Classification of materials
The symmetry of materials whether it is a crystal, a thin film, or a polycrystalline, af-fects its properties. Based on symmetry elements of crystals, there are 230 space groups, divided into 32 point groups, which are subdivisions of 7 crystal systems (triclinic, mon-oclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, and cubic). Among these 32 crystal classes, 11 are centrosymmetric containing an inversion center, that do not exhibit any polar properties. The remaining 21 noncentrosymmetric point groups have polar properties with the exception of the cubic point group 432. These 20 point groups are often called piezoelectric point groups. Piezoelectricity results from the coupling of me-chanical stress and electrical energy in the material. Among these piezoelectric point groups, 10 groups have a unique polar axis and may exhibit a spontaneous polarization vector PS in the absence of an external electric field, this is referred to as the pyroelectric effect. Pyroelectric crystalline materials belong to 10 polar point groups: 1, 2, m, 2mm, 4, 4mm, 3, 3m, 6, and 6mm. On the other hand, polycrystalline and ceramics materials can’t be described by the same discrete symmetry elements as crystals. It is more complex to describe the orientation of grains within a ceramic material, their structures belong to a textural or basic point groups. In this case, the symmetry axis is of an infinite order with an ∞ symbol, meaning that the material can be rotated by any angle around this infin-ity axis without changing its properties. Ceramics with randomly oriented grains have a spherical symmetry ∞∞m which is centrosymmetric and does not exhibit any piezoelec-tric effects even if each grain orientation belongs to a polar point group. If the ceramic is ferroelectric, the polarization of each grain can be oriented by an external electric field in the direction of the field. The polarized ceramic possesses a cone symmetry ∞m display-ing both piezoelectric and pyroelectric effects[6–8].
Fig. 1.1 shows a general representation of dielectric materials classification. Ferroelectrics form a subgroup of pyroelectrics that are a subgroup of piezoelectrics. The main charac-teristic of a ferroelectric material is having a spontaneous polarization that can be reversed by an applied electric field.
In summation, the symmetry of the materials plays an important role in defining their properties; ferroelectrics are a subclass of pyroelectrics and piezoelecrics. They are an im-portant class of materials that exhibit better pyroelectric and piezoelectric properties than nonferroelectrics.
Theory of ferroelectricity
An introduction is given on the important parameters used to describe the ferroelec-tricity phenomenon. The theoretical approach is described using thermodynamic con-cepts, which are the building blocks for the theory of thermodynamics in ferroelectrics. Moreover, the ferroelectric phenomenon is described with specific details on the phase transitions in ferroelectric materials and a main focus on the second-order(continuous) phase transition.
Let us introduce some important dielectric parameters that are going to be used in the thermodynamic relations later on in this section [6, 7].
A dipole moment is a measure of the separation of two opposite electrical charges in a molecule or an atom. The magnitude of the dipole moment vector µ is equal to the electric charge q multiplied by the distance d between the charges and the direction is from negative charge to positive charge.
Figure 1.2: Electric dipole moment
In polar dielectric materials, dipole moments are present in molecules or atoms be-cause the centers of positive and negative charges do not coincide. The summation of these electric dipole moments per unit volume of the material gives the electric polariza-tion P.
P = Pi µ (1.1)
where V is the volume of the material.
Electric displacement and dielectric constant
Upon the application of an external electric field on the dielectric material, the expres-sion of the polarization Pi induced in the insulating material by an electric field vector Ej is given by:
Pi = χijEj (1.2)
χij is the dielectric susceptibility of the material.
The electric displacement D developed inside the material due to the application of the electric field E is written as follows:
Di = ε0Ei + Pi (1.3)
0 = 8.854×10−12 F.m−1 is the permittivity of free space, another expression of D can be written using Eq.(1.2) and (1.3):
Di = ε0Ei + χijEj = εijEj (1.4)
where εij = ε0 δij + χij is the dielectric permittivity of the material with 1, if i=j
δij= ε0 δij << χij in most ferroelectric materials so εij ≈ χij.
0, if i 6= j
The relative dielectric permittivity ζij, also known as the dielectric constant of the ma-terial is more often used than the dielectric permittivity.
ζij = εij/ε0 (1.5)
The dielectric permittivity εij and the relative dielectric permittivity ζij are second rank tensors.
The coupling of the thermal, elastic and electrical effects is introduced using the ther-modynamic approach to define the pyroelectric and ferroelectric effects. Let us assume that the thermal, elastic and dielectric behavior of a homogeneous dielectric material can be described by six parameters: temperature T, entropy S, stress X, strain x, electric field E and electric displacement D.
According to the first and second laws of thermodynamics, assuming that the change in the internal energy U of a dielectric is reversible, dU is given by Eq.(1.6) as: dU = T dS + Xdx + EdD (1.6)
In most experimental situations, the temperature T, stress X and electric field E are most likely to be manipulated. For that reason, it is more convenient to switch the independent variables1 from (S,x,D) to (T,X,E). This change in the set of variables will affect the ther-modynamic potential of the internal energy U, by adding the terms -TS – Xx -ED to U. A new thermodynamic potential is defined as : G = U − T S − Xx − ED (1.7)
It is known as the Gibbs free energy , the differential form of G together with the Eq.(1.6) gives the following: dG = −SdT − xdX − DdE (1.8)
From Eq.(1.8) we can obtain the following terms: S=− @T ! x = − @X ! D=− @E! (1.9)
The coefficients in the equations (1.10) to (1.12) have physical interpretation for the dif-ferent coupled effects. We can note the most important coefficients, those relating strain x to stress X (elastic compliance), strain x to electric field E (piezoelectric coefficient), elec-tric displacement D to temperature T (pyroelectric coefficient), electric displacement D to electric field E (dielectric constant or permittivity) and strain x to temperature T (thermal expansion coefficient).
1 variables related to the bulk properties of the material unlike dependent variables which take into account the material properties and dimensions.
Ferroelectrics are dielectrics which are polar materials that posses a spontaneous po-larization vector PS, existing inherently in the material without the application of an ex-ternal electric field. The distinct characteristic of a ferroelectric material is the ability of the PS to switch between at least two equilibrium orientations in the presence of an ap-plied electric field. These materials go through a structural phase transition from a high temperature phase (paraelectric non-polar phase) to a lower temperature phase (ferro-electric polar phase). Phase transitions are based on the change of the symmetry inside the material, for example, the most common transition is from cubic to tetragonal sym-metry. The transition temperature is called the Curie temperature TC . Fig.(1.3) (a) shows how the dielectric permittivity drops above TC . It follows the Curie-Weiss law: ε=ε0+ C . (1.13)
C is the Curie constant.
The phase transitions could be of the first or second order, the order is determined by the discontinuity in the partial derivatives of the Gibbs free energy of the ferroelectric. First order transitions are discontinuous, while second order transitions are continuous. In the case of ferroelectric phase transitions, the independent parameters are often chosen to be (D, X, T) and by choosing this set, the corresponding free energy is the elastic Gibbs energy G1, which can be obtained like the Gibbs free energy from the internal energy U (see section 1.3.2). The detailed thermodynamic calculations are found elsewhere [5, 6].
In an ideal ferroelectric crystal, it is assumed that the spontaneous polarization is uni-formly aligned throughout the entire crystal along the same direction. However, this is not true for real ferroelectrics, where imperfections and inhomogeneities are present in the structure, thus near those defects, the spontaneous polarization may differ from the perfect crystal. The start of spontaneous polarization at the transition temperature leads to surface charges which in their turn, create an electric field called the depolarization field ED. The depolarizing fields arise from the nonhomogeneous distribution of spon-taneous polarization in the crystals (grains in ceramics and thin films) oppositely to the direction of the PS. The energy associated with that field is given by:
WE = 1 ZV D.E dV . (1.14)
When cooling from the paraelectric phase to the ferroelectric phase, different regions with uniformly oriented spontaneous polarization in different directions form. These regions are known as ferroelectric domains. They form in order to minimize the electrostatic energy W of the depolarizing field and the elastic energy attached to the mechanical con-straints to which the ferroelectric material is subjected to during the phase transition. The boundaries separating domains are referred to as domain walls associated with a domain wall energy Ww depending on the domain geometry, if the domains have oppositely ori-ented polarization, the separation is called 180° walls and those who separate domains with mutually perpendicular polarization are called 90° walls as shown in Fig.(1.3) (b).
Figure 1.3: Illustration of (a): Ferroelectric- paraelectric phase transition from tetragonal to cubic symmetry and (b): 90° and 180° domain walls formation in a ferroelectric material with tetragonal symmetry.
The geometry of the domain is affected by several factors including crystal symmetry, defects, the magnitude of mechanical stress, dielectric and elastic compliances, in addition to sample preparation and geometry. If the width of a domain approaches the thickness of a domain wall, ferroelectricity may cease to exist because it is no longer possible to compensate the depolarizing field in the crystal.
In summation, the ferroelectric splits into domains to minimize the electrostatic energy associated with the depolarizing field, also it occurs due to mechanical stresses. The en-ergy of domain walls can alter the ability of the ferroelectric domains to minimize the depolarizing energy due to domain width [5, 6].
The most distinguished characteristic of ferroelectrics is that the spontaneous polar-ization can be reversed with an applied electric field. A ferroelectric hysteresis loop will occur when the domains of the ferroelectric material switch. Fig.(1.4) shows a typical ferroelectric hysteresis loop. At low electric field, polarization switching does not occur, the field is not strong enough to reorient the domains, thus the ferroelectric behaves like an ordinary dielectric. As the electric field increases, the polarization increases in a non-linear fashion with a curvature. Once all the domains are aligned, the polarization reaches a saturation point. Some domains start to back switch when the electric field is decreased and the value of the polarization at zero field is called the remanent polarization Pr. The field necessary to bring the polarization to zero is called the coercive field Ec. The spon-taneous polarization is equal to the saturation value of the polarization extrapolated to zero field as shown in Fig.(1.4).
The coercive field, spontaneous and remanent polarization and shape of the loop can be affected by many factors including the film thickness, the presence of charged defects, mechanical stresses, preparation conditions and thermal treatment.
Charge-voltage response in true ferroelectrics
As mentioned previously, the P-E loop is a plot of the charge or polarization as a func-tion of the electric field E at a certain frequency. The charge and polarization responses are assumed to be equal for high relative permittivity materials. The understanding of the P-E measurement significance is made easier with some linear devices examples. For an ideal capacitor, the curve is a straight line whose gradient is proportional to the capac-itance (Fig.5.26 (a)). This is because the current leads the voltage by 90°, hence, the charge in an ideal capacitor is in phase with the voltage. In the case of an ideal resistor, the cur-rent and voltage are in phase and so the P-E loop becomes a circle. Fig.5.26 (b) shows the circular P-E loop with the center at the origin. When combining these two components in parallel, a lossy capacitor (Fig.5.26 (c)) is obtained where the area within the loop is pro-portional to the loss tangent of the device, and the slope proportional to the capacitance. Loss can be due to dielectric hysteresis or leakage current or both. Fig.5.26 (d) shows the P-E loop of a true non-linear ferroelectric. These loops are usually centered around zero and for both the lossy capacitor and the ferroelectric they cross the y axis at a non-zero value. In the ferroelectric case, this crossing point provided a measure of the remnant polarization. For the lossy capacitor the non-zero crossing point does not indicate any remanence. Caution must be exercised in interpreting the crossing point on the charge (polarization) axis as ferroelectric remanence, particularly where there may be leakage currents or the ferroelectric behavior is not clearly established. There are many examples where lossy dielectric loops have been incorrectly presented as evidence of ferroelectric behavior [9–11].
Figure 1.5: Schematic P-E response (in arbitrary units) of (a) linear capacitor, (b) linear resistor, (c) lossy capacitor and (d) non-linear ferroelectric.
Dielectric breakdown mechanisms
There are three basic mechanisms by which an insulating material breaks down un-der the application of an electric field : intrinsic breakdown, thermal breakdown and discharge breakdown. During real breakdown, all of these may occur in combination and, perhaps in the case of sintered ceramics, will be dominated by residual porosity or surface asperities, rather than characteristic properties of the bulk material. Porosity has been shown to be the key factor to initiate breakdown in most common ceramics. The de-pendence of the size and thickness can be explained by the fact that the electric field has a smaller chance of finding a critical defect at which breakdown may be initiated in thinner material. The mechanism by which the material then breaks down is open to debate but may include the idea of the propagation of a charge ‘streamer’ (in a similar manner to that described for lightening) progressing from pore to pore via conventional conduction routes. The permittivity of the sample has been shown to play a role in the breakdown phenomenon, but this has not been satisfactorily developed. Breakdown may be caused by longer term effects such as gradual reduction in resisitivity at a continuous applied high stress, as well as environmental effects such as moisture, temperature, electrochemi-cal reactions between electrodes and the material, and structural effects such as sharp and point discontinuities which might have the effect of amplifying the electric stress in cer-tain regions. Field emission injection of electrons from the electrodes can cause avalanche ionisation and subsequent breakdown [12, 13]. Other causes of breakdown can be related to the presence of carbonate species and organic residue from the precursor solution such as Na+, Cl−, F− and OH−. Those species act like mobile ions which can also be the ori-gin of leakage current. Intrinsic defects, microscopic cracks, metallic impurities and dust particle on the surface of the thin film samples can also lead to electrical breakdown.
Table of contents :
1 Ferroelectricity versus structure
1.1 Historical background
1.2 Classification of materials
1.3 Theory of ferroelectricity
1.3.1 Important parameters
1.3.2 Thermodynamic approach
1.3.3 Ferroelectric phenomenon
1.4 Ferroelectric materials
1.4.1 Single crystals
1.4.4 Thin films
1.5 Lead free thin film materials
1.5.1 Barium strontium titanate thin films
126.96.36.199 Perovskite structure
188.8.131.52 Composition dependent TC
184.108.40.206 Microstructure of CSD processed BST thin films
1.5.2 Strontium barium niobate
220.127.116.11 Structure and Curie temperature
18.104.22.168 Dielectric properties of SBN thin films
2 Thin film capacitor elaboration and characterization methods
2.2 Elaboration of thin films
2.2.1 Thin film deposition methods
2.2.2 Sol gel based method
2.2.3 MOD method
22.214.171.124 Solution coating techniques
2.2.4 Processing of solution based perovskite thin films
126.96.36.199 Solution chemistry effects
188.8.131.52 Heat treatment
2.2.5 Technological process of thin film formation
184.108.40.206 Equipments and materials
220.127.116.11 Thin film deposition
18.104.22.168 Film annealing process
22.214.171.124 Technological difficulties and solutions
2.3 Functional ferroelectric thin film capacitors
2.3.1 Thin film capacitors
2.3.2 Electrode choice
126.96.36.199 Experimental work
188.8.131.52 Top electrode deposition
2.4 Characterization techniques of thin films
2.4.1 Morphological and structural characterization
2.4.2 Physico-chemical characterization
2.4.3 Electrical characterization
184.108.40.206 Dielectric measurements
220.127.116.11 Current density
18.104.22.168 Ferroelectric measurements
3 Carboxylate based sol gel chemistry: from solutions to thin film formation
3.2 Alkoxide and carboxylate chemical approaches
3.3 Synthesis routes of metal carboxylates
3.4 Solution chemistry of SBN carboxylates
3.4.1 Choice of carboxylic acids
3.4.2 Synthesis of SBN precursor solutions
3.4.3 Preparation of SBN thin films
3.5 Characterization of SBN thin films
3.5.1 Morphological study
3.5.2 Composition analysis
3.6 BST solutions
4 Effect of thermal annealing on the morphology of sol–gel processed BST thin films: Consequences on electrical properties
4.2 BST thin films
4.3 Fundamental study of BST thin films
4.3.1 Decomposition of BST solution
4.3.2 Thin film preparation
4.3.3 GISAXS study of BST films
22.214.171.124 In situ GISAXS
126.96.36.199 Ex situ GISAXS
188.8.131.52 Quantitative film porosity
4.3.4 Structural study of BST films
4.3.5 Morphology study and modeling
4.4 BST thin film capacitor study
4.4.1 Morphology and structure
4.4.2 Electrical properties
5 Investigating the dilution effect on the morphological, structural and electrical properties of BST thin films
5.2 Precursor solution dilution study
5.2.1 Diluted BST thin film preparation
5.2.2 Diluted thin films morphology and structure
184.108.40.206 Roughness and grain size
5.3 Electrical properties
5.3.1 Dielectric properties
5.3.2 Current density
5.3.3 Poling of the BST diluted thin films
5.3.4 Ferroelectricity vs structure
220.127.116.11 Capacitance vs Bias
18.104.22.168 Polarization-field hysteresis loop
A Clean room equipments and materials
A.1 Spin coater
A.2 Hot plate
A.3 Platinized silicon wafers
B Electrical characterization setup
B.1 LCR meter
B.2 Setup for the hysteresis loop measurements
C GISAXS equipment
C.1 GISAXS setup
C.2 Anton Paar