Sneak path current is a significant remaining obstacle to the utilization of large crossbar arrays for non-volatile memories and other applications of memristors. A two-terminal selector device with an extremely large current-voltage nonlinearity and low leakage current could solve this problem. We present here a Ag/oxide-based threshold switching (TS) device with attractive features such as high current-voltage nonlinearity (~1010), steep turn-on slope (less than 1 mV/dec), low OFF-state leakage current (~10-14 A), fast turn ON/OFF speeds (<75/250 ns), and good endurance (>108 cycles). The feasibility of using this selector with a typical memristor has been demonstrated by physically integrating them into a multilayered 1S1R cell. Structural analysis of the nanoscale crosspoint device suggests that elongation of a Ag nanoparticle under voltage bias followed by spontaneous reformation of a more spherical shape after power off is responsible for the observed threshold switching of the device. Such mechanism has been quantitatively verified by the Ag nanoparticle dynamics simulation based on thermal diffusion assisted by bipolar electrode effect and interfacial energy minimization.

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In niobium oxide-based capacitors non-linear switching characteristics can be observed if the oxide properties are adjusted accordingly. Such non-linear threshold switching characteristics can be utilized in various non-linear circuit applications, which have the potential to pave the way for the application of new computing paradigms. Furthermore, the non-linearity also makes them an interesting candidate for the application as selector devices e.g. for non-volatile memory devices. To satisfy the requirements for those two areas of application, the threshold switching characteristics need to be adjusted to either obtain a maximized voltage extension of the negative differential resistance region in the quasi-static I-V characteristics, which enhances the non-linearity of the devices and results in improved robustness to device-to-device variability or to adapt the threshold voltage to a specific non-volatile memory cell. Those adaptations of the threshold switching characteristics were successfully achieved by deliberate modifications of the niobium oxide stack. Furthermore, the impact of the material stack on the dynamic behavior of the threshold switches in non-linear circuits as well as the impact of the electroforming routine on the threshold switching characteristics were analyzed. The optimized device stack was transferred from the micrometer-sized test structures to submicrometer-sized devices, which were packaged to enable easy integration in complex circuits. Based on those packaged threshold switching devices the behavior of single as well as of coupled relaxation oscillators was analyzed. Subsequently, the obtained results in combination with the measurement results for the statistic device-to-device variability were used as a basis to simulate the pattern formation in coupled relaxation oscillator networks as well as their performance in solving graph coloring problems. Furthermore, strategies to adapt the threshold voltage to the switching characteristics of a tantalum oxide-based non-volatile resistive switch and a non-volatile phase change cell, to enable their application as selector devices for the respective cells, were discussed.:Abstract I Zusammenfassung II List of Abbrevations VI List of Symbols VII 1 Motivation 1 2 Basics 5 2.1 Negative differential resistance and local activity in memristor devices 5 2.2 Threshold switches as selector devices 8 2.3 Switching effects observed in NbOx 13 2.3.1 Threshold switching caused by metal-insulator transition 13 2.3.2 Threshold switching caused by Frenkel-Poole conduction 18 2.3.3 Non-volatile resistive switching 32 3 Sample preparation 35 3.1 Deposition techniques 35 3.1.1 Evaporation 35 3.1.2 Sputtering 36 3.2 Micrometer-sized devices 36 3.3 Submicrometer-sized devices 37 3.3.1 Process flow 37 3.3.2 Reduction of the electrode resistance 39 3.3.3 Transfer from structuring via electron beam lithography to structuring via laser lithography 48 3.3.4 Packaging procedure 50 4 Investigation and optimization of the electrical device characteristic 51 4.1 Introduction 51 4.2 Measurement setup 52 4.3 Electroforming 53 4.3.1 Optimization of the electroforming process 53 4.3.2 Characterization of the formed filament 62 4.4 Dynamic device characteristics 67 4.4.1 Emergence and measurement of dynamic behavior 67 4.4.2 Impact of the dynamic device characteristics on quasi-static I-V characteristics 70 5 Optimization of the material stack 81 5.1 Introduction 81 5.2 Adjustment of the oxygen content in the bottom layer 82 5.3 Influence of the thickness of the oxygen-rich niobium oxide layer 92 5.4 Multilayer stacks 96 5.5 Device-to-device and Sample-to-sample variability 110 6 Applications of NbOx-based threshold switching devices 117 6.1 Introduction 117 6.2 Non-linear circuits 117 6.2.1 Coupled relaxation oscillators 117 6.2.2 Memristor Cellular Neural Network 121 6.2.3 Graph Coloring 127 6.3 Selector devices 132 7 Summary and Outlook 138 8 References 141 9 List of publications 154 10 Appendix 155 10.1 Parameter used for the LT Spice simulation of I-V curves for threshold switches with varying oxide thicknesses 155 10.2 Dependence of the oscillation frequency of the relaxation oscillator circuit on the capacitance and the applied source voltage 156 10.3 Calculation of the oscillation frequency of the relaxation oscillator circuit 157 10.4 Characteristics of the memristors and the cells utilized in the simulation of the memristor cellular neural network 164 10.5 Calculation of the impedance of the cell in the memristor cellular network 166 10.6 Example graphs from the 2nd DIMACS series 179 11 List of Figures 182 12 List of Tables 194

Les matériaux à changement de phase montrent la combinaison exceptionnelle d’un contraste énorme dans leurs propriétés physiques entre la phase amorphe et cristalline allié à une cinétique de changement de phase extrêmement rapide. La grande différence en résistivité permet leur application dans les mémoires numériques. De plus, cette classe de matériaux montre dans leur état vitreux des phénomènes de transport électronique caractéristiques. Le seuil de commutation dénote la chute de la résistivité dans l’état amorphe au delà d’un champ électrique critique. Le phénomène de seuil de commutation permet la transition de phase en appliquant des tensions relativement faibles. Au-dessous de cette valeur critique l’état désordonné montre une conductivité d’obscurité activée en température ainsi qu’une résistance - dans les cellules mémoires et les couches minces également – qui augmente avec le temps. Cette évolution de la résistivité amorphe entrave le stockage à plusieurs niveaux, qui offrirait la possibilité d'accroître la capacité ou la densité de stockage considérablement. Comprendre les origines physiques de ces deux phénomènes est crucial pour développer de meilleures mémoires à changement de phase. Bien que ces deux phénomènes soient généralement attribués aux défauts localisés, la connaissance de la distribution de défauts dans les matériaux amorphes à changement de phase est assez limitée. Cette thèse se concentre sur la densité des défauts mesurée dans différents verres chalcogénures présentant l’effet de seuil de commutation. Sur la base d’expériences de photo courant modulé (MPC) et de spectroscopie par déviation photothermique, un modèle sophistiqué des défauts a été développé pour GeTe amorphe (a-GeTe) mettant en évidence les états de la bande de valence et plusieurs défauts. Cette étude sur a-GeTe montre que l’analyse des données MPC peut être grandement améliorée en prenant en compte la variation de la bande de l’énergie interdite avec la température. Afin de mieux appréhender l’évolution de la résistivité amorphe, la présente étude porte sur l’évolution avec les recuits et le vieillissement de la résistivité, de l’énergie d’activation du courant d’obscurité, de la densité des défauts, du stress mécanique, de l'environnement atomique et de l’énergie de la bande interdite mesurée par des méthodes optiques sur les couches minces de a-GeTe. Le recuit d’un échantillon entraîne un élargissement de la bande interdite et de l’énergie d’activation du courant d’obscurité. De plus, la technique MPC a révélé une diminution des défauts profonds dans les couches minces de a-GeTe vieillies. Ces résultats illustrent l’impact de l’annihilation des défauts et de l’élargissement de la bande interdite sur l’évolution de la résistivité des matériaux à changement de phase amorphe. Cette thèse présente également une étude sur les alliages à changement de phase GeSnTe. En augmentant la concentration d’étain, on observe une décroissance systématique de la résistivité amorphe, de l’énergie d’activation du courant d’obscurité, de la largeur de bande interdite et de la densité des défauts, qui conduisent à une résistivité amorphe plus stables dans les compositions riches en étain comme a-Ge2Sn2Te4. L’étude sur les alliages GeSnTe montre que les matériaux à changement de phase ayant une résistivité amorphe plus stable présentent une faible énergie d’activation du courant d’obscurité. À l’exemple du Ge2Sn2Te4 et GeTe la présente étude montre un lien étroit entre l’évolution de la résistivité et la relaxation du stress mécanique. L’étude sur les verres chalcogénures montrent que les matériaux ayant un grand champ d’électrique de seuil, bien connu d’après la littérature, présentent aussi une grande densité de défauts. Ce résultat implique que l’origine du phénomène de seuil de commutation se trouve dans un mécanisme de génération à travers la bande interdite et de recombinaison dans les défauts profonds comme proposé par D. Adler. / Phase change materials combine a pronounced contrast in resistivity and reflectivity between their disordered amorphous and ordered crystalline state with very fast crystallization kinetics. Due to this exceptional combination of properties phase-change materials find broad application in non-volatile optical memories such as CD, DVD or Bluray Disc. Furthermore, this class of materials demonstrates remarkable electrical transport phenomena in their disordered state, which have shown to be crucial for their application in electronic storage devices. The threshold switching phenomenon denotes the sudden decrease in resistivity beyond a critical electrical threshold field. The threshold switching phenomenon facilitates the phase transitions at practical small voltages. Below this threshold the amorphous state resistivity is thermally activated and is observed to increase with time. This effect known as resistance drift seriously hampers the development of multi-level storage devices. Hence, understanding the physical origins of threshold switching and resistance drift phenomena is crucial to improve non-volatile phase-change memories. Even though both phenomena are often attributed to localized defect states in the band gap, the defect state density in amorphous phase-change materials has remained poorly studied. This thesis presents defects state densities measured on different amorphous phase-change materials and chalcogenides showing electrical threshold switching. On the basis of Modulated Photo Current (MPC) Experiments and Photothermal Spectroscopy a sophisticated band model for a-GeTe has been developed, which is shown to consist of defect bands and band tail states. This study on a-GeTe has shown that the data analysis within MPC experiments can be drastically improved by taking the temperature dependence of the optical band gap into account. To get a better understanding of resistance drift phenomena this study focuses on the evolution of resistivity on heating and ageing, activation energy of electronic conduction, optical band gap, defect state density, mechanical stress and nearest neighbour ordering in a-GeTe thin films. After heating the samples one hour at 140°C the activation energy for electric conduction increases by 30 meV, while the optical band gap increases by 60 meV. Additionally, MPC experiments revealed a decreasing concentration of mid gap states in aged a-GeTe thin films. These findings demonstrate the impact of band gap opening and defect annihilation on resistance drift. Furthermore, the stoichiometric dependence of resistance drift phenomena in a-GeSnTe phase-change alloys is studied in this thesis. A systematic decrease in the amorphous state resistivity, activation energy for electric conduction, optical band gap and defect density is observed with increasing tin content resulting in a low resistance drift for tin rich compositions such as a-Ge2Sn2Te4. This study on GeSnTe systems demonstrates, that phase change alloys showing a more stable amorphous state resistivity are characterized by a low activation energy of electronic conduction. This finding found in GeSnTe alloys holds also true for GeSbTe and AgInSbTe systems. On the example of a-Ge2Sn2Te4 and a-GeTe exhibiting a strong resistance drift, the evolution of the amorphous state resistivity is shown to be closely linked to the relaxation of internal mechanical stresses resulting in an improving structural ordering of the amorphous phase. For the investigated alloys showing electrical switching, the measured density of midgap states is observed to decreases with decreasing threshold field known from literature. This result favours a generation-recombination model behind electrical switching in amorphous chalcogenides as originally proposed by Adler.

<div> <div> <p>Phase transition materials (PTM) have garnered immense interest in concurrent post-CMOS electronics, due to their unique properties such as - electrically driven abrupt resistance switching, hysteresis, and high selectivity. The phase transitions can be attributed to diverse material-specific phenomena, including- correlated electrons, filamentary ion diffusion, and dimerization. In this research, we explore the application space for these materials through extensive device-circuit co-design and propose new ideas harnessing their unique electrical properties. The abrupt transitions and high selectivity of PTMs enable steep (< 60 mV/decade) switching characteristics in Hyper-FET, a promising post-CMOS transistor. We explore device-circuit co-design methodology for Hyper-FET and identify the criterion for material down-selection. We evaluate the achievable voltage swing, energy-delay trade-off, and noise response for this novel device. In addition to the application in low power logic device, PTMs can actively facilitate non-volatile memory design. We propose a PTM augmented Spin Transfer Torque (STT) MRAM that utilizes selective phase transitions to boost the sense margin and stability of stored data, simultaneously. We show that such selective transitions can also be used to improve other MRAM designs with separate read/write paths, avoiding the possibility of read-write conflicts. Further, we analyze the application of PTMs as selectors in cross-point memories. We establish a general simulation framework for cross-point memory array with PTM based <i>selector</i>. We explore the biasing constraints, develop detailed design methodology, and deduce figures of merit for PTM selectors. We also develop a computationally efficient compact model to estimate the leakage through the sneak paths in a cross-point array. Subsequently, we present a new sense amplifier design utilizing PTM, which offers built-in tunable reference with low power and area demand. Finally, we show that the hysteretic characteristics of unipolar PTMs can be utilized to achieve highly efficient rectification. We validate the idea by demonstrating significant design improvements in a <i>Cockcroft-Walton Multiplier, </i>implemented with TS based rectifiers. We emphasize the need to explore other PTMs with high endurance, thermal stability, and faster switching to enable many more innovative applications in the future.</p></div></div>