Raphaël Renoud

Monte Carlo simulation of the charge distribution induced by a high-energy electron beam in an insulating target

We have developed a simulation model of the implantation of a negative charge into an insulating target by a fixed and well-focused high-energy electron beam. We are particularly interested in the evolution of the distribution of the charges trapped during the bombardment. Our simulation is based on a Monte Carlo method permitting us to account for the various electron-insulator interactions. The charge carriers, unless they are emitted into vacuum, are followed until they have lost most of their kinetic energy. After that, they drift along the internal electric field lines before getting trapped. The field generated by these trapped charges is calculated self-consistently by solving the appropriate Poisson equation. When the trapping site density is sufficiently high, the dynamics of the charge is principally governed by the self-regulation of the total secondary emission yield. The total number of implanted charges is therefore limited and a quasi-stationary regime arises. The charge distribution builds up, forming a negative semi-ellipsoidal shell whose extent is directly related to the maximum penetration of the primary electrons. The internal region corresponds to a mixing zone with a weak positive mean charge. This characteristic distribution appears at all the primary beam energies considered. On the other hand, when the trapping site density is too low, the whole region under the beam is saturated and the mixing zone is completely occupied by electrons before the self-regulation of the total secondary yield acts.

Description of the low field nonlinear dielectric properties of ferroelectric and multiferroic materials

Ferroelectric and multiferroic materials present a nonlinear variation in their permittivity due to domain wall motion. Currently, this variation is described either by the Rayleigh law for fields above a threshold or by a power law for soft ferroelectrics. We propose a hyperbolic law based on the contributions of domain walls and intrinsic lattice which includes the two classic approaches. The threshold field is clearly defined by considering reversible and irreversible components of the permittivity. A good agreement between the hyperbolic law and experimental data is obtained. Moreover, we show that the threshold field obeys to the Volgel–Fulcher law.

Influence on the secondary electron yield of the space charge induced in an insulating target by an electron beam

The building up of the space charge induced by electron bombardment in an insulating target is due to the stabilization of self-trapped electrons and holes in polaronic traps. For the energies considered, the target charges positively and the secondary electrons emitted at low energies can be attracted back to the surface. This results in a self-regulation effect where the total secondary yield tends to unity and the surface potential stabilizes at a low positive value. This conclusion is checked for various experimental conditions. The electrons landing on the target form a ring of negative charges that progressively spread out on the surface of the sample.

Effect of Manganese Doping of BaSrTiO 3 on Diffusion and Domain Wall Pinning

In the present paper, the influence of manganese doping on the dielectric properties of BaSrTiO 3 thin films is presented. The real and imaginary parts of the materials permittivity have been measured in a large frequency range (100 Hz – 1 MHz) and as a function of the electric field. The tunability and the figure of merit of the material have been obtained from the measurement of the permittivity under an applied DC bias electric field. For the undoped material, the dielectric losses become important for a large DC bias which leads to breakdown. At a suitable dopant rate, this effect disappears. In order to better understand the origin of the related phenomena, we measure the permittivity as a function of the AC excitation amplitude and we decompose the obtained permittivity with the hyperbolic law. This enables to extract the different contributions of the bulk (low frequency diffusion and high frequency lattice relaxation) and of the domain wall motions (vibration and pinning/unpinning) to the materials dielectric permittivity and to understand the effect of manganese doping on each contribution. Knowledge of the related mechanisms allows us to establish the optimum dopant rate (mainly conditioned by the lattice contribution) and to reduce the domain wall motion, which finally is beneficial for the desired properties of the ferroelectric thin film. A particular attention is paid to low frequency diffusion, an especially harmful effect when a DC biasing is mandatory (tunable electronic component in mobile telecommunication devices for example).

Measurement and modeling of dielectric properties of Pb(Zr,Ti)O 3 ferroelectric thin films

In this study, the real and imaginary parts of the complex permittivity of lead zirconate titanate ferroelectric thin films are studied in the frequency range of 100 Hz to 100 MHz. The permittivity is well fitted by the Cole-Cole model. The variation of the relaxation time with the temperature is described by the Arrhenius law and an activation energy of 0.38 eV is found. Because of its nonlinear character, the dielectric response of the ferroelectric sample depends on the amplitude of the applied ac electric field. The permittivity is composed of three different contributions: the first is due to intrinsic lattice, the second is due to domain wall vibrations, and the third is due to domain wall jumps between pinning centers. This last contribution depends on the electric field, so it is important to control the field amplitude to obtain the desired values of permittivity and tunability.

Decomposition of the different contributions to permittivity, losses, and tunability in BaSrTiO3 thin films using the hyperbolic law

In this paper, the different contributions to the permittivity of a 1% manganese-doped BaSrTiO3 thin film are presented as a function of the applied DC field. The hyperbolic law has been used to discern the lattice, domain wall vibration, and pinning/unpinning contributions. This decomposition permits us to study the weight of the respective contribution in the total permittivity, the losses, and the tunability. By determining the figure of merit (FoM) of each contribution, the ratio between tun-ability and losses, it is possible to identify the phenomenon which should be limited or enhanced in order to optimize the materials dielectric properties. It is shown that the tunability of the domain wall contribution (approximately 80%) is very important compared to the lattice contribution (41%), the associated dissipation factor, however, is also much larger (0.2 instead of 0.014). Even if the domain wall contribution has been shown to be weak in the investigated thin film (less than 3% in permittivity and tunability), the weight of the losses is not negligible (around 18%). Hence, the domain contribution has to be limited in order to conserve a high FoM for the material. Moreover, it is shown that the AC field used for the materials characterization is important because it governs the weight of the domain wall losses and thus the FoM.

Domain wall motions in BST ferroelectric thin films in the microwave frequency range

The existence of domain wall motion at microwave frequencies and its contribution to the ferroelectric complex permittivity is shown by evaluating the dielectric properties of BaSrTiO 3 (BST) thin films as a function of the incident power. Even at low AC field amplitudes, the presence of the domain walls and the correlated motions (vibration and jumps) result in sensitivity of the dielectric properties to the incident field amplitude. Although the contribution of domain wall motion to the real part of the permittivity is not preponderant (less than 10 %), it represents more than 50 % of the materials global dielectric losses. This illustrates the importance to consider domain wall motion even in the microwave frequency region and the necessity to take into account the applied AC field amplitude (and thus the incident power) when characterizing ferroelectric materials. The present study has been realized on BST thin films, elaborated by pulsed laser deposition on MgO/Ir substrates.

Effect of the incident power on permittivity, losses and tunability of BaSrTiO 3 thin films in the microwave frequency range

Domain wall motions in ferroelectrics participate to the materials complex permittiv-ity and are responsible for their sensitivity of the dielectric properties to the driving electric field and thus to the incident power at microwave frequencies. In the present study, the dependence of the permittivity, the dielectric losses and the tunability of Ba 2/3 Sr 1/3 TiO 3 (BST) thin films on the incident power and on the bias fields is examined at a frequency of 500 MHz. While, the domain wall motion participates only slightly to the permittivity (< 5 %), it strongly influences the losses due to its very dissipative behavior. As a consequence, the Figure of Merit (FoM , ratio between tunability and dielectric losses) of the material depends on the applied microwave power. In the present study, a decrease of the FoM from 29 to 21 is observed for an incident power varying from −20 dBm to 5 dBm. When characterizing ferroelectric materials, the incident power has to be considered; moreover, domain wall motion effects should be limited in order to achieve a high FoM and less power sensitivity.

Ferroelectric tunability: From characterization to telecomunication application

Advanced dielectric spectroscopy enables studying of the ferroelectric complex permittivity. Interpretation with the hyperbolic law provides a better fundamental understanding of the materials tunability: bulk contribution, domain wall vibration and displacements may be discerned. Applications, like mobile telecommunication terminals may profit for the design of miniaturized and tunable antennas. As an example, conception and realization of a notch slot antenna with an integrated ferroelectric thin film varactor is presented.

Domain wall motion in Pb(Zr0.20Ti0.80)O3 epitaxial thin films

Two Pb(Zr0.20Ti0.80)O3 samples of different thickness and domain configuration have been studied. The c-domain sample was found to have a higher coercive field Ec and higher dielectric losses than the other which presents approximately 60% of c-domains and 40% of a-domains as observed by piezo force microscopy (PFM) characterization. Hyperbolic law measurements reveal that the higher coercive field is due to domain wall pinning in deeper defects and hence a higher field Eth is required for unpinning. The dissipation factors due to domain wall motion, however, are similar in both samples since the domain wall density is low and there is almost no interaction between domain walls. The higher dielectric losses in the c-domain oriented sample are a result of a greater contribution from the lattice and seem to be due to strain from the substrate, which is not relieved in a thin sample. PFM and dielectric characterization are complementary methods which provide a better understanding of the domain wall motion.