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  Abstract-Thispaper presents a new analytical model of 2D Poisson equation to represent theboundary condition, physical values and the electrical properties of the OrganicField Effect Transistor (OFET).

The parabolic approximation technique is usedto solve the 2D Poisson equation for preserves a close link to know about thephysical parameters of the device. The proposed method mainly focus on thedevelopment of organic materials with high carrier mobility and downscaledshort channel devices to achieve high output current with fast switching speed.I.INTRODUCTION                Organic Field Effect Transistor is the recent area ofscience and technology that aims the electronic devices based on organicmaterials. It is attractive due to it fabrication process, flexible substrateand a wide range of applications such as RFID tags, bendable displays and smartcards. OFET circuit integration over large area and the metal contacts areformed before deposition of the Organic Semiconducting (OSC) layer. Surfacemodifications of metal contacts with thiol Self Assembled Monolayer (SAM) canbe used for obtaining low resistive and good quality semiconductor films on thetop of the source to drain electrodes for higher performance and betteruniformity of the electrical characteristics. One of the most importantparameters of the OFET is contact resistance (RC), which can limit the chargecarrier mobility and switching speed of the device.

The contact resistance hastwo main resistive components: (1) a component from the unavoidable chargeinjection barrier at the metal-organic interface and (2) the bias dependentcomponent, which models the carrier transport through the amorphous organiclayer to the conducting channel between the drain and source electrodes. Thecharge mobility in an OS is temperature dependent and carrier-concentrationdependent. This dependency is due to the charge transport mechanism in organicsemiconductors, which is the thermally assisted hopping of carriers between thelocalized molecular states.Thispaper is divided into six sections. Section II presents the related worksregarding the mobility and characteristics of the charge carriers.

In sectionIII, background information regarding the proposed 2D Poisson equation andanalytical model presented in section IV. The proposed structural functions arepresented in Section V. Section VI contains the conclusion.II.RELATED WORKS                Transconductance and the thickness of the organicmaterials mentioned by Anu Assis 1 and Shaul Hameed et al.

3. According toFransiska, threshold voltage is derived depending on the density of chargetraps that can be used to know about the performance of the charge particlemovements in the threshold region. Hamidreza et al. 4 presented contactresistance in the staggered organic field effect transistor and currentcrowding mechanism for determine the gate bias conditions and the potential andconcentration of the accumulated charges in the active layer.   III.METHODOLOGY                The carrier mobility of charges during theirtransport through the high-density accumulation layer at the semiconductordielectric interface is evaluated in this method.

Gatedielectric is another component in OFET because it serves as a barrier between thecharge carriers transporting at the semiconductor-dielectric interface.A.     Device StructureThepatterned source/drain can be deposited above to the organic semiconductor andthe scaling of the channel length may depends on the effect of contact. A newstructure named Source-Gated Transistor (SGT) is formed when a barrier at thesource is used to restrict the current.  Undernormal operation, at low drain bias, the source barrier is reverse biased andthe semiconductor is depleted of carriers across its whole thickness, leadingto saturation of output current.

This allows energy-efficient operation whilemaintaining high intrinsic gain, from lower drain voltages than conventionalFETs. The figure shows that the gate used in this work Ti/Au on which the gatedielectric material (PDI-8CN2) deposited with a thickness of 200nm.Over that, pentacene the organic semiconductor with a thickness  of 50nm placed with gold electrodes forsource and drain contacts.

The channel length and width were 200nm and 600nmrespectively. The bottom layer gate contact is with the thickness of 10nmTi/100nm Au. The variation in the characteristics of the OFET with thethickness of the dielectric layer was studied by using the MATLAB software. Fig.

1Device structure for OFETThe result of thecurrent control method, drain current is virtually independent of source-drainseparation, which increases performance uniformly in high-throughputtechnologies with low-resolution patterning. The source gated transistorstructure was normally realized in inverted staggered structure, and would alsopossible to be made in staggered structure.B.     Gate Dielectric                Variation in dielectric layer thickness has aprofound influence in performance of OFETs and reducing the dielectricthickness results in improvement in the current and mobility of the device.

Thefollowing table shows the value for the different dielectric material. And theinterface at the dielectric/semiconductor has profound influence on themorphological formation of the semiconductor film and the charge transportalong the  channel. Table1.

Polymergate dielectric used for OFETs. By applying varies dielectric material to theorganic semiconductor we can know the different behavior of the OFET.C.     Analytical model An analytical model was developedby considering the effect of trap states at the grain boundaries of the organicsemiconductor layer.                Thegate consist of two materials M1 and M2 with gate lengths L1 and L2 with twodifferent work function  and .

Based on the positive or negativepotential applied to the gate terminal, the device behaves as n type OFET and ptype OFET respectively. Increasing positive voltage on the gate narrows theenergy barrier between the source and intrinsic region. The electrons tunnelfrom the valence band of the p-doped source to the conduction band in theintrinsic body and then move towards the n-doped drain by drift diffusion.

                Thepotential profile in the vertical direction is assumed to be a second-orderpolynomial,    Where, The boundary conditionsin the channel region are: (a)Electric flux at the front-oxide gate interfaceis continuous for OFET and Electric flux at the back gate-oxide            (b) The back channel interface is continuousfor both the material      (c) The potential at the source and drain end.                The electric-field distribution along the channellength can be obtained by differentiating the surface potential. Where Vbi isthe built in potential, Eg is Band gap energy, q is elementarycharge, VGS is Gate to Source Voltage, VDS is Drain toSource voltage ,  isrelative permittivity of silicon and ,  isrelative permittivity of silicon dioxide. These are the parameters used in theanalytical model equation.

The potential of the metal 1 and metal 2 is given as     Theelectric-field distribution along the channel length can be obtained bydifferentiating the surface potential. The values of C11, C12,C21, C22 can be determined by solving  the above equation 8 and 9 . Potential    and  underM1 and M2 can be obtained by solving the Poisson’s equation (3.1) usingboundary conditions (3.7), (3.8) and (3.9), therefore,     Thegate work function of metal1 (  is 4eV and metal2  is 4.6eV.

? is the electron affinity. The coefficients of A, B,C and D can be expressed as       Electric Field                The electric field distribution along the channel canbe obtained by differentiating the surface potential Thevertical electric field can be written as Drain currentThe mechanism offlow of current IDS in OFET is based on Band-to-BandTunnelingof electrons from the valence band of the source to the conduction band ofchannel region. Therefore,  Then the value for theG(E) is given as Eg is the energyband gap.

The parameters used for MATLAB simulation are A=8.1×1017eV1/2/cm.s.V2and B= 3.057×107V/cm-(eV)3/2.

   IV RESULT AND DISCUSSION                Inthis section , describe results of applying the proposed work of OFET usingparabolic abstraction method. The variation of the vertical electric field formetal 1 with the channel length results are obtained y MATLAB simulation. Fig : Variationof vertical electric field as a function of the position along with channel atmetal 1.                At metal 2 the vertical electricfield changes according to the channel length then there is momentous change inthe potential. The rise within the electric field close to the junction of themetal ends up in an increase within the carrier transport potency.

Fig:Variation of vertical electric field as a function of the position along withchannel at metal 2.                The surface potential fordifferent drain voltage of the device structure along with the simulatedpotential. The potential in the region under metal 1 increases but there is nosignificant change in potential under metal 2. Fig:Variation of the surface potential as a function of the position along withchannel for metal 1.                The step changes in surfacepotential of metal 2 indicates various values surface potential decreases thenit shifted towards the supply side . Then the drain current reduces by an orderwhen a thinner oxide is used, from 7nm to 5nm or 5nm to 2nm. Fig:Variation of the surface potential as a function of the position along withchannel for metal 2.

                Drain current vs the generationrate provides the enhanced carrier transport potency to supply. The rise withinthe sub threshold drain current causes an increase in the sub threshold leakagecurrent and a decrease in the sub threshold swing . Fig:Variation of  the sub threshold draincurrent IDS as a function of gate source voltage for metal 1.                The lower sub threshold  leakage for a thinner oxide thickness thedrain current reduces by order of 7nm to 5nm. This may attribute to greatergate control and lower in oxide thickness.

Fig:Variation of the sub threshold drain current IDS as a function ofthe gate to source voltage for metal 2. V.CONCLUSIONThe result of the proposed method accurately fitbetween the measured I-V characteristics and simulation output. In this projectparabolic approximation technique used for OFET architecture in which thestructure has been analyzed and the performance improvements over differentparameter are discussed.

The analytical model is based on two-dimensionalPoisson’s equation which is solved by using parabolic approximation. Theanalytical  expression for surfacepotential , vertical electric field have been calculated. Based on thegeneration rate and electric field , we obtained the IDS-VGscharacteristics. From the presented results, it can be concluded that thestructure provides wide range of benefits to the OFET performance. The resultclearly demonstrate the excellent immunity against short channel effect offeredby the structure while decreasing channel length. 

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