A signals-systems perspective to electronic band structure theory and Mitigation of directional MLC operation in a novel variant of double mushroom PCM cells

다국어 초록 (Multilingual Abstract)

The present Master Thesis deals with two widely separated topics which is also why, the work has been divided into two parts.

The first part focuses on developing a deeper understanding of electronic band structure theory. However, in contrast to the conventional perspective, a detour is taken in this thesis to visualize a perfectly crystalline material as a Linear Translation Invariant (LTI) system. To the best of the author’s knowledge, it is for the first time that an attempt has been made to see materials from such a perspective. Since the theory is particularly used for obtaining the electronic band structures of materials, validity of the proposed perspective to this theory is demonstrated through achievement of the band structures for a one dimensional chain of atoms as well as through a more complicated example of a two dimensional material- that being MoS2. The folding of band structures for super cells is also a phenomenon which is witnessed as part of this work for both the cases concerned.

The first part starts off with providing the reader with a broad understanding of signals and systems, in general. Following this, a description of electronic band structure theory is provided ensuring that the calculations are all generic until the step of expansion of atomic orbitals. In order to describe these orbitals, the tight binding theory (TBT) is then employed without loss of any generality. Thereafter, merging of these two widely separated domains is attempted to obtain an understanding of the theory from a whole new perspective of LTI systems. While the idea of impulse response in materials isn’t new in itself (since the Green’s functions- popularly known for electron transport physics- are also impulse responses), such a method of visualizing band folding definitely is new as it allows one to bypass an O(N) loop matrix diagonalization owing to the eigenvalue decomposition achieved through this perspective. To conclude with, the first part of this thesis is then summarized and an outlook is provided.

The second part, on the other hand, deals with a computational study of phase change memory (PCM) devices. Owing to big data era and the buzz created because of Industry 4.0, artificial intelligence (AI) has gained a lot of attention lately. There have been great advancements- in hardware as well as software- ever since the initialization of Machine Learning in 1960s. Nonetheless, it has now become evident that the advancements in hardware for AI need to buck up to match those in the software. On that note, the major hurdle is von Neumann bottleneck which essentially separates computational unit from the storage unit. Several emerging memory devices have been proposed in literature among which one of the most mature is PCM technology.

Essentially, this part is a Finite Element Method (FEM) study carried out on COMSOL for a better understanding of the thermoelectric effects in these devices. The work starts off with a description of jargon required to understand FEM in general and then, takes a deeper dive into the set-up of the work for modeling the RESET operation in mushroom shaped PCM cells. In line with previous literature, directional behavior of the device is observed depending on the bias applied to the device. In this work, as a next step, the dependence of multi-level cell (MLC) operation on polarity is investigated. On that note, contrasting results are obtained emphasizing that gradual RESET is possible with positive polarity but results in abrupt RESET with negative polarity. More interestingly, though, as a culmination of this thesis, a new variant of the double mushroom shaped cell is also proposed that can mitigate this directional behavior. Electrical characteristics of these devices obtained through calculations are presented thereafter which is then followed up by prospective applications of the proposed geometry. Just as the first part, a conclusion is provided to the second one in the end while also providing future possible directions of research in this domain.

While the main text ends with these chapters, there is additional information prescribed in the supplementary texts to certain chapters. These are complemented with pictorial as well as verbal descriptions of the background work that the author underwent to obtain the results presented in the main text- be it part one or two.

목차 (Table of Contents)

• I A signals-systems perspective to electronic band structure theory 1
• 1 Introduction to Signals & Systems 2
• 1.1 Linear Time Invariant (LTI) Systems 3
• 1.2 Fourier/Laplace Transform . 4
• 1.2.1 Eigenvalue decomposition using Fourier transform 5
• 2 The Conventional Perspective 8
• 2.1 Formulation of conventional perspective 9
• 2.2 Implementation of conventional perspective . 11
• 2.2.1 1D chain of atoms 11
• 2.2.2 2D Mono-layer MoS2 16
• 3 The New Perspective 20
• 3.1 Formulation of the new perspective 20
• 3.2 Implementation of the new perspective . 22
• 3.2.1 1D chain of atoms 23
• 3.2.2 2D Mono-layer MoS2 28
• 3.3 Novelty of the new perspective 31
• 4 Conclusion and Outlook 34
• 4.1 Future work . 35
• II Mitigation of directional MLC operation in a novel variant of double
• mushroom PCM cells 37
• 5 Introduction to Phase Change Memory (PCM) 38
• 5.1 Information Storage: An Age-Old Need 38
• 5.2 Memory Hierarchy & the Emerging Memories 40
• 5.2.1 Phase Change Materials (PCMs) 41
• 6 Conventional mushroom PCM cells 43
• 6.1 Thermoelectric modeling of mushroom PCM cells . 43
• 6.1.1 Cell specifications 44
• 6.1.2 Modules in COMSOL 46
• 6.1.3 Modeling in COMSOL 46
• 6.1.4 The crucial role of Events Interface 47
• 6.2 Directional RESET in mushroom-shaped PCM cells 47
• 6.3 Physical reasoning behind the directional RESET . 49
• 7 Novel double mushroom PCM cells 52
• 7.1 Motivation for a novel geometry . 52
• 7.2 Thermoelectric modeling in the novel geometry 52
• 7.3 Directional RESET mitigated in novel geometry . 53
• 7.4 The boundary conditions employed 59
• 7.5 Applications of the novel geometry 62
• 8 Conclusion and Outlook 66
• 8.1 Future work . 67
• List of Figures 69
• List of Tables 71
• A Supplementary Text 72
• A.1 Supplement to chapter 2 72
• A.2 Supplement to chapter 3 78
• A.3 Supplement to chapter 6 83
• A.4 Supplement to chapter 7 90
• B Bibliography 113
• Acknowledgements 117
• Declaration 119