Difference between revisions of "Electrical Properties"

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=== Bandgap and conductivity ===
In order to have a net electrical current electrons must jump from completely filled levels to empty levels across the bandgap. If the bandgap (Eg) is large, upon applying an external electric field at room temperature, there will be few electrons that have the necessary energy to jump from valence band to conduction band.
Thermal Energy is :
at 300K: kT ~ 0.025 eV (1/40 eV)
~ 0.6 kcal/mol
~ 2.5 kJ/mol
For '''E<sub>g</sub> >=2eV ''' is considered an insulator. Very few electrons can jump the bandgap.
&Sigma;<sub>RT</sub>  is typically <= 10<sup>-10</sup> &Omega; <sup>-1</sup> cm<sup>-1</sup><= 10-10 S/ cm
The best insulators go down to 10<sup>-16</sup> S/cm
'''0 < Eg ≤ 2eV: semiconductor'''
10-10 ≤ σ<sub>RT</sub> ≤ 102 S/cm
polyacetylene Eg ~ 1.5 eV
Si Eg ~ 1.1 eV
for Eg → 0: metal
σ<sub>RT</sub> ≥ 10<sup>2</sup> S/cm
Electrical conductivities vary over 25 orders of magnitude from the best insulator to the best conductor. A single crystal of copper at room temperature has a conductivity of 6 x 10<sup>5</sup> S/cm
σ<sub>RT</sub> Cu ~ 6 x 10<sup>5</sup> S/cm
Ag, Au ~ 10<sup>6</sup> S/cm
=== Conductivity Defined ===
Electrical conductivity (sigma) can be described with 3 terms.
<math>\sigma  =  n  \middot  \mu  \middot    q\,\!</math>
'''Where'''
n= density of charge carriers (cm-3)
&mu;= mobility of charge carrier (cm2/Vs)
q= charge (Coulombs, Cb)
To have conduction you must have charge carriers. For example in transpolyacetylene at 0&deg;K  has valence band that is completely full and a conduction band that is completely empty. You have electrons but they can not participate in the charge transfer process. If an electron is elevated to the excited state it enters the conduction band (LUMO level) becomes a charge carrier. If you then apply an electric field the charges need to be able to move in order for there to be a current. It the bond between the ethylene subunits were much longer there would be no overlap between their atomic orbitals and there would be zero electronic coupling between the  pi orbitals. The mobility of the charge would be zero.
In fact the bond is only 1.45 angstrom and there is a bonding and antibonding  level that allows for electronic coupling between subunits. Energy splitting is of these levels is a measure of the strength of electronic coupling between the subunits. In transpolyacetyline the bandwidth  of the valence and conduction bands is about 5eV, which corresponds to an energy splitting electronic coupling (t) of 2t. In organic semiconductors you may have an electronic coupling of t= 2.5eV, which is quite large.
Charge mobility  is the average speed of diffusion of the charge carriers (cm/s) as a function of applied electric field (V/cm). Organic transistors or an electronic device made from organic material must have good mobility of the charge carriers. There are many papers in the literature which characterize the charge mobility of organic compounds. A good mobility is 1 or larger.
<math>\mu = \frac \frac {{cm} {s}}  {\frac {V}  {cm}} = \frac {cm^2} {V \middot s} \,\!</math>
We can use dimensional analysis to make sure that all the units reflect the components of the equations.
Sigma = s / cm  = 1/ ohm cm  equiv q mu n
Equiv Cb / vs  dot 1 cm3
1/ohm cm  equiv Cb/Vs  dot 1/cm

Revision as of 15:20, 21 May 2009

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Bandgap and conductivity

In order to have a net electrical current electrons must jump from completely filled levels to empty levels across the bandgap. If the bandgap (Eg) is large, upon applying an external electric field at room temperature, there will be few electrons that have the necessary energy to jump from valence band to conduction band.

Thermal Energy is :

at 300K: kT ~ 0.025 eV (1/40 eV) ~ 0.6 kcal/mol ~ 2.5 kJ/mol

For Eg >=2eV is considered an insulator. Very few electrons can jump the bandgap.

ΣRT is typically <= 10-10 Ω -1 cm-1<= 10-10 S/ cm

The best insulators go down to 10-16 S/cm


0 < Eg ≤ 2eV: semiconductor 10-10 ≤ σRT ≤ 102 S/cm

polyacetylene Eg ~ 1.5 eV Si Eg ~ 1.1 eV

for Eg → 0: metal σRT ≥ 102 S/cm

Electrical conductivities vary over 25 orders of magnitude from the best insulator to the best conductor. A single crystal of copper at room temperature has a conductivity of 6 x 105 S/cm

σRT Cu ~ 6 x 105 S/cm Ag, Au ~ 106 S/cm


Conductivity Defined

Electrical conductivity (sigma) can be described with 3 terms.

<math>\sigma = n \middot \mu \middot q\,\!</math>

Where n= density of charge carriers (cm-3) μ= mobility of charge carrier (cm2/Vs) q= charge (Coulombs, Cb)


To have conduction you must have charge carriers. For example in transpolyacetylene at 0°K has valence band that is completely full and a conduction band that is completely empty. You have electrons but they can not participate in the charge transfer process. If an electron is elevated to the excited state it enters the conduction band (LUMO level) becomes a charge carrier. If you then apply an electric field the charges need to be able to move in order for there to be a current. It the bond between the ethylene subunits were much longer there would be no overlap between their atomic orbitals and there would be zero electronic coupling between the pi orbitals. The mobility of the charge would be zero.

In fact the bond is only 1.45 angstrom and there is a bonding and antibonding level that allows for electronic coupling between subunits. Energy splitting is of these levels is a measure of the strength of electronic coupling between the subunits. In transpolyacetyline the bandwidth of the valence and conduction bands is about 5eV, which corresponds to an energy splitting electronic coupling (t) of 2t. In organic semiconductors you may have an electronic coupling of t= 2.5eV, which is quite large.

Charge mobility is the average speed of diffusion of the charge carriers (cm/s) as a function of applied electric field (V/cm). Organic transistors or an electronic device made from organic material must have good mobility of the charge carriers. There are many papers in the literature which characterize the charge mobility of organic compounds. A good mobility is 1 or larger.


<math>\mu = \frac \frac {{cm} {s}} {\frac {V} {cm}} = \frac {cm^2} {V \middot s} \,\!</math>

We can use dimensional analysis to make sure that all the units reflect the components of the equations.


Sigma = s / cm = 1/ ohm cm equiv q mu n Equiv Cb / vs dot 1 cm3 1/ohm cm equiv Cb/Vs dot 1/cm