Atomic Layer Deposition of Nanostructured Materials E-Book

• Herausgeber: Wiley-VCH
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 940

Veröffentlichungsjahr: 2012

Beschreibung

Atomic layer deposition, formerly called atomic layer epitaxy, was developed in the 1970s to meet the needs of producing high-quality, large-area fl at displays with perfect structure and process controllability. Nowadays, creating nanomaterials and producing nanostructures with structural perfection is an important goal for many applications in nanotechnology. As ALD is one of the important techniques which offers good control over the surface structures created, it is more and more in the focus of scientists. The book is structured in such a way to fi t both the need of the expert reader (due to the systematic presentation of the results at the forefront of the technique and their applications) and the ones of students and newcomers to the fi eld (through the first part detailing the basic aspects of the technique).

This book is a must-have for all Materials Scientists, Surface Chemists, Physicists, and Scientists in the Semiconductor Industry.

Leseprobe

Contents

Cover

Related Titles

Title Page

Copyright

Foreword

Preface

Introduction

1 Introduction

2 Basic Features of ALD

3 Short History of the ALD Technology

4 The ALD Community in the Academia and Industry

5 Conclusions

References

List of Contributors

Part One: Introduction to ALD

Chapter 1: Theoretical Modeling of ALD Processes

1.1 Introduction

1.2 Overview of Atomistic Simulations

1.3 Calculation of Properties Using Quantum Simulations

1.4 Prediction of ALD Chemical Mechanisms

1.5 Example of a Calculated ALD Mechanism: ALD of Al2O3 Using TMA and Water

References

Chapter 2: Step Coverage in ALD

2.1 Introduction

2.2 Growth Techniques

2.3 Step Coverage Models in ALD

2.4 Experimental Verifications of Step Coverage Models

2.5 Summary

References

Chapter 3: Precursors for ALD Processes

3.1 Introduction

3.2 General Requirements for ALD Precursors

3.3 Metallic Precursors for ALD

3.4 Nonmetal Precursors for ALD

3.5 Conclusions

References

Chapter 4: Sol–Gel Chemistry and Atomic Layer Deposition

4.1 Aqueous and Nonaqueous Sol–Gel in Solution

4.2 Sol–Gel and ALD: An Overview

4.3 Mechanistic and In Situ Studies

References

Chapter 5: Molecular Layer Deposition of Hybrid Organic–Inorganic Films

5.1 Introduction

5.2 General Issues for MLD of Hybrid Organic–Inorganic Films

5.3 MLD Using Trimethylaluminum and Ethylene Glycol in an AB Process

5.4 Expansion to an ABC Process Using Heterobifunctional and Ring-Opening Precursors

5.5 Use of a Homotrifunctional Precursor to Promote Cross-Linking in an AB Process

5.6 Use of a Heterobifunctional Precursor in an ABC Process

5.7 MLD of Hybrid Alumina–Siloxane Films Using an ABCD Process

5.8 Future Prospects for MLD of Hybrid Organic–Inorganic Films

Acknowledgments

References

Chapter 6: Low-Temperature Atomic Layer Deposition

6.1 Introduction

6.2 Challenges of LT-ALD

6.3 Materials and Processes

6.4 Toward Novel LT-ALD Processes

6.5 Thin Film Gas Diffusion Barriers

6.6 Encapsulation of Organic Electronics

6.7 Conclusions

Acknowledgments

References

Chapter 7: Plasma Atomic Layer Deposition

7.1 Introduction

7.2 Plasma Basics

7.3 Plasma ALD Configurations

7.4 Merits of Plasma ALD

7.5 Challenges for Plasma ALD

7.6 Concluding Remarks and Outlook

Acknowledgments

References

Part Two: Nanostructures by ALD

Chapter 8: Atomic Layer Deposition for Microelectronic Applications

8.1 Introduction

8.2 ALD Layers for Memory Devices

8.3 ALD for Logic Devices

8.4 Concluding Remarks

Acknowledgments

References

Chapter 9: Nanopatterning by Area-Selective Atomic Layer Deposition

9.1 Concept of Area-Selective Atomic Layer Deposition

9.2 Change of Surface Properties

9.3 Patterning

9.4 Applications of AS-ALD

9.5 Current Challenges

Acknowledgment

References

Chapter 10: Coatings on High Aspect Ratio Structures

10.1 Introduction

10.2 Models and Analysis

10.3 Characterization Methods for ALD Coatings in High Aspect Ratio Structures

10.4 Examples of ALD in High Aspect Ratio Structures

10.5 Nonideal Behavior during ALD in High Aspect Ratios

10.6 Conclusions and Future Outlook

References

Chapter 11: Coatings of Nanoparticles and Nanowires

11.1 ALD on Nanoparticles

11.2 Vapor–Liquid–Solid Growth of Nanowires by ALD

11.3 Atomic Layer Epitaxy on Nanowires

11.4 ALD on Semiconductor NWs for Surface Passivation

11.5 ALD-Assisted Formation of Nanopeapods

11.6 Photocorrosion of Semiconductor Nanowires Capped by ALD Shell

11.7 Interface Reaction of Nanowires with ALD Shell

11.8 ALD ZnO on NWs/Tubes as Seed Layer for Growth of Hyperbranch

11.9 Conclusions

References

Chapter 12: Atomic Layer Deposition on Soft Materials

12.1 Introduction

12.2 ALD on Polymers for Passivation, Encapsulation, and Surface Modification

12.3 ALD for Bulk Modification of Natural and Synthetic Polymers and Molecules

12.4 ALD for Polymer Sacrificial Templating: Membranes, Fibers, and Biological and Optical Structures

12.5 ALD Nucleation on Patterned and Planar SAMs and Surface Oligomers

12.6 Reactions during Al2O3 ALD on Representative Polymer Materials

12.7 Summary

Acknowledgment

References

Chapter 13: Application of ALD to Biomaterials and Biocompatible Coatings

13.1 Application of ALD to Biomaterials

13.2 Biocompatible Coatings

13.3 Summary

Acknowledgments

References

Chapter 14: Coating of Carbon Nanotubes

14.1 Introduction

14.2 Purification and Surface Functionalization of Carbon Nanotubes

14.3 Decoration/Coating of Carbon Nanotubes by Solution Routes

14.4 Decoration/Coating of Carbon Nanotubes by Gas-Phase Techniques

14.5 Atomic Layer Deposition on Carbon Nanotubes

14.6 Coating of Large Quantity of CNTs by ALD

14.7 ALD Coating of Other sp2-Bonded Carbon Materials

14.8 Conclusions

References

Chapter 15: Inverse Opal Photonics

15.1 Introduction and Background

15.2 Properties of Three-Dimensional Photonic Band Structures

15.3 Large-Pore and Non-Close-Packed Inverse Opals

15.4 Experimental Studies

15.5 Tunable PC Structures

15.6 Summary

Acknowledgments

References

Chapter 16: Nanolaminates

16.1 Introduction

16.2 Optical Applications

16.3 Thin Film Encapsulation

16.4 Applications in Electronics

16.5 Copper Electroplating Applications

16.6 Solid Oxide Fuel Cells

16.7 Complex Nanostructures

16.8 Summary

Acknowledgments

References

Chapter 17: Challenges in Atomic Layer Deposition

17.1 Introduction

17.2 Metals

17.3 Nonmetal Elements

17.4 Binary Compounds

17.5 Ternary and Quaternary Compounds

17.6 Nucleation

17.7 Conclusions

References

Index

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Foreword

Atomic layer deposition (ALD) is a relatively new and low-temperature growth method capable of depositing a variety of thin films on virtually any substrate. Although it is a vapor-based technique like chemical vapor deposition (CVD), there are two main differences that make it a particularly powerful method for very thin and conformal film growth. First, precursor molecules react only with the surface (not with themselves) under deposition temperatures. Second, growth is achieved by sequential introduction of typically two precursors, separated by a thorough inert gas purge, so that different precursors are not present together in the gas phase. These characteristics are in fact responsible for generating much interest from researchers? belonging to scientific areas that had thus far been considered unrelated, thus creating a stimulating interdisciplinary environment. These are gas-phase chemistry, surface science, solid-state chemistry, kinetics of thin film growth, and engineering of gas flow reactors.

The community that is responsible for the development of ALD came from organometallic chemists. They were responsible for identifying or synthesizing precursors capable of reacting at moderate temperatures with specific surface groups while remaining stable in the gas phase (no self-reaction), which is key for the ALD process. The challenge for this community has been to produce complementary precursors that react with complete ligand exchange at moderate temperatures, essential to grow pure films. Incomplete reactions lead to the incorporation of carbon or other impurities into the films.

Surface scientists have quickly been drawn to ALD because the process is based on surface reactions. As is now recognized, surface processes can be substantially different from gas-phase chemistry because the surface structure and steric interactions dramatically affect chemical reactions at surfaces. In situ characterization is therefore necessary to verify choices based on gas-phase chemistry and to quantify surface reactivity with precursors. Furthermore, it has now been shown in several instances that the substrate can also play an active role. Specifically, at typical process temperatures reactions with the substrate can take place, such as formation of SiO2 during deposition of metal oxides on oxide-free Si substrates. Therefore, much thought is being given to developing diffusion barriers to prevent oxidation of and/or ion penetration into the substrate, including surface functionalization and even self-assembled monolayers. Given the diversity of approaches and complexity of the mechanisms, the whole arsenal of surface techniques has been brought to bear: vibrational spectroscopy (infrared, Raman), electron spectroscopy (X-ray photoelectron, photoemission, Auger), ion scattering (Rutherford backscattering, medium- and low-energy ion spectroscopies), imaging (transmission electron microscopy, atomic and in some cases scanning tunneling spectroscopies), mass spectroscopy, and quartz crystal mass analysis. Much needed fundamental work continues to be performed as new precursors and systems (e.g., metal films) are considered.

Solid-state chemists and modelers are also engaged in ALD processes because the simple picture of alternative deposition of element A and element B to form an amorphous AxBy film is not strictly correct. Atoms A and B require substantial rearrangement and rebonding as their ligands are removed, which is not always consistent with layer-by-layer growth and is certainly more complicated than the simple ALD models typically presented. Kinetics play a central role. A striking example of complex, kinetically controlled surface mechanism is the agglomeration of metal atoms upon thin metal film deposition, making it virtually impossible to initiate a uniform thin metal film growth. A combination of measurements and advanced modeling is needed to develop a mechanistic understanding of the processes with some predictive power.

Chemical engineers have played an important role in addressing the gas flow requirements that are much more stringent in ALD than in any other vapor-phase growth method. Indeed, the complete removal of one precursor gas before the other is introduced into the reactor requires that flow patterns are optimized such that the purge gas can efficiently remove all traces of the precursor gas. For industrial applications, uniform supply of precursor gas over large wafers also demands careful optimization of precursor delivery rates and flow.

The chapters in the first part of this book involve authors from this wide community and address many of the issues outlined above, including the growth of organic thin films. The focus of the book, however, is related to the extraordinarily diverse ALD-based applications that have emerged over the past few years. While the initial work was motivated by metal oxide film deposition for microelectronic applications (ALD was initially adopted by industry for the growth of high-k dielectrics, for instance), the ALD technique has begun to contribute to a wide range of systems. It is now used for sensor fabrication, fiber coating, and biomedical device fabrication, with a focus on highly structured material and nanomaterials. The second part of the book brings together a diversity of topics that underscore the value and importance of the ALD technique and foreshadows its growing popularity.

With such an explosion of applications and a growing community using ALD, it is clear that fundamental studies of ALD processes are needed to provide the necessary understanding for progress and success. This book is therefore a motivation for researchers in other fields to bring their discipline and expertise to critically evaluate and address the complex issues arising in all these applications. It constitutes an excellent reference book for students and young scientists interested in ALD, and its applications and challenges. Much remains to be done, well beyond precursor development, to fully implement this powerful technique for the current and future applications.

Dallas, Texas

January 2011

Prof. Yves J. Chabal

Preface

Atomic layer deposition (ALD) is a coating technology that in the past two decades rapidly developed from a niche technology to an established method. The method itself is not too difficult to understand and apply. The basic requirements are a vacuum chamber, at least two reactive precursors, and valves for alternate dosing of the precursors, since the different precursors must never be present in the chamber at the same time. For most of the processes, one metal-containing chemical is used as metal source and subsequently reacted with another chemical, which is the source of, for example, oxygen, nitrogen, sulfur, and so on. The chemistry is normally very simple and often shows hydrolysis, oxidation, reduction, or an organic coupling reaction in the particular case of molecular layer deposition (MLD). There are some restrictions for the chemicals: One has to ensure that the precursors have a reasonably high vapor pressure in order to allow saturation of the chamber volume upon dosing and a good thermal stability to avoid decomposition prior to the next step. A further requirement is that the precursor must chemisorb onto the substrate to be coated. Once these preconditions are fulfilled, the coating process, consisting of alternating pulse and purge steps for each precursor, can be started. The timely separation of the precursors is necessary in order to achieve a saturation (self-termination) of the substrate surface with the precursor and thus to enable a very precise thickness control, which is normally on the angstrom scale. Since ALD is not a line-of-sight coating technology, even complicated 3D structures with not easily accessible surfaces (e.g., trenches, grooves, pores, aerogels, etc.) can be uniformly and conformally? coated.

The chemistry used for ALD is often derived from the chemical approaches used for chemical vapor deposition (CVD) and one may argue that it is a modified form of CVD. This comparison is indeed correct as demonstrated from the fact that all ALD precursors can be used for CVD; however, not necessarily vice versa. On the other hand, (i) the timely separation of the precursors and the resulting film thickness control with the number of cycles instead of processing time, (ii) the often much higher compactness of the deposited films compared to CVD, and (iii) the exceptionally good step coverage make ALD an outstanding subset of CVD that surely deserves particular attention as an individual coating technology.

The rapid increase of popularity of ALD in the past two decades is clearly demonstrated by the number of articles published every year (Figure P.1). An almost linear increase is observed, reaching a maximum of around 900 articles published in 2010. Although the number of articles per year is around five times larger, a similar trend can be observed for CVD. The only difference is that since 2004 the number of papers has remained somehow constant. The development of publications related to ALD promises a bright future for research and development.

Figure P.1 Number of articles per year published on ALD (gray bars) and CVD divided by five (black bars).

Source: Web of Science accessed on December 20, 2010.

The book is divided in two parts: the first part (Chapters 1–7) deals with all the basic aspects of the technique, while the second part focuses on ALD-based nanostructured materials and their fields of application (Chapters 8–17).

The introductory chapter, written by J. Niinistö and L. Niinistö is an introduction to ALD and its development since its discovery in 1976. The following two chapters describe theoretical modeling of ALD processes (Chapter 1) and step coverage (Chapter 2). Chapter 3 describes the precursors used in ALD and their requirements. Chapter 4 describes the soft chemistry routes to oxides and the comparison of the chemistry taking place in ALD and in solution. Chapter 5 introduces molecular layer deposition, which is equivalent to ALD for the deposition of hybrid organic–inorganicthin films. The features and the relevance of low-temperature processes are discussed in Chapter 6. Chapter 7 describes the plasma-enhanced ALD.

The second part of the book (Chapter 8) starts with the applications of ALD in microelectronics; these are without any doubt the reasons why ALD became so popular nowadays. Chapter 9 introduces area-selective ALD and shows how it can be used for the formation of nanopatterns. Chapters 10, 11, and 14 describe the coatings of high aspect ratio nanostructures, nanoparticles and nanowires, and carbon nanotubes. Chapters 12 and 13 describe the coatings of soft materials such as polymers and biological materials. Chapter 15 describes the coating of nanostructures for optical applications such as opals. Chapter 16 describes the fabrication and properties of multilayers or nanolaminates. Finally, Chapter 17 discusses the challenges ALD is currently facing and possible novel directions and applications.

The book is structured in such a way to fit both the need of the expert reader (due to the systematic presentation of the results at the forefront of the technique and their applications) and the ones of students and newcomers to the field (through the first part detailing the basic aspects of the technique).

Halle, Germany

December 21, 2010

Dr. Mato Knez

Prof. Dr. Nicola Pinna

Introduction

Basic Features and Historical Development of Atomic Layer Deposition

Jaakko Niinistö and Lauri Niinistö

1 Introduction

Atomic layer deposition (ALD) has gained wide interest as an advanced thin film growth technique for various applications in modern technology. The strength of the method relies on its unique growth process where alternate, self-limiting surface reactions of the precursors, separated by inert gas purging, form a growth cycle whereupon thin, up to one atomic layer of material is grown. Precise thickness control can be achieved by repeating the growth cycle a desired number of times. The unique growth mode leads to perfectly conformal films [1--4].

The ALD technology was developed and patented almost 40 years ago in Finland by Suntola and coworkers [5]. The goal in the early development of the ALD technology was strictly application-oriented, namely, the need to develop flat panel displays for mass production. However, the breakthrough of the technology was driven by the semiconductor industry some 10 years ago and industrial applications for ALD are now emerging.

This chapter describes briefly the basic principles of the ALD method, including the benefits and limitations. As it is quite interesting to understand how the ALD technology has evolved over the years, a short historical perspective to ALD technology is also given. In addition, we try to emphasize the development of the ALD community, and novel processes and applications studied by a large number of research groups in industry and academia. Especially, answer is sought for the question: Which research areas of ALD were in main focus in the past and which seem to be emerging in the future?

2 Basic Features of ALD

ALD processes and their possible as well as industrial applications have been reviewed numerous times in the past and even very extensive reviews have been published. [1, 6, 7] ALD is a special variant of the well-known chemical vapor deposition (CVD) method. However, the differences between ALD and CVD are obvious. Whereas in CVD the precursors react at the same time on the surface or in the gas phase and precursors can decompose, in ALD the highly reactive precursors react separately by saturating surface reactions without self-decomposition. The method is surface controlled rather than process parameter controlled as in the case of CVD. In ALD the growth process proceeds in a cyclic manner and can be described as follows (exemplified with Figure 1).

Figure 1 Sketch of a typical ALD growth cycle leading to ZrO2 from ZrCl4 and H2O precursors. Reproduced with permission from ref. [3].

An ideal ALD growth cycle is characterized by

exposure of substrate surface to pulse of the first gaseous precursor;chemisorption of the first precursor onto the substrate;inert gas purge;introduction of the second precursor;surface reaction to produce the thin film;inert gas purge to remove gaseous reaction by-products.

In order to achieve a surface saturative ALD-type process, the growth rate has to be independent of the precursor dose provided that the dose is sufficiently large so that all the available surface sites have been occupied (Figure 2a). In other words, the precursor decomposition leading to a CVD-type growth mode should be avoided.

Often, but not always, a region with a constant deposition rate, also known as ALD window, is observed [2, 8, 9]. The ALD window certainly is not a requirement for an ALD-type growth mode, but it is a desirable feature that leads to the reproducibility of the film growth. Especially, if a ternary material is to be deposited, overlapping ALD windows of the constituent binary processes offer a good starting point for the development of a ternary process. The observed growth rates vs. temperature in ALD processes are shown in Figure 2b.

2.1 Limitations and Benefits of ALD

Compared to CVD, the deposition rate in ALD is rather low: An ALD cycle requires some time, typically few seconds, and the resulting thickness after one cycle is ideally one monolayer but in practice, due to steric effects, only a distinct factor of a monolayer. On the other hand, in modern technology the required film thickness is often from a couple of nanometers up to few tens of nanometers, thus the low growth rate is not seen as severe problem any more. In addition, large batch processing is a rather straightforward way to increase throughput [10].

Another limitation often considered is the limited materials selection, that is, the available materials that can be grown effectively by ALD. Several technologically interesting materials such as Si, Ge, Cu, multicomponent oxide superconductors, and many transition metals are lacking effective and production-worthy processes. However, the list of available processes [1, 6] is expanding continuously and process development through precursor chemistry is increasingly studied by many research groups, in academia and the chemical industry. In addition, with plasma processing the materials selection is likely to be increased [11].

During the recent years, many research groups have been studying growth characteristics during the early stages of growth in order to understand the growth mechanism and to better control the growth process (Figure 2). In many cases, poor nucleation has been observed that can lead to rough surfaces and in the case of many metals a discontinuous film when the thickness is only couple of nanometers. Also, in the case of high-k dielectric growth on bare silicon can suffer from inhibited growth and it can be difficult to obtain a sharp interface without a mixed interfacial layer between the material and the Si substrate [12, 13]. Such process-specific deviations are not characteristic to the method itself, but rather the precursor chemistry should be considered as one of the reasons. Other deviations related to precursor chemistry include reactive by-products that could etch the growing film or readsorb on the surface. Even small partial decomposition of the precursor can change the growth mechanism substantially. However, it should be noted that some applications can tolerate some of these deviations and “an ideal ALD growth” is not always needed.

Figure 2 Growth per cycle as a function of the pulse time (a) and temperature (b) for different growth modes.

The list of advantages of ALD is long. The characteristic feature of ALD, the self-limiting growth mode, leads to a precise control of the film thickness, a large area capability, and uniformity also in batch processes as well as to a good reproducibility. The excellent conformality is the main feature that distinguishes ALD from other thin film deposition methods and possible applications related to that are numerous. Separate dosing of highly reactive precursors allows production of high-quality materials (e.g., pinhole-free materials) at relatively low temperatures. The growth temperatures can often be reduced using, for example, plasma-generated radicals. Further benefits include the possibility to produce multilayer structures and the straightforward doping.

2.2 The Impact of Precursor Chemistry

As noted previously, a successful ALD process relies on the underlying chemistry. The alternately introduced precursors undergo saturative surface reactions. Thermal decomposition of the applied precursor destroys this self-limiting growth mode and thus the thermal stability of the precursor is the key issue in the ALD process. Naturally, being a vapor-phase method, ALD requires sufficient volatility of the precursors. Fast and complete reactions are mandatory; first of all, precursors must adsorb or react with the surface sites and these intermediates must be reactive toward the other precursor, for example, H2O in the case of many oxide processes. To maintain film uniformity, precursor molecules or reaction by-products should not etch the growing film.

In general, volatile metal-containing ALD precursors can be divided into five categories: elements (only Zn and Cd), halides, oxygen-coordinated precursors (alkoxides and beta-diketonates), true organometallics (carbon-coordinated precursors, such as alkyls and cyclopentadienyls), and nitrogen-coordinated precursors (alkylamides, silylamides, and acetamidinates). For nonmetal precursors, hydrides are most widely used. Many successful oxide processes apply water as an oxygen source. Usually O2 is found too inert in thermal ALD but it is used as a radical source in plasma-enhanced ALD and, for example, in growth of noble metals. Ozone has gained increasing interest as a powerful oxygen source and some industrial oxide processes rely on the use of ozone. The other most commonly used nonmetal precursors include H2 and NH3, also as a radical source. For sulfide film growth, H2S should be mentioned.

As the precursor chemistry is extremely important factor in ALD processing, more detailed description on different aspects is given elsewhere in this book.

3 Short History of the ALD Technology

The purpose of the development of ALD technology in the 1970s by T. Suntola and coworkers was to meet the needs of producing improved thin films and structures based thereupon for thin film electroluminescent (TFEL) flat panel displays. The first Finnish patent application was filed in November 1974 and the first US patent was granted in 1977 [5]. The name of the technology then was named by T. Suntola as atomic layer epitaxy (ALE). The word epitaxy can be translated as “on arrangement” and thus Dr. Suntola used this broad definition even though usually ALD is used to grow nonepitaxial films. Until the end of the twentieth century, the method was mostly called ALE, which was not universally accepted because mostly polycrystalline and amorphous films are deposited rather than single crystalline growth on single crystalline substrate. Other names were used as well, for example, atomic layer CVD. For the past 15 years, the term ALD became generally accepted.

The above-mentioned patents showed the basis of reactor and process technology of ALD. It should be noted that in Russia, V. Aleskowski and others had published papers in Russian language about “molecular layering,” describing alternate surface reactions characteristic to ALD. This work has been reviewed extensively by R. Puurunen earlier [6]. Here we focus on the development of ALD technology, especially reactor and process development for various applications.

3.1 ALD Reactor Development

The strength of T. Suntola's work inventing the ALD technology is clearly based on the development of feasible reactors for the processing. The aim of the first patent by Suntola and Antson was to describe a method for producing compound thin films using pure elements as reactants. The reactor configuration is shown in Fig. 3. In a rotating substrate reactor, the substrates are moved from one precursor flux to another and thus high-speed valving of pulses is not needed. This kind of concept is getting more interest again when roll-to-roll ALD or spatial ALD reactors are being developed.

Usually ALD reactors are based on valving the precursors and purges into the reaction chamber. Pulsing of the precursors separately, especially if the precursor has high vapor pressure, is simple with pneumatic or solenoid valves. Thus, it is possible to use CVD reactors as ALD reactors and many ALD reactor configurations are modified pulsed CVD reactors. The development of an inert gas valving system in early 1980s can be considered as a breakthrough for introducing low-pressure precursors. This invention led to the introduction of first commercial ALD research-scale reactors few years later. The reaction chamber and thus ALD reactors can be roughly divided into cross-flow (traveling-wave) or perpendicular-flow (e.g., showerhead) type reactors. The benefit of the cross-flow reactor is the higher throughput, and both precursor pulsing and inert gas purging are fast. However, the film thickness uniformity can be difficult to control, as CVD-type growth components may be present. Thus, careful optimization of the gas flow dynamics is needed. Batch reactors were introduced in the 1990s to overcome the major limitation of ALD technology, the low throughput. Currently, large batch reactors are used for various applications in volume production [14]. Carefully optimizing the configuration with multiple flow channels, it is possible even to reach nearly as fast cycle times as in single-wafer systems.

Figure 3 An early reactor configuration. Courtesy of Tuomo Suntola.

As the plasma became popular giving additional energy in CVD processing, the first reports of plasma-enhanced ALD became available in the late 1990s [15]. Many reactor manufacturers are introducing their PEALD reactors into the market. Using remote hydrogen plasma, for example, can overcome some problems related to ALD of transition metals. It should be noted that the PEALD techniques can be roughly divided to two categories, direct and remote PEALD. Among those, remote PEALD has gained wider interest, as mainly radicals are reaching the growing film during plasma exposure and ion bombardment can be avoided.

3.2 The Early Years – ALE

As mentioned earlier, TFEL displays were the key issue when inventing ALD technology. The research in ALE (the definition used originally) was focused on developing these devices and patents were mainly applied rather than research articles published. ALD showed its significance as a method producing dense and pinhole-free films for TFEL displays, where insulator–luminescent layer–insulator films should withstand high electric fields. The ALD grown layers for this rather thick (even >1 µm) structure were Al2O3 or AlxTiyO, ZnS:Mn, and Al2O3 [1]. The commercial ALD-based production for TFEL displays started already in the early 1980s [16]. In 1984, the first scientific meeting, First Symposium on Atomic Layer Epitaxy, was organized in Finland (Figure 4 a). The contributed talks concentrated mainly on TFEL displays and only half a dozen groups participated in the meeting [17].

Figure 4 First pages of the book of the abstracts of the first ALE symposium held in Espoo in 1984 (a) and the first international symposium on ALE held in Espoo in 1990 (b).

At the same time, besides the ALE research related to EL displays, interest toward polycrystalline II–VI semiconductors, such as CdTe, also rose.

3.3 Novel Method Still Unknown – ALE/ALD in the 1980s and 1990s

The epitaxial growth of III–V and II–VI compounds began to gain interest internationally from mid-1980s until mid-1990s. The research was extremely active in this area in Japan and the United States. The First International Symposium on ALE was arranged in summer 1990 in Finland (Figure 4 b). The majority of contributed papers focused on III–V compounds, especially the growth of epitaxial GaAs [18]. In addition, during that time one major research focus was the deposition of Si and Ge. Superconductor research was also of interest.

At the same time, research efforts focusing on polycrystalline and amorphous oxides increased. This research was extremely important in the later stage, when microelectronics industry realized the potential of ALD. In a review published in 1996, growth processes for a dozen of binary oxide materials such as HfO2 and TiO2 were listed [19]. In addition, surface chemistry of ALD processes began to gain interest [20]. However, in the 1990s the full recognition for ALD was still to be seen and the interest was growing rather slowly.

3.4 Breakthrough for ALD – Microelectronics

The final breakthrough for the ALD technology can be timed to approximately the beginning of the twenty-first century. The reason for the increase in interest was the continuous scaling of microelectronic devices. The major semiconductor companies started their research already in the end of the 1990s and soon more and more research groups in industry and academia established ALD research in their laboratories. The expanding ALD community is discussed in more detail in Section 4.

The first microelectronic application was related to memories, to be more specific, an ALD Al2O3 insulating layer in DRAM capacitors [14]. The need for rather thin conformal coating on high aspect ratio structures is perfectly suited for ALD. The technology is used in high-volume production, current state-of-the-art ALD material as DRAM high-k dielectric materials being ZrO2-based [21, 22]. Future materials include SrTiO3 in a metal–insulator–metal (MIM) capacitor structure and ALD is the method of choice for conformal coatings with such materials.

However, largest publicity around ALD was reached somewhat later, when the semiconductor company Intel announced adaptation of ALD in manufacturing HfO2-based high-k gate oxide in CMOS transistors [23]. The research efforts for this application started more than 10 years earlier and the most likely ALD process for this gate oxide process was published in 1994 [24]. Implementing novel manufacturing technology, such as ALD, in microelectronics industry took time, but it seems that now novel ALD processes can be adapted into production somewhat faster.

Due to the obvious need for ALD processed materials, a large number of ALD journal articles were related to those applications. High-k oxides, especially HfO2, seemed to dominate the field in the beginning of the 2000s. Wide research efforts have been put not only on oxides, but also on metals for microelectronic applications. Many novel processes were developed, such as Ru processes. Copper for interconnects was also studied intensively.

In spite of the numerous research groups studying ALD for microelectronic applications, there are still many goals to be achieved. Better processes for future materials need to be developed and integration problems need to be solved. For example, SrTiO3 for DRAM applications is extensively studied, and whether the industry will use ALD SrTiO3 in high-volume production is to be seen. It should be noted that not only volatile memories but also nonvolatile memories offer a lot of possibilities for ALD to solve many problems, phase-change memories with ALD GST being a good example.

3.5 Emerging Applications for the Future

As microelectronic applications dominated the ALD technology field in the past decade, the current research efforts are going into the direction of much wider application areas. Nanotechnology applications seem to be well suited for ALD and more and more research papers are covering these topics. Photovoltaics is certainly an emerging field for ALD. Also, energy-related applications are research fields where ALD is applied. Other possible breakthrough fields for ALD include MEMS, biotechnological applications, and applications related to growth on nanotubes and graphene. Various interesting topics are covered later in this book. It seems that ALD has become a mainstream technology, and the possible application areas are very broad.

4 The ALD Community in the Academia and Industry

As mentioned several times earlier, the ALD community, groups concentrating on various ALD research topics, precursor and reactor manufacturers, and industrial “end users” of ALD technology, has increased dramatically during the past 15 years. In the early days of ALD, only few groups were more or less active. For example, the first ALD patent was applied in 1974 and the first research paper was published in 1980 [25]. In spite of the small number of groups in the field, the first ALD symposium was held in 1984 (Figure 4 a). This national symposium in Finland mainly consisted of talks related to EL displays. As mentioned, the interest rose slowly, but already in 1990 the first international conference was held in Finland [26] and it acted as a start for first series of ALD conferences. This international symposium series was held four times, latest in 1996 [27]. At the same time, longest lasting conference series was established, first as a small symposium between Finnish and Estonian ALD groups and then expanding as a Baltic ALD conference series, latest organized in Germany in 2010. The international ALD conference series was established in 2001, and the first international conference on ALD was held in Monterey, CA [28], and it gathers the expanding ALD community every summer. In addition, many large international materials science conferences do have special ALD sessions annually.

A review article from the year 1998 shows the number of ALD groups at that time more or less actively using ALD and publishing ALD-related papers or patents [29]. Out of those groups (about 40), which were mainly concentrated in Finland, the United States, and Japan, some pioneering groups are still strongly studying ALD. However, from the end of the 1990s, the number of groups and ALD reactors in use has increased at such a pace that it would be impossible to gather such data. Hundreds of ALD reactors have been distributed and groups working in industry and academia are constantly expanding. This can be easily seen in Figure 5, where the number of scientific papers per year is plotted. From the early years, where only couple of ALD publications appeared, number approaching 1000 publications is the current status. For patents and patent applications, the increase has been even more intense during the recent years.

Figure 5 Number of articles per year published on ALD (keywords: “atomic layer deposition” or “atomic layer epitaxy”). Source Web of Science accessed on 2011.

5 Conclusions

As a method for producing high-quality thin films, ALD has in the recent 35 years increased to a mainstream technology. Its future seems bright, and more and more materials scientists are using this method for numerous applications. Its importance for modern technology has been proved, and the number of industrial ALD applications is constantly increasing. However, there are many topics where ALD need to be further improved. Especially, the development of novel ALD processes through precursor chemistry is important. In addition, the development of ALD reactor technology should provide more and more advantages in terms of productivity for ALD compared to many other film deposition techniques.

References

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10. Granneman, E., Fischer, P., Pierreux, D., Terhorst, H., and Zagwijn, P. (2007) Batch ALD: Characteristics, comparison with single wafer ALD, and examples, Surf. Coat. Technol., 201, 8899.

11. Kessels, W.M.M., Heil, S.B.S., Langereis, E., van Hemmen, J.L., Knoops, H.C.M., Keuning, W., and van de Sanden, M.C.M. (2007) Opportunities for plasma-assisted atomic layer deposition, ECS Trans., 3, 183–190.

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14. Ritala, M. and Niinistö J. (2009) Industrial applications of atomic layer deposition, ECS Transactions, 25 (8), 641–652.

15. Sherman, A., Atomic layer deposition for nanotechnology (2008) Ivoryton Press, Ivoryton, USA, 239 p.

16. Pakkala, A., AVS 4th International Conference on Atomic Layer Deposition, Helsinki, Finland, 2004, presentation available on CD-ROM.

17. Paananen, R. (Ed.) Proceedings of the First Symposium on Atomic Layer Epitaxy, VTT, Espoo, 1984, 46 p.

18. Niinistö L., (Ed.): Proceedings of the First International Symposium on Atomic Layer Epitaxy, Acta Chem. Scand., Helsinki, 1990, 209 p.

19. Niinistö, L., Ritala, M., and Leskelä, M. (1996) Synthesis of oxide thin films and overlayers by atomic layer epitaxy for advanced applications, Mater. Sci. Eng. B, 41, 23–29.

20. George, S.M., Ott, A.W., and Klaus, J.W. (1996) Surface chemistry for atomic layer growth, J. Phys. Chem., 100, 13121–13131.

21. Kuesters, K. H., et al. (2009) New materials in memory development sub 50 nm: trends in flsh and DRAM, Adv. Eng. Mater., 11, 241–248.

22. Niinistö, J., Kukli, K., Heikkilä, M., Ritala, M., and Leskelä, M. (2009) Atomic layer deposition of high-k oxides of the group 4 metals for memory applications, Adv. Eng. Mater., 11, 225–234.

23. Bohr, M. T., Chan, R. S., Ghani, T., and Mistry, K. (2007) The high-k solution, IEEE Spectrum, 44 (10), 29–35.

24. Ritala, M., Leskelä, M., Niinistö, L., Prohaska, T., Friedbacher, G., and Grasserbauer, M. (1994) Develoment of crystallinity and morphology in hafnium dioxide thin films grown by atomic layer epitaxy, Thin Solid Films, 250, 72.

25. Ahonen, M, Pessa, M., and Suntola, T. (1980) Thin Solid Films, 65, 301.

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List of Contributors

Aziz I. Abdulagatov University of Colorado Departments of Chemistry and Biochemistry and Chemical and Biological Engineering Boulder, CO 80309-0215 USA

Stacey F. Bent Stanford University Department of Chemical Engineering 381 North-South Mall Stanford, CA 94305 USA

Guylhaine Clavel University of Aveiro Department of Chemistry and CICECO Campus Universitario de Santiago 3810-193 Aveiro Portugal

Jeffrey W. Elam Argonne National Laboratory Communications & Public Affairs 9700 S. Cass Avenue Argonne, IL 60439 USA

Hong Jin Fan Nanyang Technological University School of Physical & Mathematical Sciences Division of Physics and Applied Physics 21 Nanyang Link Singapore 637371 Singapore

Davy P. Gaillot University of Lille 1 (USTL Lille 1) TELICE Group IEMN/UMR 8520, Bâtiment P3 59655 Villeneuve d'Ascq Cedex France

Steven M. George University of Colorado Departments of Chemistry and Biochemistry and Chemical and Biological Engineering Boulder, CO 80309-0215 USA

Zachary M. Gibbs University of Colorado Departments of Chemistry and Biochemistry and Chemical and Biological Engineering Boulder, CO 80309-0215 USA

Robert A. Hall University of Colorado Departments of Chemistry and Biochemistry and Chemical and Biological Engineering Boulder, CO 80309-0215 USA

Cheol Seong Hwang Seoul National University Department of Materials Science and Engineering and Inter-university Semiconductor Research Center 151-744 Seoul Korea

Erwin Kessels Eindhoven University of Technology Department of Applied Physics 5600 MB Eindhoven The Netherlands

Mato Knez Max-Planck-Institute of Microstructure Physics Weinberg 2 06120 Halle Germany

Byoung H. Lee University of Colorado Departments of Chemistry and Biochemistry and Chemical and Biological Engineering Boulder, CO 80309-0215 USA

Han-Bo-Ram Lee Stanford University Department of Chemical Engineering 381 North-South Mall Stanford, CA 94305 USA

Younghee Lee University of Colorado Departments of Chemistry and Biochemistry and Chemical and Biological Engineering Boulder, CO 80309-0215 USA

Markku Leskelä University of Helsinki Department of Chemistry 00014 Helsinki Finland

Catherine Marichy University of Aveiro Department of Chemistry and CICECO Campus Universitario de Santiago 3810-193 Aveiro Portugal

Jens Meyer Princeton University Department of Electrical Engineering Olden Street Princeton, NJ 08544 USA

Charles B. Musgrave University of Colorado at Boulder Department of Chemical and Biological Engineering Boulder, CO USA

Kornelius Nielsch University of Hamburg Institute of Applied Physics Jungiusstrasse 11 20355 Hamburg Germany

Jaakko Niinistö University of Helsinki Department of Chemistry 00014 Helsinki Finland

Lauri Niinistö Aalto University School of Chemical Technology Laboratory of Inorganic Chemistry 02015 Espoo Finland and Picosun Oy Tietotie 3 02150 Espoo Finland

Sovan Kumar Panda School of Advanced Materials Engineering and Center for Materials and Processes of Self-Assembly Kookmin University Jeongneung-Gil 77, Seoul, 136702 South Korea

Gregory N. Parsons North Carolina State University Department of Chemical and Biomolecular Engineering Raleigh, NC 27695 USA

Nicola Pinna University of Aveiro Department of Chemistry and CICECO Campus Universitario de Santiago 3810-193 Aveiro Portugal and Seoul National University (SNU) School of Chemical and Biological Engineering College of Engineering World Class University (WCU) Program of Chemical Convergence for Energy & Environment (C2E2) 151-744 Seoul Korea

Stephen Potts Eindhoven University of Technology Department of Applied Physics 5600 MB Eindhoven The Netherlands

Harald Profijt Eindhoven University of Technology Department of Applied Physics 5600 MB Eindhoven The Netherlands

Andrea Pucci University of Aveiro Department of Chemistry and CICECO Campus Universitario de Santiago 3810-193 Aveiro Portugal

Matti Putkonen Beneq Oy 01511 Vantaa Finland and Aalto University School of Science and Technology Laboratory of Inorganic Chemistry 00076 Aalto, Espoo Finland

Thomas Riedl University of Wuppertal Institute of Electronic Devices Rainer-Gruenter-Str. 21 42119 Wuppertal Germany

Dragos Seghete University of Colorado Departments of Chemistry and Biochemistry and Chemical and Biological Engineering Boulder, CO 80309-0215 USA

Hyunjung Shin School of Advanced Materials Engineering and Center for Materials and Processes of Self-Assembly Kookmin University Jeongneung-Gil 77, Seoul, 136702 South Korea

Christopher J. Summers Georgia Institute of Technology School of Materials Science and Engineering Atlanta, GA 30338-0245 USA

Adriana V. Szeghalmi Max-Planck-Institute of Microstructure Physics Weinberg 2 06120 Halle Germany and Chemnitz University of Technology Institute of Physics Chemnitz Germany

Richard van de Sanden Eindhoven University of Technology Department of Applied Physics 5600 MB Eindhoven The Netherlands

Marc-Georg Willinger University of Aveiro Department of Chemistry and CICECO Campus Universitario de Santiago 3810-193 Aveiro Portugal and Fritz Haber Institute of the Max Planck Society Department of Inorganic Chemistry Faradayweg 4-6 14195 Berlin Germany

Byunghoon Yoon University of Colorado Departments of Chemistry and Biochemistry and Chemical and Biological Engineering Boulder, CO 80309-0215 USA

Part One

Introduction to ALD

Chapter 1

Theoretical Modeling of ALD Processes

Charles B. Musgrave

1.1 Introduction

This chapter describes simulations of atomic layer deposition (ALD) using quantum chemical electronic structure methods. Section 1.2 provides a brief overview of the quantum chemistry methods useful in the study of chemical processes and materials behavior. Although this section includes a summary of quantum chemical methods, it is not meant to be a comprehensive review of quantum chemistry and the reader is encouraged to examine the many excellent textbooks and reviews of quantum chemistry [1–3]. Section 1.3 overviews the use of quantum chemistry for predicting the properties of molecules and materials, while Section 1.4 specifically overviews the use of these methods to study ALD mechanisms, and Section 1.5 provides several examples of the determination of ALD mechanisms using quantum chemical methods. Again, this section is not meant to provide a comprehensive review of the use of electronic structure theory to study ALD and the motivated reader can examine the literature to explore what has specifically been done in this area. In addition to the various manuscripts our group has published on this topic [4–24], the groups of Esteve and Rouhani [25–29] and Raghavachari [30–35] have published many excellent articles on using quantum chemical methods to study ALD. While the overview of simulations presented here is meant to be helpful in understanding the approaches used to theoretically study the chemistry of ALD, it can be skipped for those who are already familiar with these methods or who do not seek a deeper understanding of electronic structure theory.

1.2 Overview of Atomistic Simulations

While simulations can be aimed at developing a description and understanding of the ALD process or at predicting the properties of the resulting ALD film, we here specifically focus on simulations intended to explain the chemistry of the ALD process. The unique features of ALD specifically rely on the nature of the half-reactions that describe the chemistry of each half-cycle. Specifically, ALD relies on the self-limiting nature of the surface reactions that result from the use of reagents that each do not self-react and that are introduced into the ALD reactor in separate pulses, temporally separated from each other by a reactor purge [36]. During each precursor pulse, the precursor reacts selectively with the functional groups remaining from the previous precursor pulse, but not with itself. For a successful ALD process, each half-reaction must produce a surface functional group reactive toward the subsequent precursor and deposit at most one atomic layer. Ideally, because reactants do not self-react and are introduced into the reactor separately, chemistry and transport are decoupled in ALD reactors. Thus, the nature of the surface reactions is the central feature of the ALD process that provides it with its ideal attributes – uniformity, conformality, and nanometer-scale control of film thickness and composition. Consequently, a fundamental understanding of an ALD process involves a detailed description of the ALD chemical mechanism, and accordingly, we focus on summarizing methods that describe these surface reactions that provide ALD with its unique advantages.

1.2.1 Quantum Simulations

The most fundamental approach to describing chemical reactions is based on using quantum mechanics to describe the electronic structure of the reacting system. During a chemical reaction, the reactants transform into products by rearranging their atomic coordinates from that of the reactants to that of the products. The actual trajectory followed by the reacting species is variable as atomic motion is a highly dynamical process. Each intermediate structure along the trajectory followed during the reaction involves a unique ground-state electronic wave function. That is, the electron density of the system is dynamically redistributed as the atomic structure evolves from that of the reactants to that of the products. Because the electrons have much lower mass than the nuclei, the reacting system typically stays in its electronic ground state during the course of reaction. In other words, the redistribution of electron density along the trajectory of atomic configurations is adiabatic. Nonetheless, the key point is that this complex process is intrinsically quantum mechanical, despite being electronically adiabatic because the properties along the trajectory of the reaction, and specifically the energy, depend exclusively on the wave function at each atomic configuration.

Because chemical reactions are inherently quantum mechanical, any method used to simulate chemical reactions must either be quantum mechanical or somehow empirically incorporate the quantum mechanical nature of the process of reaction into its description. Classical molecular dynamics (MD) potentials are generally not capable of accurately describing chemical reactions, except in the very few cases where potentials have been designed and trained specifically to describe a particular chemical reactivity. Fortunately, over the past few decades the meteoric rise in computational power together with significant advances in electronic structure methods and algorithmic progress has made the direct application of quantum mechanics to describing atomistic systems of reasonable size practical, although nowhere as efficient as classical MD. In fact, high-quality quantum calculations that required supercomputers to execute just 20 years ago can now be performed on desktop computers. Another major development that enabled the ongoing revolution in quantum chemistry is the development of high-quality quantum mechanical density functional theory (DFT) methods that have been implemented in reasonably priced simulation packages with relatively simple graphical interfaces. This, combined with the availability of affordable modern computers, has enabled researchers on even the most modest budgets access to the power of quantum chemical calculations. The result is an explosion in the quantity of research conducted using quantum chemical simulations. Thus, the computational approaches we focus on are quantum chemical methods, both because of their now widespread use and because they are the most appropriate and reliable approaches for describing the chemistry of ALD.

A large number of different quantum chemical methods, including DFT, are now available in a variety of software packages. These can be categorized as being either semi-empirical or ab initio (from first principles). Semi-empirical methods approximately solve the Schrödinger equation, but use empirically derived parameters to compute the effects of terms that are either neglected or approximated in the specific approximations used within the method. These methods have the advantage of being extremely fast relative to ab initio methods. They can also be relatively accurate if the system and property of interest are within or not too different from the training set used to parameterize the method. Unfortunately, semi-empirical methods are generally not reliable for the prediction of activation barriers, which of course are central to predicting the chemistry of a reacting ALD system as the energies of the various possible transition states (TS) determine whether a reaction is active. Consequently, we do not discuss the application of semi-empirical methods to simulate ALD.

In contrast to semi-empirical methods, first principles methods are by definition not empirically fit to any experimental data set. Ab initio methods start with a fundamental quantum mechanical description of the system and then employ various approximations to make the solution of the quantum mechanical problem tractable. While approximations are employed, they do not involve fitting to any data. As we will see shortly, many DFT methods involve an empirical component in the development of the exchange correlation (XC) functionals that define each DFT method. Nevertheless, DFT methods are still typically called ab initio methods. Despite the fact that most DFT methods do not strictly conform to the definition of ab initio, we will also adhere to the general convention of calling these methods first principles methods.

1.2.2 Wave Function-Based Quantum Simulations

Quantum simulation methods are classified as either wave function or density functional methods. Ab initio wave function methods involve directly solving the Schrödinger equation using various approximations with the quality of the method depending on the degree of approximation. Thus, ab initio wave function methods can be ranked within a hierarchy that depends on the extent of the approximations used, ranging from the mean field approximation of the Hartree–Fock (HF) method [37–39] to exact methods that include nth-order perturbation theory [40] (in the limit of large n and if the perturbation is small), full configuration interaction (CI), and quantum Monte Carlo methods [41]. The most approximate ab initio wave function method is the HF method. The HF wave function is the lowest energy single Slater determinant wave function for an n-electron system, where the wave function is the determinant of the n-by-n matrix where each column is a different electron orbital and each row a different electron. A determinant form for the wave function guarantees that it is antisymmetric, a requirement for fermions, and that the electrons are treated as identical, indistinguishable particles. Unfortunately, despite being ab initio, the mean field approximation that defines the HF method causes it to severely overestimate activation barriers in the vast majority of reactions, among other inaccuracies, which thus makes it unsuitable as a method for accurately describing chemical reactivity. On the other hand, HF serves as the basis for almost all wave function-based methods. Generally, these approaches combine the n-electron HF ground-state wave function with excited HF wave functions constructed by replacing occupied orbitals of the ground state with up to n unoccupied (virtual) orbitals to improve the quality of the wave function. The mixing in of excited HF wave functions with the HF ground state to improve the description of the wave function is usually accomplished using perturbation theory or variationally using configuration interaction.

Because a detailed description of wave function methods is beyond the scope of this chapter and because the application of these methods to simulate ALD has been much more limited than the application of density functional methods, we will forgo a more extensive account of these methods. However, we note that ab initio wave function methods have the advantage that they can be systematically improved. That is, we can methodically climb the hierarchical ladder of methods from the base Hartree–Fock method up toward the exact methods by, for example, increasing the order of the many-body perturbation theory (MBPT) or increasing the order of excitations in a configuration interaction method, which include coupled cluster and complete active space methods. Thus, we can robustly determine whether a method accurately describes the system by systematically improving it and analyzing its approach to convergence. Unfortunately, the accurate wave function methods are generally prohibitively expensive for many systems of interest. This is especially true for the case of ALD because the systems of interest are surface reactions, and thus involve a model of the reacting surface containing too many atoms for practical simulation using the higher quality wave function methods. However, they can still play the role of calibrating more approximate methods practical enough for simulating ALD processes to validate the choice of method and provide error bars on the predicted reaction energetics.

1.2.3 Density Functional-Based Quantum Simulations

An alternative to using the electronic wave function as the basis of a quantum mechanical method is to use the electron density. Methods based on this approach are called DFT methods. Hohenberg and Kohn first showed that the electron density uniquely determines the number of electrons and the location and identity of the atoms, that is, the potential, and thus the system Hamiltonian and its associated Schrödinger equation [42]. Consequently, the electron density uniquely determines the wave function and thus all information contained in the wave function must also be contained in the density! The key is to construct an energy functional equivalent to the Hamiltonian that includes all important contributions to the electronic energy. A functional is essentially a function of a function; in this case, the energy is a function of the electron density, which is itself a function of position. Kohn and Sham proved that the exact energy functional exists [43], but unfortunately proof of its existence did not prescribe an approach to its determination. However, knowing that an exact energy functional exists motivated the development of DFT where the key challenge has been to derive energy functionals that accurately describe the system.

The general approach to developing DFT energy functionals has been to exploit the fact that energy is an extensive property in order to separate the energy functional into its component energy contributions, including the kinetic energy, electron–electron repulsions, electron–nuclear attractions, the exchange energy, and the correlation energy. The explicit inclusion of the exchange and correlation energy through the exchange and correlation density functionals, called the exchange correlation functional when combined, may appear strange here because they are not explicitly included in the Hamiltonian of wave function methods. This is because no antisymmetry requirement is imposed on the density, so exchange does not naturally arise in DFT as it does when using a Slater determinant form of the wave function and so it must be explicitly added. On the other hand, correlation is an opportunistic addition to the energy functional used to improve the quality of a density functional to help it reproduce the properties of the system. This explicit addition of correlation energy is remarkably computationally efficient compared to the approaches for incorporating additional correlation energy into wave function methods that rely on mixing large numbers of excited states into the ground-state wave function. Furthermore, density functional methods are computationally efficient because they not only use a single Slater determinant description of the electronic structure, but also do not involve calculating any “two-electron integrals,” which is a requirement of all orbital-based wave function methods, making the wave function methods scale with at least the fourth power of the system size.