Charge Transport and Related Phenomena in Organic Devices Noam Rappaport, Yevgeni Preezant, Yehoram Bar, Yohai Roichman, Nir Tessler Microelectronic & Nanoelectronic Centers, Electrical Engineering Department, Technion, Haifa 32000, Israel Oren Tal, Yossi Rosenwaks, Dept. of Physical Electronics, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel Calvin K. Chan and Antoine Kahn Dept. of Electrical Engineering, Princeton University, Princeton NJ 08544, USA

Charge Transport Short Introduction (or the things we tend to neglect) Simplified Device-Oriented Approach FETs (charge density & Electric Field) PN Diodes Thin film device Highlight Inconsistencies

Hopping conduction model Conjugated segments  “States” Charge conduction  non coherent hopping x 

What are the important factors? 1.Energy difference 2.Distance 3.Similarity of the Molecular structures 1.What is the statistics of energy-distribution? 2.What is the statistics of distance-distribution? 3.Is it important to note that we are dealing with molecular SC? Do we need to use the concept of polaron?

Detailed Equilibrium Anderson: EiEi EjEj

Polaron Picture Anderson (Miller Abrahams) E Q Configuration co-ordinate

Morphology or Topology Spatial (Off Diagonal) Disorder 20% 100% 20% H. Bassler, Phys. Stat. Solid. (b), 175,15, (1993)

Mean Medium Approximation X0X0 X0-XX0-X X0+XX0+X Energy Physical picture is GREATLY relaxed to allow for Charge Density and Electric Field effects is a single model Y. Roichman & Nir Tessler 2003

 /kT Mean Medium Approximation (at low charge density) C=2.5*10-4  = Dashed line – Fit using Y. Roichman, et. al., Phys. Stat. Solidi a-201 (6), (2004)

Mean Medium Approximation  =5kT  =4kT  =7kT PkPk “Unified” percolation models predict much higher density dependence:

Limitations of the MMA Assumes equilibrium –Can not model intrinsically non-equilibrium density of states (as exponential). –Can not model a sample with preferential paths (percolation). Assumes that the sample is uniform on the length scale defined by the distance between contacts. But it actually shares the assumptions used with any device model

Choose material that shows less mixed phases. Shaked et. al., Adv mat, 15,913, 2003 Role of MW

Eliminate parasitic currents Close topology

V DS = Mobility = ? Need to account for: 1.It is density dependent (varies along the channel) 2.Real DOS is not single Gaussian (density dependence is “unknown”)  Develop a method for a general density dependence Transistors O. Katz, Y. Roichman, et. al, Semicond. Sci. Technol. 20, (2005) N. Tessler & Y. Roichman, Organic Elect., 2005.

Deduced  Model 120meVMMA Roichman et. al. 75meVPercolation Pasveer et. al. Coehoorn et. al. K= 0.38 PkPk But the polymer is MEH-PPV Extracting  1.Use low V DS 2.Do not use  Field dependent at 2-3x10 3 V/cm. A longer length scale, as in correlation, is required -4

Can we use MMA to describe LEDs too Can we use Semiconductor Device model to describe 100nm thick device?

Current continuity Eq. To model LEDs we need to be able to predict the charge density distribution inside the device charge density distribution inside a device is governed by D/  Y. Roichman and N. Tessler, Applied Physics Letters 80, 1948 (2002). Generalized Einstein-Relation:

Simple expression to fit them all For the MMA model: N. Tessler & Y. Roichman, Organic Elect., 2005.

Use General Einstein Relation to Model Junctions Semiconductor / Semiconductor (PN diode) Metal / Semiconductor (contact)

nKnK Ideality Factor: Exponential DOS Organic /Organic Junction PN

N. Tessler & Y. Roichman, Organic Elect., 2005.

Model the contact to LED as a transport problem Fimage UU  -ExU F  max,eff  Energy Distance,x x o Fimage UU  max,eff  Energy Distance,x x o U Band

Model the contact to LED as a transport problem Equilibrium at the contact interface defines the charge density on the organic side Transport in contact region & bulk is modeled using semiconductor equations Gaussian nature   and D (or D/  ) are functions of density Y. Preezant and N. Tessler, JAP 93 (4), (2003). Y. Roichman, et. al., Phys. Stat. Solidi a-201 (6), (2004)

Model the contact to LED as a transport problem Results: We could reproduce effects of – barrier temperature …. BUT – each experiment required a different physical set of parameters to make the fit quantitative. Take home message: 1. The Device Model doesn’t work well 2. The contact region and bulk may be governed by a different picture Arkhipov – non equilibrium at the contact leads to injection that is limited by hops into a Gaussian DOS (1nm insulating gap will make it valid). Baldo – The metal enhances disorder at the contact region only V. I. Arkhipov, et. al., Phys. Rev. B 59 (11), (1999). B. N. Limketkai and M. A. Baldo, Phys. Rev. B 71, (2005

Anything else could be wrong?

Are there Concerns Regarding LEDs ~10nm 100nm Filaments ?

Current Time  Time of flight measurement (excitation = step function) But step function is better suited for the understanding of devices as it has the same steady state! A linear part  a dominant mobility

Transient measurement (in thin, 300nm, films) Low excitation density Hard to find a linear slope Photocurrent

Mobility Distribution Saturated PathwaysUnsaturated Pathways 1.Thick Films: V.I. Arkhipov, E.V. Emelianova, G.J. Adriaenssens, H. Bässler, J. of Non-Crystalline Solids (2002) 2. Thin Films (experimental): R. Österbacka et al., Synthetic Metals 139, , 2003

Fitting with Model Transient Fit to Measurement Mobility Distribution Function

Low excitation density Medium excitation density Higher excitation density Hard to find a linear slope linear slope appears Clear linear slope Dispersive Less-Dispersive Charge Density Measuring 300nm thick MEH-PPV Device Under device densities the transport is “better-behaved”

Are there Concerns Regarding LEDs ~10nm 100nm Filaments ?

Motion on a 3D grid Note: the “long jumps” are due to the cyclic conditions at Y & Z axis

Monte Carlo (Hopping in Gaussian DOS) Monte-Carlo Drift-diffusion

Conclusion Are all types of devices “seeing” the same microscopic physical picture? (don’t think so) New description for dispersive transport (Filaments, Stability?)

Thank You

C=3x10 -4 (cm/Vs) 0.5 Spatial (Off Diagonal) Disorder

C=3x10 -4 (cm/Vs) 0.5

Current continuity Eq. To model LEDs we need to be able to predict the charge density distribution inside the device Equilibrium conditions (existence of a Fermi level + constant temperature) Generalized Einstein-Relation (Ashcroft, solid state physics) charge density distribution inside a device is governed by D/  Y. Roichman and N. Tessler, Applied Physics Letters 80, 1948 (2002).