5 0

1 6 s

0 .6 0 .2

2 0 0

x s T T IP - 4 s p u rg e - 1 2 s H

8 s

0 .4 0 .0

2 s T T IP p u ls e

A L D w in d o w

4 s

0 .6 0 .2

1 5 0

O 2

2 4 s 4 8 s

ACS Paragon Plus Environment 1 0 0

1 5 0

2 0 0

s u b s tra te te m p e ra tu re [°C ]

2 5 0

2

O

A L D W in d o w

- T e m p e r a t u r e L im it

U p p e r T e m p e r a t u r e L im it [° C ]

The Journal of Physical Chemistry Page 36 of 40 1 0 %

2 8 0

1 2 2 6 3 4 5 2 4 6 7 2 2 8 9 2 0 10 11 0

5 %

x %

M ix e d

1 % 0

o f p r e c u r s o r d e c o m p o s e d t h e r m a lly d u r in g T T IP p u ls e d u r in g T T IP p u r g e

C V D / A L D R e g im e lit e r a t u r e

v a lu e : 2 4 0 ° C

A L D

0

0

R e g im e

ACS Paragon Plus Environment 0 .1

1 T T IP P u ls e &

1 0 P u r g e T im e [s ]

1 0 0

T T IP

H

2

O

2 0 0 °C u rg e

Page 37 The ofJournal 40 4 s T of T I P Physical - 4 s p u r g e - Chemistry 1 2 s H O - 4 s p P r e c u r s o r F lu x [c m

-2

s ] -1

1 0 1 0

2 0

2

1 8

1 S u r f a c e C o v e r a g e 1 .0 2 0 .5 3 [r e la t iv e ] 0 .0 4 8 0 5M a s s U p t a k e 2 6 [n g c m ] 4 0 7 0 8 0 .7 9 Å / c y c le 9 6 R 10 e a c t e d S p e c ie s 11[ 1 0 1 4 c m - 2 ] G P C 3 h y d r o ly s is ACS Paragon Plus Environment 12 0 13 c y c le 1 c y c le 2 c y c le 14 p r o c e s s t im e [s ] 3

G r o w t h p e r C y c le [Å ]

1 2 3 4 5 6 7

1 .5

4 s T T IP - 4 s P u rg e - 1 2 s H

T T IP d e c o m p o s it io n d u r in g ...

O

- x s P u rg e

2 0 0 °C

T T IP P u rg e

1 .0

T T IP P u ls e

0 .5 0 .0

2

The Journal of Physical Chemistry Page 38 of 40

0

p u r g in g o p t im u m

H 2 O P Paragon u ls e ACS Plus Environment 2

H 2

O

4 6 p u r g e d u r a t io n [s ]

8

1 0

PageThe 39 of Journal 40 of Physical Chemistry 1 .0

m a s s u p t a k e [ a .u .]

1 2 0 3 4 5 6 0 7 1 8 9 10 11 0 12 13 14 0 15 16 17

.5

2 0 0 °C

.0 .0 2 7 5 °C

.5 .0

s im u la t e d m a s s u p t a k e -2 0

Q C M

s ig n a l fr o m

lit e r a t u r e

ACS Paragon Plus Environment 0

2 0 p r o c e s s t im e [s ]

4 0

precursor adsorption pyrolytic The Journal of Physical Chemistry and desorption decomposition 1 2 3 4 5 6

dΓTTIP = dt dΓH2O = dt

( (

JH2OsH2O

(

ΓTTIP 2 (2) -kkdes - kpyrolysis ΓTTIP TTIPΓTTIP 0 ΓTTIP ΓH O Plus Environment - kdes 1- 0 2 ACS Paragon H2OΓH2O Γ H2 O

JTTIP sTTIP 1-

(

hydrolytic Page 40 of 40 decomposition

- khydrolysis ΓTTIPΓH2O - khydrolysis ΓTTIPΓH2O

Surface Reaction Kinetics of Titanium Isopropoxide and Water in

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