Thermal Modeling of Heat Transfer in 3ω and MPTR experiments

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Overview on Phase Change Memory

Although their commercial success remains somewhat questionable, numerous memory technologies have been competing in the field of Non Volatile Memory (NVM) market as reported in Figure 2.This specific microelectronic application is divided into two categories, namely volatile and non-volatile. Volatile memory does not retain data when power is turned off. On the contrary Non-volatile memory devices are expected to guarantee data retention along a measurable time even when power is turned off.
One of the most interesting non-volatile technologies is the Phase Change Memory (PCM). As mentioned in the literature, these novel technologies offerreliable and more promising alternatives to replace Flash memory and even Double Data Rate Random Access Memory (DDR-RAM)[2]-[7]. This fact stands on the scalability of PCMs compared to MRAMs (Magnetic-RAM) and FRAMs (Ferroelectric-RAM), as reported in Table 1. PCMs have alsohigh cycles with respect to Flash memories though the endurance is lower than in the cases of FRAM and MRAM. In addition, few mask steps are required in photolithography for film deposition in PCM technology in contrast to FRAM and MRAM technologies that require the integration of ferroelectric and magnetic materials within the Complementary Metal–Oxide–Semiconductor (CMOS).As maybe the most interesting feature, PCM increases the write speed by at least one order of magnitude compared to Flash memories. In addition PCM is suitable for very low-voltage technologies[14]. To summarize, with the performances in fast SET-RESET process, high-speed random access times, long lifetime [18][19]andpotential extended scalability[20][21], PCM technology is a credible alternative to the Flash technology.
Intel-Ovonyx Corporation presented the first memory array with PCM memory cellsin the early of the 2000s [15]. STMicroelectronics[16]and Samsung[17]also launched their products shortly after. Figure 3shows an evolution of PCMs cell size as a function of year compared to the competitive Flash technology. The figure shows the first starting point in 2001 with the 180 nm technology node.The PCM cell size reached the 32 nm node in 2012 and the 16nm technology node is expected in a very short time.An extraordinary scaling is also achievable very soon due to the income of nanowire technology thanks to the Metal Organic Chemical Vapour Deposition technique (MOCVD). Such a realization has been made at MDM laboratory in the framework of the Synapse European project. Finally, among all those promising expectations one has to emphasize the capability of PCM to store more than two levels per cell, thus giving extra options to further reduce the cost per bit[22].
However, several critical issues remain to be resolved before PCM becomes fully commercially competitive. Among these, the challenge of increasing the data density in phase change cells is strongly related to the resistivity drift phenomenon. The drift is not due to cycling, but to structural relaxation of the amorphous. At each cycle the drift restarts from beginning due to the resetting of the resistance. The multi-level storage we discussed just before seems also an interesting approach to overcome this limitation[7]. Its is not however the only one but it has the advantage to solve an issue as well as to offer a higher storage of bit without increasing the number of cell. Another issue met in PCM is the lower temperature of crystallization (150°C in case of the Ge-Sb-Te alloy) that makes the PCM misfit with applications involving high functioning temperature. This point will be one of the most interest of the present work in this thesis.
Figure 3: Scaling trends for NAND, NOR and PCM. The phase change memory technology is expected to reach the same Flash NAND size at the 32 technology feature size[18].

How does it work?

Although this is not the subject of the present work, in order to understand the key challenging issues related to the practical implementation of such materials the main principles of PCM must be presented. Phase change memory (PCM) is relying on the reversible, thermally assisted phase transitions of specific phase change materials. Stanford Ovshinsky was the first to investigate phase change alloys in the 1960sand he discovered their ability to switch between in two stable states of the matter: the amorphous and crystalline state. This process isthe so-called phase tranformation. Let us remind that if a solid possesses long range, regularly repeating units, it is classified as a crystalline material. Crystalline solids are only produced when the atoms, ions, or molecules have an opportunity to organize themselves into regular arrangements, or lattices. On the other side, if there is no long-range structural order throughout the solid, the material is best described as amorphous. The phase change is a reversible phenomenonthat is achieved by stimulating the cell with suitable electrical pulses that appropriately heat the material, monitoring the phase change. We must emphasize that phase change relies on a solid-solid phase change asfor instancetheeutectic or eutectoid transformations in alloys.The key point is that there existsan extreme contrast,over several orders of magnitude, between amorphous and crystalline phase in terms of the electrical resistivity(a few MΩin amorphous phase and a few kΩ in crystalline state) while the optical [9]reflectivity can change up to 30% (this discovery has been successfully exploited in rewritable optical media (CD, DVD)[10][11]).An example of the electrical resistivity change of a Ge-Sb-Te alloy with temperature, starting from the amorphous state, is represented in Figure 4. The variation lies on a logarithm scale making the resistivity to vary along several decades [13].
Phase change materials are inevitably composed by chalcogenide materials that are allotropic (the property of some chemical elements to exist in two or more different forms, in the same physical state)semiconducting elements and alloys belonging to the IV, V, and VI group of the periodic classification, i.e. indium, germanium, tin, antimony, tellurium. Figure 5shows the ternary phase diagram of the Ge-Sb-Te, In-Sb-Te, Ag-Sb-Te and Sn-Sb-Te systems.
Alloys along the pseudo-binary line between Sb2Te3 and GeTe with compositions (GeTe)m(Sb2Te3)nhave been intensely studied already and they have been implemented in PCM electronic devices. Among them, the Ge2Sb2Te5 ternary is very well known and has been studied for several years also at the MDM and I2M laboratories.
Figure 5: An overview of the phase change alloys that have been investigated using the ternary phase change diagram. It is clearly seen that the In3Sb1Te2(that is investigated in this thesis) shows distinctively different properties from the other alloys. Figure inspired from [37].
It must also be said that a lot of doped binary or ternary systems have been the subject of several studies. This “doping” is expected to improve some features as the switch rate and the data retention. However the term “doping” must be understood mainly as the addition of atomic elements whose some are even constituents of the alloy (as Ge for instance in case of the Ge-Te or Ge-Sb-Te systems).
The incredible electrical resistivity phase change finds its origin at the microscopic scale. Indeed,it is related to a bonding mechanism in the crystalline phase, called resonance or mesomerism) bonding by Linus Pauling. For instance, in the configuration of amorphous Ge2Sb2Te5 system, Ge atoms can occupy both threefold and tetrahedral sites with principally covalent bonding (high electrical resistivity). When switching to the cubic crystalline phase at 150°C structure comes to octahedral sub-units described as being ‘resonantly’ bonded.This bonding is characterized by the fact that a single half-filled p-band forms two bonds to its left and right neighbours (low electrical resistivity). Nevertheless, this bonding mechanism is met only for a small subset of group V and VI compounds, which explains the limited numberofpossible systems, as those presented in Figure 5[26]. A more physical interpretation of this phenomenon is given in[27][28][29].Such a phenomenon explains why the amorphous phase is stable for 10 years at about 100°C, while this state recrystallizes into the crystalline phase in less than 10 ns at elevated temperatures [30][31](the fastest known switching reported in the literature isless than 1 ns [32]).
Figure 6: Three critical temperatures are observed versus temperature: glass transition temperature (Tg), crystallization temperature (Tc) and melting temperature (Tm)[23].
Figure 6 shows the three critical temperatures during the operational condition of PCMs[23]. According to its structural change, the switch from the crystalline phase to the amorphous phase is achieved through intense localized Joule heating caused by a controlled current injection making the phase change material above the melting temperature Tm followed by a fast quench. This occurs as the atomic viscosity increases and therefore the atomic mobility decreases drastically with decreasing temperature. The temperature, at which a viscosity threshold value of 1012Pa.s is reached, is known as the glass transition temperature Tg. Herein, glass transition temperature is a signature of significant softening of glasses; it is measured by probing the viscosity of glasses. At this temperature the mobility of the atoms is so low in the order of timescales and would be required to induce the crystallization in the next ten years. Therefore a high Tg is required for memory applications. Alternatively heating an amorphous sample gives rise to crystallization when enough time/energy is available for the system. As said previously, when temperature of the material is higher than the crystallization temperature Tc, crystallization can occur on very short timescales [24].

Phase Change Memory Operation

Implementation of the phase change material to achieve the phase change memory device is represented inFigure 7 a). The resistivity difference between the amorphous and the crystalline states of a chalcogenide glass is used to encode the logic ‘0’ and ‘1’ levels. The device consists of a top electrode, the chalcogenide phase change layer, and a bottom electrode. The heater is attached to the underside of the PCM. Heating/melting affects only a small area around the tip of the heater displayed as a mushroom.
As presented inFigure 7 b)and Figure 8, the phase change write operation consists of:
• RESET state: the chalcogenide glass is momentarily melted by a short (ns) electric pulse and then quickly quenched into amorphous solid with high resistivity
• SET state: a lower amplitude but longer pulse (>100 ns) re-crystallizes the amorphous layer back to the crystalline state with low resistance level [22],[25],[36]-[39].
The resistance state of the memory cell is read with a sufficiently small current pulse, which does not alter the state of the memory cell.
As presented in Figure 8, this change of state is only possible because of the threshold switching effect that leads,within a few nanoseconds,to a reduction of the resistance of the amorphous phase when a certain threshold field is surpassed, at a given threshold voltage VT. Otherwise, it would be impossible to heat the amorphous material using Joule heating with reasonably low voltages.
Figure 8: Electrical program of the cell. Starting from the amorphous phase with large resistance R (100 Ω.cm), a current pulse is applied. At the threshold voltage VT, the resistance drops suddenly, and a large current (I) flows that heats the material above the crystallization temperature Tc for a sufficiently long time to crystallize (SET operation). In the crystalline state, the resistance is low (1mΩ .cm). A larger, short current pulse is applied to heat the material above the melting temperature Tm. The material is melt-quenched and returns to the amorphous, high resistance state (RESET operation). Figure comes from reference [37].
The threshold voltage in current typical PCM cells is on the order of 1 V, but if devices are scaled to much smaller dimensions, the threshold voltage scales with the size of the amorphous region, and for very small cells, it could become comparable to the read voltage such that every read operation could alter the cell state.

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The In-Sb-Te alloy

One of the main issues of PCM is related to the crystallization temperature that need to be high enough in order to have a better stability of the amorphous phase, thus enabling the fulfilment of high temperature applications requirements. It has been demonstrated that doping the chalcogenide with nitrogen, oxygen, carbon and silicon markedly increased the crystallization temperature, from 150 °C of un-doped Ge2Sb2Te5[42], to above 290 °C [44][44].Recent studies revealed that In3Sb1Te2 demonstrated a high crystallization temperature (290°C) and melting temperature (626°C)[41], enhancing the stability of the amorphous phase and the data retention in phase change memory (PCM) devices for high-temperature applications; it also allows multi-bit storage in a single cell, due to intermediate phases during operation. Therefore, a straightforward way to achieve this same purpose consists of replacing germanium with indium in the Ge-Sb-Te system. Furthermore, the IST system has the same space group number and atomic structure as the Ge-Sb-Te (GST) and it has nearly same lattice parameter (a=b=c=6.12 A° for IST and a=b=c=6.03 A° for GST).The In3Sb1Te2is called the 4thgeneration of ternary phase-change material.Interest in this alloy was renewed when Maeda et al. started to successfully apply this alloy in optical discs, exploiting the advantageous properties like high crystallization temperature, phase stability, short writing times and high numbers of writing cycles [46][47]. Recent interest was renewed due to the possibility of multilevel storage in In-Sb-Te alloys but also the production of nano wire via metal organic chemical vapour deposition (MOCVD)[41], [48]-[51]. The observed multi resistance states, represented inFigure 9, is due to InSb/InTe segregation [50]. The crystal structure of cubic In3Sb1Te2 has a rocksalt geometry with In occupying the cation sub-lattice and Sb and Te atoms occupying the anion sub-lattice in a random manner as shown by recent X-ray and neutron diffraction experiments [41]. It is interesting to note that Ge2Sb2Te5 also crystallizes in a metastable rocksalt phase in which, however, the cation sub-lattice is occupied in a random manner by Sb, Ge, and 20% of vacancies, the anionic sub-lattice being occupied by Te only. Antimony is thus cationic in In3Sb1Te2 and anionic in Ge2Sb2Te5. The octahedral-like bonding geometry of the cubic ternary In3Sb1Te2 has to be contrasted with the tetrahedral bonding geometry of the binary compounds InTe and InSb. In fact, InSb crystallizes in a zinc-blende structure, while crystalline InTe is made of chains of edge-sharing InTe4 tetrahedra intercalated by weakly bound, interstitial-like In ions.
Measured current versus Voltage curve of the In3Sb1Te2 PRAM cell. The inset shows the I-V curve of the Ge2Sb2Te5 cell. Results obtained by [41]

Thermal properties of the PCM

The functioning of PCM is a thermally assisted process. Temperature dependent thermal properties of the PCM are thus key parameters thathave to be perfectly known in order to simulate the electro-thermal behaviour of the cell. Much work has been done in that sense. Since the process is time dependent, not only the thermal conductivity k but also the thermal diffusivity a or the specific heat Cp have to be measured. As everybody knows, those three parameters are linked as a=k/Cp. Obviously, defining the thermal conductivity means that one assumes implicitly that the mean free path (mfp) of the heat carriers (phonon and electrons or holes) is lower than the characteristic length of the material (the thickness in case of a film). Indeed, the thermal conductivity is a “macroscopic” parameter that allows relating the heat flux and the temperature gradient in the material. In Chalcogenides alloys, the mfp is very small (the order of the nanometer) at room temperature. This means that the thermal conductivity of very thin films can be rigorously defined even for films whose thickness is of the order of some tenth nanometers. One can ask therefore about the meaning of measuring the thermal conductivity on such films whereas a bulk measurement would have been easier to implement. The response is double. First, the alloys are generally deposited from specific processes as: sputtering, Atomic Layer Deposition (ALD), Chemical Vapour deposition (CVD), Metal-Organic Chemical Vapour deposition (MOCVD that will be used in this work) that do not allow depositing thick layers. Secondly, the PCM films thickness must be representative of that implemented in the memory device. This point is quite important since structural configuration of the film could be slightly modified by superimposed layers at the bottom and the top of the PCM layer. Indeed, the PCM is in contact with dielectric materials in the real device that play the role of thermal and electrical insulators (see Figure 7). The classical dielectric materials used in PCM are SiO2, Al2O3 or Si3N4. On the other hand, the PCM layer is also in contact with metal electrodes that ensure the current to flow through the PCM. Those metallic materials are TiN or Al. The influence of the contact between layers on the thermal conductivity of the PCM layer can be viewed as an isotropy of the film with respect to the in-plane and transverse values. However, such an anisotropy has never been observed on the PCM film whatever the contact layers and the thickness of the film.

Table of contents :

1 Chapter 1: Phase Change Memory – From Scientific Context to Application
1.1 Introduction
1.2 Overview on Phase Change Memory
1.3 How does it work?
1.4 Phase Change Memory Operation
1.5 The In-Sb-Te alloy
1.6 Thermal properties of the PCM
1.7 Objectives of this research work
1.8 References
2 Chapter 2: Thermal characterization of IST thin films
2.1 Introduction
2.2 Description of the 3ω method
2.3 Photothermal Radiometry technique
2.3.1 Principle
2.3.2 MPTR setup working at high temperature
2.3.3 Optical Transducer
2.3.4 Phase-lag calibration
2.4 Conclusion
2.5 References
3 Chapter 3: Thermal Modeling of Heat Transfer in 3ω and MPTR experiments
3.1 Introduction
3.2 Heat diffusion model in a composite stack of thin films
3.2.1 General formulation
3.2.2 From time to frequency
3.3 From the general formulation to the 3ω and MPTR experimental configurations
3.3.1 Practical considerations about the heat diffusion length
3.3.2 Dealing with spatial coordinates with 3ω method
3.3.3 Dealing with spatial coordinates with MPTR method
3.4 Practical estimation of RT in the 3ω and MPTR methods
3.4.1 Sensitivity to RT using the 3ω method
3.4.2 Sensitivity to RT using the MPTR method
3.5 Identification of RT
3.6 Evaluation of k and TBR
3.7 Conclusion
3.8 References
4 Chapter 4: Experiments, results and discussions
4.1 Introduction
4.2 Useful thermophysical properties for further studies
4.3 IST film deposition
4.4 Thermal characterization using the 3ω technique
4.4.1 Sample preparation
4.4.2 Structural analysis of the samples
4.4.3 3ω Measurements
4.4.4 Discussion on the thermal conductivity
4.4.5 Discussion on the thermal boundary resistance
4.5 Thermal Characterization using Modulated Photothermal Radiometry (MPTR)
4.5.1 Introduction
4.5.2 Structural and chemical analysis
4.5.3 MPTR Measurements
4.5.4 Discussion on thermal conductivity
4.5.5 Discussion on the TBR
4.6 Conclusion
4.7 References
5 Conclusions and perspectives
6 Appendix A: Methodologies for structural and interface characterization
6.1 Introduction
6.2 Scanning Electron Microscopy and X-ray microanalysis
6.3 X-Ray Diffraction and Reflectivity Techniques
6.4 Raman Spectroscopy
6.5 Time of Flight Secondary Ion Mass Spectroscopy (ToF-SIMS)
7 Appendix B: Growth MOCVD technique for In-Sb-Te thin film deposition


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