1 Modeling of Organic Metal-Insulator-Semiconductor Capacitor Prashanth Kumar Manda, Logesh Karunakaran, Sandeep Thirumala, Anjan Chakravorty, Member, IEEE, and Soumya Dutta, Member, IEEE, Abstract—In this paper, we demonstrate the principle of ( a ) operation of a metal-insulator-semiconductor (MIS) capacitor ( b ) 1 5 R e g i o n - 1 R e g i o n - 2 R e g i o n - 3 V based on undoped organic semiconductor. In spite of low charge C a t h o d e g ) 1 4 2 - concentration within the semiconductor, this device exhibits a m t S e m i c o n d u c t o r S t r o n g M o d e r a t e W e a k s c 1 3 a c c u m u l a t i o n capacitance variation with respect to applied gate voltage Vg, a c c u m u l a t i o n a c c u m u l a t i o n F n I n s u l a t o r ( 1 2 resembling the capacitance-voltage C-V characteristics of a t i C ≈ ≈ traditional doped semiconductor based MIS capacitor. A physics 1 1 C C i C C m i n based model is developed to derive charge concentration, surface G a t e 1 0 potential s and the capacitance of organic MIS capacitor. The S u b s t r a t e model is validated with TCAD simulation results and is further 9 - 3 - 2 - 1 0 1 2 3 verified with experimental results obtained from fabricated V ( V ) organic MIS capacitor consisting of poly(4-vinylphenol) and g poly(3-hexylthiophene-2,5-diyl) as insulator and semiconductor, Fig. 1: (a) Device structure, (b) C-V characteristics of a MIS respectively. capacitor. Index Terms—Organic MIS capacitor, Surface potential, Schot- tky contacts, Device simulation. the observed C-V characteristics of organic MIS capacitor along with its variation with semiconductor thickness. The I. INTRODUCTION model is validated with TCAD simulation and is further ETAL -insulator-semiconductor capacitors are consid- verified with experimental results that are obtained from the M ered to be a model device structure as a preamble organic MIS capacitor, fabricated in our laboratory. to study the field effect transistors. Substantial progress of The schematic of an organic MIS capacitor and its typical organic field-effect transistor, which consists of undoped or- C-V characteristics are shown in Figs. 1(a) and (b), respec- ganic semiconductor as an active material, strongly invokes tively. Based on the applied gate voltage (Vg) and the flat the analysis of MIS capacitors. Till now there have been few band voltage (Vfb), C-V characteristics can be divided into reports on the capacitance-voltage (C-V ) characteristics of three regions: 1) Vg << VFB (strong accumulation region), 2) organic semiconductor based MIS capacitors, which have been Vg < VFB (moderate accumulation region) and 3) Vg > VFB explained based on doping concentration [1]–[3] and empir- (weak accumulation region). In strong accumulation regime, ical models [4]–[7] under the framework of Mott-Schottky the capacitance approaches to insulator capacitance (Ci). On analysis. However, Mott-Schottky analysis, which has been the other hand, in weak accumulation regime the capacitance widely accepted to explain C-V characteristics of doped reduces to Cmin, which is a series combination of Ci and semiconductor based MIS capacitor, cannot be employed in geometrical capacitance of the semiconductor (Csc), as given undoped semiconductor based MIS capacitor as it leads to by (1) [8]. erroneous results, reported by [8]. Thus there has been no CiCsc Cmin = ; (1) report on physics based model describing C-V characteristics, Ci + Csc which is indispensable to understand the principle of operation "i"0 "s"0 Ci = ;Csc = ; of organic semiconductor based MIS capacitor. ti ts In this work, we develop a physics based analytical model where "0 is the permittivity of free space, "i, "s correspond arXiv:1810.12120v1 [cond-mat.mes-hall] 26 Oct 2018 to explain C-V characteristics of MIS capacitor, consisting of to relative dielectric constants of insulator and ti, ts are organic semiconductor, which is typically intrinsic in nature. In thicknesses of insulator and semiconductor, respectively. the context of the present model, the mathematical expression However, there is no model to explain the capacitance be- of charge profile, surface potential and the capacitance are havior in the moderate accumulation regime in consistent with evaluated enabling an equivalent circuit model that can explain the regions 1 and 3. This work focuses on developing physics based model to describe the capacitance behavior covering the Prashanth Kumar Manda, Logesh Karunakaran, Anjan Chakravorty, and Soumya Dutta are with the Department of Electrical Engineering, Indian entire voltage range (regions 1-3) under consideration. Institute of Technology Madras, Chennai 600036, India. Sandeep Thirumala was with the Department of Physics, Indian Institute of II. MODEL DEVELOPMENT Technology Madras, Chennai 600036, India (e-mail: [email protected]). The authors would like to acknowledge Department of Science & Technol- In this study, we consider an intrinsic organic semiconduc- ogy (DST, Govt. of India) and IIT Madras for financial support. tor, which forms a Schottky type contact with the cathode 2 Charge density (cm−2 ) Fixed charge 푄푓 Csc Gate charge 푄푔 Semiconductor charge 푄푠푝 Cathode charge 푄푠푐 Ci −푡푖 0 푡푠 푥 Csp Fig. 2: Schematic of the different charge densities. Fig. 3: Equivalent circuit diagram according to (5). metal [8]–[10], having a large barrier height φe (= 1.72 eV) for electrons compared to that for holes φh (= 0.28 eV). Equation (5) can be manifested by an equivalent circuit, Upon formation of the contact, the charge carriers (electrons representing organic MIS capacitor, as shown in Fig. 3. It and holes) are injected into the semiconductor via thermionic is evident from (5) that the capacitance variation with Vg emission process maintaining electron (nd) and hole (pd) (especially in region 2 of Fig. 1(b)) is due to Csp, arising from carrier concentration at the semiconductor-cathode interface the variation of injected mobile charge carriers with respect to depending on the barrier height [8]–[10]. Since φh φe, Vg. Thus a complete model for capacitance of organic MIS the injected hole concentration is more than the electron capacitor can be achieved by modeling Qsp (so p(x)) and s. concentration (i.e., pd nd) and the contribution of electrons can be neglected. The injected holes undergo diffusion due to A coupled equation for the electric field (E(x)) within the concentration gradient and drift due to the electric field present semiconductor (0 ≤ x ≤ ts) can be obtained by combining inside the semiconductor simultaneously, establishing a steady Poisson’s equation (@E(x)=@x = q p(x)="s"0) along with the state charge concentration profile under equilibrium. hole transport equation under equilibrium as Upon applying negative Vg, positive charges get induced E(x)@E(x) @2E(x) − V = 0; (9) on the cathode metal (Qsc) as shown in Fig. 2. Subse- @x t @x2 quently the injected holes are attracted towards the insulator- where V is the thermal voltage. Equation (9) is integrated semiconductor surface resulting hole accumulation within the t R ts once to get semiconductor (Qsp = 0 qp(x) dx, where q is the charge of electron). Different charge densities present within the device 1 2 1 @E(x) E(x)2 − = k2; (10) are illustrated schematically in Fig. 2, where Qg and Qf 2Vt 2Vt @x represent the charge density at gate metal and the fixed charge with k as a constant of integration. For a semiconductor with density at the insulator-semiconductor interface, respectively. finite thickness, a general solution for (10) was given by [11] The charge density at the cathode metal Q can be expressed sc as in terms of the potential drop across the semiconductor ( s) E(x) = −2Vtk coth (k [x − 2Vtξ]) : (11) and the capacitance Csc as where ξ is a constant to be evaluated. Subsequently, p(x) can Q = − C : (2) sc s sc be written as Using Kirchhoff’s voltage rule, applied Vg can be related to 2 2"s"0Vt k i and s as p(x) = : (12) q sinh (k [x − 2Vtξ]) Vg = i + s: (3) Using the boundary condition at the semiconductor-metal where can be replaced by −(Q +Q )=C , in the presence i sp sc i interface (p(ts) = pd), (12) further takes the form of of Q and φ (work-function different between gate and f gc 2 cathode) (3) can be modified to kxd p(x) = pd ; (13) sinh (k [x − ts ± x1]) Qsp + Qsc Vg − Vfb = s − ; (4) r Ci arg sinh (kxd) 2"s"0Vt where x1 = and xd = . where Vfb = φgc − Qf =Ci. k qpd By integrating E(x) and p(x) within the semiconductor, s Differentiating (4) with respect to Qg one obtains and Qsp can be obtained respectively, as given below 1 1 1 = + : (5) sinh (k [±x1 − ts]) C Ci Csp + Csc = 2V log : (14) s t sinh (k [±x ]) where 1 C = @Qg=@Vg; (6) s ! − s 2 p 2 Csp = −@Qsp=@ s; (7) Qsp( s) = Q0 exp + (kxd) − 1 + (kxd) : Vt @Qg = −@(Qsp + Qsc): (8) (15) 3 ( a ) 1 8 L i n e s : m o d e l ( c ) L i n e s : m o d e l ( a ) ( c ) L i n e s : m o d e l 1 0 2 . 5 S y m b o l s : T C A D 0 S y m b o l s : T C A D S y m b o l s : T C A D 1 0 ) 3 ) 2 2 - - ) ) 2 7 n m 2 2 7 n m 2 - - m 3 6 n m 0 m 2 .