Macroscopic Theory of Charged Domain Walls in Ferroelectrics

This thesis consists of a theoretical analysis of charged domain walls in ferroelectrics based on Landau theory and the theory of semiconductors. First, the internal structure of a 180-degree charged domain wall is considered. It is shown that different regimes of screening and different dependences for width of charged domain walls on the temperature and parameters of the system are possible, depending on spontaneous polarization and concentration of carriers in the material. In typical perovskites the screening is provided by a degenerate electron gas in the nonlinear screening regime. The corresponding width of charged domain walls is about one order of magnitude larger than the width of neutral domain walls. The formation energies of "head-to-head" walls in an isolated sample under different regimes of screening are derived, neglecting the poling ability of the surface. In the nonlinear regimes of screening, this energy is equal to the energy necessary for the creation of electron-hole pairs in a sufficient amount to screen the spontaneous polarization, which is proportional to the band gap of the ferroelectric. It is shown that if the poling ability of the surface is large enough, either "head-to-head" or "tail-to-tail" configurations can be energetically favorable in comparison with the monodomain state of the ferroelectric. For the case of a surface with weak poling ability the existence of charged domain walls in bulk ferroelectrics is merely a result of domain-growth kinetics. It is shown that, at large enough sample thicknesses, a charged domain wall can be energetically favorable in comparison to other possible states: a multidomain state with antiparallel domains separated by neutral walls and a state with zero polarization. This size effect provides a possible explanation of the reason for experimental observation of 180-degree charged domain walls in bulk lead titanate but not in barium titanate. The results obtained for the case of an isolated ferroelectric sample are compared with the results for a sample with electrodes. It is shown that a charged domain wall in an electroded sample can either be metastable or stable, depending on the work function difference between the electrodes and the ferroelectric and the poling ability of the surface. The interaction of an electric field with charged domain walls in ferroelectrics is also addressed. A general expression for the force acting per unit area of the a charged domain wall carrying free charge is derived. It is shown that in proper ferroelectrics, the free charge carried by the wall dependeds on the size of the adjacent domains. As a result, it is found that the mobility of such a domain wall (with respect to the applied field) is sensitive to the parameters of the domain pattern containing this wall. The problem of the force acting on a planar charged 180° domain wall normal to the polarization direction in a periodic domain pattern in a proper ferroelectric is solved analytically. It is shown that, in the linear regime under small applied field, the forces acting on walls in such a pattern increase with decreasing wall spacing. The direction of the forces coincides with those for the case of the corresponding neutral walls. At the same time, for large enough wall spacings and large enough fields, these forces can be of the opposite sign. It is shown that the domain pattern under consideration is unstable in a defect-free ferroelectric. The poling of a crystal containing such pattern, stabilized by the pinning pressure, is also considered. It is shown that, except for a special situation, the presence of charge domain walls can make poling more difficult. It is demonstrated that the results obtained are also applicable to "zig-zag" walls under the condition that the "zig-zag" amplitude is much smaller than the domain wall spacing. A mechanism that leads to a strong enhancement of the dielectric and piezoelectric properties in ferroelectrics with increasing density of charged domain walls is proposed. It is demonstrated that an incomplete compensation of bound polarization charge at these walls creates a stable built-in depolarizing field across each domain leading to increased electromechanical response. This model clarifies a long-standing unexplained effect of domain wall density on macroscopic properties of domain engineered ferroelectrics. It is demonstrated that lead-free ferroelectrics like barium titanate with dense patterns of charged domain-walls are expected to have strongly enhanced piezoelectric properties, thus suggesting a new route to high-performance, lead-free ferroelectrics. The problem of the screening of ferroelectric bound charge on a ferroelectric-semiconductor interface is considered. It is shown that the screening ability of the interface can be drastically improved due to the presence of a built-in potential in the semiconductor, which depends on the electron affinities and surface state density and can be controlled by a judicious choice of materials.

Head-to-head and tail-to-tail 180^{°} domain walls in an isolated ferroelectric

Maxim Gureev, Nava Setter, Alexander Tagantsev

Head-to-head and tail-to-tail 180 degrees domain walls in a finite isolated ferroelectric sample are theoretically studied using Landau theory. The full set of equations, suitable for numerical calculations, is developed. The explicit expressions for the polarization profile across the walls are derived for several limiting cases and wall widths are estimated. It is shown analytically that different regimes of screening and different dependences for the width of charged domain walls on the temperature and parameters of the system are possible, depending on spontaneous polarization and concentration of carriers in the material. It is shown that the half-width of charged domain walls in typical perovskites is about the nonlinear Thomas-Fermi screening length and about one order of magnitude larger than the half-width of neutral domain walls. The formation energies of head-to-head walls under different regimes of screening are obtained, neglecting the poling ability of the surface. In the nonlinear regimes of screening, this energy is equal to the energy necessary for the creation of electron-hole pairs in the amount sufficient to screen the spontaneous polarization, which is proportional to the band gap of the ferroelectric. It is shown that either head-to-head or tail-to-tail configurations can be energetically favorable in comparison with the monodomain state of the ferroelectric if the poling ability of the surface is large enough. If this is not the case, the existence of charged domain walls in bulk ferroelectrics is merely a result of the domain-growth kinetics. Formation energies of the other possible states, i.e., the multidomain state with antiparallel domains separated by neutral walls and the state with the zero polarization, were compared with the formation energy of the charged domain wall. It was shown that, at large enough sample thicknesses, a charged domain wall can be energetically favorable in comparison with the states mentioned above. This size effect could explain why charged domain walls were observed experimentally in bulk lead titanate but not in barium titanate. The results obtained for the case of an isolated ferroelectric sample were compared with the results for an electroded sample. It was shown that a charged domain wall in an electroded sample can be either metastable or stable, depending on the work-function difference between electrodes and ferroelectrics and the poling ability of the electrode-ferroelectric interface.

2011

Ferroelectric charged domain walls in an applied electric field

Maxim Gureev, Pavel Mokry, Nava Setter, Alexander Tagantsev

The interaction of electric field with charged domain walls in ferroelectrics is theoretically addressed. Ageneral expression for the force acting per unit area of a charged domain wall carrying free charge is derived. It is shown that, in proper ferroelectrics, the free charge carried by the wall is dependent on the size of the adjacent domains. As a result, the mobility of such domain wall (with respect to the applied field) is sensitive to the parameters of the domain pattern containing this wall. The problem of the force acting on a charged planar 180 degrees domain wall normal to the polarization direction in a periodic domain pattern in a proper ferroelectric is analytically solved in terms of Landau theory. In small applied fields (in the linear regime), the force acting on the wall in such pattern increases with decreasing the wall spacing. It is shown that the domain pattern considered is unstable in a defect-free ferroelectric. The poling of a crystal containing such pattern, stabilized by the pinning pressure, is also considered. Except for a special situation, the presence of charge domain walls makes poling more difficult. The results obtained are also applicable to zigzag walls under the condition that the zigzag amplitude is much smaller than the sizes of the neighboring domains.

American Physical Society2012

Ferroelectric gate on AlGaN/GaN heterostructures

Lisa Malin

The capability of switching the spontaneous polarisation under an applied electric field in ferroelectric materials can be exploited for the use in low power, non-volatile, re-writable memory devices. Currently available commercially is ferroelectric random access memory, FeRAM, which allows for high speed, low voltage and greater write-erase endurance compared to its two main competitors, Flash and EEPROM, when using the one transistor – one capacitor configuration. However, it is desired to further optimise the configuration in order to obtain better densification, faster access time and better reliability. One way to do such is to pass from the ferroelectric capacitors and develop ferroelectric field effect transistors. Exploiting the phenomenon of ferroelectricity and integrating ferroelectrics with the semiconductor technology has not been simple. The FeFET has been demonstrated using a silicon-based transistor, however commercial devices are not available. Challenges arise mainly due to the high temperature deposition of perovskite ferroelectrics causing the degradation of the ferroelectric/semiconductor interface due to inter-diffusion. Acquiring long term retention of the transistor behavior has also been problematic due to phenomenons such as charge injection and depolarisation. In this thesis a new approach to the problem of semiconductor devices with a ferroelectric gate is explored. Instead of using a silicon-based device, semiconductor heterostructures are investigated. Combining the high mobility channel existing in semiconductor heterostructures, with the non-volatile switching of the polarisation in the ferroelectric gate can pave the way to novel future devices. The AlGaN/GaN semiconductor heterostructure was chosen for two main reasons. The first is a two dimensional electron gas, 2DEG, located at the AlGaN/GaN interface which possesses better transport properties than a single layered semiconductor. Secondly, GaN and its alloys are known to have large chemical and temperature stability making them ideal to withstand the high temperature deposition process of perovskite ferroelectrics. The deposition of two ferroelectric layers onto the AlGaN heterostructure were investigated. Lead zirconium titanate, PZT, a traditional perovskite ferroelectric deposited at high temperature, was chosen for its high remanent polarisation and low coercive field. An alternative ferroelectric gate, the co-polymer poly(vinylidene fluoride/trifluoroethylene), P(VDF/TrFE)(70:30) was deposited and of interest due its low crystallisation temperature and low dielectric constant. Its remanent polarisation is smaller and coercive field larger than that of PZT, but were determined sufficient to observe the depletion effect in the two dimensional electron gas. The goals accomplished in this research were: Development of Ferroelectric Gate Processing: Deposition processes of the ferroelectric layers were developed and optimised in order to obtain a high quality ferroelectric, while maintaining the original transport properties of AlGaNs 2DEG. The processing of HfO2 and MgO buffer layers were developed and investigated for their effects on limiting unwanted inter-diffusion and charge injection. PZT Gate on Al0.3Ga0.7N: The first successful development and observation of a PZT gate on a Al0.3Ga0.7N/GaN heterostrucutre was accomplished. A (111) oriented PZT(40:60) ferroelectric gate on the Al0.3Ga0.7N heterostructure depleted the sheet resistance of the 2DEG by a factor of three when poling the PZT layer with –40V directly to the conductive cantilever used in a piezoresponse force microscope. This decrease in sheet resistance was stable for more than three days. P(VDF/TrFE)(70:30) Gate on Al0.3Ga0.7N: The ferroelectric co-polymer P(VDF/TrFE) (70:30) was investigated as a gate on the Al0.3Ga0.7N heterostructure. When the P(VDF/TrFE) was poled with –30V to a top electrode the sheet resistance was modulated by a factor three, however there was no retention of this modulation. Ferroelectric Spontaneous Polarisation on a Semiconductor Heterostructure: It was theoretically derived that when depositing a ferroelectric layer onto a semiconductor heterostructure its spontaneous polarisation is dramatically reduced due to the depolarisation field and may be suppressed completely. This decay in spontaneous polarisation can be minimised by using a ferroelectric layer with a small dielectric constant, which justifies the use of ferroelectric polymers as the gate material. Domain Writing:The technique of domain writing using piezoresponse force microscopy showed that it was possible to create domain patterning on the ferroelectric layers that were deposited onto the Al0.3Ga0.7N heterostructure with sub-micron line resolution, on the order of 300nm or better. Using ferroelectrics on semiconductors is not only limited to ferroelectric memory devices. Other applications could be ferroelectric nano-lithography, where a ferroelectric pattern is written with a piezoresponse force microscope, PFM, and this pattern is projected onto the transistors channel, potentially creating quantum/ballistic devices. The challenge of integrating ferroelectrics with semiconductors has yet to be fully understood. One of the main advancements that was reached with this research is the understanding of the decrease of the spontaneous polarisation when a ferrroelectric layer is deposited onto a semiconductor heterostructure of finite thickness. The maximisation of the ferroelectrics polarisation on 20nm of Al0.3Ga0.7N can be obtained when minimising the dielectric constant of the ferroelectric layer. The current challenge is to get a better physical understanding of the limitation of the retention of the spontaneous polarisation, while discovering methods for its improvement.