cahen; erice,5-2014 bioelectronics; solid state we’ll start from the atom
TRANSCRIPT
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
Cahen; Erice,5-2014 bioelectronics; solid state
The hydrogen molecule
H + H H2
Cahen; Erice,5-2014 bioelectronics; solid state
r0 : distance between atoms where system’s energy is minimized
The hydrogen molecule
H + H H2
Cahen; Erice,5-2014 bioelectronics; solid state
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
Cahen; Erice,5-2014 bioelectronics; solid state
From atomic levels to bands
Cahen; Erice,5-2014 bioelectronics; solid state
What do the energy levels represent?
Cahen; Erice,5-2014 bioelectronics; solid state
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/
Cahen; Erice,5-2014 bioelectronics; solid state
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
Dan Thomas, Univ. Guelph, Canadahttp://www.chembio.uoguelph.ca/educmat/chem7234/
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
Cahen; Erice,5-2014 bioelectronics; solid state
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
Cahen; Erice,5-2014 bioelectronics; solid state
Semiconductor ifEg < 4-5 eV (@ RT)
Remember: kBT @RT ≅ 26 meV ~ 200 cm-1
Bands distinguish different Electronic Materials
Conductionband
Conductionband
Valenceband
Cahen; Erice,5-2014 bioelectronics; solid state
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
Cahen; Erice,5-2014 bioelectronics; solid state
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
Dan Thomas, Univ. Guelph, Canadahttp://www.chembio.uoguelph.ca/educmat/chem7234/
Cahen; Erice,5-2014 bioelectronics; solid state
The concept of the Fermi level
Cahen; Erice,5-2014 bioelectronics; solid state
Cahen; Erice,5-2014 bioelectronics; solid state20
Potential energy and charge carrier distribution
Conduction band
Valence band
CBM
VBM
EG
position
Electron potentialenergy
Conduction band
CBM
VBM
EG
position
Electron potentialenergy
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
Cahen; Erice,5-2014 bioelectronics; solid state
Two Conductors in Contact
electron flow+ –+ –+ –+ –+ –
leads to charge separation
Contact potential difference
Fermi level equal throughout sample @ electronic equilibrium
Dan Thomas, Univ. Guelph, Canadahttp://www.chembio.uoguelph.ca/educmat/chem7234/
Cahen; Erice,5-2014 bioelectronics; solid state
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
Dan Thomas, Univ. Guelph, Canadahttp://www.chembio.uoguelph.ca/educmat/chem7234/
Cahen; Erice,5-2014 bioelectronics; solid state
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
Dan Thomas, Univ. Guelph, Canadahttp://www.chembio.uoguelph.ca/educmat/chem7234/
Cahen; Erice,5-2014 bioelectronics; solid state
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.
Dan Thomas, Univ. Guelph, Canadahttp://www.chembio.uoguelph.ca/educmat/chem7234/
Cahen; Erice,5-2014 bioelectronics; solid state
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
Cahen; Erice,5-2014 bioelectronics; solid state
Why are materials with semiconducting properties important?
It is all about CONTROLwith minimal energy
expenditure
Cahen; Erice,5-2014 bioelectronics; solid state
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
Cahen; Erice,5-2014 bioelectronics; solid state
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
Cahen; Erice,5-2014 bioelectronics; solid state
Semiconductor dopingImpurities introduce free charge carriers
P
Donor impurities
Negative charge carriers
n-type semiconductor
Ofer Sinai, 11-2013
Cahen; Erice,5-2014 bioelectronics; solid state
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
Cahen; Erice,5-2014 bioelectronics; solid state
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
Cahen; Erice,5-2014 bioelectronics; solid state
What is the effect of doping?Donor impurities add occupied levels near the CB edge
Added free electrons Fermi level is raised
Conduction band (CB)
Valence band (VB)
E E
EFermi
Ofer Sinai, 11-2013
Cahen; Erice,5-2014 bioelectronics; solid state
What is the effect of doping?Acceptor impurities add unoccupied levels near VB edge
Added free holes Fermi level is lowered
Conduction band (CB)
Valence band (VB)
E E
EFermi
Ofer Sinai, 11-2013
Cahen; Erice,5-2014 bioelectronics; solid state
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
Cahen; Erice,5-2014 bioelectronics; solid state
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
Cahen; Erice,5-2014 bioelectronics; solid state
The p-n junctionCharge carriers diffuse in both directions
Conduction band
Valence band
Local vacuum level
n-type side p-type side
Conduction band
Valence band
Local vacuum level
+ –E
≈Conduction band
Valence band
Local vacuum level
Ofer Sinai, 11-2013
Cahen; Erice,5-2014 bioelectronics; solid state
Conduction band
Valence band
Local vacuum level
The p-n junctionA space-charge region (SCR) is formed
EFermi
n-type side p-type side
E
≈
Ofer Sinai, 11-2013
Cahen; Erice,5-2014 bioelectronics; solid state
The p-n junctionThe junction is rectifying:
n-type side p-type side
Ofer Sinai, 11-2013
Cahen; Erice,5-2014 bioelectronics; solid state
The p-n junctionForward bias:
n-type side p-type side
+–
Ofer Sinai, 11-2013
Cahen; Erice,5-2014 bioelectronics; solid state
The p-n junctionReverse bias:
n-type side p-type side
+ –
Ofer Sinai, 11-2013
Cahen; Erice,5-2014 bioelectronics; solid state
Plot of I-V of Diode with Small Negative Applied Voltage
Cahen; Erice,5-2014 bioelectronics; solid state
Plot of I-V of Diode with Small Positive Applied Voltage
Cahen; Erice,5-2014 bioelectronics; solid state
OHM’S LAW
Cahen; Erice,5-2014 bioelectronics; solid state
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)
Cahen; Erice,5-2014 bioelectronics; solid state
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
Cahen; Erice,5-2014 bioelectronics; solid state
Calculating Resistance from Resistivity
Cahen; Erice,5-2014 bioelectronics; solid state
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.
Cahen; Erice,5-2014 bioelectronics; solid state
Diode and resistor Current-Voltage plot
Cahen; Erice,5-2014 bioelectronics; solid state
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 .
Cahen; Erice,5-2014 bioelectronics; solid state65
Electric field and drift current
CBM
VBM
E
g
position
Electron potentialenergy
+ -
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
Cahen; Erice,5-2014 bioelectronics; solid state66
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
Cahen; Erice,5-2014 bioelectronics; solid state67
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
Cahen; Erice,5-2014 bioelectronics; solid state
• 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
Cahen; Erice,5-2014 bioelectronics; solid state
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.
Cahen; Erice,5-2014 bioelectronics; solid state
-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
Cahen; Erice,5-2014 bioelectronics; solid state
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;
·