My Ph.D research is focused on condensed matter physics and materials science. In particular, I am interested in applications of density functional theory to technologically important problems such as high-k materials and epitaxial systems. Using density functional theory I study surfaces, interfaces, and various types of defects. I will describe some of the projects I have been working so far.

  1. High-k materials

    2. High-k materials (oxides with the high dielectric constant) are replacing SiO2 as a gate dielectric in Complementary Metal Oxide Semiconductor (CMOS) devices. One of the most promising materials is HfO2. Theoretical calculations are very helpful in understanding the underlying physics associated with HfO2 as a gate oxide. Even though real structures are more complicated than atomistic models we build we still can extract the basic physics, and answer many questions of practical interests.

    SiO2/HfO2 interface

    Main results: I determined the valence band offset between silica and hafnia with the average potential method and site projected density of states method. It varies from -2.0eV (valence band top of hafnia is below that of silica) to 1.0eV (the valence band top of hafnia is above) from interface to interface.

    interface structure
    I found that the band offset is completely controlled by the average coordination of oxygen at the interfacial layer: the higher the coordination the larger the band offset and it increases almost linearly. If the average coordination were 3 then the Schottky limit for the valence band offset (1.6eV for our case) would be recovered.As one would expect the dipole (extracted from the plane average charge density) at the interface is smaller for highly coordinated structures. In addition, the structures with higher coordination have lower interface energy.

    Impact: HfO2 is grown on top of Si substrate with atomic layer deposition. During the growth a thin SiO2 layer is created. The presence of this thin silica layer completely changes the band alignment, and it can completely change electronic characteristic of a device. Understanding governing factors of the band alignment can help us finding a method to modulate the band alignment and thus improve device characteristics, such as threshold voltage and flat band voltage.

    Details: In order to study this problem I have built multiple atomistic models of hafnia/silica interface starting form the beta-cristobalite (C9) structure of silica and two polymorphs of hafnia, cubic and monoclinic.

    interface structure

    One of the atomistic models of the SiO2/HfO2 interface.

    The main requirement I impose on the interfacial layer is the right stoichiometry, most importantly Si and Hf atoms are connected though O atoms. The requirement of right stocihimetry implies that at the interface there should be only three oxygen atoms per 1x1 cell (bulk SiO2 has two O atoms in a layer per surface cell and HfO2 has four). I found that the most important feature which distinguishes these interfaces from one another is the coordination of interfacial oxygen atoms. The minimal coordination an oxygen atom can have is one and the maximal is three. Average coordination of these three atoms varies form 1.67 to 2.67 for different structures. To explain these ab-initio results I propose that the correction to the Schottky rule has two sources. First, the charge transfer across the interface lowers hafnia states and raises those of silica resulting in a dipolar shift. Second, the subsequent polarization of the interfacial oxygen atoms in response to the dipole layer's field reduces the dipolar shift. I suggest that highly coordinated oxygen atoms screen the interfacial dipole field stronger. Using this model I extract from the results of the ab-initio calculations the oxygen Born effective charge and its dependence on the coordination. In two limiting cases (silica and hafnia) this procedure gives correct values.

    Effects of aluminum incorporation on band alignment at the SiO2/HfO2 interface

    Among other challenges associated with the integration of novel gate dielectric materials into the standard transistor fabrication process is the need to identify metal electrodes, which would exhibit the Si band edge work function values (matching the ones of the n- and p- type of Si substrate). Due to the inherent instability of metals in contact with hafnia under high temperature processing conditions, the focus has shifted towards developing a metal gate stack with appropriate effective work functions, which would provide required low transistor threshold voltage. One of these methods is doping SiO2/HfO2 stack with metal atoms. In this study I demonstrated that incorporation of Al atoms into the SiO2/HfO2 stack may significantly change the band discontinuity between silica and hafnia, and thus affect the effective work-function.

    Main results: I determined that doping at the interface has much lower energy than away from the interface. Therefore, we expect migration of Al atoms towards the interface. For each structure I determine the valence band offset and find that the doping near the interface can change the band offset as much as 2eV with respect to the undoped structure. Obviously, doping away from the interfacial layer has no effect on the band discontinuity. These results suggest that by choosing doping with right amount of Al atoms one can tune the band alignment and improve electrical characteristics of the CMOS device.

    interface structure

    An atomistic model of Al incorporation at the SiO2/HfO2 interface. Two silicon atoms are substituted with alumina atoms and one oxygen atom is removed.

    Details: I constructed several stoichimetric Al doping complexes in the SiO2/HfO2 gate stack starting with one of my SiO2/HfO2 models (one with the lowest interface energy and smallest interface dipole). This is achieved by substituting two Si atoms with Al atoms and removing one oxygen. Another way to create a stoichiometic doping complex is to substitute only one Si atom with Al atom and incorporate one Al atom and one O atom interstitially. I considered doping in different places: at the interface, in the bulk SiO2, and in the bulk HfO2. For each of them I consider several versions. I calculated formation energies for each structure with respect to different reactions, and also as a function of oxygen chemical potential. Qualitatively I explain this result in the same manner as the previous one with a plane capacitor model. Since Al has higher electronegativity than Hf(1.6 for Al and 1.3 for Hf), by substituting Si atoms with Al we still will have charge transfer from Hf to Al atoms. This charge is screened by oxygen layer. However, now oxygen content is lower because we had to remove oxygen to maintain the stoichiometry. Therefore, the screening is reduced and the overall dipole is increased. This means that the valence band of HfO2 moves down and that of SiO2 moves up.

    HfO2/Rh interface

    (coming soon)

  2. Growth of Sr layer on stepped Si(001) surface

    3. Side view of Si(001) surface with double steps.

    a) Top view of stepped Si(001) surface, dimers shift at the step edge. b) One Sr atom on top of the step edge.