MT-201A MATERIALS SCIENCE Electrical and Electronic Materials Module 7 Dielelctric Materials Compiled by Dr. Vikram Dabhade Dept. of Metallurgical and Materials Engineering, Indian Institute of Technology Roorkee, Roorkee-247667, Uttrakhand.
INTRODUCTION• Dielectric material: is one that is electrically insulating (non-metallic)and exhibits or may be made to exhibit an electric dipole structure; that is,there is a separation of positive and negative electrically charged entitieson a molecular or atomic level.• While insulating materials are used to resist the flow of current, dielectricmaterials are used to store electrical energy.Capacitance• When a voltage is applied across a capacitor, one plate becomes positivelycharged, the other negatively charged, with the corresponding electric fielddirected from the positive to the negative. The capacitance C is related to thequantity of charge stored on either plate Q by C=Q/Vwhere V is the voltage applied across the capacitor. The units of capacitanceare coulombs per volt, or farads (F).
• Now, consider a parallel-plate capacitor with a vacuum in the region between the plates. The capacitance may be computed from the relationship C = εo A lwhere A represents the area of the plates and l is the distance between them.• The parameter εo is called the permittivity of a vacuum, is a universalconstant having the value of 8.86 x 10-12 F/m.
If a dielectric material is inserted into the region within the plates then C=ε A lwhere ε is the permittivity of this dielectric medium, which will be greaterin magnitude than εo. The relative permittivity εr often called the dielectricconstant, is equal to the ratio εr = ε εowhich is greater than unity and represents the increase in charge storingcapacity by insertion of the dielectric medium between the plates. Thedielectric constant is one material property that is of prime consideration forcapacitor design.
Dielectric Constant (Permittivity)As explained above, dielectric constant or permittivity of a material is definedas the “ratio of capacitance of a capacitor with that material as dielectricbetween the conducting plates, to the capacitance of the same capacitor withvacuum as dielectric medium.” εr = ε / εo or εr = c / coThe relative permittivity of vacuum is 1.00 and that of air is 1.00058 whichis taken as unity. Gases have a relative permittivity slightly higher than unity,while polar liquids and ionic solids have high values of permittivity.
Dielectric Strength (breakdown voltage)• Dielectric strength of an insulating material is the maximum electric fieldstrength that it can withstand intrinsically without breaking down, i.e., withoutexperiencing failure of its insulating properties or it is the minimum electricfield that produces breakdown in a given configuration of dielectric material.• The dielectric strength is also know as the breakdown voltage i.e. the voltagebelow which the dielectric material remains stable but above which it results inthe destruction of insulating properties.• The theoretical dielectric strength of a material is an intrinsic property of thebulk material and is dependent on the configuration of the material on whichthe field is applied.• At breakdown, the electric field frees bound electrons. If the applied electricfield is sufficiently high, free electrons may become accelerated to velocitiesthat can liberate additional electrons during collisions with neutral atoms ormolecules in a process called avalanche breakdown.
• Breakdown occurs quite abruptly (typically in nanoseconds)., resulting inthe formation of an electrically conductive path and a disruptive dischargethrough the material. For solid materials, a breakdown event severelydegrades, or even destroys, its insulating capability.• Factors affecting dielectric strength1. It increases with the increase in thickness of the specimen. (Directly proportional)2. It decreases with the increase in operating temperature. (Inversely proportional)3. It decreases with the increase in frequency. (Inversely proportional)4. It decreases with the increase in humidity. (Inversely proportional)The field strength at which break down occurs in a given case is dependenton the respective geometries of the dielectric (insulator) and the electrodeswith which the electric field is applied, as well as the rate of increase at whichthe electric field is applied. Because dielectric materials usually containminute defects, the practical dielectric strength will be a fraction of theintrinsic dielectric strength seen for ideal, defect free, material.
Table: Dielectric strength (in MV/m) of various common materials: Substance Dielectric Strength (MV/m)Helium 0.15Air 3.0 (depends on pressure)Alumina 13.4Window glass 9.8 - 13.8Silicone oil, Mineral oil 10 - 15Benzene 16Polystyrene 19.7Polyethylene 18.9 - 21.7Neoprene rubber 15.7 - 27.6Ultra pure Water 30High Vacuum (field emission limited) ] 20 - 40 (depends on electrode shape)Fused silica 25 - 40Waxed paper 40 - 60PTFE (Teflon) 60Mica  20 - 70Thin films of SiO2 in ICs > 1000
Dielectric Loss• The dielectric material separating two electrodes / conductors / plates isstressed when subjected to a potential. When the potential is reversed, thestress is also reversed.• This change of stress involves molecular rearrangement within thedielectric. This involves energy loss with each reversal. This is because themolecules have to overcome a certain amount of internal friction in theprocess of alignment. The energy expended in the process is released as heatin the dielectric.“The loss appearing in the form of heat due to reversal of electric stressescompelling molecular rearrangement is known as dielectric loss”• The dielectric loss is not appreciable at ordinary frequency of 50 Hz, but incommunication systems where frequencies of mega hertz are used, the heatreleased will be very high and can be observed by the increase in thetemperature of the dielectric material.
Dielectric Polarization• A material is made up of atoms; each atom consists of a cloud of negativecharge (electrons) bound to and surrounding a positive point charge at itscenter. Because of the comparatively huge distance between them, none of theatoms in the dielectric material interact with one another.• In the presence of an electric field the charge cloud is distorted, as shown inthe top right of the figure.• This can be reduced to a simple dipole using the superposition principle. Adipole is characterized by its dipole moment, a vector quantity shown in thefigure as the blue arrow labeled M. It is the relationship between the electricfield and the dipole moment that gives rise to the behavior of the dielectric Figure: Electric field interaction with an atom under the classical dielectric model
Polar and Non-Polar DielectricsPolar Dielectrics• Like water, alcohol, CO2, NH3, HCl etc. aremade of polar atoms/molecules.• In polar molecules when no electric field isapplied centre of positive charges does notcoincide with the centre of negative charges.• A polar molecule has permanent electric dipole moment in the absence ofelectric field also. But a polar dielectric has net dipole moment is zero in theabsence of electric field because polar moleculesare randomly oriented as shown in figure.• In the presence of electric field polar molecules tends to line up in thedirection of electric field, and the substance has finite dipole moment.
Non - Polar Dielectrics• Like N2, O2, Benzene, Methane etc. are made of non-polar atoms/molecules.In non-polar molecules, when no electric field is applied the centre of positivecharge coincides with the centre of negative charge in the molecule. Eachmolecule has zero dipole moment in its normal state.• When electric field is applied, positive charge experiences a force in thedirection of electric field and negative charge experiences a force in thedirection opposite to the field i.e., molecules becomes induced electricdipole.
7.1 Matter Polarization and Relative PermittivityRelative PermittivityConsider a parallel plate capacitor with vacuum as the dielectric mediumbetween the plates (Fig.(a)). The plates are connected to a constant voltagesupply V. Let Qo be the charge on the plates. The capacitance Co of theparallel plate capacitor in free space is defined by Co = Qo / V Co = capacitance of a parallel plate capacitor in free space Qo = charge on the plates V = voltage
When a dielectric slab (slab of non-conducting material) is inserted into thisparallel plate capacitor (Fig.b & c) with V kept the same. Now due to theinsertion of the dielectric slab, there is an external current flow that indicatesthat there is additional charge being stored on the plates. The charge on theelectrodes increases from Qo to Q. Because now there is greater amount ofcharge stored on the plates, the capacitance of the system in Fig.(a) is largerthan that in Fig.(b) by the ratio Q to Qo.The relative permittivity (or the dielectric constant) εr is defined to reflect thisincrease in the capacitance or the charge storage capacity by virtue of having adielectric medium. If C is the capacitance with the dielectric medium (Fig.(c))then: εr = Q/Qo = C/CoThe increase in the stored charge is due to the polarization of the dielectric bythe applied field.
Dipole Moment and Electronic PolarizationAn electrical dipole moment is simply a separation between a negative andpositive charge of equal magnitude Q in a system of charges. In the simple caseof two point charges, one with charge + q and one with charge − q, the electricdipole moment p is: p = Qawhere a is the displacement vector pointing from the negative charge to thepositive charge (a in the scalar form is the bond length in the molecule whichhas got polarized)
• The net charge within a neutral atom is zero. In the absence of an electric fieldthe center of negative charge of the electrons coincides with the positivenuclear charge, means that the atom has no net dipole moment (Fig.7.3(a)).• With an application of electric field induced dipole moment will take placecausing electrons being much lighter than the positive nucleus to get displacedby the field. This results in the separation of the negative charge center from thepositive charge center as shown in Fig.7.3(b).• This separation of negative and positive charges and the resulting induceddipole moment are termed polarization. An atom is said to be polarized if itpossesses an effective dipole moment, that is, if there is a separation betweenthe centers of negative and positive charge distributions.• The induced dipole moment depends on the electric field causing it. We definea quantity called the polarizability α to relate the induced dipole momentpinduced to the field E causing it, pinduced = αEwhere α is a coefficient called the polarizability of the atom. Since thepolarization of a neutral atom involves the displacement of electrons α isgenerally called electronic polarization denoted as αe.
Polarization Vector P• When a material is placed in an electric field, the atoms and molecules of thematerial become polarized, so we have a distribution of dipole moments in thematerial. We can visualize this effect with the insertion of a dielectric slab intothe parallel plate capacitor as shown in Fig.(a).• The placement of the dielectric slab into an electric field polarizes themolecules in the material. The induced dipole moments all point in the directionof the field.
• Consider a polarized medium alone, as shown in Fig.(b) in which everypositive charge has a negative charge next to it and vice versa. There istherefore no net charge within the bulk. But the positive charges of the dipolesappearing at the right hand face are not canceled by negative charges of anydipoles at this face. There is therefore a surface charge +Qp on the right handface that results from the polarization of the medium.• Similarly, there is a negative charge -Qp with the same magnitude appearingon the left hand face due to the negative charges of the dipoles at this face.These charges are bound and are a direct result of the polarization of themolecules. They are termed surface polarization charges.• Fig(c) emphasizes this aspect of dielectric behavior in an electric field byshowing the dielectric and its polarization charges only.• We represent the polarization of a medium by a quantity called polarizationP, which is defined as the total dipole moment per unit volume, P = 1 [p1 + p2 + ……+ pN] VolumeWhere p1, p2,….pN are the dipole moments induced at N molecules in thevolume.
• If pav is the average dipole moment per molecule, then an equivalentdefinition of P is P = Npav• To calculate the polarization P for the polarized dielectric we need to sum allthe dipoles in the medium and divide by the volume Ad as in eqn.1. Howeverthe polarized medium can be simply represented as in Fig.(c) in terms ofsurface charge +QP and -QP, which are separated by the thickness distance d.• We can view this arrangement as one big dipole moment per unit volume, themagnitude of P is P = ptotal / volume = Qpd / Ad = Qp / ABut Qp / A is the surface polarization charge density σp, so P = σp• Polarization is a vector and the above equation only gives its magnitude. Forthe rectangular slab in Fig.7.5., the direction of P is normal to the surface. For+σp (right face), it comes out from the surface and for -σp (left face), it isdirected into the surface. If Pnormal is the component of P normal to the surfacewhere the polarization charge density is σp, as shown in Fig.7.6, then, Pnormal = σp
Local Field Eloc• The electronic polarizability αe is related to relative permittivity εr by therelation εr = 1 + Nαe / εo. Relative permittivity εr is a macroscopic propertywhile electronic polarizability αe is related to microscopic polarizationmechanisms. This equation assumes that the field acting on an individualatom or molecule is the field E, which is assumed to be uniform within thedielectric.• However the induced polarization depends on the actual field experiencedby the molecule. But there are polarized molecules within the dielectic withtheir negative and positive charges separated so that the field is not constanton the atomic scale as we move through the dielectric. This is depicted inFig.7.7.• The field experienced by an individual molecule is actually different than E,which represents the average field in the dielectric. As soon as the dielectricbecomes polarized, the field at some arbitrary point depends not only on thecharges on the plates (Q) but also on the orientations of all the other dipolesaround this point in the dielectric. When averaged over some distance, say athousand molecules, this field becomes E, as shown in Fig.7.7.
• The actual field experienced by a molecule in a dielectric is defined as thelocal field and denoted by Eloc. It depends not only on the free charges on theplates but also on the arrangement of all the polarized molecules around thispoint. In evaluating Eloc we simply remove the molecule from this point andcalculate the field at this point coming from all sources, including neighbouringpolarized molecules as shown in Fig.7.7.
7.2 Electronic Polarization: Covalent Solids• When a field is applied to a solid substance, the constituent atoms ormolecules become polarized as shown in Fig.7.8. The electron clouds withineach atom becomes shifted by the field, and this gives rise to electronicpolarization.• This type of electronic polarization within an atom, however, is quite smallcompared with the polarization due to the valence electrons in the covalentbonds within the solid.• For example, in crystalline silicon, there are electrons shared withneighboring Si atoms in covalent bonds as shown in Fig.7.8. These valenceelectrons form bonds (i.e. become shared) between the Si atoms because theyare already loosely bound to their parent atoms. Thus, they readily respond toan applied field and become displaced.• This type of electronic polarization, due to the displacement of electrons incovalent bonds is responsible for the large dielectric constants of covalentcrystals.
(a) Valence electrons in covalent bonds in the absence of an applied field.(b) When an electric field is applied to a covalent solid, the valence electrons in thecovalent bonds are shifted very easily with respect to the positive ionic cores. Thewhole solid becomes polarized due to the collective shift in the negative chargedistribution of the valence electrons.
7.3 Polarization MechanismsIn addition to electronic polarization, there are a number of other polarizationmechanisms such as:1. Ionic polarization2. Orientational (Dipolar) Polarization3. Interfacial Polarization and4. Total Polarization (which is the sum of electronic, ionic and dipolar)
Ionic Polarization• This type of polarization occurs in ionic crystals such as NaCl, KCl and LiBr.Ionic crystals have distinctly identifiable ions, ex, Na+ and Cl-, located at welldefined lattice sites, so each pair of oppositely charged neighboring ions has adiple moment.• As an example, we consider the one-dimensional NaCl crystal depicted as achain of alternating Na+ and Cl- ions as shown in Fig.7.9a. In the absence ofand applied field, the solid has no net polarization because the dipole momentsof equal magnitude are lined up head to head and tail to tail so that the netdipole moment is zero. The dipole moment p+ in the positive direction has thesame magnitude as p- in the negative x direction, so the net dipole moment pnetis zero.• In the presence of a field E along the x direction, however, the Cl- ions arepushed in the –x direction and the Na+ ions in the +x direction about theirequilibrium positions. Consequently, the dipole moment p+ in the +x directionincreases to p+ and the dipole moment p- decreases to p- as shown in Fig.7.9b.The net dipole moment, or the average dipole moment, per ion pair is now (p+ -p-), which depends on the electric field E.
(a) A NaCl chain in the NaCl crystal without an applied field. Average or net dipole moment per ion is zero.(b) In the presence of an applied field the ions become slightly displaced which leads to a net average dipole moment per ion.
Orientational (Dipolar) Polarization• Certain molecules exhibit permanent dipole moments as discussed earlier. Forexample HCl molecule shown in Fig.7.10a has a permanent dipole moment pofrom the Cl- ion to the H+ ion.• In the liquid or gas phases, these molecules, in the absence of an electric field,are randomly oriented as a result of thermal agitation as shown in Fig.7.10b.• When a electric field E is applied E tries to align the dipoles parallel to itself,as depicted in Fig.7.10c. The Cl- and H+ charges experience forces in oppositedirections. But the nearly rigid bond between Cl- and H+ holds them together,which means that the molecule experiences a troque τ about its center of mass.• This torque acts to rotate the molecule to align po with E. If all the moleculeswere to simply rotate and align with the field, the polarization of the solidwould be P = NpoWhere N is the number of molecules per unit volume.• However, due to their thermal energy, the molecules move around randomlyand collide with each other and with the walls of the container. These collisionsdestroy the dipole alignments. Thus the thermal energy tries to randomize theorientations of the dipole moments.
• A snapshot of the dipoles in the material in the presence of a field can bepictured in Fig.7.10d in which the dipoles have different orientations. There is,never less, a net average dipole moment per molecule Pav that is finite anddirected along the field. Thus the material exhibits net polarization, which leadsto a dielectric constant that is determined by this orientational polarization.
Interfacial Polarization• Interfacial polarization occurs whenever there is accumulation of charge at aninterface between two materials or between two regions within a material. Thesimplest example is interfacial polarization due to the accumulation of chargesin the dielectric near one of the electrodes, as shown in Fig.7.11a and b.• Invariably all materials, however perfect, contain crystal defects, impurities,and various mobile charge carriers such as electrons, holes, or ionized host orimpurity ions.• Consider a material which has equal number of positive ions and negativeions, but the positive ions are more mobile because they are relatively smallerthen the negative ions. Under the presence of an applied field, these positiveions migrate to the negative electrode. The positive ions, however cannot leavethe dielectric and enter the crystal structure of the metal electrode. Theytherefore simply pile up at the interface and give rise to a positive space chargenear the electrode.• These positive charges at the interface attract more electrons to the negativeelectrode. This additional charge on the electrode, of course, appears as anincrease in the dielectric constant.
• The term interfacial polarization arises because the positive chargesaccumulating at the interface and the remainder of negative charges in the bulktogether constitute dipole moments that appear in the polarization vector P.• Grain boundaries frequently lead to interfacial polarization as they can trapcharges migrating under the influence of an applied field, as indicated inFig.7.11c. Dipoles between the trapped charges increase the polarization vector.(a) A crystal with equal number of mobile positive ions and fixed negative ions. In the absence of a field, there is no net separation between all the positive charges and all the negative charges.(b) In the presence of an applied field, the mobile positive ions migrate toward the negative charges and positive charges in the dielectric. The dielectric therefore exhibits interfacial polarization.(c) Grain boundaries and interfaces between different materials frequently give rise to interfacial polarization.
Total Polarization• In the presence of electronic, ionic, and dipolar polarization mechanisms,the average induced dipole moment per molecule will be the sum of all thecontributions in terms of the local field, Pav = αeEloc + αiEloc + αdEloc• Each effect adds linearly to the net dipole moment per molecule. Interfacialpolarization cannot be simply added to the above equation as it occurs atinterfaces and cannot be put into an average polarization per molecule in thebulk.