Design, characterization and simulation of electronic and optoelectronic nanodevices based on bidimensional materials

Resumen

1– Introduction Each progress in the solid state device development has approached us to the actual society. The transistor's technology, more specifically the field effect transistors (FET), based on Silicon, have seen how their first concept was muted and adapted, in an effort to meet a law, or better a promise, known as Moore's law, in honour to Gordon Moore, who quite rightly estimated the market tendency: that every 12 months, the number of components per chip will duplicate [1]. One decade later, this formula was revised to every 18 months. Almost like a dogma of faith, the companies and research centres have striven to accomplish this law. Today, complex designs endeavour to solve the different issues that technological nodes have faced [2]. Some of these improvements are straining the Silicon to improve its mobility; the use of high-κ oxides between the gate and the channel to reduce the loss currents; or the placement of more than one gate surrounding the channel, instead of only placing the gate on top of the channel, forming a Multiple Gate transistor. In this way, the Silicon technology has been stretched to achieve the market and society demands, making lives more comfortable and productive. The progress in the different fields mentioned before is mainly based on the great understanding we have of Silicon. However, this material has some physical limitations that preclude its effective usage in some applications, and brakes its potential in others [3]. Due to these facts, some alternative steps have been considered, like the study of other materials that complement or substitute Silicon for certain applications. One of these alternatives is the precursor of works like this Thesis, the isolation of a material known today from Boehm et al.'s work as graphene, or sp2-hybridized Carbon [4]. Its astonishing properties inspired a debate about the usage of this and other new materials in the world of electronics, which still remains. The word graphene refers to a portion of a much better known material: graphite. Typically used to make pencils, it is composed of multiple Carbon layers arranged in hexagonal honeycomb panels, with an in-plane distance of 1.42 Angstrom and 3.45 between layers. The covalent bonds that keep the atoms united inside the layer are very strong, but the forces between layers, known as van der Waals forces, are not as intense. The weak interconnection facilitates an easy exfoliation, up to only one layer thick, known as graphene. The key of this monolayer material, the property that makes it so interesting, is related to its band structure [5]. Free-standing monochrystalline graphene presents a conical band diagram, where the conduction and valence bands are in touch with each other at the so called Dirac-point, which makes that electrons in graphene behave as massless two-dimensional particles. This makes graphene behave as a semi-metal, and confers two important properties: very large electron and hole mobilities, over hundreds of thousands of cm2/Vs in ideal conditions; and ambipolarity, because the Fermi level can be easily tuned using a gate bias. The fascinating properties of graphene are fuelling applications in a wide variety of emerging fields, not so far just theoretical entelechies, as e.g. topological insulators or valleytronic-based devices. The two-dimensional (2D) nature of graphene encloses as many advantages as technological challenges, and has paved the way to other 2D materials with similar structure, in such a way that some of the intrinsic lacks of graphene can be overcome. A new family of 2D materials has appeared to complement graphene, each of them with their own peculiarities. Some of these new materials are native insulators, like the hexagonal Boron Nitride h-BN, or semiconductors, as it happens with most of the Transition Metal Dichalcogenides (TMDs), as well as metals, superconductors and topological insulators [6]. The weak interaction between layers due to the van der Waals forces allows to stack different materials, making new van der Waals heterostructures. The palette is very rich, and offers a wide variety of applications, from optoelectronic devices for light sensing and harvesting, to logical circuits. Learning the physics concerning to the new 2D materials is essential to understand how far we can progress with them. Both theoretical and experimental results can complete the remaining pieces of the puzzle, providing us with new and smart solutions to complement or even surpass the Silicon technology. This PhD Thesis is focused on the study of the electronic and optoelectronic properties of different devices based on Two-Dimensional Materials, with emphasis on photodiodes and phototransistors. The targets of this work are: -The development of a numerical simulator to study the electrostatics and transport capacities of electronic and optoelectronic devices, paying special attention to the charge transport process between heterostructures. -The numerical analysis of 2D semiconductors applied to different devices, to study different properties, including: -The electron mobility limited by different scattering mechanisms in back-gated transistors formed by few-layer MoS2 semiconductor as channel. -The interface influence in light harvesting and sensing capabilities of hybrid bulk-2D heterojunctions interdigitated by Schottky and gated regions. -The interface trap influence in the photogating effect in phototransistors based on few-layer 2D Materials. -The contact resistance and Schottky barrier in phototransistors based on few-layer 2D Materials. Here we include the development of new techniques to make symmetrical, low cost, n-type contacts for 2D Materials. 2– Theory Numerical tools have become essential to evaluate the behaviour of complex electronic systems, where the material physical properties and devices features mix in an intricate way. In this Thesis, we have designed and implemented from scratch a simulation tool to study the electrostatics and transport properties of arbitrary structures made of metals, oxides and semiconductors in a two dimensions system. We have called it SAMANTA: Simulator for All Modern Assembled Nanodevices Transport Applications. The simulator comprises the Poisson and continuity equations, with the transport evaluated in a drift-diffusion scheme [7]. In the case of metal-semiconductor, semiconductor-semiconductor and semiconductor-oxide-semiconductor junctions, a thermionic emission (TE) plus direct tunnel model (TFE, Thermionic-Field Emission) is used to simulate the charge transport [8]. The direct tunnel is complemented with the local and non-local band-to-band tunnelling model. In addition, several generation and recombination models are added to the continuity equations [9]: light generation; Shockley-Read-Hall SRH recombination; surface SRH recombination; Auger recombination; and Radiative recombination. Additionally, SAMANTA is able to evaluate trap profiles at the interfaces of the device, including oxides, metals or other semiconductors [9]. There is one extra module, called SAMANTA-SP1D, which can solve the one dimensional Schrödinger-Poisson equations, useful to obtain the wavefunctions and energy levels of a confined system [10], and which can be thus used as a preliminary step to evaluate the carrier mobility for a certain material system. Finite differences are employed, together with a Newton linearisation method, to self-consistently solve the equations [7]. 3– Results Electron mobility in few-layers MoS2 MOSFET Few-layer channel of MoS2, back-gated transistors have been analysed in its one-dimensional confinement direction using the SAMANTA-SP1D solver [11]. The band structure of the semiconductor has been modelled using the effective mass approach. By applying the Kubo-Greenwood formula, the phonon-limited mobility was calculated, giving a solution in good agreement with experimental data for medium and high temperatures, which gives an excellent approach for non-monolayer devices. Our results demonstrated that the polar optical phonons governs the phonon-limited mobility for high temperatures, and acoustic phonons play an important role for low temperatures. The phonon-limited mobility has also shown a non-monotonic dependence with thickness, with a maximum for around T_sc=5 nm. This effect is related with the form factor behaviour in the polar optical phonons scattering mechanism. Thinner flakes drop their mobility due to the strong quantum confinement. Coulomb scattering, including the screening effect, is modelled considering anisotropic bands and a scalar dielectric function. Here we conclude this scattering effect is the most important degradation element of the electron mobility for low temperatures. Graphene-Silicon Photodiodes For non-degraded interfaces, the graphene-Silicon heterojunctions [12] can provide the best performance as the photogenerated carriers are collected directly by the graphene contact. In this situation, the presence of the GIS stack forces the carriers to flow to the contacts, first by drift and as they accumulate below the gate insulator as a lateral diffusion current. This longer path makes carriers prone to suffer recombination. During the fabrication procedure, the interface between graphene and Silicon can be seriously degraded affecting a variety of parameters that have been analysed. Thermionic velocity and graphene workfunction degradation can modify the short-circuit current and the saturation voltage. Carrier lifetime and mobility reduce the maximum photocurrent achievable. Traps and doping density at the interface originate an S-shaped I-V characteristic, due to the screening of the electric field. Laser analysis shows how the degradation of the silicon surface in contact with the graphene layer affect the device performance when that region is locally illuminated. The presence of the SiO2 with a high quality interface increases the available photocurrent in good agreement with the experimental results. This fact is especially noticeable for high light densities. Photogating in MoTe2 Phototransistors We have checked the impact of interface traps in the behaviour of a MoTe2 photosensor [13]. In particular, the device parameters have been calibrated against experimental results using a distributed direct metal-semiconductor tunnelling model with an image charge barrier lowering. Using this model, we have reproduced to a very good degree of accuracy the experimental transfer and output curves in dark and illumination conditions, respectively. We have seen the photogating effect is an important feature of the devices based on 2D materials, which must be considered to properly use them as photosensors. These traps have been placed at the interface between the oxide and the deposited sheet. Especially for low light intensities, the total photocurrent is dominated by the photogating effect. It has been analysed using different trap profiles, which have shown that the photoconductive gain is more severe with very deep level traps and narrower energy profiles. Final responsivity is enhanced due to this effect, making necessary a calibration of the sensor prior to its practical usage. It is desirable to combine this material with a non-bulk metal to avoid its Fermi level pinning and ensure the desired workfunction. We have then investigated the photogating effect as an important feature of photodevices based on 2D materials, which must be considered to properly model them. The traps have been placed at the interface between the oxide and the channel sheet. For low light intensities, we have observed that the total photocurrent is dominated by the photogating effect, especially for lower metal workfunctions. The photogating has been analysed for different trap profiles, showing that the photoconductive gain is more severe with very deep level traps and narrower energetic profiles. Graphene-MoS2 Phototransistors A novel, low-cost technique to fabricate sub-micron channel length 2D-materials-based devices has been presented. After depositing a few-layer graphene flake between two bulk metal contacts, it is sliced to form the device contacts employing an AFM tip The 2D material forming the channel is deposited then in touch with the resulting graphene layers to form a sub-micron FET structure Using this technique, few-layer MoS2 flake is deposited to fabricate a phototransistor, which can be used as photosensor. The electrical and optoelectronic properties of the resultant device have been studied both experimentally and theoretically. It has been showed that the intermediate graphene layer enables a low Schottky barrier height with the selected semiconductor, providing a low contact resistance [14]. In addition, the fabrication of both contacts from the same graphene flake results in symmetrical contacts, which would be more complicated to get from different mechanically exfoliated graphene. When illuminated, the device shows a high photoresponse, owing to the sub-micron narrow channel length that makes it possible for the photogenerated carriers to flow to the graphene contacts before they are recombined. 4– Conclusions In this Thesis, we have studied, both theoretically and experimentally, several optoelectronic devices based on 2D materials. First we have analysed the performance capabilities of TMD semiconductors, which are limited by the phonon and Coulomb scattering. After that, we have studied a hybrid technology combining graphene and Silicon to make a photodiode, which shows improved capabilities when combined with GIS stacks. We have checked the importance of the access regions in TMD semiconductors, despite the high natural doping density, and the environment adverse effects in the photoresponse of MoS2 and MoTe2 phototransistors, which is the source of photogating effects that can ultimately uncalibrate the light sensor device. Finally, we have experimentally studied a phototransistor made of MoS2 as channel semiconductor and graphene as access regions, proving the advantages of using non-bulk metals with 2D materials.