Modeling of Organic Metal-Insulator-Semiconductor

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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 ψs 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 εiε0 εsε0 Ci = ,Csc = , of organic semiconductor based MIS capacitor. ti ts

In this work, we develop a physics based analytical model where ε0 is the permittivity of free space, εi, εs 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.MODELDEVELOPMENT 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 ψs. 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)/εsε0) 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 (ψs) 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 = −ψ C . (2) sc s sc be written as Using Kirchhoff’s voltage rule, applied Vg can be related to 2 2εsε0Vt k ψi and ψs as p(x) = . (12) q sinh (k [x − 2Vtξ]) Vg = ψi + ψs. (3) Using the boundary condition at the semiconductor-metal where ψ 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 = ψs − , (4) r Ci arg sinh (kxd) 2εsε0Vt where x1 = and xd = . where Vfb = φgc − Qf /Ci. k qpd By integrating E(x) and p(x) within the semiconductor, ψs 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 ψ = 2V log . (14) s t sinh (k [±x ]) where 1 C = ∂Qg/∂Vg, (6) s ! −ψs 2 p 2 Csp = −∂Qsp/∂ψs, (7) Qsp(ψs) = 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 . 0 3 6 n m 1 6 1 0 c c ) ) m m

3 - 1 3 1 0 6 0 n m - - c c 6 0 n m 1 1

1 0 1 1

1 1 2 9 7 n m m m 0 0 1 1 . 5 9 7 n m 1 c c 1 1

1 4 0 0 ( ( ( (

1 0 1 1 - 3 V ) ) ( ( - 2 p p

s s x 1 . 0 x

p - 2 V p

( 1 0 (

- 3 V s s Q Q p p - 1 V 1

- 2 V Q Q - 1 - 1 V 0 . 5 L i n e s : m o d e l 0 V 1 0 0 V 1 0 - 3 S y m b o l s : T C A D 1 0 1 0 1 0 1 2 ( b ) ( d ) ( b ) ( d ) 0 . 8 L i n e s : m o d e l L i n e s : m o d e l ) 0 . 0 )

1 0 . 6 1 - S y m b o l s : T C A D - S y m b o l s : T C A D m m

c 2 7 n m c 0 2 7 n m 0 . 4

V 3 6 n m V 3 6 n m ) 0 . 4 ) 5 - 0 . 5 5 - 3 V

V 6 0 n m 6 0 n m 0 0 V - 3 V ( 0 . 2 - 2 V ( s

1 9 7 n m 1 9 7 n m s

( - 2 V ( L i n e s : m o d e l ؙ

- 1 V ؙ ) S y m b o l s : T C A D - 1 V ) x 0 . 0 x L i n e s : m o d e l 0 V ( 0 V ( S y m b o l s : T C A D E - 1 . 0 E 0 . 0 - 0 . 2 - 1 0 2 5 5 0 7 5 - 4 - 3 - 2 - 1 0 1 2 0 2 5 5 0 7 5 - 4 - 3 - 2 - 1 0 1 2 x ( n m ) x ( n m ) V g ( V ) V g ( V )

Fig. 4: (a) p(x) and (b) E(x) for different Vg with ts = 97 nm, Fig. 5: (a) p(x) and (b) E(x) for different Vg with ts = 97 nm, (c) Qsp-V characteristics in linear (left axis) and logarithmic (c) Qsp-V characteristics in linear (left axis) and logarithmic (right axis) scales and (d) ψs variation with Vg for different (right axis) scales and (d) ψs variation with Vg for different ts for xd > ts case. The symbols are TCAD simulation and ts for xd < ts case with φh = 0.15 eV, and Vfb = -0.52 V. solid lines are model. The parameters used for the simulation The symbols are TCAD simulation and solid lines are model. are ti = 287 nm, εi = 4.81, εs = 3.3, φh = 0.28 eV, NC = NV 19 −3 = 10 cm and Vfb = -0.52 V. match between the model (lines) and TCAD simulation results (symbols). The constant electric field profile throughout where the semiconductor for Vg > Vfb supports the fact that at p higher voltages the semiconductor resembles an insulator. The Q0 = 2qεrε0Vtpd variations of Qsp and ψs with respect to Vg for different It is to be noted that the unknown parameter k needs to be semiconductor thickness (ts) are shown in Figs. 4(c) and (d), evaluated to calculate Qsp and ψs. k can be calculated by respectively. Upon decreasing Vg, more holes are attracted solving (4) with the help of (14) and (15). The developed towards the interface, which results in an increase in Qsp model is valid for xd > ts. and a decrease in ψs, as expected from (15). In contrast, For xd < ts (is realized by reducing the barrier height for with the increase in Vg, holes are repelled from the insulator- holes )and in strong accumulation, the charge concentration semiconductor interface making Qsp much lower than Qsc. at x = d becomes significant and comparable to the charge This turns the semiconductor to behave like an insulator (Fig. concentration within the device as shown in Fig. 5(a). More- 4(b)). Consequently ψs increases linearly with Vg (Fig. 4(d)), over the charge concentration is sufficient to screen the gate which can be understood from (4) by neglecting Qsp term and field as shown in Fig. 5(b) and gate looses the control over replacing Qsc in terms of ψs using (2). The dependences of the cathode charge. Hence in this case the cathode charge is Qsp and ψs on semiconductor thickness, as expected from invariant with the gate voltage. (15) and (14), are clearly observed in Figs. 4(c) and (d) respectively. It is to be noted that all ψs vs Vg curves for different thicknesses intersect at ψ =0. The corresponding III.MODEL VALIDATION AND DISCUSSION s value of Vg is the flatband voltage Vfb, which, in principle, The model, developed in the preceding section, is validated should be independent of thickness of the semiconductor. using Sentaurus TCAD simulation [12]. The variation of hole The total capacitance C, calculated using Qsp, ψs and concentration profile with respect to Vg, calculated from the (5), is plotted with respect to Vg for different semiconductor model (solid lines), is in good agreement with the TCAD thicknesses, as shown in Fig. ??(a). Excellent agreement be- simulation results (symbols), as shown in Fig. 4(a). It is tween the analytical model (solid lines) and TCAD simulation evident that the hole concentration at x = ts is bias independent results (symbols), in all the figures (Figs. 4 and ??) ensures as it is solely decided by thermionic emission. On the contrary, the consistency, scalability and robustness of the proposed the hole concentration at the insulator-semiconductor interface model. Moreover, the model captures the physics behind (x = 0) varies exponentially with ψs as C-V characteristics over the entire voltage range, covering regions 1-3. It is noteworthy to mention that the variation −ψs p(0) = pd exp . (16) of C and slope of C-V characteristics in the moderate V min t accumulation region with respect to semiconductor thickness Similarly, the variation of electric field profiles with Vg across is quite different from traditional MIS capacitor consisting of the semiconductor are plotted in Fig. 4(b) showing a good doped semiconductor. 4

IV. EXPERIMENTAL RESULTS ACKNOWLEDGEMENTS The authors would like to acknowledge Centre for NEMS We extend our study to validate the present model with and Nanophotonics (CNNP) for providing fabrication facility. experimental data. Organic semiconductor based MIS capaci- Authors would like to thank Nidhin K. for fruitful discussion. tors were fabricated on cleaned glass substrates by evaporating aluminum of thickness 50 nm as gate metal, followed by spin REFERENCES coating of cross linked Poly(4-vinylphenol) (PVP) with spin speed 6000 r/min. Subsequently, the samples were annealed at [1] W. Hill and C. Coleman, “A single-frequency approximation for o interface-state density determination,” Solid-State Electronics, vol. 23, 200 C for 20 minutes that resulted in a thickness of 290 nm no. 9, pp. 987 – 993, 1980. (measured using an ellipsometer). Poly(3-hexylthiophene-2,5- [2] M. Estrada, F. Ulloa, M. vila, J. Snchez, A. Cerdeira, A. Castro- diyl) (P3HT), a widely studied undoped organic semiconduc- Carranza, B. Iguez, L. F. Marsal, and J. Pallars, “Frequency and voltage dependence of the capacitance of mis structures fabricated with tor, was spun from a solution of concentration 15 mg/ml polymeric materials,” IEEE Transactions on Electron Devices, vol. 60, in 1,2-Dichlorobenzene. The spin speed was set to 1000, pp. 2057–2063, June 2013. 3000 and 4000 r/min to achieve P3HT thickness of 97, 56 [3] M. Devynck, B. Rostirolla, C. P. Watson, and D. M. Taylor, “Photo- response of a p3ht:pcbm blend in metal-insulator-semiconductor capac- and 27 nm, respectively. The samples were then annealed itors,” Applied Physics Letters, vol. 105, no. 18, p. 183301, 2014. at 120 oC for 20 minutes prior to thermal evaporation of [4] E. J. Meijer, A. V. G. Mangnus, C. M. Hart, D. M. de Leeuw, and T. M. gold of thickness 50 nm as the top metal contact (cathode Klapwijk, “Frequency behavior and the mottschottky analysis in poly(3- hexyl thiophene) metalinsulatorsemiconductor diodes,” Applied Physics in particular). All the fabrication processes were carried out Letters, vol. 78, no. 24, pp. 3902–3904, 2001. inside the glove box with controlled oxygen (< 1 ppm) [5] D. M. Taylor and N. Alves, “Separating interface state response and moisture (< 1 ppm) levels. The fabricated devices were from parasitic effects in conductance measurements on organic metal-insulator-semiconductor capacitors,” Journal of Applied Physics, characterized inside a vacuum probe station using Agilent vol. 103, no. 5, p. 054509, 2008. B1500A parameter analyzer at 1 kHz frequency. [6] I. Torres and D. M. Taylor, “Interface states in polymer metal-insulator- semiconductor devices,” Journal of Applied Physics, vol. 98, no. 7, The measured C-V characteristics of the fabricated organic p. 073710, 2005. MIS capacitors with different semiconductor thicknesses are [7] E. J. Meijer, A. V. G. Mangnus, C. M. Hart, D. M. de Leeuw, and T. M. shown in Fig. ??(b) (star symbol), exhibiting the similar trend Klapwijk, “Frequency behavior and the mottschottky analysis in poly(3- hexyl thiophene) metalinsulatorsemiconductor diodes,” Applied Physics qualitatively to C-V characteristics described using TCAD Letters, vol. 78, no. 24, pp. 3902–3904, 2001. simulation results and the analytical model in Fig. ??(a). The [8] A. Nigam, M. Premaratne, and P. R. Nair Org. Electron., vol. 14, no. 11, dielectric constants of PVP and P3HT were extracted using the pp. 2902 – 2907, 2013. [9] P. K. Manda, S. Ramaswamy, and S. Dutta, “Extraction of the built- measured thicknesses, Cmax and Cmin, showing consistency in potential for organic solar cells from current-voltage characteristics,” with the reported values [13]. Analyzing the proposed model IEEE Transactions on Electron Devices, vol. 65, pp. 184–190, Jan 2018. and the measured data, Vfb and φh were extracted to reproduce [10] A. Nigam, P. Nair, M. Premaratne, and V. Rao Elec. Dev. Lett., IEEE, vol. 35, pp. 581–583, May 2014. C-V characteristics (lines) in Fig. ??(b). The same parameters [11] S. M. Skinner, “Diffusion, static charges, and the conduction of electric- were used for TCAD simulation results, as represented by ity in nonmetallic solids by a single charge carrier. i. electric charges in the symbols in Fig. ??(b). Appreciable coherence between the plastics and insulating materials,” Journal of Applied Physics, vol. 26, no. 5, pp. 498–508, 1955. experimental result (solid stars), TCAD simulation (symbols) [12] . Sentaurus TCAD Release H-2013.03 Ed.Synopsys Mountain View and analytical model (lines) validates the applicability of the CA USA presented model in case of organic semiconductor (undoped) [13] A. Facchetti, M.-H. Yoon, and T. Marks, “Gate dielectrics for organic ﬁeld-effect transistors: New opportunities for organic electronics,” Ad- based MIS capacitors. vanced Materials, vol. 17, no. 14, pp. 1705–1725, 2005.

V. CONCLUSION

In conclusion, the C-V characteristics of undoped organic semiconductor based MIS capacitor is thoroughly investigated. Even though the nature of the characteristic seems very similar to that of doped semiconductor based MIS capacitor, there are distinct differences between the underlying device physics of doped and undoped semiconductor based MIS capacitors. A physics based model, incorporating the injection of mobile charge carriers through metal-semiconductor Schottky contact and their accumulation within the semiconductor under the inﬂuence of gate voltage, is developed to explain C- V characteristics over entire voltage range. The model is consistently validated with TCAD simulation results. Variation of C-V characteristics of organic MIS capacitor with the semiconductor thicknesses, which is unlikely in traditional MIS capacitor, is veriﬁed with the experimental data obtained from P3HT based MIS capacitor.