cahen; erice,5-2014 bioelectronics; solid state we’ll start from the atom

Cahen; Erice,5-2014 bioelectronics; solid state

Some basics of solid state electronics

• Molecules in solid state

• Bonds

• Energy levels

• Fermi level

• Bands

• Insulators, semiconductors and metals

• Doping

• Junction basics


The hydrogen molecule

H + H H2


r0 : distance between atoms where system’s energy is minimized

The hydrogen molecule

H + H H2


Types of Bonding

Ionic van der Waals

Metallic

Covalent

Hydrogen

High Melting Point

Hard and Brittle

Non conducting

solid

NaCl, CsCl, ZnS

Usually

400-4000 kJ/mol

Low Melting Point

Soft and Brittle

Non-Conducting

Ne, Ar, Kr and Xe

Usually

2-4 kJ/mol

Variable Melting

Point

Variable

Hardness

Conducting

Fe, Cu, Ag

Usually

75-1000 kJ/mol

Very High Melting

Point

Very Hard

Usually not

Conducting

Diamond, Graphite

Usually

150-1100 kJ/mol

Low Melting Point

Soft and Brittle

Usually

Non-Conducting

İce,

organic solids

Usually

5-30 kJ/mol


From atomic levels to bands


What do the energy levels represent?


Energy Levels

An Atom

Ene

rgy

E = 0

A SmallMolecule

A LargeMolecule

FilledStates

EmptyStates

HOMO

LUMO

FermiLevel

VacuumLevel

Chemistry is controlled by the states around the filled/empty transition,i.e., the electronic charge neutrality level, around the …… Fermi Level

BulkMaterial

Dan Thomas, Univ. Guelph, Canadahttp://www.chembio.uoguelph.ca/educmat/chem7234/


Bands distinguish different Electronic Materials

Metal

CoreBands

ValenceBand

Infinitesimalenergy difference (ΔE)

between filled andempty states

Small, but non-zeroΔE between

filled andempty states

Large ΔE betweenfilled andempty states

Band Gap

Semiconductor Insulator


Cahen; Erice,5-2014 bioelectronics; solid state13

Inorganic semiconductors: energy bands

S i A T O M

yB

yB

yA

yAy

hyb

C O N D U C T IO N B A N D

V A L E N C E B A N D

E nerg y gap , Eg

) a ( ) b ( ) c ( ) d (

3 p

3 s

S i C R Y S T A L

yh yb

Principles of Electronic Materials and Devices, S.O. Kasap, McGraw Hill.

Semiconductor crystal made of atoms that share electrons to form (at least partially) covalent bonds. The structure depends on the valency of constituent atoms

Ev: valence band maximum

Ec: conduction band minimum

A. Kahn, Princeton


Organic semiconductors: molecular levels

Small molecules

Zn

N

N

NN

NN

N N

ZnPc

Pentacene

Energy gap; 1-5 – 3.5 eVLUMO: lowest unoccupied molecular orbitalHOMO: highest occupied molecular orbital

Semiconductor crystal made of molecules held together by weak van der Waals forces. The electronic structure of the solid derives in large part

from the molecular moiety .

14

A. Kahn, Princeton


Semiconductor ifEg < 4-5 eV (@ RT)

Remember: kBT @RT ≅ 26 meV ~ 200 cm-1

Bands distinguish different Electronic Materials

Conductionband

Conductionband

Valenceband


Each allowed energy level can be occupied by no more than 2 e-s of opposite “spin”. This means that, @ low temperatures, all available electronic energy levels in the material, up to a certain energy level will be occupied by 2 e-s . This is the Fermi level, EF.The probability of e-s occupying a level @ energy E, @ a certain temperature, T, is given by the Fermi-Dirac distribution function, f(E):

Fermi Level I

http://solarwiki.ucdavis.edu/@api/deki/files/119/solar_bands_green.jpg


Fermi Level II •focus on the electrons near the filled/empty boundary.

E=0 (vacuum level)

EF (Fermi level)

Minimumenergy toremoveelectronfromSample

=Work Function

•each material’s energy state distribution is unique; different EF.

Metal 1 Metal 2

EF (Fermi level)

the closer an electron is to the vacuum level, the weaker it is bound to the solid

or, the more energetic is the electron



The concept of the Fermi level


Potential energy and charge carrier distribution

Conduction band

Valence band

CBM

VBM

EG

position

Electron potentialenergy

Conduction band

CBM

VBM

EG

position


Semiconductor @ 0 K .No thermal excitation across the energy gap.

Valence band: full; conduction band: empty; Systems always want to minimize energy; electrons go to lowest potential energy configuration (valence band)

Filled bands do not conduct ; @0 K semiconductor is insulator

Intrinsic (undoped) semiconductor @ finite T:Some thermal excitation of electrons across EG

Electrons in conduction, holes in valence band

)ni = intrinsic carrier concentration; Nc, Nv = effective density of states @

conduction, valence band edges(Partially filled bands conduct finite conductivity

Valence band

Valence band

EF

EF kT

E

vci

g

eNNn 2

A. Kahn, Princeton


Two Conductors in Contact

electron flow+ –+ –+ –+ –+ –

leads to charge separation

Contact potential difference

Fermi level equal throughout sample @ electronic equilibrium



Metal in an Electrolyte Solution

Fermi levelsare aligned

For electronic equilibrium in the system ,

charge is transferred toequilibrate (solid’s) Fermi level with the

)solution (redox potential,producing charge

separation and a contactpotential difference.

– +– +– +

Redox potential=

Electrochemical potential of the electron=

Fermi level



An Ion in Solutionion’s electronic structure: HOMO, LUMO, HOMO-LUMO gap.

Lowest Unoccupied Molecular Orbital

Highest Occupied Molecular Orbital

HOMO-LUMO Gap “Fermi” level



Electrochemical ThermodynamicsEvery substance has a unique propensity to contribute to a system’s energy. We

call this property Chemical Potential.

m

When the substance is a charged particle (such as an electron or an ion) we must include the response of the particle to an electrical field in addition to its

Chemical Potential. We call this Electrochemical Potential.

These are perhaps the most fundamental measures of thermodynamics.



Semiconductor doping• “Doping” – deliberate introduction of

impurities into a high-purity, low-defectsemiconductor crystal

• Impurity content is low host chemical/crystallineproperties preserved

• Nevertheless, impuritiescompletely dominate theelectrical behavior

Ofer Sinai, 11-2013


Why are materials with semiconducting properties important?

It is all about CONTROLwith minimal energy

expenditure


Semiconductor doping

Intrinsic semiconductor very low conductivity

At room T,Si intrinsic carrier concentration ≈ 1010 cm-3

(Cu: ~1023 cm-3)

Ofer Sinai, 11-2013


Semiconductor dopingImpurities introduce free charge carriers

P B

Donor impurities

Negative charge carriers

n-type semiconductor

Acceptor impurities

Positive charge carriers (holes)

p-type semiconductor

Ofer Sinai, 11-2013


Semiconductor dopingImpurities introduce free charge carriers

P

Donor impurities

Negative charge carriers

n-type semiconductor

Ofer Sinai, 11-2013


Impurities determine conduction

Si intrinsic carriers: ~1010 cm-3

Si atom density: ~5∙1022 cm-3

E.g., a ppm impurity can increase the amount of carriers a million-fold!

Between doping rates of 1013 – 1020 cm-3, doping determines

Carrier concentrationCarrier polarity

Ofer Sinai, 11-2013


What is the effect of doping?The Fermi level, EF, is a key parameter

Intrinsic EF is near the center of the forbidden gap

Conduction band (CB)

Valence band (VB)

E E

EFermi

1

1

kTEE fe

Ef

Egap

Fermi-Dirac distribution

Ofer Sinai, 11-2013


What is the effect of doping?Donor impurities add occupied levels near the CB edge

Added free electrons Fermi level is raised


Valence band (VB)

E E

EFermi

Ofer Sinai, 11-2013


What is the effect of doping?Acceptor impurities add unoccupied levels near VB edge

Added free holes Fermi level is lowered


Valence band (VB)

E E

EFermi

Ofer Sinai, 11-2013


The p-n junctionBasic component in electronics

Conduction band

Valence band

Local vacuum level

EFermi

p-type side

E

≈ Conduction band

Valence band

Local vacuum level

n-type side

EFermi

Ofer Sinai, 11-2013


The p-n junctionBasic component in electronics

Conduction band

Valence band

Local vacuum level

n-type side p-type side

Conduction band

Valence band

Local vacuum level

E

≈

Ofer Sinai, 11-2013


The p-n junctionCharge carriers diffuse in both directions

Conduction band

Valence band

Local vacuum level


Conduction band

Valence band

Local vacuum level

+ –E

≈Conduction band

Valence band

Local vacuum level

Ofer Sinai, 11-2013


Conduction band

Valence band

Local vacuum level

The p-n junctionA space-charge region (SCR) is formed

EFermi


E

≈

Ofer Sinai, 11-2013


The p-n junctionThe junction is rectifying:


Ofer Sinai, 11-2013


The p-n junctionForward bias:


+–

Ofer Sinai, 11-2013


The p-n junctionReverse bias:


+ –

Ofer Sinai, 11-2013


Plot of I-V of Diode with Small Negative Applied Voltage


Plot of I-V of Diode with Small Positive Applied Voltage


OHM’S LAW


What is Ohm’s law?

• Ohm’s Law explains the relationship between voltage (V or E), current (I) and resistance (R)

• Used by electricians, automotive technicians, stereo installers

• Ohm’s Law explains the relation between voltage (V or E), current (I) and resistance (R)


The Electrical Components of Ohm’s Law

Voltage The electrical "pressure" thatcauses free electrons to travel

through an electrical circuit. Alsoknown as electromotive force (emf).

It is measured in volts.

Resistance That characteristic of a medium

which opposes the flow ofelectrical current through itself.Resistance is measured in ohms.

Power The amount of current times the

voltage level at a given pointmeasured in wattage or watts.

Current The amount of electrical charge(the number of free electrons)moving past a given point in an

electrical circuit per unit of time.Current is measured in amperes


Calculating Resistance from Resistivity


2.82× 3.5× 1.72× 2.44× 9.7× 95.8× 100× 1.59× 5.6× 3×Table 20.1 Resistivitiesa of Various Materials

Material Resistivity r (W·m) Material Resistivity r (W·m)

Conductors Semiconductors

Aluminum 10–8 Carbon 10–5

Copper 10–8 Germanium 0.5bc

Gold 10–8 Silicon 20–2300bc

Iron 10–8 Insulators

Mercury 10–8 Mica 1011–1015

Nichrome (alloy) 10–8 Rubber (hard) 1013–1016

Silver 10–8 Teflon 1016

Tungsten 10–8 Wood (maple) 1010

aThe values are for temperatures near 20 °C.bDepending on purity.cDepending on purity.


Diode and resistor Current-Voltage plot


Current Density

•Current density is to study the flow of charge through a cross section of the conductor at a particular point

•It is a vector which has the same direction as the velocity of the moving charges if they are positive and the opposite direction if they are negative.

•The magnitude of J is equal to the current per unit area through that area element .


Electric field and drift current

CBM

VBM

E

g

position


+ -

Vbias

EEpnqj pn )(

n, p: charge carrier densityq: unit chargeμn, μp: charge carrier mobilityE: electric field

Conductivity:

)( pn pnq

Drift current density

Mobility:

m*: effective massτ: scattering time

A. Kahn, Princeton


Inorganic semiconductors

strongcovalentbonds

•Strong inter-atomic covalent bonds•Strong overlap of wave functions centered over

neighboring atoms•Electronic and optical properties of the solid

determined by long range order/structure•Wide energy bands (5-10 eV)

•Large charge carrier mobilities (102-103 cm2/V.sec)•Carriers delocalized over the whole crystal

•In general, one-electron approximation to describe the behavior of the carriers in the crystal potential is valid the presence of a charge carrier at any point in the solid does not perturb significantly the band structure of the solid

•Rigid bands

CBM

VBM

Key characteristics of inorganic semiconductors

Bloch wave function, where k is the propagation vector, unk a periodic function

with periodicity of crystal lattice A. Kahn, Princeton


But….. at inorganic SC surfaces surface states

•Surfaces (interfaces) of most inorganic semiconductors include defects and/or dangling bonds that give rise to active electronic surface states in the gap of the material

•Surface (interface) states capture electrons (acceptor-type) or holes (donor-type) and induce band bending at the SC surface (interface)

VBM

CBM

EF

p-type SC with surface gap states

donor-type states

QSS > 0-

QSC < 0--

A. Kahn, Princeton


• Closed-shell molecular units bound by weak vdW intermolecular interaction

Þ no dangling bonds if molecular unit is intactÞ no surface statesÞ small intermolecular overlap of electron wave

functions; overlap of π-electron system responsible for charge transport

Þ Strong on-molecule localization of charge carriers (very low mobility: 10-5 - few cm2/V.s)

Þ Narrow energy bands

van der Waals (vdW)intermolecular bonding

HOMO

LUMO

EF

•Electronic and optical properties of the films determined to first approximation by molecular moiety

•Single electron approximation breaks down :

Molecule is a small entity with a finite number of electrons (as compared to macroscopic solid). Addition or subtraction of an electron significantly impacts the electronic structure of the small system

Key characteristics of organic semiconductors

68

A. Kahn, Princeton


Two conditions to make organic materialelectronically conductive

1- Sequence of alternating single and double bonds,

CONJUGATION.

In conjugation, the bonds between the C atoms are alternately single and double. Every bond contains a localised “sigma” (σ) bond which forms a strong chemical bond. In addition, every double bond also contains a less strongly localised “pi” (π) bond which is weaker.


-2- DOPING – e.g., :

1-oxidation, e.g., with halogen (p-doping).

2- reduction, e.g., with alkali metal (n-doping).

Doping Proteins ?

xNaCHxNaCH xnn

32

3ICHI

xCH nn


PART II

• Surfaces; self-assembly; characterization of surfaces (CPD, ellipsometry, XPS, UPS, IEPS, IR)

• Surfacesà Interfaces / contacts;; Measurements setups - contacts for molecular electronics; molecules as surface/ interface modifiers, molecules as transport media

• Solid state electronic measurements, diodes; current-voltage; conductance-voltage; IETS; capacitance-voltage;

·

cahen; erice,5-2014 bioelectronics; solid state we’ll start from the atom

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