st05 – electronic properties of materials (from a 'microscopic' aspect) 1 electronic...

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ST05 – Electronic properties of materials (from a 'microscopic' aspect)

Electronic properties of materials from a 'microscopic' aspect

Lecturer:Smilen Dimitrov

Sensors Technology – MED4

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Introduction

• The model that we introduced for ST

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Introduction

• Goal – establish transition between electronic properties of materials on microscopic (molecular) and macroscopic (circuit theory) level

• Discuss concept of conductors and insulators• Discuss behavior of conductors and insulators in electrostatic field• Process of electric charging – induction and contact • Concept of electric current – convection and conduction; transient

and steady state• Short circuit• Concept of electric resistivity (microscopic parameter) and

resistance (macroscopic parameter)• Water flow – electric current analogy

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Materials as geometric distribution of charge - conductors and insulators

• So far, we have considered fields and interaction of few charges at a time... however:

• We are more interested in fields and interaction of objects' – materials – collections of great numbers of charged particles.

• Focus in: Materials science - “electronic materials” - solid state physics

• Basic classes of materials:

– Conductors – materials in which electrons can be easily transported (flow)

– Insulators – materials in which electrons cannot be easily transported (no flow)

• Typical methods in these discussions: Gauss' law to relate the electric field at a surface to the total charge enclosed within the surface; relate derivatives of the electric field to the

charge density via Maxwell's equations and vector calculus divergence; Poisson's equation ; Laplace's equation.

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Materials as geometric distribution of charge - conductors and insulators

• Materials in which every atom is whole – where the number of negative electrons and positive protons is equal – will in general be electrically neutral (that is, there will be no detectable field around a neutral object).

• A material/object becomes charged: – Positively – when electron(s) is/are removed from a neutral

object– Negatively - when electron(s) is/are added to a neutral object

• So we are basically interested in:

– The electrostatic field of charged objects – conductors or insulators

– Behaviour of uncharged, electrically neutral objects – conductors or insulators – placed in an external electrostatic field

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Conductors

• Main representatives of conductors are metals• Simplified model of a metal :

– A negative electron gas/cloud, surrounding a positive crystal lattice composed of ions

– The material is kept together due to the force between negative cloud and positive lattice

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• Best known metal conductor – copper (but also gold, silver)• Non-metallic conductors: solutions of salts, plasmas (and resistive

- graphite)

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Conductors

• Metal ions have a free valence zone, which for electrons is both easy to fill, and easy to leave

• So electrons can easily move through the material, by successively occupying and leaving free valence zones of ions.

• Metals have, at room temperatures, already a large number of free electrons in interatomic space, that are in constantly random motion.

• Even the slightest imbalances of the electric field can cause the free electrons in a metal material to move along the field.

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Conductor in electrostatic equilibrium

• Electrostatic equilibrium – idealization, related to an ideally isolated conductor– Formulation: In an isolated conductor, excess charges quickly achieve a

state where there is no net motion of charge.

• “No net motion” means that there is no directed motion of many free electrons; the individual free electrons still move randomly in a conductor in equilibrium.

• If excess charges are put in the material – they will quickly move, reposition, and optimally distance themselves, until conditions for no net motion are achieved within the material

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• Several conclusions:

• The electric field is zero everywhere inside a conductor (otherwise the charges would not be stationary, since F = qE). -> then the potential inside a conductor must be constant – Faraday's cage

• If an isolated conductor carries excess charge, the charge resides on its surface. Gauss’ law tells us that if there is no field within the conductor there can be no charge contained within it.

• The electric field just outside a charged conductor is perpendicular to the surface of the conductor (the tangential component of E at the surface must be zero, otherwise the charges would move). The conductor surface is then an equipotential surface.

• On an irregularly shaped conductor, the charge accumulates at at sharp points (that is, locations where the radius of curvature of the surface is smallest)

• Conductors through which current flows are not in electrostatic equilibrium – which also holds for the first moments after extra charge is placed on a conductor

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•

No field Strongest

field

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Field of a charged conductor

• Typically, in engineering a method known as Gauss' law is applied• For objects with certain symmetries (spherical, cylindrical and

planar) the field follows the shape of the object

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Conductor in electrostatic field

• A neutral conductor placed in an external field experiences separation of charge – which results with induced charge (electrostatic induction)

• There will be internal redistribution of free electrons, until the condition of electrostatic equilibrium is achieved.

• So inside the conductor we will still have E=0 and V=const

• For a neutral conductor, the induced charge is its own free electrons – just redistributed.

• This still holds even if the conductor was previously charged.

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Insulators (dielectrics)

• In conductors, atoms had loosely bound valence electrons – which easily became free and could move through the material; the cause of conductivity

• In insulators – all of the atom's electrons are tightly bound – it is very difficult to release them as free

• Typical insulators are materials like glass, mica, rubber, quartz, air etc.• Also: semiconductors at low temperatures; teflon (almost ideal);

plastics and rubber-like polymers

• Meaning of dielectric and insulator – almost the same; dielectric simply points out that under an influence of field, otherwise neutral atoms/molecules will be deformed and will possess “both” positive and negative charge

• Electrical insulation is the absence of electrical conduction. Electronic band theory (a branch of physics) predicts that a charge will flow whenever there are states available into which the electrons in a material can be excited. This allows them to gain energy and thereby move through the conductor (usually a metal). If no such states are available, the material is an insulator.

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Dielectric in electrostatic field - polarisation

• Dielectric materials will react to an external electrostatic field through the process of polarisation - an internal redistribution of charge which aims to weaken the field in the material. Since there are no free charges however, there will not be translatory motion of charge.• Polarisation: The positive nuclei of a dielectric are pushed on one side by an external field, and the electrons pulled to the other side.

• There are two principal methods by which a dielectric can be polarized: stretching and rotation.

• Stretching an atom or molecule results in an induced dipole moment added to every atom or molecule

• Rotation occurs only in polar molecules — those with a permanent dipole moment like the water molecule

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Dielectric in electrostatic field - polarisation

• Polarisation can also be seen by taking into account only the centers of negative and positive charge in an atom, respectively

• Polarisation causes the external field to weaken in a dielectric, in comparison to vacuum, (as some of the energy is used on rotating/stretching the atoms of the dielectric)

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Field of a charged dielectric

• In general, none of the conclusions for a charged conductor hold for a charged dielectric – charge (electrons) inserted at some point, have no way of redistributing quickly

• The same holds for a dielectric placed in an external field• There are cases, where field of a dielectric will look like that of a

conductor (example: planar symmetry)

• For a dielectric:– The polarity of the charge may be different from point to point– The field in the interior may be different from zero– The field is not necessarily perpendicular to the surface– The integral of the field strength from a point on or in the

insulator to ground is usually different from point to point (local potential)

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Process of electrification (charging)

• We already discussed that:– An electrically neutral object is an object which has a balance of

protons and electrons.

– In contrast, a charged object has an imbalance of protons and electrons

• the process of charging (electrification) is the process through which an electrically neutral object is made a charged object - through addition or removal of charge (mostly electrons).

• in general two ways to charge a body - through:– Charging by contact (contact electrification – through

physical contact), or – Charging by induction (which would use an external

electrostatic field to induce charge disbalance)

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Process of electrification (charging)

• Some sources include additional methods of charging, (apart from

contact and induction):

– Triboelectricity: different materials originally in contact that are then separated; one becomes positive, the other negative

– Electrochemical (as in batteries)– Polarity / polarization– Piezoelectricity - charge separation in materials under

mechanical stress – Pyroelectricity - charge separation brought about by

heating

• although, the above could also be narrowed down to the first two categories.

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Charging by contact

• Can be defined as: When two objects are touched together, sometimes the objects became spontaneously charged. One object develops a net negative charge, while the other develops an equal and opposite positive charge.

• Classified in categories: • Triboelectric contact - If two different insulators are touched

together, they develop equal, but opposite charges; not well understood.

• Electrolytic-metallic contact - If a piece of metal is touched against an electrolyte material, both materials develop equal but opposite charges

• Metallic contact - If two metals having differing work functions are touched together, one steals electrons from the other, and the opposite net charges grow larger and larger; this is the Volta effect.

• Semiconductor contact - If metal touches a semiconductive material, or if two different semiconductors are placed into contact, both materials develop equal but opposite charges (basis for diodes).

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Charging by contact

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• For an electric contact between two pieces of the same metal, we have the condition of electrostatic equilibrium that applies

– which leads to the process of charge sharing: charge is shared between two conductors that are electrically connected with a conductor (and left alone), until they arrive at mutual electrostatic equilibrium.

– This effect is what makes implementing electric circuits by connecting pieces of wire together possible!

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• Special issue – when a charged object is connected to a theoretically infinite reservoir of electrons, like the Earth. This process is known as grounding.

• When a charged object is grounded, the excess charge is balanced by the transfer of electrons between the charged object and a ground.

Charging by contact - Grounding

• If the object is negative – has extra electrons – the earth will take them in...

• If the object is positive – lacks electrons – the earth will supply as many are needed..– … given we

assume the Earth is an infinite reservoir of electrons...

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• Electrostatic induction is a method by which an electrically charged material can be used to create an electrical charge in a second material, without physical contact between the two materials.

Charging by induction

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• So far, in our discussion we touched upon issues of transfer of charge (free electrons) from one object to another; – in the process, some objects would become electrically

charged. • However, we should be aware that in such processes, we have

neither created, nor destroyed electric charge; we have simply moved it from one place to another.

• The recognition that electrical charge can be neither created nor destroyed - it can only be transferred from one object to another – is known as the Law of conservation of charge.

• In other words, the law says that: the total amount of charge amidst objects (participating in an electric process) is the same before the process starts, as it is after the process ends.

Law of conservation of charge

∑i

Q i=0

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• Some visualizations on Internet

Visualisation of fields and potential from materials

st05 – electronic properties of materials (from a 'microscopic' aspect) 1 electronic...

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