Band Regime versus Hopping Regime - Revision history

Cmditradmin: /* Band regime versus Hopping regime */

2010-08-10T23:11:54Z

Band regime versus Hopping regime

← Older revision		Revision as of 16:11, 10 August 2010
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	See Chemical Reviews 2004<ref>Bredas, JL; Beljonne, D; Coropceanu, V; Cornil, J, "Charge-Transfer And Energy-Transfer Processes In Pi-Conjugated Oligomers And Polymers: A Molecular Picture, Chemical Reviews, 104, 4971-5003 {{Doi:10.1021/cr040084k}}</ref>		See Chemical Reviews 2004<ref>Bredas, JL; Beljonne, D; Coropceanu, V; Cornil, J, "Charge-Transfer And Energy-Transfer Processes In Pi-Conjugated Oligomers And Polymers: A Molecular Picture, Chemical Reviews, 104, 4971-5003 {{Doi\|10.1021/cr040084k}}</ref>

	See Chemical Reviews 2007<ref>Chemical Reviews 107, 926-952 (2007)</ref>		See Chemical Reviews 2007<ref>Chemical Reviews 107, 926-952 (2007)</ref>

Cmditradmin: /* Band regime versus Hopping regime */

2010-08-10T23:11:22Z

Band regime versus Hopping regime

← Older revision		Revision as of 16:11, 10 August 2010
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	See Chemical Reviews 2004<ref>Chemical Reviews 104, 4971-5003 ~~(2004)~~</ref>		See Chemical Reviews 2004<ref>Bredas, JL; Beljonne, D; Coropceanu, V; Cornil, J, "Charge-Transfer And Energy-Transfer Processes In Pi-Conjugated Oligomers And Polymers: A Molecular Picture, Chemical Reviews, 104, 4971-5003 {{Doi:10.1021/cr040084k}}</ref>

	See Chemical Reviews 2007<ref>Chemical Reviews 107, 926-952 (2007)</ref>		See Chemical Reviews 2007<ref>Chemical Reviews 107, 926-952 (2007)</ref>

Smhunter: /* Band regime vs Hopping regime */

2010-06-22T20:19:49Z

Band regime vs Hopping regime

← Older revision		Revision as of 13:19, 22 June 2010
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	The '''band regime''' and '''hopping regime''' are the two limiting systems for transport although there are variations of each. They represent two ways that electricity can be conducted through an organic molecule or material.		The '''band regime''' and '''hopping regime''' are the two limiting systems for transport although there are variations of each. They represent two ways that electricity can be conducted through an organic molecule or material.

	== Band regime vs Hopping regime ==		== Band regime versus Hopping regime ==
	In band regime the charge carrier (wave function) is delocalized over the entire molecule or system. The delocalization over the whole system means there is only a probability of finding the charge carrier in any location. This results in coherent transport. In a sense the charge carrier has a “memory” of where it was before.		In band regime the charge carrier (wave function) is delocalized over the entire molecule or system. The delocalization over the whole system means there is only a probability of finding the charge carrier in any location. This results in coherent transport. In a sense the charge carrier has a “memory” of where it was before.

Cmditradmin: /* Band regime vs Hopping regime */

2010-01-06T17:59:27Z

Band regime vs Hopping regime

← Older revision		Revision as of 10:59, 6 January 2010
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	In hopping regime there is a localized charge carrier on a single molecule and you can follow the movement of the charge from molecule to molecule or chain segment to chain segment. Depending on the geometry and orientation of crystals hopping may result in differing mobilities in different directions or when hopping between layers. The band regime has the highest charge mobility and it is critical to understand the circumstances that encourage it. The transport is incoherent because each hop is random and has no correlation to the immediately preceding hop.		In hopping regime there is a localized charge carrier on a single molecule and you can follow the movement of the charge from molecule to molecule or chain segment to chain segment. Depending on the geometry and orientation of crystals hopping may result in differing mobilities in different directions or when hopping between layers. The band regime has the highest charge mobility and it is critical to understand the circumstances that encourage it. The transport is incoherent because each hop is random and has no correlation to the immediately preceding hop.

	'''Electronic coupling''' is large in the band regime and is the dominant factor. Whereas in the hopping regime coupling of charge carrier with vibrations, caused by geometry relaxations, is the dominant factor. In π conjugated systems with a charge localized somewhere on a chain or a molecule there will be a geometry relaxation around that charge leading to the formation of a phonon. A '''phonon''' is a mode of vibration in an ordered solid material or molecular substance that involve then entire lattice.		'''Electronic coupling''' is large in the band regime and is the dominant factor. Whereas in the hopping regime coupling of charge carrier with vibrations, caused by geometry relaxations, is the dominant factor. In π conjugated systems with a charge localized somewhere on a chain or a molecule there will be a geometry relaxation around that charge leading to the formation of a [[phonon]]. A '''phonon''' is a mode of vibration in an ordered solid material or molecular substance that involve then entire lattice.

	Geometry relaxations can lead to intramolecular vibrations as well as intermolecular vibrations in which adjacent molecules move with respect to one another.		Geometry relaxations can lead to intramolecular vibrations as well as intermolecular vibrations in which adjacent molecules move with respect to one another.

Cmditradmin at 21:05, 7 December 2009

2009-12-07T21:05:18Z

← Older revision		Revision as of 14:05, 7 December 2009
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	! hopping regime		! hopping regime
	\|-		\|-
	\| delocalization of the charge carrier ~~wavefunctions~~		\| delocalization of the charge carrier wave functions
	\| localization of the charge carrier ~~wavefunctions~~		\| localization of the charge carrier wave functions
	\|-		\|-
	\| coherent transport		\| coherent transport
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	In order to achieve a band regime (which has the largest carrier mobility) you must have a highly ordered structure or single crystal with few impurities. Low temperature is required because vibrations in adjacent coupled molecules due to temperature will decrease the electronic coupling and therefore decrease the mobility. For this reason mobility decreases with increasing temperature. In the case of methyl, which has a high charge carrier density, the decrease in mobility means the conductivity also decreases with temperature. The increase in intermolecular and intramolecular vibrations has generally a negative impact on the mobility of charge carriers.		In order to achieve a band regime (which has the largest carrier mobility) you must have a highly ordered structure or single crystal with few impurities. Low temperature is required because vibrations in adjacent coupled molecules due to temperature will decrease the electronic coupling and therefore decrease the mobility. For this reason mobility decreases with increasing temperature. In the case of methyl, which has a high charge carrier density, the decrease in mobility means the conductivity also decreases with temperature. The increase in intermolecular and intramolecular vibrations has generally a negative impact on the mobility of charge carriers.

	The second requirement for a band regime is the well ordered structure provides a large electronic coupling between adjacent sites on adjacent molecules or polymer repeat units. In a perfectly ordered polyacetylene the ~~wavefunctions~~ for the charge carriers are delocalized over the whole system. The presence of polarons and solitons means there must not be a perfect crystalline structure because these polaronic structures are associated with a geometry relaxation of the system. Charge polarons and solitons dissappear when there is complete delocalization. Polysulfur nitride ((SN)<sub>x</sub>) has crystals with strong interactions between the chains and no distortions. As a result there are no solitons. Normally samples of polyacetylene and transpolyacetylene are somewhat disordered and soliton and polaron behavior is observed.		The second requirement for a band regime is the well ordered structure provides a large electronic coupling between adjacent sites on adjacent molecules or polymer repeat units. In a perfectly ordered polyacetylene the wave functions for the charge carriers are delocalized over the whole system. The presence of polarons and solitons means there must not be a perfect crystalline structure because these polaronic structures are associated with a geometry relaxation of the system. Charge polarons and solitons dissappear when there is complete delocalization. Polysulfur nitride ((SN)<sub>x</sub>) has crystals with strong interactions between the chains and no distortions. As a result there are no solitons. Normally samples of polyacetylene and transpolyacetylene are somewhat disordered and soliton and polaron behavior is observed.

	== Evidence for band regime vs hopping regime ==		== Evidence for band regime vs hopping regime ==

Cmditradmin: /* Band regime vs Hopping regime */

2009-12-07T21:05:00Z

Band regime vs Hopping regime

← Older revision		Revision as of 14:05, 7 December 2009
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	== Band regime vs Hopping regime ==		== Band regime vs Hopping regime ==
	In band regime the charge carrier (~~wavefunction~~) is delocalized over the entire molecule or system. The delocalization over the whole system means there is only a probability of finding the charge carrier in any location. This results in coherent transport. In a sense the charge carrier has a “memory” of where it was before.		In band regime the charge carrier (wave function) is delocalized over the entire molecule or system. The delocalization over the whole system means there is only a probability of finding the charge carrier in any location. This results in coherent transport. In a sense the charge carrier has a “memory” of where it was before.

	In hopping regime there is a localized charge carrier on a single molecule and you can follow the movement of the charge from molecule to molecule or chain segment to chain segment. Depending on the geometry and orientation of crystals hopping may result in differing mobilities in different directions or when hopping between layers. The band regime has the highest charge mobility and it is critical to understand the circumstances that encourage it. The transport is incoherent because each hop is random and has no correlation to the immediately preceding hop.		In hopping regime there is a localized charge carrier on a single molecule and you can follow the movement of the charge from molecule to molecule or chain segment to chain segment. Depending on the geometry and orientation of crystals hopping may result in differing mobilities in different directions or when hopping between layers. The band regime has the highest charge mobility and it is critical to understand the circumstances that encourage it. The transport is incoherent because each hop is random and has no correlation to the immediately preceding hop.

Cmditradmin: /* Band regime vs Hopping regime */

2009-09-15T22:02:37Z

Band regime vs Hopping regime

← Older revision		Revision as of 15:02, 15 September 2009
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	See Chemical Reviews 2007<ref>Chemical Reviews 107, 926-952 (2007)</ref>		See Chemical Reviews 2007<ref>Chemical Reviews 107, 926-952 (2007)</ref>

			See Wikipedia [http://en.wikipedia.org/wiki/Organic_semiconductor Organic Semiconductor]
	=== Requirements for Band Regime ===		=== Requirements for Band Regime ===

Cmditradmin: /* Time domain */

2009-09-15T18:31:48Z

Time domain

← Older revision		Revision as of 11:31, 15 September 2009
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	The wider the bandwidth the larger the electronic coupling between adjacent units.		The wider the bandwidth the larger the electronic coupling between adjacent units.

	If W, the conduction bandwidth (for electrons) (and, or) the valance bandwidth (for holes) is large enough (.2-.3 eV) then τ is ~~'''~~shorter than 10<sup>-13</sup> s and this ~~makes~~ band transport is possible~~'''~~.		If W, the conduction bandwidth (for electrons) (and, or) the valance bandwidth (for holes) is large enough (.2-.3 eV) then τ is shorter than 10<sup>-13</sup> s and this means band transport is possible.

	This is because the carrier will not “sit” long enough on any single molecule for that molecule to have time to geometrically relax (relaxaton for C-C requires 20 ms) making band transport possible.		This is because the carrier will not “sit” long enough on any single molecule for that molecule to have time to geometrically relax (relaxaton for C-C requires 20 ms) thus making band transport possible.

	In a simple tight-binding approximation:		In a simple tight-binding approximation:

Cmditradmin: /* Band regime vs Hopping regime */

2009-09-15T18:30:21Z

Band regime vs Hopping regime

← Older revision		Revision as of 11:30, 15 September 2009
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	== Band regime vs Hopping regime ==		== Band regime vs Hopping regime ==
	In band regime the charge carrier (wavefunction) is delocalized over the entire molecule or system.		In band regime the charge carrier (wavefunction) is delocalized over the entire molecule or system. The delocalization over the whole system means there is only a probability of finding the charge carrier in any location. This results in coherent transport. In a sense the charge carrier has a “memory” of where it was before.

	In hopping regime there is a localized charge carrier on a single molecule and you can follow the movement of the charge from molecule to molecule or chain segment to chain segment. Depending on the geometry and orientation of crystals hopping may result in differing mobilities in different directions or when hopping between layers. The band regime has the highest charge mobility and it is critical to understand the circumstances that encourage it.		In hopping regime there is a localized charge carrier on a single molecule and you can follow the movement of the charge from molecule to molecule or chain segment to chain segment. Depending on the geometry and orientation of crystals hopping may result in differing mobilities in different directions or when hopping between layers. The band regime has the highest charge mobility and it is critical to understand the circumstances that encourage it. The transport is incoherent because each hop is random and has no correlation to the immediately preceding hop.

	In a band regime the delocalization over the whole system means there is only a probability of finding the charge carrier in any location. This results in coherent transport. In a sense the charge carrier has a “memory” of where it was before.		'''Electronic coupling''' is large in the band regime and is the dominant factor. Whereas in the hopping regime coupling of charge carrier with vibrations, caused by geometry relaxations, is the dominant factor. In π conjugated systems with a charge localized somewhere on a chain or a molecule there will be a geometry relaxation around that charge leading to the formation of a phonon. A '''phonon''' is a mode of vibration in an ordered solid material or molecular substance that involve then entire lattice.

	~~In the case of hopping the transport is incoherent because each hop is random and has no correlation to the immediately preceding hop.~~

	Electronic coupling is large in the band regime and is the dominant factor. Whereas in the hopping regime coupling of charge carrier with vibrations, caused by geometry relaxations, is the dominant factor. In π conjugated systems with a charge localized somewhere on a chain or a molecule there will be a geometry relaxation around that charge leading to the formation of a phonon. A phonon is a mode of vibration in an ordered solid material or molecular substance that involve then entire lattice.

	Geometry relaxations can lead to intramolecular vibrations as well as intermolecular vibrations in which adjacent molecules move with respect to one another.		Geometry relaxations can lead to intramolecular vibrations as well as intermolecular vibrations in which adjacent molecules move with respect to one another.
Line 50:		Line 46:
	=== Requirements for Band Regime ===		=== Requirements for Band Regime ===

	In order to achieve a band regime (which has the largest carrier mobility) you must have a highly ordered structure or single crystal with few impurities. Low temperature is required because vibrations in adjacent coupled molecules due to temperature will decrease the electronic coupling and therefore decrease the mobility. For this reason mobility decreases with increasing temperature. In the case of methyl, which has a high charge carrier density, the decrease in mobility means the conductivity also decreases with temperature. The increase in intermolecular and intramolecular vibrations has generally a negative impact on the mobility of charge carriers.		In order to achieve a band regime (which has the largest carrier mobility) you must have a highly ordered structure or single crystal with few impurities. Low temperature is required because vibrations in adjacent coupled molecules due to temperature will decrease the electronic coupling and therefore decrease the mobility. For this reason mobility decreases with increasing temperature. In the case of methyl, which has a high charge carrier density, the decrease in mobility means the conductivity also decreases with temperature. The increase in intermolecular and intramolecular vibrations has generally a negative impact on the mobility of charge carriers.

	The second requirement for a band regime is the well ordered structure provides a large electronic coupling between adjacent sites on adjacent molecules or polymer repeat units. In a perfectly ordered polyacetylene the wavefunctions for the charge carriers are delocalized over the whole system. ~~If there are~~ polarons and solitons ~~this~~ means there must not be a perfect crystalline structure because these polaronic structures are associated with a geometry relaxation of a the system. Charge polarons and solitons dissappear when there is complete delocalization. Polysulfur nitride ( (SN)<sub>x</sub> ) has crystals with strong interactions between the chains and no distortions. As a result there are no solitons. Normally samples of polyacetylene and transpolyacetylene are somewhat disordered and soliton and polaron behavior is observed.		The second requirement for a band regime is the well ordered structure provides a large electronic coupling between adjacent sites on adjacent molecules or polymer repeat units. In a perfectly ordered polyacetylene the wavefunctions for the charge carriers are delocalized over the whole system. The presence of polarons and solitons means there must not be a perfect crystalline structure because these polaronic structures are associated with a geometry relaxation of the system. Charge polarons and solitons dissappear when there is complete delocalization. Polysulfur nitride ((SN)<sub>x</sub>) has crystals with strong interactions between the chains and no distortions. As a result there are no solitons. Normally samples of polyacetylene and transpolyacetylene are somewhat disordered and soliton and polaron behavior is observed.

	== Evidence for band regime vs hopping regime ==		== Evidence for band regime vs hopping regime ==

Cmditradmin at 17:15, 15 September 2009

2009-09-15T17:15:32Z

← Older revision		Revision as of 10:15, 15 September 2009
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	</table>		</table>

	The '''band regime''' and '''hopping regime''' are the two limiting systems for transport although there are variations of each.		The '''band regime''' and '''hopping regime''' are the two limiting systems for transport although there are variations of each. They represent two ways that electricity can be conducted through an organic molecule or material.

			== Band regime vs Hopping regime ==
	In band regime the charge carrier (wavefunction) is delocalized over the entire molecule or system.		In band regime the charge carrier (wavefunction) is delocalized over the entire molecule or system.

	In hopping regime there is a localized charge carrier on a single molecule and you can follow the movement of the charge from molecule to molecule or chain segment to chain segment. Depending on the geometry and orientation of crystals hopping may result in differing mobilities in different directions or when hopping between layers. The band regime has the highest charge mobility and it is critical to understand the circumstances that encourage it.		In hopping regime there is a localized charge carrier on a single molecule and you can follow the movement of the charge from molecule to molecule or chain segment to chain segment. Depending on the geometry and orientation of crystals hopping may result in differing mobilities in different directions or when hopping between layers. The band regime has the highest charge mobility and it is critical to understand the circumstances that encourage it.

	~~== Band regime vs Hopping regime ==~~

	In a band regime the delocalization over the whole system means there is only a probability of finding the charge carrier in any location. This results in coherent transport. In a sense the charge carrier has a “memory” of where it was before.		In a band regime the delocalization over the whole system means there is only a probability of finding the charge carrier in any location. This results in coherent transport. In a sense the charge carrier has a “memory” of where it was before.