Electrical investigation of p-type 4H-SiC heavily doped by ion implantation

In the last decades, an increasing interest in the research field of wide bandgap semiconductors was observed, mostly due to the progressive approaching of silicon-based devices to their theoretical limits. 4H-SiC is an example among these, and is a mature compound for applications. The main advantages offered 4H-SiC in comparison with silicon are an higher breakdown field, an higher thermal conductivity, a higher operating temperature, very high hardness and melting point, biocompatibility, but also low switching losses in high frequencies applications and lower on-resistances in unipolar devices. Then, 4H-SiC power devices offer great performance improvement; moreover, they can work in hostile environments where silicon power devices cannot function. Ion implantation technology is a key process in the fabrication of almost all kinds of SiC devices, owing to the advantage of a spatially selective doping. This work is dedicated to the electrical investigation of several differently-processed 4H-SiC ion- implanted samples, mainly through Hall effect and space charge spectroscopy experiments. It was also developed the automatic control (Labview) of several experiments. In the work, the effectiveness of high temperature post-implant thermal treatments (up to 2000°C) were studied and compared considering: (i) different methods, (ii) different temperatures and (iii) different duration of the annealing process. Preliminary p + /n and Schottky junctions were also investigated as simple test devices. 1) Heavy doping by ion implantation of single off-axis 4H-SiC layers The electrical investigation is one of the most important characterization of ion-implanted samples, which must be submitted to mandatory post-implant thermal treatment in order to both (i) recover the lattice after ion bombardment, and (ii) address the implanted impurities into lattice sites so that they can effectively act as dopants. Electrical investigation can give fundamental information on the efficiency of the electrical impurity activation. To understand the results of the research it should be noted that: (a) To realize good ohmic contacts it is necessary to obtain spatially defined highly doped regions, which must have conductivity as low as possible. (b) It has been shown that the electrical activation efficiency and the electrical conductivity increase with the annealing temperature increasing. (c) To maximize the layer conductivity, temperatures around 1700°C are generally used and implantation density high till to 10 21 cm -3 . In this work, an original approach, different from (c), is explored by the using very high annealing temperature, around 2000°C, on samples of Al + -implant concentration of the order of 10 20 cm -3 . Several Al + -implanted 4H-SiC samples, resulting of p-type conductivity, were investigated, with a nominal density varying in the range of about 1-5∙10 20 cm -3 and subjected to two different high temperature thermal treatments. One annealing method uses a radiofrequency heated furnace till to 1950°C (Conventional Annealing, CA), the other exploits a microwave field, providing a fast heating rate up to 2000°C (Micro-Wave Annealing, MWA). In this contest, mainly ion implanted p-type samples were investigated, both off-axis and on-axis <0001> semi-insulating 4H-SiC. Concerning p-type off-axis samples, a high electrical activation of implanted Al (50-70%) and a compensation ratio below 10% were estimated. In the work, the main sample processing parameters have been varied, as the implant temperature, CA annealing duration, and heating/cooling rates, and the best values assessed. MWA method leads to higher hole density and lower mobility than CA in equivalent ion implanted layers, resulting in lower resistivity, probably related to the 50°C higher annealing temperature. An optimal duration of the CA treatment was estimated in about 12-13 minutes. A RT resistivity on the lowest reported in literature for this kind of samples, has been obtained. 2) Low resistivity data: variable range hopping Notwithstanding the heavy p-type doping levels, the carrier density remained less than the critical one required for a semiconductor to metal transition. However, the high carrier densities obtained was enough to trigger a low temperature impurity band (IB) conduction. In the heaviest doped samples, such a conduction mechanism persists till to RT, without significantly prejudice the mobility values. This feature can have an interesting technological fall, because it guarantee a nearly temperature- independent carrier density, it being not affected by freeze-out effects. The usual transport mechanism occurring in the IB conduction is the nearest neighbor hopping: such a regime is effectively consistent with the resistivity temperature behavior of the lowest doped samples. In the heavier doped samples, however, a trend of the resistivity data compatible with a variable range hopping (VRH) conduction has been pointed out, here highlighted for the first time in p-type 4H-SiC. Even more: in the heaviest doped samples, and in particular, in those annealed by MWA, the temperature dependence of the resistivity data is consistent with a reduced dimensionality (2D) of the VRH conduction. In these samples, TEM investigation pointed out faulted dislocation loops in the basal plane, whose average spacing along the c-axis is comparable with the optimal length of the hops in the VRH transport. This result suggested the assignment of such a peculiar behavior to a kind of spatial confinement into a plane of the carrier hops. 3) Test device the p + -n junction In the last part of the work, the electrical properties of 4H-SiC diodes were also studied. In this case, a heavy Al + ion implantation was realized on n-type epilayers, according to the technological process applied for final devices. Good rectification properties was shown from these preliminary devices in their current-voltage characteristics. Admittance spectroscopy and deep level transient spectroscopy measurements showed the presence of electrically active defects other than the dopants ones, induced in the active region of the diodes by ion implantation. A critical comparison with the literature of these defects was performed. Preliminary to such an investigation, it was assessed the experimental set up for the admittance spectroscopy and current-voltage investigation and the automatic control of these measurements.

Studies on Wilson loops, correlators and localization in supersymmetric quantum field theories

In this thesis we study at perturbative level correlation functions of Wilson loops (and local operators) and their relations to localization, integrability and other quantities of interest as the cusp anomalous dimension and the Bremsstrahlung function. First of all we consider a general class of 1/8 BPS Wilson loops and chiral primaries in N=4 Super Yang-Mills theory. We perform explicit two-loop computations, for some particular but still rather general configuration, that confirm the elegant results expected from localization procedure. We find notably full consistency with the multi-matrix model averages, obtained from 2D Yang-Mills theory on the sphere, when interacting diagrams do not cancel and contribute non-trivially to the final answer. We also discuss the near BPS expansion of the generalized cusp anomalous dimension with L units of R-charge. Integrability provides an exact solution, obtained by solving a general TBA equation in the appropriate limit: we propose here an alternative method based on supersymmetric localization. The basic idea is to relate the computation to the vacuum expectation value of certain 1/8 BPS Wilson loops with local operator insertions along the contour. Also these observables localize on a two-dimensional gauge theory on S^2, opening the possibility of exact calculations. As a test of our proposal, we reproduce the leading Luscher correction at weak coupling to the generalized cusp anomalous dimension. This result is also checked against a genuine Feynman diagram approach in N=4 super Yang-Mills theory. Finally we study the cusp anomalous dimension in N=6 ABJ(M) theory, identifying a scaling limit in which the ladder diagrams dominate. The resummation is encoded into a Bethe-Salpeter equation that is mapped to a Schroedinger problem, exactly solvable due to the surprising supersymmetry of the effective Hamiltonian. In the ABJ case the solution implies the diagonalization of the U(N) and U(M) building blocks, suggesting the existence of two independent cusp anomalous dimensions and an unexpected exponentation structure for the related Wilson loops.