The classically used techniques to obtain the thermodynamic data
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He has carried out a great deal of research and technical survey work as well as several studies in the aforementioned areas with over 170 published international academic works in different languages.",coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"110471",title:"Dr.",name:"Amjad",middleName:"Zaki",surname:"Almusaed",slug:"amjad-almusaed",fullName:"Amjad Almusaed",profilePictureURL:"https://mts.intechopen.com/storage/users/110471/images/system/110471.png",biography:"Amjad Almusaed was born in 1967. He holds a PhD degree in Architecture (Environmental Design) from Ion Mincu University, Bucharest, Romania. He completed postdoctoral research in 2004 on sustainable and bioclimatic houses, from the School of Architecture in Aarhus, Denmark. His research expertise is sustainability in architecture and urban planning and design. He has carried out a great deal of research and technical survey work, and has performed several studies in the above-mentioned areas. He has edited many international books and is an active member of many worldwide architectural associations. He has published more than 170 international academic works (papers, research, books, and book chapters) in different languages.",institutionString:"Jönköping University",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"8",totalChapterViews:"0",totalEditedBooks:"9",institution:{name:"Jönköping University",institutionURL:null,country:{name:"Sweden"}}}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"11",title:"Engineering",slug:"engineering"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"259492",firstName:"Sara",lastName:"Gojević-Zrnić",middleName:null,title:"Mrs.",imageUrl:"https://mts.intechopen.com/storage/users/259492/images/7469_n.png",email:"sara.p@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. 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Theophanides",coverURL:"https://cdn.intechopen.com/books/images_new/1591.jpg",editedByType:"Edited by",editors:[{id:"37194",title:"Dr.",name:"Theophanides",surname:"Theophile",slug:"theophanides-theophile",fullName:"Theophanides Theophile"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"39516",title:"Thermodynamics Simulations Applied to Gas-Solid Materials Fabrication Processes",doi:"10.5772/51377",slug:"thermodynamics-simulations-applied-to-gas-solid-materials-fabrication-processes",body:'The development and the design of materials and/or the processes of their fabrication are generally very time consumer and with expensive operations. Various methods of development can be conceived. Often, "empirical" approaches are adopted: the choice of the experimental parameters is established either on technological or commercial criteria, the optimization being the results of a “trial and error” approach, or on the results of design of experiments (DOE) approach targeted at a property of a material or a parameter of a very particular process. Another approach is to use process modeling: to simulate the process by a more or less simplified model. The modeling of gas-solid materials fabrication processes brings together several physical and chemical fields with variable complexity, starting from thermodynamics and\\or kinetics studies up to the mass and heat transport coupled with databases and with thermodynamic and/or kinetics transport properties.
The objective of this chapter is to illustrate the interest areas computer-aided materials design and of processes optimization based on the thermodynamic simulation and giving some interesting examples in different domains. Databases as well as their necessary tools for the implementation of the thermodynamic calculations will be described.
The thermodynamic simulations of multicomponent systems contribute at two important points: the selection of the material and the optimization of the conditions of fabrication. In order to obtain a finely targeted product which meet specific functionalities, it is necessary to answer the following questions:
what type of composition, quantity, and microstructure of the material allow to obtain such properties?
it is possible to elaborate the material? By what process, with which reagent/ species and which operating conditions?
is stable this material during a treatment in temperature, and under a given atmosphere?
does this material react with its environment (substrate, oven, atmosphere)?
These questions are connected because the properties of the material, essentially conditioned by the microstructure of the final material, are going to depend on its chemical composition, to the process, to the operating conditions and on dimensions of the fabrication equipment.
The answers to these questions can be provided and shown from calculation of phase diagrams, evaluation of chemical reactions, calculation of equilibrium pressures, and from reaction diagrams.
To evaluate equilibrium state, two possible approaches exist. The first one is to choose
The second approach, more complex, is based on the analysis and the consideration of all the species belonging to the chemical system in the studied process.
The optimization procedure must have the following stages:
The analysis of the system with the inventory of all the species reasonably susceptible to be present during the reactions taking place in the process.
The construction of a consistent set of thermodynamic data for these species.
The thermodynamic calculations at equilibrium of complex system
The best representation of the results for the users
Thus, the thermodynamic calculations often give satisfactory results for processes which use high temperatures and residence time or reaction but for processes at low temperature, the kinetic factors must be not neglected. That is why the recent developments of thermodynamic softwares tend to include descriptions of phenomena of diffusion and reaction kinetics.
The thermodynamic approach gives the superior limit of possibilities of process (considering the reaction rates as infinite). It can be the only way of modeling for a complex system where the mechanisms of reaction and the kinetic data are badly known.
To include some dynamic aspects (mass transport) in the modeling, an approach which takes into account the evaluation of flows will be presented. It concerns applications where the total pressure is low (<10 Pa).
The analysis of the system consists in listing the following points: the range of temperature T, range of pressure P or of volume V, the duration of the process, the list of the reagent species, the inventory of the components of the reactor and the nature of the atmosphere. For these last points, it means elaborating a list of all the compounds, the gaseous species, the elements and the solid solutions which result from the combination of the basic elements of the system.
This list is automatically generated thanks to interfaces with databases. However, it is advisable to make sure that the used database is very complete. As an example, the list corresponding to the chemical system Si-C-H-Ar (proceeded CVD (Chemical Vapor Deposition) contains about sixty species – excluding the hydrocarbons CxHy where x>3 [1].
In a process reactor, at constant pressure, the balance is reached when the total free Gibbs energy function of the system is minimal (equation 1). To determine the nature and the proportion of the present phases at equilibrium, it is necessary to have the description of the energies of Gibbs of all these phases.
where qj the number of moles of the species j, Gj the molar free energy of Gibbs of the species j, Ne total number of species.
The Gibbs energy can be described from the enthalpy (H) and the entropy (S):
The necessary data are thus: Cp(T), ∆H(298K), S(298K) and the data of possible phases transitions Ttrans, ∆Htrans(T).
Various formalisms are adopted for the analytical expression of the function Cp (T). Among them, the formalisms of the SGTE (Scientific Group Thermodata Europe ) [2] (equation 5) and of the NASA [3](equation 6) are :
where a, b, c, d, e are adjustable parameters.
So, it can be described analytically the Gibbs energy G for a stoichiometric compound (equation 7), for a gas (equation 8) and a solution phase (equation 9):
Besides, as neither the enthalpy nor the entropy can be described in an absolute way, a reference state must be used for these two functions of state. For the entropy, the adopted convention consists in taking a zero value at 0 K. In the case of the enthalpy, the most common convention is to choose the stable structure of the element at T = 298K, as standard reference state (e.g. Al cfc, Ti hcp, O2 gas …). For the reference state, ∆H(298K)=0 and S(0K)=0.
As the reliability of the results of the thermodynamics simulation depends widely on the quality and on the consistence of the necessary data, it is advisable to attach an importance to the consistence of the available information: thermodynamics measurements, theoretical calculations, characterizations (X-ray diffraction, Environmental Scanning Microscopy), balance of phases (diagrams). In the Table 1 are given some experimental and theoretical techniques usually used to obtain the thermodynamic data.
The thermodynamic information are accessible in compilations of binary phases diagrams (for example Hansen [5], Elliot [6], Massalski [7]), ternary (Ternary Alloys [8]), or specialized journals (CALPHAD, Journal of Phase Equilibria, Intermetallics…), or tables (JANAF Thermochemical Tables [9], Barin [10], Gurvich [11]).
Today, most of data are available in international electronic databases. In Europe, the economic interest group "Scientific Group Thermodata Europe [12]" proposes common data bases for compounds, pure substances and for solutions. Also let us quote the “Coach” data bank ( more than 5000 listed species) proposed by Thermodata [1], well adapted to simulate gas/solid processes, the FACT bank (oxides/salts) proposed by the company GTT [13] and the Research Center in Calculation Thermodynamics [14], base TCRAS [15], bases NASA combustion [16], NIST [17].
Experimental | Theory | |
∆H(T) | Calorimetry (dissolution) | Ab initio calculations Estimations : Miedema [4], analogy |
Cp(298K), S(298K) | Temperature measurement at low temperature | |
Cp(T) | Estimations : Neumann-Kopp law(ΔCp=0 for a condensed compound) | |
Cp, S(T) | Differential Scanning Calorimetry (DSC) | volume-specific heat capacity calculations |
G(T) | Electromotive force, Mass Spectrometry (activity data, partial pressures at equilibrium) | |
Ttrans, Htrans (T) | Differential Thermal Analysis (DTA) Thermogravimetric analysis (TGA) |
The classically used techniques to obtain the thermodynamic data
The software of complex equilibrium is based on the minimization at constant temperature T of the Gibbs energy and constant pressure P (equation 1) or Helmholtz energy (equation 10), at constant volume:
qj the number of moles of the species j.
The constraints of mass equilibrium of each present element in the chemical system expressed according to the number of atoms on the pure element i (C elements) are translated by the equation (11 ):
where
These C equations can be translated under the matrix shape (equation 12):
There are multiple algorithms allowing this minimization. Various classifications were given, the most exhaustive having been supplied by Smith and Missen [18]. In a simple way, two groups of algorithms can be distinguished: on one hand the methods of direct minimization, about zero order for the calculation of the function G, on the other hand, the methods of the first order based on the equality of the chemical potential which require the calculation of the function derivatives. These last ones also include the methods of second order, using among others the algorithm of Newton-Ralphson which is based on the second derivatives. It is necessary to note that the methods of the first order must be perfectly controlled because they can lead to a maximum instead of a minimum and consequently to a wrong result.
A method of the first group is described below: the matrix T is decomposed into a regular square matrix Tp of dimension C and a matrix Td of dimension (C, Ne-C) such as:
The C species which constitute the matrix column qp are called the “main species” because they are chosen among the most important species and have by definition a linear independent stoichiometry. The Ne-C remaining species of the matrix Td is called “derived species” although they are chosen as variables from the minimization. So the Ne-C values qd are given by the procedure of minimization, C values qp is calculated by resolving the linear system:
An iteration of this method is divided into two steps. Firstly, the phase of exploration, every variable is modified by a value + or - h.
If Xn-1 is the vector representing the variables after n-1 iterations: the species i having a step hi and Gi the value of the function
if Gi+<Gi either,
When the exploration phase is ended, the next step is to move to the second algorithm phase where from the values of G + and Xn\n\t\t\t\t\t+ issued from the exploration phase, we calculate X++ = Xn-1 + (Xn+-Xn-1) as well as the corresponding value G++ to obtain the optimal set [19]. To proceed the mimimization procedure, a certain number of more and more friendly softwares are available commercially. It can be listed as example:
Thomas [22], Bernard [23] and Pons [24] present few examples on CVD processes to illustrate the use of an a priori thermodynamic analysis. In the following paragraphs, it was chosen to show other few examples which evidence the help of thermodynamic modeling in industrial bottlenecks:
Thermal stability of Metal-Organic Precursors used in CVD and ALD processes.
Stability of SiC in H2 atmosphere
HfO2 plasma etching
SiO2 PVD evaporation-condensation deposition process.
In the last two examples which correspond to processes operating at low pressure (<1 Pa), in addition to pure thermodynamic approach, a dynamic approach was presented which includes calculations of the major species flows.
In the pursuit of smaller and faster devices manufacture, microelectronics industry scales down feature sizes and thus has to develop new materials and processes. Nowadays, organometallic precursors are widely used in ALD (Atomic Layer Deposition) and CVD (Chemical Vapor Deposition) deposition processes due to low deposition temperature (generally below 523 K). The objective of computational modeling for gaseous phase processes like ALD or CVD is to correlate the as-grown material quality (uniformity, growth rate, cristallinity, composition, etc) to general parameters such as growth conditions, reactor geometry, as well as local parameters that are actual flow, thermal fields and chemical kinetics at the solid/gas interface.
The gaseous precursors compounds used for the transport of the elements to be deposited by these processes have to meet several physicochemical properties requirements including relatively high volatility, convenient decomposition behavior and thermal stability. The tantalum organometallic precursor pentakis dimethylamino tantalum (PDMAT), remains an attractive solution for tantalum nitride films deposition. Unfortunately, information on physical and chemical behavior of this kind of precursor is scarce and namely species that are formed during vaporization and transported to the deposition chamber remain generally unknown. Thus, the knowledge of thermodynamics of these gaseous compounds could help in the understanding of the transport and growth mechanisms. Indeed, thanks to thermodynamics, it is possible to evaluate what evolves at equilibrium in the precursor source, in the input lines and in the deposition chamber where deposition reactions occur. To control, optimize and understand any ALD or CVD processes, thermodynamic simulations are very useful and therefore data should be primarily assessed.
In order to deposit thin layers of TaN using PDMAT, ALD experiments evidenced a cracking of this precursor in the ALD reactor [25].
Cracking reactions of PDMAT can be complex and occur at the same time. A quantitative interpretation of cracking reactions can be deduced from observed molecules by mass spectrometry [26, 27] with the condition that all products and reactants of the reaction are observed and measured by the mass spectrometer at the same time. Without additional hydrogen contribution, the two following cracking reactions of Ta [N(CH3)2]5(g) could occur:
either the Ta- [N(CH3)2] bond breaks with the additional break of H-CH2 to produce HN(CH3)2 (the so-called β substitution):
or the only bond break of Ta- [N(CH3)2],
As no N(CH3)2 (g) radical was detected, the observed HN(CH3)2 (g) molecule could be formed by the following complete and rapid reaction,
Consequently, it could be assumed that the measured HN(CH3)2 (g) amount is the same as the initial produced amount of N(CH3)2 (g): this radical spontaneously reacts totally according to the reaction (20) after being produced by reaction (19). This mechanism could explain why N(CH3)2 (g) was not detected. So, in this study, the total cracking reaction was finally considered:
Another cracking reaction could be noticed: OTaN4C8H24 (g) molecule broke down into OTaN3C6H18 (g) according to the following reaction,
because the energy of the Ta-N bond is lower than the Ta-O bond.
The experimental study of these two reactions (21) and (22) requires to know or measure H2(g) pressure. Hydrogen could come from either equilibrium with cracking cell deposits or either molecules losing one or more hydrogen atoms. In this last case, a new molecule should be present. In this study, as no hydrogen was detected or introduced intentionally in the cell, it was assumed that the amino radical is totally consumed and produces HN(CH3)2 (g) with just a sufficient hydrogen amount. So, it can be assumed that the partial pressure of p(HN(CH3)2) is quite equal to the partial pressure of p(N(CH3)2). That allows us to calculate the equilibrium constant of reaction (19):
Pressure measurements of these three molecules by mass spectrometry lead to the evaluation of standard enthalpy at 298 K from the third law of thermodynamics:
Measured partial pressures of Ta [N(CH3)2]5 (g), Ta [N(CH3)2]4 (g) and HN(CH3)2 (g) are elsewhere reported [26, 27].
From this, the average value of ΔrH°298 K was evaluated to be equal to (85±5) kJ/mol.
Thermodynamic simulations, based on the Gibbs free energy minimization of the Ta-C-N-H-(O)-(Ar) system were performed using GEMINI software [1] to provide the nature of the species that should be present at equilibrium under experimental conditions. The sets of thermodynamic data which have been used come from SGTE 2007 database [28] and from the mass spectrometry study for Ta [N(CH3)2]5(g), Ta [N(CH3)2]4(g),and NC2H6 (g) gaseous species [26]. Without any available literature data or any estimates, it cannot be considered any thermodynamic description of OTaNxCyHz (g) gaseous species and intermediate TaNxCyHz (g) species such as TaN3C6H16 (g), even though these species are expected to appear as observed in mass spectrometric measurements and to play a role in PDMAT cracking and in Ta containing solid formation [26]. Two kinds of simulations have been performed within a temperature range from 400 to 750 K and at 10 Pa, which is our typical mass spectrometric total pressure in the cracking cell. First, homogeneous equilibrium was investigated - no solid phase is allowed to be formed - which corresponds to no deposition i.e. transport in gas lines held at temperature above the saturated one (Figure 1).
Second, a heterogeneous equilibrium - the solid phase is allowed to be formed - has also been simulated, which corresponds to the deposition process occurring in the ALD reactor and in the cracking cell.
In all these thermodynamic simulations, it appeared that Ta [N(CH3)2]5(g), (PDMAT) is not stable. In Figure 1 the homogeneous equilibrium calculation show that Ta [N(CH3)2]4(g) is stable but disappears after 450 K and Ta(g) is the only one main tantalum containing species after 415 K - but this species will soon be condensed due to large over saturation-. Added to Ta(g), a lot of cracking gaseous species such as N2 (g), CH4 (g), H2 (g) originate from the complete amine decomposition and indeed among these species, NC2H7 (g) and NC2H6 (g) do not appear. The heterogeneous equilibrium calculations shows the formation of C solid that corresponds to the amine decomposition and this amount of free carbon increases with increasing temperature. Also, the formation of solid TaN was observed within the whole investigated temperature range and no gaseous tantalum containing species pertained contrary to mass spectrometric experiments.
Homogeneous thermodynamic simulations performed starting from 1 mole of the compound Ta [N(CH3)2]5(g) and 0.001 mol of Ar and for an applied total pressure equal to 10 Pa in order to be compared with the mass spectrometric experiments.
It is to be concluded that discrepancies exist between thermodynamic simulations and mass spectrometric experiments. Indeed, thermodynamics predicted total cracking of both Ta [N(CH3)2]5(g) and amine molecules in the whole investigated temperature ranges, while in mass spectrometric experiments, Ta [N(CH3)2]5(g) and NC2H7 (g) amine have been observed only in the low temperature below 623 K [26, 29]. The deviation vs. equilibrium could be analyzed experimentally by the use of various sizes of cracking cell as well as the deliberate and controlled introduction of H2(g). However, despite these limitations, these results indicate the main features of the precursor thermal behavior which can be very useful in the first stages of the development of any new ALD or CVD (for precursor transport) processes.
Silicon carbide (SiC) possesses many favorable properties making it interesting for a multitude of applications, from high temperature to high frequency and high power device. Among them, its excellent physico-chemical and electronic properties such as wide band gap and high breakdown field, together with the degree of maturity of technology, makes SiC a good candidate for mass production of Schottky diodes [30].
SiC device processing is conditioned to the fabrication of large area single crystal wafers with the lowest defect density associated to deposition of epitaxial thin films which present good structural quality and controlled doping level [31]. The most common processes used to develop SiC wafers and SiC thin films are the seeded sublimation growth technique so called the “Modified Lely method” and the Chemical Vapor Deposition technique from propane and silane, respectively.
Huge improvements for both processes have been observed in the last decades. They come mainly from extensive experimental effort, all over different groups in the world. However, macroscopic modeling has given valuable information to understand the impact of some growth parameters and propose new design of experiment to enlarge wafer size and deposition area.
On both processes [32-35], some modeling trends were largely reported combined with experimental results obtained in our research’s groups.
Special emphasis is given to chemical related results. To carry out modeling, it was followed the different levels of complexity procedure described in the earlier paragraphs. Owing to the similarity of the two systems, studies on species and material databases have been naturally used for both processes.
CVD- grown SiC films can be obtained from a variety of precursors which are generally part of the Si-C-H system. However, to obtain high crystal quality of 4H and 6H SiC layers, which are the most interesting polytypes for the power devices applications, experimental investigations have demonstrated that silane (SiH4(g)) – propane (C3H8(g)) gave the most stable growth, in the typical conditions (temperature higher than 1700K, pressure between 10 kPa to 100kPa, hydrogen as carrier gas) [36]. Operations are separated in two steps, first an in situ etching step to prevent epitaxy-induced defects, then the deposition step.
A great body of literature dealing with both theoretical and experimental results has been devoted to understanding chemistries relevant to the separate Si-H and C-H systems.
However, it appears that most is unknown about the chemical reactions in which organosilicon species, that include the three elements, can be involved. This is related to the difficulty to measure thermochemical properties of such reactive, short life time, species. Most of the thermodynamic data that have been used for these species come from ab initio electronic structure calculations combined with empiric bond additivity corrections [37, 38]. Mass spectrometry measurements have been carried out to estimate the thermodynamic data of the gaseous species Si2C(g), SiC2(g), SiC(g) and the condensed SiC(s) phase [39, 40].
With a purely thermodynamic approach, it was examined the preliminary operation of in situ etching. It was found that the H2(g) etching of SiC(s) at 1700 K under 100 kPa can lead to the formation of a condensed silicon phase, as shown on Figure 2. Thermodynamic study was made to understand the impact of the temperature, the pressure and the composition of the gas mixture [41].
Heterogeneous thermodynamic calculations show that the mixture (H2(g) + condensed SiC(s)) ends in the formation of gaseous species such as CH4(g) for the C-containing species and SiH2(g), SiH4(g), SiH(g), Si(g) and Si(s) in condensed phase for the Si-containing species. With the etching, the amount of the gaseous C-species formed (mainly CH4(g)) is three times higher than the gaseous Si-species one. So, there is Si in excess which is condensed at the SiC(s) surface in a solid or liquid phase depending whether the etching temperature is higher or below the Si melting temperature. When the temperature is higher than 1800K, at atmospheric pressure, the quantity of formed gaseous Si-species becomes equal to the quantity of formed gaseous C-species. Consequently, the formation of liquid silicon is avoided.
Thermodynanic simulations have revealed the main phenomena and indicated some solutions. Reducing pressure would provide the same beneficial effect, though the etching rate decreases, as illustrated in Figure 3.
To compensate the formation of gaseous CH4(g), the addition of an hydrocarbon species such as propane in the initial gaseous mixture would prevent the formation of condensed silicon.
All these effects have been confirmed with experimental studies (Figure 2).
Optical Micrograph of SiC(s) surface etched with H2(g) at 1700 K under 100 kPa, showing silicon droplets (right). The silicon phase is identified by Raman spectroscopy (left) [
Heterogeneous equilibrium of the SiC(s) - H2(g) system at 1685K. Gaseous species created by the etching are represented as a function of the pressure [
With the constant downscaling of Complementary Metal-Oxide-Semiconductor (CMOS) devices and the consequent replacement of SiO2 many high-
In the case of the etching of HfO2, one of the main issues is the low volatility of halogenated based etch by-products [42].
Compared to SiO2 halide based etching process, thermodynamic data shows that, Hf based etch by-products (HfCl4(g), HfBr4(g), HfF4(g)) are less volatile than Si etch by products (SiCl4(g), SiBr4(g), SiF4(g)) [43]. Therefore, for HfO2(s) etching, the choice of the halogenated based chemistry and substrate temperature are crucial parameters. In this work, thermodynamic studies have been carried out in the pressure (0.5 Pa) and temperature range (425 K to 625 K) conditions in order to select the most appropriate gas mixture and temperature leading to the formation of Hf and O based volatile products. Based on thermodynamic calculations in a closed system, the HfO2(s) etching process has been simulated.
With this thermodynamic analyses, it is possible to determine an etch chemistry leading to volatile compounds and to estimate an etch rate under pure chemical etching conditions. It should be noted that the thermodynamic approach does not take into account the ion bombardment of the plasma.
For example, let’s consider the etching of HfO2(s) in CCl4(g) plasma at 400 K and 0.5Pa. In such case, the thermodynamic system is composed by four elements Hf, O, C, and Cl. The thermodynamic calculation inputs are:each element of CCl4(g) (C and Cl atoms) with HfO2(s) as a solid phase. The main gaseous species are CO2(g) and HfCl4(g) and the main condensed species are HfCl4(s) on HfO2(s) in a solid phase. There are other gaseous species in very low amount so that they can be neglected as (CO, Cl2, Cl). These results show that carbon and chlorine containing chemistries can lead to the etching of HfO2(s) by forming CO2(g) and HfCl4(g). Similar results have been obtained for the other halide chemistries CCl3F(g), CCl2F2(g), CCl3F(g), CCl4(g).
To point out the more promising chemistry among the usually adopted halogens precursors, the etch rate has been estimated from the flow calculations of each gaseous and condensed species under open conditions assuming molecular flow and the validity of the Hertz-Knudsen relation [44].
For these processes operating at low pressure (<10 Pa), it is possible to associate the incident and emitted flows from a given surface to the equilibrium partial pressures [45].
These calculations are based on the effusion calculations principles from the gas kinetic theory.
For a gaseous species e, the total flow
Where pe et Me are the partial pressure and molar mass of the species e, respectively.
For each etched or deposited element i, there is equality between the incident flow and the emitted or produced from reactions flows:
on the deposited or etched surface
For example, in the case of HfO2(s) etching by CHCl3(g) with Ar(g), the system is Hf, O, C, H, Cl, Ar
For the previous thermodynamic calculations (HfO2(s) and CHCl3(g)) the major species at equilibrium are:
CO2(g), HCl(g), HfCl4(g), Ar(g) in the gaseous phase
C(s), HfO2(s), HfCl4(s) in the solid phase
for a temperature of 300 K and a pressure of 5 Pa.
The flow equations are in this case (principle of mass conservation) :
Flow of incident C = flow of evaporated C + flow of condensed C:
Flow of incident H = flow of evaporated H :
Flow of incident Cl = flow of evaporated Cl + flow of condensed Cl :
with F(.(s)) the flow in solid phase species and
So five unknowns are obtained:
To be able to solve this system, five equations are needed. Already, three equations with these ones of flow exist. For the both missing, it’s enough to consider:
The equation of total pressure:
And the value of the equilibrium constant for the assessment of mass equation of the system, the fifth global equation is supplied by:
the equilibrium constant of this equation is :
The system of five equations and five unknowns is obtained:
The partial pressures of the main species are obtained. To determine the etch rate, it is needed to use the calculated values for the pressures of the gases containing the elements of material to etch.
In our example, the following gases CO2(g) and HfCl4(g) are considered.
The theoretical etch rate ER is given by the lowest value between:
ER = flow HfCl4(g).molar volume HfCl4(g) or flow CO2(g).molar volume CO2(g) (in m/s)
Where:
with
Figure 4 shows the evolution of the calculated HfO2(s) etch rate as a function of temperature for different F/Cl ratios in CClxFy(g) based chemistries. The etch rate is lower when the F/Cl ratio increases in the gas mixture at temperature higher than 400 K. The decrease in the etch rate is explained by the non volatility of HfF4(g) in the investigated temperature range.
From these results, thermodynamic studies predict that a chlorocarbon gas mixture -such as CCl4 -seems to be the most promising chemistry to etch HfO2(s) under pure chemical etching conditions.
Evolution of the thermodynamically calculated HfO2(s) etch rate as a function of F-Cl ratio in CCl
From optics applications, the example of the evaporation/condensation process to obtain SiO2 films is chosen. In that process, the surface of the evaporating source is heated by electronic bombardment, while the substrate is held at low temperature.
The control and the reproducibility of this type of process is based on the following points:
Stability of the source with time (chemical composition, morphology of surface of the evaporating zone)
Temperature and surface of the evaporated area (what is linked to the parameters of the electronic bombardment).
The object of this study is to simulate the evaporation of a source of glassy silica with the aim of depositing SiO2. The heated zone is about 3-7 cm2, the reactor has a volume about 1 m3, the substrate is located at 1 m from the source.
The first paragraph is dedicated to the pure thermodynamic simulations to determine the major species originated from the evaporation. In the second one, the calculations of the flows of evaporation at equilibrium as well as exchanged flows between source and substrate surfaces are presented.
The thermodynamic simulations corresponding to the SiO2(s) evaporation are realized by considering an excess of solid SiO2(s) at a given temperature, in a constant volume. The range of tested temperature is 1600 - 2500 K. The results of the simulation indicate that the only solid present at equilibrium is SiO2(s) and that there is no formation of solid silicon.
In the range of selected temperature, the evaporation of the silica is thus congruent (the ratio of the quantity of silicon and oxygen produced in the gaseous form is equal to 2). Figure 5 presents the nature and the partial pressures of the gaseous species formed at equilibrium.
Calculated partial pressures for SiO2 vaporization.
The major species in this range of temperature are SiO(g), O2(g), O(g) and SiO2(g), with trace of Si(g). It can be noted that the mainly evaporated species is not SiO2(g) as it could believed to justify the stoichiometric composition of the deposits. From the results of the molar fractions calculated for various species, the gas phase reaction which takes place is globally the following:
These curves show that the evaporated material quantity and consequently the evaporation rate increases with temperature. That explains the best results obtained with sources carried beyond their melting point (besides the higher quality of the surface with regard to a solid source).
The calculated total pressure above silica is represented on the figure 5.
For the temperatures of evaporation above 1600 K, the total pressure over the silica is superior to 0.1 Pa. If the total pressure is fixed to a lower value, there is then complete consumption of the quantity of silica carried at the evaporation temperature from a thermodynamic point of view.
Calculated total pressure for SiO2(s) vaporization
The evaporation flows of the gaseous species originating from the SiO2(s) evaporation should respect the congruent vaporization relation (ratio Si/O in the gaseous phase = 2), demonstrated by the previous approach.
where
As illustrated by the previous etching case, it is possible to calculate all the species partial pressures (pe) which verify the equation (37).
From the calculated flows from equation (37), the molar volume of SiO2(s), the reactor geometry, and the temperature conditions on the surface, it is possible to estimate the growth rate and the deposition profile (Figure 7). The growth rate on the substrate is given from the exchanged flows between the two surfaces source and substrate, from basic assumptions of molecular flows.
With coaxial source and substrate, the exchanged flow between the r0 radius source and r1, radius substrate, separated by a distance h is given by the relation (38).
Deposition profile vs deposition temperature for two evaporation temperatures; Substrate radius r0= 0.5 m; evaporating source surface= 3cm2, h= 1m
The results of the simulations are the same order as the obtained experimental values.
The simulations of the evaporation of SiO2(s) show that it is congruent and that there is thus no evolution of the load in time. The mainly produced gaseous species are SiO(g), O2(g), and O(g). Their proportions remain constant but their quantities increase with the temperature of evaporation. Simulations of the evaporation/condensation process provide good estimations of the deposition rate.
This review illustrates the interest to operate a priori an thermodynamic approach to determine the feasibility and optimize a fabrication process, specially gas-solid fabrication process. Kinetic approaches will give rise to more realistic simulations but are often difficult to implement, for lack of reliable information. The classic pure thermodynamic can provide useful information. It can be the only approach in the case of complex chemical systems for which few kinetic data are available. To take into account the dynamic character of the processes, the approaches mixing thermodynamics simulations and calculations of exchanged flows are possible. In every case, the methodology has to contain continuous comparisons between experimental results and simulations.
This paper was inspired by the collaborative works with the colleagues of the SIMaP (Laboratoire de Science et Ingénierie des Matériaux et Procédés): Jean-Noël Barbier, Claude Bernard, Christian Chatillon, Alexander Pisch, Arnaud Mantoux, Raphaël Boichot, Michel Pons.
Thomas Neuhann and Howard Gimbel, considered as pioneers in the development of the centered continuous curvilinear capsulorhexis (CCC) technique, first published their paper on the technique in 1990 [1]. The use of CCC technique makes the rim of the anterior capsule (AC) much stronger and decreases the risk of tearing, thus providing a solid foundation for applying the “chip and flip,” “divide and conquer,” “phaco chop,” and “phaco pre-chop” techniques. What is more, the IOL could be more correctly positioned and stability with the centered continuous curvilinear anterior opening. [2, 3, 4, 5]. In terms of improving the prognosis, CCC technique could supply a continuous opening with more smooth edges [6]. The morphology of anterior capsule affect position of lens and refractive outcome greatly [7]. CCC helps maintain the intraocular lens (IOL) in the correct position and overlaped by anterior capsule as showed in Figure 1 which providing a more predictable effective lens position (ELP) [6]. In addition, The CCC technique could reduce the incidence of posterior capsular opacification (PCO) [8, 9, 10]. With the current widespread-use of multi-focus intraocular lenses and astigmatism-correcting intraocular lenses, Cataract surgery has entered the refractive age. Centered CCC(CCCC) play a crucial role in obtaining good postoperative visual quality. Tilt and decentration of the IOL can decrease visual acuity which could result in astigmatism [11, 12]. Okada et al. [13] confirmed that decentration of optic center by 0.4 mm could produce 0.25D change in spherical equivalent.
Color photo of patient 3 months after CCCC. The margin of optic region was overlaped by anterior capsule full-circlely.
In this chapter, we will elaborate on several aspects include: preoperative preparation; the effects of incision on capsulorhexis. The two parts above mainly discuss the tools, head position of patient, exposure of surgical field of vision, red reflex of microscope, hand position of surgeon and importance of incision. Then capsulorhexis technique and special cases of capsulorhexis will be interpreted. In the end, we will introduce the advantage of femtosecond laser system in capsulorhexis and precautions.
Initially, a type of irrigating cystotome (designed by Charles Kelman) and a needle were employed in CCC. The first forceps, specifically used to conduct capsulorhexis, were designed by Peter Utrata in 1988,and are still used today.
Forceps were designed in different lengths, with columnar and flat handle (Figure 2) and the tips were curved and flat (Figure 3). Compared with columnar handle, the flat handle is easier for thumb and index finger to hold and middle finger to support and relatively more lighter. After the viscoelastic agent was injected into the front chamber, the anterior capsule is flattened. The flat tip has more room to move around in the anterior chamber. The curved tip generate height difference in the anterior chamber. Limited by the incision, the movement of curved tip is restricted. The choice of length, depends on the habit and hand size of the operator and the last choice of columnar and flat handle or curved and flat tip depends on the habit too.
Different designs of forceps handle. A is columnar and B is flat.
Different designs of forceps tip. A is flat and B is curved.
Aim to reduce the incidence of infection after operation especially to decrease surgically induced astigmatism and the influence on corneal optical performance in refractive cataract surgery, corneal incision size was reduced from over 3 mm to less than 2 mm. [14, 15, 16, 17, 18, 19]. The related equipment is also required to be further improved. Smaller incisions limit the movement of traditional capsular forceps. Calladine-Inamura Capsulorhexis Forceps increases the opening and closing range of the tip in the anterior chamber by the hinge design on the forearm as showed in Figure 4 to complete capsulorhexis through small incision. Ikeda MICS Capsulorhexis Forceps is tube designed with small diameter as 0.7 mm (showed in Figure 5) could enter anterior chamber for capsulorhexis through small paracentesis.
Calladine-Inamura Capsulorhexis forceps. Hinge design on the forearm in a and the detail in B.
Ikeda MICS Capsulorhexis forceps. Tube design without joint in A and the detail of tip in B.
Scales of 5 mm and 2.5 mm are marked on some of the flat-tipped forceps, as shown in Figure 6,which can be useful as a measurement reference for the operator.
The scaleis marked on the tip of forceps as scratches. The distal one is 2.5 mm, the proximal is 5 mm.
The position of the head is vital to ensure the centrality of the AC opening. The patient’s head should be kept horizontal for the lens plane to remain horizontal (Figure 7). The AC opening could be decentered downwards if the jaw is too elevated (Figure 8), or upwards if the forehead is too elevated (Figure 9).
The plane of the lens should be kept level by adjusting the position of head before operation.
The AC opening would be decentered towards inferior if the jaw is too elevated.
The AC opening would be decentered towards superior if the forehead is too elevated.
The pupils must be fully dilated to expose the surgical field. One drop of 0.5%tropicamide is instilled every 15 min (four times), to maintain the diameter of the pupil greater than 6.0 mm.
The rare cases in which cataracts are complicated with uveitis, the pupil cannot be dilated adequately because the iris is atrophic and inelastic. In such cases, the pupil can be stretched by two choppers, as shown in Figure 10, which is known as the pupil-stretch technique. Moreover, alternative devices and techniques are available. For example the iris can be fixed by iris hooks through a series of side-incisions to dilate the pupil (Figure 11), and the use of the Malyugin ring can reduce the number of side incisions required (Figure 12). There are also many other pupil expansion devices, such as Hydro view Iris Protector Ring, B-HEX Pupil Expander, I-Ring pupil expander etc., can be used in clinic.
To stretch the pupil in the opposite direction (white arrow) with two chopping hook. The relevant side-effect are hemorrhage (red arrow) and tansformation of pupil after operation.
Iris hooks to fix the iris through side incision which is composed of a hook (red arrow) and gasket (white arrow).
Malyugin ring after disinfection and sealing is showed in A. Malyugin ring stretch the pupil during operation as showed in B (red arrow).
However, the use of instruments or pupil-stretch technique can lead to tears of the iris muscle fiber, resulting in pupil malformation and even the risk of hemorrhage as show in Figure 10 (red arrow). In such cases, coreoplasty can be performed using Vannas capsulotomy scissors, as shown in Figure 13.
Coreoplastyis applied by capsulotomy Vannas scissors to amplify the vision field.
Moreover, when the pupillary area of chronic uveitis is adhered to the AC by an exudative membrane, capsulorhexis forceps could be used to dilacerate the membrane (Figure 14). After both these procedures, the pupils can be dilated injection of a viscoelastic agent.
Capsulorhexis forceps is used to tear the membranes to remove its restriction on the pupil.
The red reflex test, which is performed using a microscope, is very important at each step of cataract surgery. It allows the surgeon to clearly see the capsulorhexis path by illuminating the AC (white arrow in Figure 15), and visualization of the path can be enhanced by adjusting the ratio of coaxial to paraxial light on the microscope (Figure 16).
Capsulorhexis path is clear with good red reflex (white arrow).
Coaxial light and paraxial lights on the operation microscope.
In cases of mature or hyper mature cataracts, the light reflects off the posterior segment, generating a retro-illumination of the AC, which is insufficient for correctly performing capsulorhexis. In such cases, Trypan blue dye could be used to stain the AC.
To avoid wrist dangling, the surgeon’s hands or wrists should rest steadily against the patient’s forehead. This will allow the surgeon’s hands to move synchronously with the patient’s head if the they move head abruptly. The angle at which the hands placed varies according to the practitioner’s habits.
An ideal surgical incision is the fundamental prerequisite for successful capsulorhexis. In Europe and America, a temporal incision is preferred, while in Asia it is mostly performed at an 11 o’ clock position. Regardless of the orientation, when the incision is made, the direction of the tunnel knife should be along the meridian of the cornea, as shown in Figure 17.
The direction of incision should along meridian direction (C) from positioning (A) to the process of making the incision (B).
A meridional incision does not limit the movement of capsular forceps, which ensures that the anterior opening is centered and perfectly round. When the incision deviates from the meridian, the boundaries of the inner incision will limit the track for the capsulorhexis forceps as shown in Figure 18.
Incision deviates from the meridian showed in A. the boundaries of deflective inner incision limit the movement of capsulorhexis forceps as showed in B.
In addition, if the incision is too close to the center of the cornea, the range will be affected, leading to a small and off-center capsulorhexis, as shown by the red arrows in Figure 19.
Incision (red box) is too close to the center of the cornea relative to the limbus (red circle). The irregular AC opening (red arrow) followed the non-ideal incision.
When a viscoelastic agent is injected into the eye, the needle should move inside out, while filling the whole anterior chamber with the viscoelastic to flatten the AC. Otherwise, the path of the capsulorhexis would slide in the direction of the suspensory ligament.
Coordinate your hands, hold the tweezers in your dominant hand and slightly fixate the eyeball to maintain the cornea in the middle. The hand holding the tweezers should be soft and not put pressure on the eyes. Otherwise, the viscoelastic agent can extrude from the incision, resulting in uneven force on the AC and capsular tear. However, too much pressure on the eyeball will cause folds on the cornea, which affects the surgical field of vision.
The process of capsulorhexis is equivalent to drawing a circle. With the eye in position, consider the focal point reflected by the microscope light as the center, and tear the forceps from this point (red circle in Figure 20) to open the AC, with an outward radius of approximately 2.5 mm.
The light spot (red cirlce) would be center of capsule if the position of head and eye maintain level. The radius of capsulorhexis is showed as red arrow.
The limbus can be used as reference to guide the capsulorhexis [20]. For the unexperienced surgeon, the technique is difficult given the narrow diameter of 5–5.5 mm. To aid the process, the marks on forceps in Figure 6 or the marks made on the cornea before initiation of capsulorhexis, can be used for guidance.
The following points should be considered during capsulorhexis:
If excessive pressure is applied by the forceps on the internal incision, the viscoelastic agent could spill out from the incision site. This would leave the anterior chamber partially filled, and the resulting unbalanced forces applied on the AC, will cause capsulorhexis failure.
The trajectory of the capsulorhexis will depend on the balance of two forces exerted during the movement of the forceps by the surgeon, as shown in Figure 21 by red arrows. One is the tearing force along the tangent of the circle, and the other is the pulling force perpendicular to the tangent, towards the center of the circle. Only when the two forces are balanced, will the trajectory be correct and the capsulorhexis completed successfully. If the tearing force along the tangent of the circle is larger, the trajectory of the capsulorhexis would shift laterally, causing a tear. If the pulling force is larger, the trajectory of capsulorhexis would deviate towards the center, resulting in a very small capsulorhexis.
A skilled surgeon can complete the capsulotomy in 3 to 4 attempts, while a beginner should increase the number of attempts and stop before the capsule trajectory cannot be controlled. Extra care should be taken at the joint, and an additional capsulotomy may be added if necessary.
During the movement, avoid lifting the forceps too high, to avoid scratching the corneal endothelium.
The force of capsulorhexis is composed of forces in two direction as showed by red arrows. One is along the tangent of the circle, and the other is towards the center of the circle.
Congenital cataracts in children can be a challenge for surgeons, and should not be attempted by beginners, for several reasons:
The AC of children is more flexible, which makes it difficult to cut with forceps. The discission needle made by 1 ml syringe is the preferred instrument in this case, as shown in Figure 22.
Owing to the increased toughness and flexibility of the AC, the trajectory of capsulorhexis can be difficult to control. The pulling force should be slightly increased to avoid tearing and an oversized opening.
Cataracts with congenital lens abnormality are usually associated with suspensory ligament anomaly, which can be a challenge even for a skilled operator.
A showed the discission needle made by 1 ml syringe. B showed the detail of the needle.
The challenge in this situation is the difficulty of pupil dilation due to iris degeneration caused by uveitis, which has a significant impact on the surgical field of vision. The measures recommended for this situation have been already mentioned in the
In mature cataracts, the capsular membrane is relatively brittle and often accompanied by intumescent lens, as shown in Figure 23.
Color photo of white cataract with intumescent lens and shallow anterior chamber.
Due to the excessive expansion of the surface, the AC often tears-out, forming the Argentinian flag sign. To avoid this, the method of capsule decompression is recommended as follows:
Dye the capsule with Trypan blue to increase visibility
Puncture the central area of the AC with the tip of a needle or forceps as A in Figure 24,with a resulting liquefied cortical efflux (red arrow in B of Figure 24). A blunt needle can then be used to clear this efflux.
Alternatively a discission needle can be used to puncture the AC and then clear the liquefied cortex under the AC directly. Remember to bevel the needle downwards and to maintain the operation in the central area of the AC as C in Figure 24.
When the liquefied cortex is cleared, the central area of the AC will collapse (D in Figure 24). At this point, the AC can be flattened by injection of viscoelastic, and capsulorhexis initiated. The process of capsulorhexis could be then divided into two steps as needed, beginning with a small opening, and the then extending the radius to approximately 2.5 mm.
Decompression of intumescen lens. To pierce the intumescent AC with the tip of capsulorhexis forceps (A). The liquefied cortex spills out (red arrows in B). Discission needle was applied to clear the liquefied cortex beneath AC (C). AC collapse appeared as larger annular reflections (D).
A disease that often causes difficulty with capsulorhexis is exfoliation syndrome, because of two clinical aspects. Firstly, the pupils cannot be dilated past 5 mm, generating an insufficient red reflex for the operator to perform the procedure comfortably. The Malyugin ring, as mentioned in the section on the surgical field of vision, can be used in such situations. However, skilled surgeons often perform a blind capsulorhexis. The trajectory of the capsulorhexis is covered by the iris, as shown in Figure 25.
The pupil is too small to expose the trajectory of the capsulorhexis. Skilled surgeons could perform a blind capsulorhexis.
The other difficulty is extreme relaxation or even rupture of the suspensory ligament, which can be difficult to detect, even with UBM (Ultrasound Biomicroscopy). As the pupil cannot be dilated large enough and therefore the condition of suspensory ligaments around the capsule is not clear. However, the extent of the suspensory ligament relaxation can be judged by the folds caused by the tip of the capsular tweezers when touching the surface of the AC during capsulorhexis as showed in Figure 26.
Suspensory ligament of exfoliation syndrome is extremely flabby which could appear as the radial and wrinkled reflections during capsulorhexis (red arrow).
When such a situation occurs, the surgeon should be careful, and the number of capsulorhexis should be appropriately increased to improve controllability. This method is also suitable for small pupils in diabetic patients and patients with prostatitis treated with Finasteride. Beginners should be aware of this disease and refer the cases to experienced surgeons.
Femtosecond laser capsulorhexisis superior in accuracy and precision compared with manual capsulorhexis, as well as the tensile strength of the capsule opening. An accurate circular, continuous and centered capsulorhexis as achieved by a femtosecond system cannot be achieved manually [21] (Figure 27). Because of these advantages, capsulorhexis assisted by a femtosecond laser is even more critical for premium IOLs. Presently, femtosecond laser surgery is also used in mature, traumatic, and for other cataract patients with suspensory ligament abnormalities [22, 23, 24, 25, 26].
The display interface of femtosecond laser during capsulorhexis. A perfect AC opening (red arrow) was conducted. Lens plane was also displayed by anterior OCT (yellow arrow).
This system greatly reduces the risk of capsulorhexis with due attention to the following recommendations:
The patient needs to be able to cooperate.
The patient’s head and eye position should remain absolutely horizontal, as shown in Figure 5.Excessive upturn and downturn can lead to failure of capsulorhexis. Therefore, patients with head tremor and uncooperative eye position should be cautious. We can refer to the surface of the lens shown in anterior OCT of this system as yellow arrow in Figure 27.
The pupil must be dilated to at least 5 mm.
As cataract surgery enters the refractive age, the criteria “continuous, circular, and centered” have become the basic requirement of the capsulorhexis technique. Therefore, it is extremely important for the surgeon to master the technique of capsulorhexis.
The authors declare no conflict of interest.
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