TUTORIAL I DEVICE PHYSICS, CHARGE TRANSPORT, APPLICATIONS AND PROCESSING IN ORGANIC ELECTRONICS Nir Tessler Devin Mackenzie March 28, 2005 1:30 – 5:00 PM

MRS SPRING 2005 TUTORIAL I DEVICE PHYSICS, CHARGE TRANSPORT, APPLICATIONS AND PROCESSING IN ORGANIC ELECTRONICS PART 1 DEVICE PHYSICS and CHARGE TRANSPORT Nir Tessler EE Dept. Technion www.ee.technion.ac.il/nir

Nir Tessler, EE Dept. Technion Organic Semiconductors Nir Tessler, EE Dept. Technion www.ee.technion.ac.il/nir Semiconductor High band gap Low mobility Molecular You are holding ~60 slides but we will look together only at part of them. Watch for the slide number

Reminder EFM EC EF=EFi EFi EFi EF EV If the band-gap is high Insulator Intrinsic N-type P-type Metal EC EV EF=EFi EFM EFi EF EF EFi

Semiconductor

Isolated Material E0- Vacuum level Metal EFM EC Semiconductor EF EV (not in equilibrium) E0- Vacuum level Metal EFM EF EC EV Semiconductor Metal The energy required to “lift” an electron from the metal to the semiconductor = work function The (average) energy required to extract an electron.

(creating equilibrium) Making contact (creating equilibrium) E0 Metal EFM EF EC EV Semiconductor Is there any electronic interaction?

Charging a capacitor to a voltage of: Making contact E0 EC DV Metal EFM EF Semiconductor EV Charging a capacitor to a voltage of:

What assumptions did we use? There exist equilibrium between M and SC  Fermi level is continuous. The metal is an infinite reservoir (attaching the SC is a small perturbation) The potential is continuous (no dipoles ) +Q -Q

What will occur after making contact? Isolated Materials E0- Vacuum level Metal Metal EFM EF EC EV Semiconductor What will occur after making contact? Will the semiconductor become metallic? Will the entire volume be chemically reduced?

Isolated Material Connected E0 EF EC EV EFM EFM EF EC EV (no equilibrium) Connected (equilibrium) E0 ultra-thin EF EC EV Metal EFM Metal EFM EF EC EV Ultra-thin ~ nm scale

Ultra-thin EF EC EV Metal EFM Since the ultra-thin region is negligible in size it is not drawn: EF EC EV Metal EFM Interface dipole Conclusion: the metal workfunction can not be above (below) the conduction (valence) band.

What will happen after making contact 2.7 3.5 5.2 5.2 What will happen after making contact 5.2-3.5=1.7

Thermionic Emission E EC X Current Ec Barrier Basic Assumptions: Emission from A to B does not depend on emission from B to A but only on the concentration in A and B respectively (there doesn’t have to be equilibrium across the interface). The charge density in the metal is fixed (infinite reservoir)

In Low mobility semiconductors (organics) the emission rates from metal to organic and back are much larger then the current flowing in the device: There is equilibrium at the contact interface The thermionic emission process is not important but for ensuring equilibrium. What may change the above? What may slow the emission across the interface? The presence of a thin insulating layer will make the crossing from the metal to the organic (tunneling) very slow and it will become the rate limiting factor (i.e. break the equilibrium).

Insulator N. F. Mott and R. W. Gurney, Electronic processes in ionic crystals (Oxford university press, London, 1940). M. A. Lampert and P. Mark, Current injection in solids (Academic Press, New York, 1970

A current flowing through “insulator” Without an injection: velocity When the charge is evenly distributed:

A current flowing through “insulator” Detailed description: To be consistent with previous slide, use drift current only:

The charge density at the contact interface (N0) is dictated by the contact

What does small K mean?

Minor problem We neglected diffusion currents We found that E=0 at the contact So how come there is any current? These expressions do not hold at the close vicinity of the contact and as long as the contact region is much smaller then the device it doesn’t matter.

Now the charges are in How do they move?

e Molecular  Localization x Conjugated segments  “States” Charge conduction  non coherent hopping x e

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

Detailed Equilibrium Ej Ei Anderson:

Molecular Nature of the Envelope Function The polaron picture:

Simplistic approach Elastic energy: Q is a molecular configuration coordinate Stretched Squeezed Equilibrium

Elastic Energy (spring) Q0 E0spring Configuration coordinates E=E0+B(Q-Q0)2

Adding an electron (mass) will add energy of m*g*h Q0 E0t= E0spring+E0elec Q Here the particle just entered the system (molecule) and we see the potential surface just before relaxation After the system undergoes relaxation to a new equilibrium point. The “system” gained elastic energy while the electron energy went down (mg*Dh-BQ2>0)

Q A* A Q0 E0spring E0t= E0spring+ mgQ0 A* E0= E0t + BDQ2 - mgDQ A

The electronic equivalent Stretch mode En En +dEn L L + dL For small variations in the “size” of the molecule the electron phonon contribution to the energy of the electron is linear with the displacement of the molecular coordinates. For p-conjugated the atomic displacement is ~0.1A and F=2-3eV/A. The general formalism: Ee-ph=-AQ

Linear electron-phonon interaction: The system was stabilized by DE through electron-phonon interaction  Polaron binding energy

Transfer will occur when Q1=Q2=Q Total excess energy to reach this state: Electron transfer is thermally activated process Typical number is:

If initial and final energies are different: (In disordered materials E0_e is not identical for the two molecules) Accounts for difference between the equilibrium energies

Requires the “presence” of phonons. Or the occupation of the relevant phonons should be significant Average attempt frequency Probability of electron to move (tunnel) between two molecules that are in their “best” conformation Activation of the molecular conformation

Bosons: What will happen if T<Tphonon/2 ? The relevance to our average attempt frequency: What will happen if T<Tphonon/2 ? The molecules will not reach the “best” conformation that was accessible at higher (room) temperature New activation energy New attempt frequency Typical temperature at which the transport mechanism changes is 150-200k

Sites-Energy Statistics (the most popular ones) Gaussian DOS Exponential DOS Completely ignore the issue

What is the statistical Energy-Distribution? Gaussian Exponential

The two look very different BUT – a single experiment (typically) samples only a small region of the DOS

Charge Mobility & Charge Density For low enough density: For high enough density: (Nt=1020cm-3 -> n<5x1018) (s=5kT, Nt=1020cm-3 -> n>1x1015) Power Law T0=450k  s=5.5kT M. Vissenberg and M. Matters, "Theory of the field-effect mobility in amorphous organic transistors," Physical Review B, vol. 57, pp. 12964-12967, 1998 Y. Roichman, Y. Preezant, and N. Tessler, "Analysis and modeling of organic devices," Physica Status Solidi a-Applied Research, vol. 201, pp. 1246-1262, 2004

Electric Field Mobility (a.u.) s=7kT Empirical Typical numbers Gaussian DOS H. Bassler, Phys. Stat. Sol. (b) 175, 15-56 (1993) (The range of papers by H. Bassler provide deep insight of the transport) Mobility (a.u.) Y. Roichman, Y. Preezant, and N. Tessler, "Analysis and modeling of organic devices," Physica Status Solidi a-Applied Research, vol. 201, pp. 1246-1262, 2004 s=7kT

Derivation of the Generalized Einstein Relation Current continuity Eq. In the absence of external force (J=0) Equilibrium conditions (existence of a Fermi level + constant temperature) Generalized Einstein-Relation (Ashcroft, solid state physics)

Generalized Einstein Relation Charge Diffusion & Charge Density (A) s=7kT s=5kT s=4kT Enhancement of Einstein Relation T0=600k T0=500k T0=400k Y. Roichman and N. Tessler, "Generalized Einstein relation for disordered semiconductors - Implications for device performance," Applied Physics Letters, vol. 80, pp. 1948-1950, 2002 Relative Charge Density

Diode Or: s=4kT  T0=450k

Extracting Mobility Analysis of LEDs Analysis of FETs The disorder parameter s is an established important feature Can we extract it?

LEDs Gaussian DOS at low density limit Average Density H. Bassler, Phys. Stat. Sol. (b), vol. 175, pp. 15-56, 1993 Average Density Density at the exit contact Need a formalism that accounts for both electric field and density

CIp-FET Drain Source Source Drain p - conjugated y x z L L W W W W L L Insulator SiO Insulator SiO 2 2 y x z Si Conductor Conductor Si Vg Vg Vg Vg

Charge Density & Electric Field Dependence (Gaussian DOS) s=4kT s=7kT Mobility (a.u.) The exponential prefactor depends on s as well as Charge Density Y. Roichman, Y. Preezant, N. Tessler, Phys. Stat. Sol. 2004

s/kT Exponential pre-factor Mean Medium Approximation - Low & High Density + Electric field only for LEDs thicker then 200nm (and limited voltage range) AND Exponential pre-factor ~1016÷1017cm-3 s/kT Using Low density expression The extracted s is always ≤130meV

k Use FETs to extract s At Low Electric Field: At Room Temp. Tasks: 1. Measure Mobility 2. Estimate charge density

Extracting Mobility - FETs But 100% is not always critical

Deriving the expressions for charge density dependent mobility

This procedure does NOT (i.e. general procedure) assume a given DOS Shape (i.e. general procedure) By making the best fit one finds: 1. Density dependent mobility 2. Threshold voltage (+-)

To evaluate charge density: transfer Vg to density in cm-2 and then to cm-3 Einstein relation is larger then 1 and depends on the charge density Simple to implement Accounting for it: Charge Density can not exceed the DOS Channel depth does not go below 1-2 monolayer It is too fundamental to be ignored!

Threshold Voltage Intrinsic E E C C E F E E V V Gate Voltage

E E E E E Threshold Voltage Intrinsic EF C C F V V VG Linear Gate

E E E E E Threshold Voltage – disordered material Intrinsic C C F V V EF E E C C Linear E F Exponent E E Sub- Threshold VG V V Gate Voltage

Models for Contact injection: [1] V. I. Arkhipov, E. V. Emelianova, Y. H. Tak, and H. Bassler, "Charge injection into light-emitting diodes: Theory and experiment," Journal of Applied Physics, vol. 84, pp. 848-856, 1998. [2] V. I. Arkhipov, U. Wolf, and H. Bassler, "Current injection from metal to disordered hopping system. II. Comparison between analytic theory and simulation," Phys. Rev. B, vol. 59, pp. 7514-7520, 1999 [3] M. A. Baldo and S. R. Forrest, "Interface-limited injection in amorphous organic semiconductors - art. no. 085201," Physical Review B, vol. 6408, pp. 5201-+, 2001. [4] M. A. Baldo, Z. G. Soos, and S. R. Forrest, "Local order in amorphous organic molecular thin f ilms," Chemical Physics Letters, vol. 347, pp. 297-303, 2001 [5] Y. Preezant and N. Tessler, "Self-consistent analysis of the contact phenomena in low- mobility semiconductors," Journal of Applied Physics, vol. 93, pp. 2059- 2064, 2003. [6] Y. Preezant, Y. Roichman, and N. Tessler, "Amorphous Organic Devices - Degenerate Semiconductors," J. Phys. Cond. Matt., vol. 14, pp. 9913–9924, 2002. [7] Y. Roichman, Y. Preezant, and N. Tessler, "Analysis and modeling of organic devices," Physica Status Solidi a-Applied Research, vol. 201, pp. 1246-1262, 2004 [8] J. C. Scott and G. G. Malliaras, "Charge injection and recombination at the metal-organic interface," Chemical Physics Letters, vol. 299, pp. 115-119, 1999. [9] T. van Woudenbergh, P. W. M. Blom, M. Vissenberg, and J. N. Huiberts, "Temperature dependence of the charge injection in poly-dialkoxy-p-phenylene vinylene," Applied Physics Letters, vol. 79, pp. 1697-1699, 2001 [10] J. H. Werner and H. H. Guttler, "Barrier Inhomogeneities at Schottky Contacts," Journal of Applied Physics, vol. 69, pp. 1522-1533, 1991

Transport models [1] W. D. Gill, "Drift mobilities in amorphous charge-transfer complexes of trinitrofluorenone and poly-n- vinylcarbazole," J. Appl. Phys., vol. 43, pp. 5033, 1972. [2] M. Van der Auweraer, F. C. Deschryver, P. M. Borsenberger, and H. Bassler, "Disorder in Charge-Transport in Doped Polymers," Advanced Materials, vol. 6, pp. 199-213, 1994. [3] R. Richert, L. Pautmeier, and H. Bassler, "Diffusion and drift of charge-carriers in a random potential - deviation from einstein law," Phys. Rev. Lett., vol. 63, pp. 547-550, 1989. [4] V. I. Arkhipov, P. Heremans, E. V. Emelianova, G. J. Adriaenssens, and H. Bassler, "Weak-field carrier hopping in disordered organic semiconductors: the effects of deep traps and partly filled density-of-states distribution," Journal of Physics-Condensed Matter, vol. 14, pp. 9899-9911, 2002. [5] M. Vissenberg and M. Matters, "Theory of the field-effect mobility in amorphous organic transistors," Physical Review B, vol. 57, pp. 12964-12967, 1998. [6] D. Monroe, "Hopping in Exponential Band Tails," Phys. Rev. Lett., vol. 54, pp. 146-149, 1985. [7] H. Scher, M. F. Shlesinger, and J. T. Bendler, "TIME-SCALE INVARIANCE IN TRANSPORT AND RELAXATION," Physics Today, vol. 44, pp. 26-34, 1991. [8] H. Scher and E. M. Montroll, "Anomalous transit-time dispersion in amorphous solids," Phys. Rev. B, vol. 12, pp. 2455–2477, 1975. [9] E. M. Horsche, D. Haarer, and H. Scher, "Transition from dispersive to nondispersive transport: Photoconduction of polyvinylcarbazole," Phys. Rev. B, vol. 35, pp. 1273-1280, 1987. [10] Y. Roichman, Y. Preezant, and N. Tessler, "Analysis and modeling of organic devices," Physica Status Solidi a- Applied Research, vol. 201, pp. 1246-1262, 2004. [11] Y. Roichman and N. Tessler, "Generalized Einstein relation for disordered semiconductors - Implications for device performance," Applied Physics Letters, vol. 80, pp. 1948-1950, 2002. [12] Y. N. Gartstein and E. M. Conwell, "High-Field Hopping Mobility in Molecular-Systems with Spatially Correlated Energetic Disorder," Chemical Physics Letters, vol. 245, pp. 351-358, 1995. [13] H. C. F. Martens, P. W. M. Blom, and H. F. M. Schoo, "Comparative study of hole transport in poly(p- phenylene vinylene) derivatives," Physical Review B, vol. 61, pp. 7489-7493, 2000 [14] S. V. Rakhmanova and E. M. Conwell, "Electric-field dependence of mobility in conjugated polymer films," Applied Physics Letters, vol. 76, pp. 3822-3824, 2000 [15] R. A. Marcus, "Chemical + Electrochemical Electron-Transfer Theory," Annual Review of Physical Chemistry, vol. 15, pp. 155-&, 1964. [16] R. A. Marcus, "Theory of Oxidation-Reduction Reactions Involving Electron Transfer .5. Comparison and Properties of Electrochemical and Chemical Rate Constants," Journal of Physical Chemistry, vol. 67, pp. 853- &, 1963. [17] D. Emin, "Small polarons," Phys. Today, vol. 35, pp. 34-40, 1982

Transport in FETs [1] S. M. Sze, Physics of Semiconductor Devices. New York: Wiley, 1981. [2] A. A. Muhammad, A. Dodabalapur, and M. R. Pinto, "A two-dimensional simulation of organic transistors," IEEE trans. elect. dev., vol. 44, pp. 1332-1337, 1997. [3] G. Horowitz, P. Lang, M. Mottaghi, and H. Aubin, "Extracting parameters from the current-voltage characteristics of field-effect transistors," Advanced Functional Materials, vol. 14, pp. 1069-1074, 2004. [4] G. Horowitz, M. E. Hajlaoui, and R. Hajlaoui, "Temperature and gate voltage dependence of hole mobility in polycrystalline oligothiophene thin film transistors," J. Appl. Phys., vol. 87, pp. 4456-4463, 2000. [5] Y. Roichman and N. Tessler, "Structures of polymer field-effect transistor: Experimental and numerical analyses," Applied Physics Letters, vol. 80, pp. 151-153, 2002. [6] Y. Roichman, Y. Preezant, and N. Tessler, "Analysis and modeling of organic devices," Physica Status Solidi a- Applied Research, vol. 201, pp. 1246-1262, 2004. [7] S. Shaked, S. Tal, Y. Roichman, A. Razin, S. Xiao, Y. Eichen, and N. Tessler, "Charge density and film morphology dependence of charge mobility in polymer field-effect transistors," Advanced Materials, vol. 15, pp. 913-+, 2003. [8] N. Tessler and Y. Roichman, "Two-dimensional simulation of polymer field-effect transistor," Applied Physics Letters, vol. 79, pp. 2987-2989, 2001. [9] L. Burgi, R. H. Friend, and H. Sirringhaus, "Formation of the accumulation layer in polymer field-effect transistors," Applied Physics Letters, vol. 82, pp. 1482-1484, 2003. [10] L. Burgi, H. Sirringhaus, and R. H. Friend, "Noncontact potentiometry of polymer field-effect transistors," Applied Physics Letters, vol. 80, pp. 2913-2915, 2002. [11] S. Scheinert and G. Paasch, "Fabrication and analysis of polymer field-effect transistors," Physica Status Solidi a-Applied Research, vol. 201, pp. 1263-1301, 2004. [12] E. J. Meijer, C. Tanase, P. W. M. Blom, E. van Veenendaal, B. H. Huisman, D. M. de Leeuw, and T. M. Klapwijk, "Switch-on voltage in disordered organic field-effect transistors," Applied Physics Letters, vol. 80, pp. 3838-3840, 2002. [13] C. Tanase, E. J. Meijer, P. W. M. Blom, and D. M. de Leeuw, "Unification of the hole transport in polymeric field-effect transistors and light-emitting diodes," Physical Review Letters, vol. 91, pp. 216601, 2003. [14] G. Paasch and S. Scheinert, "Scaling organic transistors: materials and design," Materials Science-Poland, vol. 22, pp. 423-434, 2004

It is very important to measure down to very low charge density Our Model (for low field limit): In FETs: It is very important to measure down to very low charge density AND not force a single power law -8 -4 -3 -2 -1 VDS 2k=0.85±0.1 s≈5kT=130meV

Q* A system that is made of two identical molecules Wa (Room Temperature) -1000 1000 2000 3000 4000 5000 6000 E Q* Reactants Products A B A B Wa As the molecules are identical it will be symmetric (charge on 1 is equivalent to charge on 2)

Q Would the electron transfer rate still follow exp(-qWa/kT) A system that is made of two identical molecules (Low Temperature) -1000 1000 2000 3000 4000 5000 6000 E Q A B A B Wa At low temperature the probability to acquire enough energy to bring the two molecules to the top of the barrier is VERY low. In this case the electron may be exchanged at “non-ideal” configuration of the atoms or in other words there would be tunneling in the atoms configuration (atoms tunnel!). Would the electron transfer rate still follow exp(-qWa/kT)

Trans-Resistor = Transistor G S D Assumed m is constant Assumed channel depth is negligible compared to insulator thickness so that C=COX (and VDS is small). Trans-Resistor = Transistor

Trans-Resistor = Transistor G S D B IDS VDS Vg1>VT Vg2>Vg1 Vg3>Vg2 Vg4>Vg3 Trans-Resistor = Transistor

y x (a) (b) - 5V - 5V Gate 0V 0V 0V - 3V 0V - 1.5V Source Drain (c) Region with no charge where all voltage beyond VG drops upon.

IDS VDS Vg>VT Ranges Saturation Linear