Organic Electronic Devices Week 3: Charge Transport Lecture 3.5: Organic Field-Effect Transistors

Bryan W. Boudouris Chemical Engineering Purdue University

1 Lecture Overview and Learning Objectives

• Concepts to be Covered in this Lecture Segment

• Introduction to the Device Geometry and Operation of Organic Field- Effect Transistors (OFETs) • Characterization of OFETs Using an Output Curve and a Transfer Curve in Order to Determine Charge Carrier Mobility • Explanation of the Difference Between the ON and OFF States and the Concept of the Subthreshold Swing

• Learning Objectives By the Conclusion of this Presentation, You Should be Able to:

1. Explain the operating mechanism of an organic field-effect transistor during p-type and n-type transport testing. 2. Derive the equation that relates the drain current to the mobility of transistor given a certain geometry and materials parameters. 3. Calculate the mobility and ON/OFF ratio of an organic semiconductor given an output curve and a transfer curve. OFET Device Structure and Operating Mechanism

Organic Field-effect Transistors (OFETs) Are Useful Devices for Testing the Properties of Organic Semiconductors

OFETs Are Three Electrode Devices

Operating Mechanism of an OFET in Hole Transporting Mode

S – Source Electrode D – Drain Electrode Gate – Gate Electrode VG – Voltage Between Source and Gate VD – Voltage Between Source and Drain L – Channel Length, Distance between Source and Drain Electrodes (Typical Value ~200 µm) W – Channel Width, Distance of the Source and Drain Electrodes in the Direction Orthogonal to the Channel Length Direction (Typical Value ~2,000 µm) Applying Different Voltages Allows for Two Typical Plots

Output (ID-VD) Curve Transfer (ID-VG) Curve

• In the linear regime the current simply • In the subthreshold regime the device is increases with voltage according to Ohm’s turning from OFF (low current) to ON (high Law current)

• In the saturation regime the current • In the high V regime the slope of the line reaches a maximum value prior to leveling G of I1/2 can be used to estimate the mobility of with increasing applied voltage the semiconductor Further Reading: Newman, C. R.; Frisbie, C. D.; et al. Chem. Mater. 2004, 16, 4436. Current and Carrier Concentration in OFETs

Output (ID-VD) Curve Applying VG Induces Charges (qind)

qind (x) = n(x)et

qind (x) = Cox (VG −VT −V (x))

n(x) Electron Density

t Thickness of Charged Layer

Cox Capacitance of the Insulator

VT Threshold Voltage

At VD values near 0 V, the carrier concentration is relatively uniform across the channel because V(x) is ~0 and VT should not be a function of the distance.

Further Reading: Newman, C. R.; Frisbie, C. D.; et al. Chem. Mater. 2004, 16, 4436. Current and Carrier Concentration in OFETs (Part II)

Output (ID-VD) Curve Applying VG Induces Charges (qind)

qind (x) = n(x)et

qind (x) = Cox (VG −VT −V (x))

Can Describe ID from Ohm’s Law L V = I R and R = so D D Aσ L V = I D D Aσ Linear Gradient in V(x) at Low VD L Channel Length A Channel Cross Sectional Area

σ Electrical Conductivity

Further Reading: Newman, C. R.; Frisbie, C. D.; et al. Chem. Mater. 2004, 16, 4436. Current and Carrier Concentration in OFETs (Part III)

Cross Sectional Area Is Just the Channel Width Times the Induced Thickness L L V = I = I D D Aσ D (tW )σ

By Definition, the Conductivity for an Electron-only Device Is:

σ = e nind ,av µ nind ,av Average Carrier Concentration in the Channel

Therefore: L L VD = I D = I D (tW )σ (tW )(e nind ,av µ) L VD = I D (µW )( nind ,av et )

Further Reading: Newman, C. R.; Frisbie, C. D.; et al. Chem. Mater. 2004, 16, 4436. Current and Carrier Concentration in OFETs (Part IV)

The Average Value of the Induced Charges in the Channel Must Be:  V  = − − D qind ,av Cox VG VT   2  Therefore, The Average Carrier Concentration in the Channel Must Be:  V  = = − − D nind ,av et qind ,av Cox VG VT   2  Substitution of This Equation into the Equation from the Previous Slide Yields: L L V = I = I or D D (µW )( n et ) D  V  ind ,av (µW )C V −V − D ox  G T 2   2  W VD I D = µ Cox (VG −VT )VD −  L  2 

Further Reading: Newman, C. R.; Frisbie, C. D.; et al. Chem. Mater. 2004, 16, 4436. Calculating the Field-Effect Mobility in the Linear Regime

Define the Transconductance (gm) and Conductance (gd) for (VG – VT) >> VD

∂I D W gm = = Cox µlin VD Use the Transfer Curve ∂VG L VD

∂I D W gd = ~ Cox µlin (VG −VT ) Use the Output Curve ∂VD L VG

By Knowing the Device Geometry and the Capacitance of the Dielectric, the Linear Regime Mobility Can Be Calculated Readily

What Happens in the Saturation Regime? Carrier Concentration in the Saturation Regime

Output (ID-VD) Curve Substituting VD = VG – VT Yields:

2 W VD ID =µ Cox( V G −− VV T) D L 2 2 W (VVGT− ) ID=µ C oxGT( VVVV −)( GT −−) L 2

W 2 I= µ CV( − V) D 2L ox G T

Further Reading: Newman, C. R.; Frisbie, C. D.; et al. Chem. Mater. 2004, 16, 4436. ION/IOFF Ratio and Subthreshold Swing

Transfer (ID-VG) Curve Define the Subthreshold Swing (S)

dV S ≡ G d(log I D )

The subthreshold swing is a measure of how rapidly the device switches from the OFF to the ON state. It is reported in terms of V decade-1.

A large value of S generally implies a large concentration of shallow traps.

The ION/IOFF ratio is the value of the OFF current to the ON current, and is reported in x terms of 10 . In general, it is important to minimizes IOFF through minimizing dopants and leak and maximizing ION through increasing the mobility of the semiconductor system. Summary and Preview of the Next Lecture

Organic field-effect transistors (OFETs) are unique devices capable of serving as testbeds to evaluate the mobility of organic semiconductors. Furthermore, they can be used as logic switches because they have a relatively large difference in current between their ON and OFF states. The three terminal geometry allows for the control of charge induction, and thus charge flow, through the gate electrode.

The performances of OFET devices generally are characterized through two distinct curves. These are the output (ID-VD) and transfer (ID-VG) curves. Both of these curves display a linear and saturation regime that correspond to different charge carry concentrations in the channel of the OFET device. Starting from Ohm’s Law, one can derive how the current should change as a function of voltage in these systems, and one can use this information to extract mobility values from the OFET devices.

Next Time: Charge Generation in Organic Photovoltaic Devices