Electron-Phonon Coupling - Revision history

Cmditradmin at 18:40, 7 July 2010

2010-07-07T18:40:53Z

← Older revision		Revision as of 11:40, 7 July 2010
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	[[category:transport properties]]		[[category:transport properties]]

			== References ==
			<references/>

	<table id="toc" style="width: 100%">		<table id="toc" style="width: 100%">
	<tr>		<tr>

Cmditradmin: /* Nonlocal electron-phonon coupling */

2010-07-07T18:40:12Z

Nonlocal electron-phonon coupling

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	<br clear='all'>		<br clear='all'>
	[[Image:napthalene_opticalmodes.png\|thumb\|500px\|Intermolecular optical modes in naphthalene]]		[[Image:napthalene_opticalmodes.png\|thumb\|500px\|Intermolecular optical modes in naphthalene<ref>Spectrochim. Acta, Part A A24, 1091 (1968)</ref>
			]]

	This shows the intermolecular optical modes in naphthalene. These can be evaluated and they have good agreement with experimental observation.		This shows the intermolecular optical modes in naphthalene. These can be evaluated and they have good agreement with experimental observation.

Cmditradmin: /* Electron phonon mechanism */

2010-07-07T18:39:08Z

Electron phonon mechanism

← Older revision		Revision as of 11:39, 7 July 2010
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	=== Electron phonon mechanism ===		=== Electron phonon mechanism ===
	[[Image:electron_phonon.png\|thumb\|400px\|Local e-ph coupling (Holstein's molecular polaron model) and nonlocal e-ph coupling (Peierls-type model Su Schrieffer-=Heeger Hamiltonian)]]		[[Image:electron_phonon.png\|thumb\|400px\|Local e-ph coupling (Holstein's molecular polaron model) and nonlocal e-ph coupling (Peierls-type model Su Schrieffer-Heeger Hamiltonian)]]

	Intramolecular and intramolecular modes of vibration are able to modify e and t. To get a complete description of the system you can look at the variation of the site energy as a function each the vibrational modes that are in the system. This equation looks at the site energy on molecule m and zero denotes the absence of vibration and then look at the impact of each of the vibrational modes (j) on the site. This shows the variation of site energy as you take into account vibrational modes. Some modes will have no impact, some will be significant. Moving to an ionized state there will be a strong geometry relaxation so there will be a strong coupling to the vibrational modes that lead to the ionized state.		Intramolecular and intramolecular modes of vibration are able to modify e and t. To get a complete description of the system you can look at the variation of the site energy as a function each the vibrational modes that are in the system. This equation looks at the site energy on molecule m and zero denotes the absence of vibration and then look at the impact of each of the vibrational modes (j) on the site. This shows the variation of site energy as you take into account vibrational modes. Some modes will have no impact, some will be significant. Moving to an ionized state there will be a strong geometry relaxation so there will be a strong coupling to the vibrational modes that lead to the ionized state.

Cmditradmin: /* Electron phonon mechanism */

2010-07-07T18:38:48Z

Electron phonon mechanism

← Older revision		Revision as of 11:38, 7 July 2010
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	=== Electron phonon mechanism ===		=== Electron phonon mechanism ===
	[[Image:electron_phonon.png\|thumb\|400px\|~~Sources of local~~ and nonlocal e-ph coupling]]		[[Image:electron_phonon.png\|thumb\|400px\|Local e-ph coupling (Holstein's molecular polaron model) and nonlocal e-ph coupling (Peierls-type model Su Schrieffer-=Heeger Hamiltonian)]]

	Intramolecular and intramolecular modes of vibration are able to modify e and t. To get a complete description of the system you can look at the variation of the site energy as a function each the vibrational modes that are in the system. This equation looks at the site energy on molecule m and zero denotes the absence of vibration and then look at the impact of each of the vibrational modes (j) on the site. This shows the variation of site energy as you take into account vibrational modes. Some modes will have no impact, some will be significant. Moving to an ionized state there will be a strong geometry relaxation so there will be a strong coupling to the vibrational modes that lead to the ionized state.		Intramolecular and intramolecular modes of vibration are able to modify e and t. To get a complete description of the system you can look at the variation of the site energy as a function each the vibrational modes that are in the system. This equation looks at the site energy on molecule m and zero denotes the absence of vibration and then look at the impact of each of the vibrational modes (j) on the site. This shows the variation of site energy as you take into account vibrational modes. Some modes will have no impact, some will be significant. Moving to an ionized state there will be a strong geometry relaxation so there will be a strong coupling to the vibrational modes that lead to the ionized state.

Cmditradmin at 18:35, 7 July 2010

2010-07-07T18:35:18Z

← Older revision		Revision as of 11:35, 7 July 2010
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	</table>		</table>

	The frontier of research in organic semiconductors is attempting to get a complete picture of electron transport by understanding intramolecular and intermolecular vibrations or [[phonon \| phonons]]. Several people have been working on this for a while.		The frontier of research in organic semiconductors is attempting to get a complete picture of electron transport by understanding intramolecular and intermolecular vibrations or [[phonon \| phonons]] and electron-phonon coupling. Several people have been working on this for a while.
	Silbey & Munn		Silbey & Munn
	Bobbert et al.		Bobbert et al.

Cmditradmin at 16:50, 6 January 2010

2010-01-06T16:50:07Z

← Older revision		Revision as of 09:50, 6 January 2010
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	</table>		</table>

	The frontier of research in organic semiconductors is attempting to get a complete picture of electron transport by understanding intramolecular and intermolecular vibrations. Several people have been working on this for a while.		The frontier of research in organic semiconductors is attempting to get a complete picture of electron transport by understanding intramolecular and intermolecular vibrations or [[phonon \| phonons]]. Several people have been working on this for a while.
	Silbey & Munn		Silbey & Munn
	Bobbert et al.		Bobbert et al.

Cmditradmin: /* Charge Transport */

2009-12-01T19:24:42Z

Charge Transport

← Older revision		Revision as of 12:24, 1 December 2009
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	=== Charge Transport ===		=== Charge Transport ===
	[[Image:chargetransport.png\|thumb\|400px\|Variation in charge mobility with temperature]]		[[Image:chargetransport.png\|thumb\|400px\|Variation in charge mobility with temperature]]
	Currently we can not predict the crystal structure of a molecule given the chemical formula of a molecule. The big challenge is to evaluate the mobility as a function temperature. ~~If you start~~ with a perfect crystal at low temperature ~~you have~~ a large mobility. As the temperature increases the molecules start vibrating and there is a reduction in electronic coupling, bandwidth and mobility. In metals as you increase temperature the vibrations get larger and mobility comes down. At some point the vibrations will reduce the electronic coupling so much that it will become favorable for the charge carrier to localize. This cross over region is difficult to describe and may not be an abrupt evolution. There is a gradual localization process. ~~Once you cross~~ over into the hopping regime (an activated regime) with localization the mobility goes back up with temperature. Here the vibrations help by preparing the two molecules to achieve essentially the same geometry so that electron transfer can take place. So the rate of electron transfer is simply the time it takes for vibrations to bring the molecules into the same geometry. In most organic materials will have decomposed before they reach a temperature where they begin to decrease in electron transfer with temperature (T<sub>2</sub>).		Currently we can not predict the crystal structure of a molecule given the chemical formula of a molecule. The big challenge is to evaluate the mobility as a function of temperature. Starting with a perfect crystal at low temperature there is a large mobility. As the temperature increases the molecules start vibrating and there is a reduction in electronic coupling, bandwidth and mobility. In metals as you increase temperature the vibrations get larger and mobility comes down. At some point the vibrations will reduce the electronic coupling so much that it will become favorable for the charge carrier to localize. This cross over region is difficult to describe and may not be an abrupt evolution. There is a gradual localization process.

			Crossing over into the hopping regime (an activated regime) with localization the mobility goes back up with temperature. Here the vibrations help by preparing the two molecules to achieve essentially the same geometry so that electron transfer can take place. So the rate of electron transfer is simply the time it takes for vibrations to bring the molecules into the same geometry. In most organic materials will have decomposed before they reach a temperature where they begin to decrease in electron transfer with temperature (T<sub>2</sub>).

	[[category:transport properties]]		[[category:transport properties]]

Cmditradmin: /* Tight-binding Hamiltonian */

2009-09-15T19:19:29Z

Tight-binding Hamiltonian

← Older revision		Revision as of 12:19, 15 September 2009
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	=== Tight-binding Hamiltonian ===		=== Tight-binding Hamiltonian ===
	[[Image:tight_hamiltonian.png\|thumb\|~~300px~~\|Tight binding Hamilitonian expression]]		[[Image:tight_hamiltonian.png\|thumb\|400px\|Tight binding Hamilitonian expression]]

	This is the second quantization form of the Hamiltonian. In Hückel calculations you describe a molecule as having an energy coulomb integral α. This is the energy of a site. To do a Hückel calculation for a polyene molecule you place an α on each carbon. The value of the α is the value of the π atomic orbital for an isolated sp2 carbon.		This is the second quantization form of the Hamiltonian. In Hückel calculations you describe a molecule as having an energy coulomb integral α. This is the energy of a site. To do a Hückel calculation for a polyene molecule you place an α on each carbon. The value of the α is the value of the π atomic orbital for an isolated sp2 carbon.

	The transfer integral (t<sub>mn</sub>) or electron coupling for adjacent molecules is the resonance integral beta in Hückel terminology. For example considering butadiene at the Hückel level there would be 4 carbons, each with a site energy α, and between carbons the resonance integral β, which can be different for double B<sub>1</sub> (shorter bonds have larger electronic coupling) and single bonds B<sub>2</sub>. The same could be done for the pentacene system. In the case of pentacene the two molecules of the units cells have slightly different surroundings and therefore the energies would slightly different. There would be β1 and β2 (for the tb and td directions). In the Hamiltonian α and β become e and t. This gives a very compact way of writing an equation.		The transfer integral (t<sub>mn</sub>) or electron coupling for adjacent molecules is the resonance integral beta in Hückel terminology. For example considering butadiene at the Hückel level there would be 4 carbons, each with a site energy α, and between carbons the resonance integral β, which can be different for double B<sub>1</sub> (shorter bonds have larger electronic coupling) and single bonds B<sub>2</sub>. The same could be done for the pentacene system. In the case of pentacene the two molecules of the units cells have slightly different surroundings and therefore the energies would slightly different. There would be β1 and β2 (for the tb and td directions). In the Hamiltonian α and β become e and t. This gives a very compact way of writing an equation.
			<br clear='all'>

	=== Electron phonon mechanism ===		=== Electron phonon mechanism ===

Cmditradmin: /* Electron phonon mechanism */

2009-09-15T19:19:14Z

Electron phonon mechanism

← Older revision		Revision as of 12:19, 15 September 2009
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	=== Electron phonon mechanism ===		=== Electron phonon mechanism ===
	[[Image:electron_phonon.png\|thumb\|~~300px~~\|Sources of local and nonlocal e-ph coupling]]		[[Image:electron_phonon.png\|thumb\|400px\|Sources of local and nonlocal e-ph coupling]]

	Intramolecular and intramolecular modes of vibration are able to modify e and t. To get a complete description of the system you can look at the variation of the site energy as a function each the vibrational modes that are in the system. This equation looks at the site energy on molecule m and zero denotes the absence of vibration and then look at the impact of each of the vibrational modes (j) on the site. This shows the variation of site energy as you take into account vibrational modes. Some modes will have no impact, some will be significant. Moving to an ionized state there will be a strong geometry relaxation so there will be a strong coupling to the vibrational modes that lead to the ionized state.		Intramolecular and intramolecular modes of vibration are able to modify e and t. To get a complete description of the system you can look at the variation of the site energy as a function each the vibrational modes that are in the system. This equation looks at the site energy on molecule m and zero denotes the absence of vibration and then look at the impact of each of the vibrational modes (j) on the site. This shows the variation of site energy as you take into account vibrational modes. Some modes will have no impact, some will be significant. Moving to an ionized state there will be a strong geometry relaxation so there will be a strong coupling to the vibrational modes that lead to the ionized state.

Cmditradmin: /* Charge Transport */

2009-09-15T19:18:52Z

Charge Transport

← Older revision		Revision as of 12:18, 15 September 2009
Line 55:		Line 55:

	=== Charge Transport ===		=== Charge Transport ===
	[[Image:chargetransport.png\|thumb\|~~300px~~\|Variation in charge mobility with temperature]]		[[Image:chargetransport.png\|thumb\|400px\|Variation in charge mobility with temperature]]
	Currently we can not predict the crystal structure of a molecule given the chemical formula of a molecule. The big challenge is to evaluate the mobility as a function temperature. If you start with a perfect crystal at low temperature you have a large mobility. As the temperature increases the molecules start vibrating and there is a reduction in electronic coupling, bandwidth and mobility. In metals as you increase temperature the vibrations get larger and mobility comes down. At some point the vibrations will reduce the electronic coupling so much that it will become favorable for the charge carrier to localize. This cross over region is difficult to describe and may not be an abrupt evolution. There is a gradual localization process. Once you cross over into the hopping regime (an activated regime) with localization the mobility goes back up with temperature. Here the vibrations help by preparing the two molecules to achieve essentially the same geometry so that electron transfer can take place. So the rate of electron transfer is simply the time it takes for vibrations to bring the molecules into the same geometry. In most organic materials will have decomposed before they reach a temperature where they begin to decrease in electron transfer with temperature (T<sub>2</sub>).		Currently we can not predict the crystal structure of a molecule given the chemical formula of a molecule. The big challenge is to evaluate the mobility as a function temperature. If you start with a perfect crystal at low temperature you have a large mobility. As the temperature increases the molecules start vibrating and there is a reduction in electronic coupling, bandwidth and mobility. In metals as you increase temperature the vibrations get larger and mobility comes down. At some point the vibrations will reduce the electronic coupling so much that it will become favorable for the charge carrier to localize. This cross over region is difficult to describe and may not be an abrupt evolution. There is a gradual localization process. Once you cross over into the hopping regime (an activated regime) with localization the mobility goes back up with temperature. Here the vibrations help by preparing the two molecules to achieve essentially the same geometry so that electron transfer can take place. So the rate of electron transfer is simply the time it takes for vibrations to bring the molecules into the same geometry. In most organic materials will have decomposed before they reach a temperature where they begin to decrease in electron transfer with temperature (T<sub>2</sub>).