Showing posts with label organic electronics. Show all posts
Showing posts with label organic electronics. Show all posts

Tuesday, July 21, 2026

Rudolph Marcus (1923-2026): theoretical chemical physicist

Rudolph Marcus died last week. He was 102. There is a nice obituary in The New York Times. He was best known for his theory of electron transfer, for which he was the sole recipient of the Nobel Prize in Chemistry in 1992.

Although the theory was proposed for electron transfer in a polar solvent it applies to a wide range of other systems, where two quantum states are coupled to one another and to an environment. One example is for Forster transfer of excitons between molecules, which is central to photosynthesis.

I will give a physics perspective, based on a talk I gave in Slovenia back in 2013. Slides are here.

Basically, Marcus proposed an effective Hamiltonian for two diabatic states and calculated a transition rate in a limit that is relevant to most chemical contexts.

The Hamiltonian can be viewed as the spin-boson model, in which a two-level system is coupled to a bath of harmonic oscillators. 

[The dense book by Weiss on Quantum Dissipative Systems makes the connection explicit in detail. A more accessible treatment may be chapter 16 in the book Chemical Dynamics in Condensed Phases by Nitzan.]

The Hamiltonian is 

This defines a spectral density, which is important for quantum decoherence, but not so much here, except it defines a timescale that determines the classical limit, which Marcus assumed.


This can be used to define a quantity central to Marcus' theory, the reorganisation energy.


The transition rate between the two quantum states is given by

I consider this to be one of the most important equations in chemical physics, particularly for the understanding and design of functional materials.

Aside. Much of this is equivalent to Holstein's 1959 treatment of incoherent polaron transport (see Mahan, Many-body physics).

A key experiment by John R. Miller, Lidia T. Calcaterra and Gerhard L. Closs in 1984 showed how good the theory was and how its predictions were counter-intuitive. The authors considered a family of molecules that allowed them to tune epsilon, the energy difference between the two electronic states. [On the graph below epsilon = - Delta G].


The vertical scale is the reaction rate on a logarithmic scale. It varies by four orders of magnitude.

What is surprising? As stated at the Nobel prize award ceremony:

"The quadratic equation predicts that electron transfer reactions will occur more slowly the larger the driving force of the reaction is. This phenomenon received its own name, “the inverted region.” To a chemist, the phenomenon is just as unexpected as when a skier finds himself gliding more slowly down a slope the steeper it is."

The theory implies an important design principle for functional materials: if optimising functionality means maximising the reaction rate, then tune the energy difference epsilon to equal the reorganisation energy E_R.

The theory illustrates two important aspects of emergence: effective theories and universality. Many different systems can be described by the same theory. The environment may involve many degrees of freedom and its coupling to the system is characterised by many parameters (the M_alpha above). However, only one parameter matters, the reorganisation energy.

For Australians, there is some ambivalence about the way Marcus' name is often solely associated with electron transfer theory. We often refer to it as Marcus-Hush or Hush-Marcus theory because Noel Hush did similar work around the same time. Some of the history is recounted here by Ian Rae and Jeff Reimers. There are also subtle debates about whether the electron transfer is adiabatic or non-adiabatic.

My only personal interaction with Marcus was in 2011 when I visited the chemistry department at Caltech. Marcus kindly took me to lunch at the faculty club, along with his research group. Then he was 84 years old. He kept publishing papers until he died.

Tuesday, March 26, 2019

Noel Hush (1924- 2019): pioneering theoretical chemist

I was sad to hear last week that Professor Noel Hush died at age 94. Noel [also known as Prof.] was a pioneer in theoretical chemistry and chemical physics. He had a profound influence on both fields, particularly in their development in Australia.

Arguably his greatest scientific contribution was in the theory of electron transfer. Depending on where you are from this is called Hush-Marcus theory, Marcus-Hush theory, or Marcus theory. In particular, in 1958 Hush derived one of the most important equations in chemical physics, which can be used for design principles for functional electronic materials. A key concept here is the notion of diabatic states.

I had the privilege of knowing and working with Prof. Hush on and off over the past decade. As I made an adiabatic transition from condensed matter into chemical physics Prof. Hush provided a lot of encouragement, wisdom, perspective, and ideas. He strongly believed that theoretical chemists and condensed matter theorists could have mutually beneficial interactions. Together with Jeff Reimers and Laura McKemmish, we co-authored seven papers together. The last papers were published when Noel was 90 years old!

Besides his significant legacy of scientific knowledge, there is an incredible legacy of people that he taught, supervised, mentored, encouraged, and collaborated with.

There is an interesting interview of Prof. Hush about his life by Robyn Williams from 2011.

Friday, February 7, 2014

Quantifying many-body effects in organic photovoltaics

Most papers about organic photovoltaics are full of discussion about HOMO's and LUMO's, their relative energies and spatial extents.  
In the early days of this blog, I asked Am I HOMO- and LUMO-phobic?

Molecular orbitals are beautiful intuitive concepts that are extremely valuable for qualitative understanding. However, they do not exist, i.e., there is no way to measure one, even in principle.
Furthermore, for typical organic molecules used in organic photonics and electronics the one-electron energies associated with these orbitals usually do not give reliable estimates of physically observable energies [associated with true many-body states] such as the ionisation energy, electron affinity, optical energy gap....

I was pleased to see that the above issues are nicely explained and quantified in a recent paper

Reassessing the use of one-electron energetics in the design and characterization of organic photovoltaics
Brett M. Savoie, Nicholas E. Jackson, Tobin J. Marks, and Mark A. Ratner
We present results showing that common approximations employed in the design and characterization of organic photovoltaic (OPV) materials can lead to significant errors in widely adopted design rules. First, we assess the validity of the common practice of using HOMO and LUMO energies in place of formal redox potentials to characterize organic semiconductors. We trace the formal justification for this practice and survey its limits in a way that should be useful for those entering the field. We find that while the HOMO and LUMO energies represent useful descriptive approximations, they are too quantitatively inaccurate for predictive material design. Second, we show that the excitonic nature of common organic semiconductors makes it paramount to distinguish between the optical and electronic bandgaps for materials design. Our analysis shows that the usefulness of the “LUMO–LUMO Offset” as a design parameter for exciton dissociation is directly tied to the accuracy of the one-electron approximation. In particular, our results suggest that the use of the “LUMO–LUMO Offset” as a measure of the driving force for exciton dissociation leads to a systematic overestimation that should be cautiously avoided.
Some of these issues were also highlighted in earlier work, led by my UQ colleague Ben Powell, but not referenced.

Friday, October 11, 2013

What does my supervisor expect of me?

Different Ph.D and postdoctoral advisors/supervisors/mentors can have very different expectations of students/postdocs who work for/with them. Furthermore, these expectations can be significantly different from what students/postdocs expect. I have written before that it is important at the beginning [or better still, before] starting to work together that these expectations are clarified and discussed. At one Australian university it is part of the formal Ph.D induction process. Unfortunately, this is often not done.

Vitaly Podzorov is a physics faculty member at Rutgers University. On his website, he has a very clear and detailed description of what he expects from group members. It is worth reading carefully. Some of it is specific to his field, experimental organic electronics. Some of it may appear a little harsh. I don't necessarily agree with some of it [e.g. TeX is outdated software!]. I worry that the tone may lead students being scared to make mistakes, to take risks and fail. But, it clearly shows things from his perspective. Potential and new group members are not left guessing. Doing good science is hard and competitive.

Are there other examples where faculty web pages spell out expectations?
I welcome comments.

Tuesday, September 4, 2012

Signatures of "band-like" transport in organic electronic materials

I used to regularly write posts about charge transport in organic electronic materials. Some of these generated lively discussion in the comments section.

This morning I read an interesting paper Band-Like Electron Transport in Organic Transistors and Implication of the Molecular Structure for Performance Optimization
by Nikolas Minder, Shimpei Ono, Zhihua Chen, Antonio Facchetti, Alberto Morpurgo

They correctly distinguish "band-like" transport where a charge carrier is delocalised over just a few molecules from true band transport where it is delocalised over a large number of molecules [or unit cells in a crystalline semiconductor such as silicon].

They claim that a signature of band-like transport is the common observation of a mobility that decreases with increasing temperature and a Hall effect signal. I agree with the former but am confused about the latter. I thought for incoherent polaron transport one could still have a Hall effect, as discussed in a classic paper by Friedman and Holstein. 

The authors overlook the fact that a signature of band-like transport is that the mobility should be larger than e a^2/hbar ~ 1 cm^2/Vsec. Ignorance of this old and important result seems to be common in the field.

Previously, I pointed out that comparing the relative magnitudes of the energy gaps respectively associated with mobility, optical conductivity, and thermopower is a nice way to distinguish coherent from incoherent transport.

Sunday, November 21, 2010

A string theorist learns basic solid state physics

The Big Bang Theory seems to be getting better all the time, both in terms of humour and scientific content. This weekend we watched The Einstein Approximation (Season 3, Episode 14). Sheldon is obsessed with understanding how the electrons in graphene are "massless". His brain is stuck and so he seeks out a mind numbing job that he hopes will remove this mental block [inspired by Einstein working in the Swiss patent office, hence the title]. Eventually, he realises the problem was that he was thinking of the electrons as particles rather than as waves diffracted off the hexagonal lattice formed by the carbon nuclei. The Big Blog Theory has a good discussion about graphene.
I could not find a clip on YouTube of the relevant scenes where the physics is discussed. Let me know if you know of one.
A synopsis is here.
Finally, I wonder if this episode helped sway the Nobel Committee?

Saturday, November 13, 2010

A grand challenge: calculate the charge mobility of a real organic material

Previously I have written several posts about charge transport in organic materials for plastic electronic and photovoltaic devices. This week I looked over two recent articles in Accounts of Chemical Research that discuss progress at the very ambitious task of using computer simulations to calculate/predict properties of real disordered molecular materials beginning with DFT calculations of specific molecules. I was pleased to see that Marcus-Hush electron transfer theory plays a central role in both papers,

Electronic Properties of Disordered Organic Semiconductors via QM/MM Simulations (from the group of Troy Van Voorhis at MIT). 

Modeling Charge Transport in Organic Photovoltaic Materials (from Jenny Nelson's group at Imperial College London).

I have several questions and concerns about the latter paper.

The authors do a rather sophisticated simulation of a time of flight experiment where they put a charge accumulation on one side of the sample, apply an electric field, and measure
the average charge velocity, and extract the mobility. Intermolecular hopping rates are given by Marcus-Hush theory with parameters extracted from DFT calculations.

1. Is this the most efficient and reliable way to calculate mobility?
Generally in solid state physics one uses the fluctuation-dissipation relation. In this case Einstein's relation the mobility can be obtained from the diffusion constant. The diffusion constant is just the intermolecular hopping rate times the square of the intermolecular distance.

2. The mobility computed depends on the thickness of the sample.

3. How was the calculation benchmarked? Does this method give reliable
results for simpler systems, e.g., a naphthalene crystal?

4. The abstract makes some very strong claims,
"these computational methods simulate experimental mobilities within an order of magnitude at high electric fields. We ... reproduce the relative values of electron and hole mobility in a conjugated small molecule... We can reproduce the trends in mobility wiht molecular weight ... we quantitatively reproduce...On the basis of these results, we conclude that all of the necessary building blocks are in place for the predictive simulation of charge transport in macromolecular electronic materials and that such methods can be used as a tool toward the future rational design of functional organic electronic materials."


But when I look at the graph above it looks to me that the method often disagrees with experiment by more than an order of magnitude and fails to capture any electric field dependence. I could not find any discussion of temperature dependence.

Thursday, November 4, 2010

Trapped by solid state physics

There is an interesting looking perspective piece in Journal of Physical Chemistry Letters
Intrinsic Charge Trapping in Organic and Polymeric Semiconductors: A Physical Chemistry Perspective by L. G. Kaake, P. F. Barbara and X.-Y. Zhu

It begins
We aim to understand the origins of intrinsic charge carrier traps in organic and polymeric semiconductor materials from a physical chemistry perspective. In crystalline organic semiconductors, we point out some of the inadequacies in the description of intrinsic charge traps using language and concepts developed for inorganic semiconductors. In π-conjugated polymeric semiconductors, we suggest the presence of a two-tier electronic energy landscape, a bimodal majority landscape due to two dominant structural motifs and a minority electronic energy landscape from intrinsic charged defects.

Monday, November 1, 2010

Dielectric relaxation in organic electronic devices

A recent post mentioned the paper Low-k insulators as the choice of dielectrics in Organic Field-Effect Transistors [by Veres et al.], in the context of the sticky point of how to determine the relative importance of disorder and polaronic effects in molecular conducting materials used in semiconductor type devices. 

A major point of the paper is something different: how the mobility measured by time of flight (TOF) measurements is distinctly different [it has a larger magnitude and smaller activation energy] from in FETs, and that the mobility in FETs can decrease significantly with increasing the dielectric constant of the material used in the gate insulator material.

The paper discusses extensively how this may be associated with different kinds of disorder at the interface [which was followed by a theoretical paper in J. Chem. Phys. by Richards, Bird, and Sirringhaus]. It is not clear to me that invoking disorder is necessary to explain the gate dielectric dependence sure this is necessary. The reorganisation energy (polaron binding energy) associated with charge transfer between neighbouring molecules varies significantly with the dielectric constant of the surrounding medium. [Reminder: the activation energy for the mobility is 1/4 of this reorganisation energy].

For molecules close to the interface between the gate insulator and organic semiconductor, this reorganisation energy will decrease with a decrease in the dielectric constant of the insulator. Furthermore, if the organic semiconductor has a dielectric constant less than the gate dielectric, the reorganisation energy associated with a bulk measurement such as TOF will be less than a FET measurement which measures charge transport close to the interface.

Indeed the observed dependence of the FET mobility on the gate dielectric constant is observed explained within the framework of small polaron theory in a 2005 Nature Materials paper, Tunable Frohlich polarons in organic single-crystal transistors [see Figure above].

Friday, October 29, 2010

Deconstructing charge transport in organic semiconductors

A key question about charge transport in organic molecular materials is:

What is the relative importance of disorder and dielectric relaxation [small polarons = Marcus-Hush theory] in determining the charge mobility?

There is a nice clear and succinct review article in Chemical Reviews from 2007 by Coropceanu et al.

The view that disorder is dominant has been advocated by Bassler and collaborators, in
terms of a Gaussian density of states. This leads to a  mobility with the temperature dependence

[I have not seen an analytical derivation, this seems to be based on curved fitting to the results of Monte Carlo simulations].
This is in contrast, to an activated form.


Aside: Coropceanu et al. claim "there is no full theoretical justification for such an Arrhenius like expression". I am mystified by this claim. Small polaron theory [and equivalently Marcus-Hush theory, together with the fluctuation-dissipation theorem] give such a form. Indeed, in the review article they later give such expressions.
But, that is not my main point.

It is also pointed out that distinguishing between these two models is difficult
with experimental data from a limited temperature range.
This can be seen clearly in the Figure below taken from a 2003 paper Low-k insulators as the choice of dielectrics in Organic Field-Effect Transistors




Hence, just because one can fit the data to one of the models one should NOT conclude that model is correct. Unfortunately, this is often forgotten...

Presumably measurements down to 1 K may help distinguish the two models, although apparently these devices can malfunction at lower temperature.

I have more to say about this data, and what it may say about the charge transport mechanism,  but will leave that for another day...

Tuesday, October 19, 2010

Lawrie Lyons (1922-2010): a pioneer in organic photonics and electronics

Professor Lawrie Lyons died last thursday in Brisbane. He was the Foundation Professor of Physical Chemistry at University of Queensland from 1963 until his retirement in 1987. Long before it became a "hot" field he made many of the first measurements the optical and electronic properties of organic molecular crystals such as anthracene.  
In 1967 with Felix Gutmann (UNSW) he published, Organic Semiconductors  (Wiley, 1967) 858 pages. This work was of sufficient influence and importance that in 1983 Hendrik Keyzer revised and expanded it, Organic Semiconductors: Part 2 (Wiley, 1983). [I think it is the ultimate compliment if you write a book and someone else publishes a later edition. Other famous examples include Coulson's Valence and Lehringer's Biochemistry].
In 1971 he was elected a Fellow of the Australian Academy of Science. 
Lawrie was the scientific "grandfather" of Andrew Taylor, Head of Rutherford Appleton Laboratory and a driving force in making ISIS the world's leading neutron and muon source. At Sydney University, Laurie supervised the B.Sc. (Honours) thesis of John White (now at ANU), who was subsequently, Taylor's D.Phil supervisor at Oxford.
Following retirement, Lawrie pursued full-time a life-long passion. In 1989  he founded ISCAST, the Institute for the Study of Christianity in an Age of Science andTechnology.


I thank John Mainstone for providing some of the chronology.

Friday, July 9, 2010

Computational photochemistry tutorial


A very effective way to start learning what computational chemistry can and cannot do is to start doing hands on tutorials of concrete examples. Last week, at the I2CAM workshop on photovoltaics, Jeff Reimers ran a hands on workshop where participants calculated photochemical properties associated with charge separation and recombination in a specific donor-acceptor molecule. Here is the tutorial sheet and you can run Jeff's CNDO (Complete Neglect of Differential Overlap) [something like a Hubbard model..] code on the nanohub.
Besides being hands on, and very chemically focused, I also like the tutorial because it discusses solvent effects, kinetics, and Marcus-Hush theory.

Wednesday, June 9, 2010

Re-inventing the wheel (with open boundary conditions...)

The Journal of Chemical Theory and Computation just published a paper,

Conjugated Molecules Described by a One-Dimensional Dirac Equation

I had a sense of deja vu reading the first two-thirds of the paper. In the 1980's there was a lot of work in this direction in the physics community, beginning with this PRB by Takayama, Liu, and Maki, which has hundreds of citations. However, the JCTC paper authors appear to be unaware of all this earlier work.

Saturday, April 24, 2010

Deconstructing charge transport in complex materials III

Previously I have written posts about the important issue of understanding (and enhancing) the charge mobility of molecular materials. Key questions include:

What determines the relative magnitude of electron and hole mobilities?

How does mobility depend on the intermolecular separation and relative orientation?

I have tried to emphasize the charge transport is largely incoherent and that consequently a quantitative and qualitative understanding can be achieved via Marcus-Hush electron transfer theory [which is essentially equivalent to Holstein's small polaron theory]. I really don't think these points are appreciated enough (or at all) by people working on these materials.

This week at the conference I was delighted to become aware of the nice work of the group of Swapan Pati (one of the organisers) on this problem. [Their work precedes my rantings on this blog].

In this 2007 J. Chem. Phys. paper they take such approach and perform electronic structure calculations to calculate the two key physical quantities H_DA, (the matrix element for charge transfer = the Huckel parameter t) and the reorganisation energy for both electron and hole transport in different single crystal polymorphs of benzene and napthalene. H_DA falls off rapidly with distance and can vary significantly with the relative orientation and position of aromatic rings. The relative mobility of electrons and holes is determined by the relative magnitude of both H_DA and the reorganisation energy. Contrary to the standard dogma there are situations where the electron mobility is larger than the hole mobility.

Mohakud and Pati also have a J. Materials Chemistry paper applying a similar approach to octathio[8]circulene.

To me, important open questions include:
  • How will these results be modified by the screening and polarisation associated with bulk crystal? [I suspect H_DA may not change much but the reorganisation energy may increase significantly].
  • How does the experimental activation energy for the mobility compare to 1/4 of the reorganisation energy?
  • Can this approach be extended to describe the observed field-dependent mobility? [see for example this 2008 PRL by Emin].

Wednesday, April 21, 2010

Estimating the conductivity of DNA

Rosa Di Felice gave an interesting talk about computational studies of the electronic structure of DNA based systems. A combined experimental-theoretical review is here.

A key quantity for calculating the electron transfer rate (and conductivity) is the transfer integral (tight binding hopping integral). Rosa mentioned this nice methodological paper from J. Chem. Phys. which shows how to extract this parameter from methods such as DFT.

Tuesday, March 30, 2010

An equation you should know

Next month I am going to India to speak at a School and Conference on “Emergent Properties and Novel Behavior at the Nanoscale” organised by I2CAM and the Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR) in Bangalore.

In the school I will give a one hour long lecture. Here is the abstract I have submitted. Any feedback welcome. Some related material is discussed in this talk I gave last year in the Black Forest.

Quantum design principles for functional electronic materials

In a complex material how does one optimise the quantum efficiency of the transition
between two different quantum states when there are many alternative transitions available to a system?

Regardless of whether or not it is explicitly stated this is the question which is at the heart of a wide range of research. Prominent examples include understanding biomolecular function, designing organic photovoltaic cells, and catalysis.

I will discuss how this optimisation problem involves a subtle interplay between quantum coherence and decoherence induced by the system environment. The essential physics involved can be understood in terms of the spin-boson model which describes two quantum states which are coupled to one another with an environment which is modelled by a collection of an infinite number of harmonic oscillators.

Qualitatively different dynamics occurs depending on the relative magnitude of the key energy and time scales in the problem: the thermal energy, energy difference between the two states (epsilon), the coupling of the two states (and the associated Rabi frequency), the reorganisation energy of the environment, and the typical relaxation time of the environment.

Perhaps it is not appreciated enough that for most systems of interest all of these energy scales are well-characterised.

The incoherent "classical" regime of the spin-boson model gives a simple expression for the transition rate which is the same as the Marcus-Hush expression for the electron-transfer rate. I consider this is one of the most important equations in chemical physics and particularly for the understanding and design of functional materials.

I will discuss several important applications of this equation.

1) A design principle:
The rate is a maximum for a specific non-zero value of the coupling to the environment where epsilon equals the reorganisation energy.

2) The temperature dependence of the charge mobility in molecular materials.
[This is the same expression as given by small polaron theory].

3) Forster resonant energy transfer between chromophores.

Friday, March 26, 2010

Deconstructing excitons in organic materials

Previously, I asked is organic semiconductors a misnomer?

One needs to be very careful about trying to apply the same concepts from inorganic semiconductors to organic materials used to make devices such as photovoltaic cells.

An important example is excitons.
In inorganic semiconductors these arise from the Coulomb interaction between an electron and a hole and that have binding energies of much less than an electron Volt and they have a spatial extent of many lattice constants. They are sometimes called Wannier-Mott excitons.
Because they are so large variation of the dielectric constant of the material has a significant effect on the binding energy and spatial extent. As a first approximation one solves the hydrogen atom problem with the band effective mass and material dielectric constant.

However, the excitons (i.e., low lying singlet excited states are produced by photon absorption and can decay radiatively) in organic materials are VERY different. They are usually spatially localised on a single molecule. They are sometimes called Frenkel excitons.
The localisation can be seen by making a dilute "solution" of the molecules in a glass or matrix. They differ little from a thin film of just the molecules. The binding energy (i.e., the energy difference between the excited state and that of an electron and a hole on two neighbouring molecules) can be of the order of an electron Volt and reflects electronic correlations on the molecule. Except in very clean single crystals, there are usually no bands (and so an effective mass cannot be defined) and the dielectric constant does not determine the binding energy or the spatial extent of the exciton.

Wednesday, March 3, 2010

Quick to save the planet

A fundamental question concerning dye-sensitized solar cells is what determines the speed and efficiency with which charge is injected from the dye to the semiconductor (such as titanium oxide) on which it is absorbed?
A nice review by Liu and Andersen contains the summary diagram.


One important point I learnt is that (at least in some dyes) the ultrafast injection (~tens fsec) from the singlet excited state of the organometallic dye complex (such as those shown above) competes with intersystem crossing to the triplet excited state, from which injection can also occur but not as quickly.

Saturday, February 20, 2010

Proton conduction in organic FETs?

This title is deliberately provocative. It is keeping with the notion of multiple alternative hypotheses. I note the following concerning organic Field Effect Transistors
  • The mobility of protons in water is 3 x 10-3 cm^2/Vs.
  • This is larger than the hole mobility in many OFETs.
  • Fabrication of many OFETs involves treatment with acids at some stage.
  • Gate dielectric surface treatments significantly affect device performance, as described in this review.
So can someone rule out the following hypothesis?
In some organic FETs there is actually a contribution to the current from protons (rather than holes) moving in the interface between the organic "semiconductor" and the gate dielectric.

Perhaps a systematic study of OFET performance as a function of humidity?

Friday, February 19, 2010

Is "organic semiconductors" a misnomer?

A wide range of organic molecular materials such as pentacene and polythiophene are attracting considerable interest because of the prospect of "plastic electronics". They can be used to fabricate devices such as light emitting diodes, photovoltaic cells, and field effect transistors, which are traditionally made with inorganic semiconductor materials such as silicon and gallium arsenide. Consequently, these organic materials are often referred to as organic semiconductors. This may seem reasonable because:
  • they have a conductivity that is activated in temperature
  • there is an energy gap of several eV to the lowest optically excited state
  • they can be used to make "semi-conductor type" devices
On the other hand, they have properties that are significantly different from inorganic semiconductor materials. These all relate to the fact that electronic states tend to be localised on single molecules whereas in inorganic semiconductors one can have states which are delocalised over many atoms.
  • they do not have well-defined conduction and valence bands (e.g., their mobility is almost always much less than that required for band transport) [just because you can calculate something does not mean it exists!]
  • they have a mobility that is thermally activated
  • energy gaps associated with optical absorption and conduction are significantly different
  • electronic correlations significantly modify the ordering of electronic states (e.g. there is a large gap between singlet and triplet excited states)
Because there is no band transport one cannot define a scattering time and one should not talk about "band bending" near an interface.

I think that referring to these materials as organic semiconductors has led a lot of confusion and debatable reasoning in the literature. I think "organic electronic materials" or "organic photonic materials" is much more appropriate.

What does this movie tell us about the modern university?

Last night, my wife and I watched the movie, Wit. You can watch the full movie here  (free with ads). I should warn that some of the conten...