Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Quantum potential wikipedia , lookup
Electron mobility wikipedia , lookup
EPR paradox wikipedia , lookup
Hydrogen atom wikipedia , lookup
Time in physics wikipedia , lookup
Bell's theorem wikipedia , lookup
Quantum vacuum thruster wikipedia , lookup
Old quantum theory wikipedia , lookup
Quantum Capacitance in Topological Insulators Faxian Xiu,1* Nicholas Meyer,1 Xufeng Kou,2 Liang He,2 Murong Lang,2 Yong Wang,3 Xinxin Yu,2 Alexei V. Fedorov,4 Jin Zou,5 and Kang L. Wang2* 1 Department of Electrical and Computer Engineering, Iowa State University, Ames, USA Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA 3State Key Laboratory of Silicon Materials and Center for Electron Microscopy, Department of Materials Science and Engineering, Zhejiang University, Hangzhou, 310027, China 4Advanced Light Source Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California, 94720, USA 5Materials Engineering and Centre for Microcopy and Microanalysis, The University of Queensland, Brisbane QLD 4072, Australia *To whom correspondence should be addressed. E-mail: [email protected], [email protected] 2 Supplementary Information 1. Figure S1| A profile of terrace height 2. Figure S2| Transport measurements for a MBE-grown Bi2Se3 thin film: surface properties 3. Figure S3| STM Measurements 4. Figure S4| A regular MOS capacitor without Bi2Se3 5. Figure S5| Theoretical calculations of quantum capacitance 6. Figure S6| Bulk properties through transport measurements 7. Figure S7| High temperature capacitance measurements 8. Figure S8| Capacitance simulations for a 2-DEG. 9. Figure S9| Notes on Fe/Al contacts 10. Figure S10| Magnetic-field-dependent capacitance measurements 11. Figure S11| Ambipolar field effect 12. More details on photolithography process 13. Theory for frequency responses of majority carriers 14. Simplified band diagrams for the MOS capacitor and notes on SdH oscillations 1 1. Figure S1| A profile of terrace height b a 2.5 Height (nm) 2.0 100 nm Figure S1. (a) An AFM image of Bi2Se3 (b) A depth profile showing the height of terrace along the green line in (a). The individual terrace is estimated to be 1 nm in height. 1.5 1.0 0.5 0.0 0 150 300 450 Distance (nm) 2. Figure S2| Transport measurements for a MBE-grown Bi2Se3 thin film: surface properties Figure S2| a, Longitudinal resistance Rxx versus magnetic field. Solid arrows indicate integer Landau levels from the valley values; open arrows give the peak values. b, Rxx versus 1/B at different temperatures. c, Landau level index plot: 1/B versus n. The open 2 (closed) circles are the Landau level of the maxima (minima) of Rxx. d, Normalized conductivity amplitude xx(T)/xx(0) as a function of temperature (at B=7.6 T). The effective mass is deduced to be ~0.07 me. e, Dingle plot of ln[(R/R0)Bsinh(] versus 1/B. The plot is used to determine carrier lifetime (τ) and mean free path (ℓ. Some parameters can be calculated F k F / mcyc 3.6 105 m / s follows, 1.3 1012 s F 4.6 10 7 m , EF mcyc F2 53meV , , as and the surface , mobility e / mcyc 13,200cm2 / V s . The estimated Fermi level of 53 meV suggests the surface carriers are electrons and the Fermi level is located inside the bulk band gap, which is closed to the extracted Fermi levels from the quantum capacitance (61.5-79.4 meV, Fig. 4h inset in the main text). Note that the sample shown in Fig. S2 was grown on a semi-insulating CdS substrate using the same growth condition as those grown on Si substrates (for the quantum capacitance measurements). There are other excellent reports on transport measurements which show methods of extracting important parameters1-19. ARPES20-31 and STM32-36 data can also be used to verify these parameters. 2. Figure S3| STM Measurements 200 STM 100 measurements 150 (acknowledge 50 This paper Analytis etc. [21] Lang etc. [28] 100 Professor Naichang Yeh from Caltech, 50 Physics). The Dirac point is about ~ 70 0 -50 0 (c) 0.8 0.7 dI/dV (a.u.) 250 E - ED (meV) Figure S3| Spatially averaged density (b) 150 measurements from of states (dI/dV) 300 -50 20 meV below the Fermi surface, in -0.8 0.0 0.8 K//(Å-1reasonable ) 1 2 3 0.5 Dirac point 0.4 0.3 -400 -300 -200 -100 0 E (meV) -100 0 0.6 4 12 -2 agreement ns (10with cm ) our 100 200 estimation from the SdH oscillations (~53 meV) and the quantum capacitance measurements (61.5-79.4meV). 3 Fig. 4 3. Figure S4| A regular MOS capacitor without Bi2Se3 Figure S4| A capacitor device without Bi2Se3. It shows a p-type characteristic originating from the Si substrate. At negative it saturates to the capacitance of COX, from Capacitance (pF) Saturate to COX 7.2 6.8 bias, 6.4 which the effective dielectric constant can be -20 -10 0 10 20 Gate voltage (V) extracted ( r 7.8 ). 4. Figure S5| Theoretical calculations of quantum capacitance 2 Cq (F/cm ) 0.8 0.6 0.4 0.2 -0.4 -0.2 0.0 0.2 0.4 Va (V) For the TI surfaces, the E-k relation can be described as E (k ) vF | k | and the g | E | , thus the quantum capacitance of the density of states is gTI ( E ) 2 ( vF ) 2 topological surface states can be described as the following37, [ q( n p )] g CQ q Va 2 ( vF ) 2 E ( f p f n ) gq kT E qVa ln[2(1 cosh F )] 2 2 ( vF ) kT 2 4 Va dE where g=gsgv is the degeneracy factor considering both spin and energy band degeneracies for TI surface states, fp and fn are probability of holes and electrons at given energy followed by the Fermi distribution rule, and Va is the voltage dropped on the TI surface. From the quantum capacitance measurements, the Fermi level is located 61.5 to 79.4 meV above the Dirac point (Fig. 4h in the main text). This corresponds to the minimum of the quantum capacitance when Va ~ 0.07 V. The resulting quantum capacitance of an ideal topological insulator is similar to that of graphene38. Note that the simulation is simplified to only consider the surface contribution. 6. Figure S6| Bulk properties through transport measurements (b) Exp Fitted (c) 20 40 200 20 100 0 -20 Exp Fitted Surface Impurity Band 0 -100 T = 220 K -40 T = 20 K -20 -4 0 4 B (T) 8 -8 -4 0 4 B (T) 8 -8 -4 8 2 Surface States Impurity Band Bulk (cm /Vs) 14 4 10 4 2 10 13 10 12 10 Surface States Impurity Band Bulk 2 3 10 T -2.0 4 11 10 0 4 B (T) (e) 15 10 -2 T = 40 K -200 -8 n2D (cm ) 0 -10 -60 (d) Exp Fitted Bulk Surface Impurity Band 10 Gxy (mS) 60 Gxy (S) Gxy (mS) (a) 2 2 4 6 8 2 10 T (K) 4 6 8 2 2 100 4 6 8 2 10 T (K) 4 6 8 2 100 Fig. 2 Figure S6| Hall conductance of a ~10 nm Bi2Se3 film, from which three conducting channels were extracted including the bulk, the impurity band and the surface states. Magnetic field dependent conductivity Gxy at temperatures of (a) 220 K, (b) 20 K and (c) 40 K. Open circles are experimental data and solid lines are fitted results. d, 2D carrier 5 density versus temperature. The solid yellow line represents the Fermi-Dirac distribution of the bulk carrier density equivalent to 2D. e, Mobility versus temperature for the three channels. The dashed line represents the power law dependence of T-2, which suggests the mechanism of phonon scattering in these temperature ranges. Figure S6d illustrates the temperature dependence of the two-dimensional carrier density of three channels. The bulk carrier densities (green triangles) decrease exponentially as carriers are frozen to the impurity band. Since the carriers in the bulk conduction band are electrons, their temperature dependent density can be described as a classic Fermi-Dirac distribution of nb n0 / e Ea / k BT 1 (solid yellow line in Fig. S6d), where n0 is the bulk carrier density of ~ 4 1015 cm-2, and Ea of 20 meV is the energy gap between the impurity band and the bottom of the bulk conduction band. The carrier densities of the impurity band (blue squares) and surface states (red circles) remain approximately constant at 1.3 1013 cm-2 and 4 1011 cm-2, respectively. Figure S6e shows the corresponding mobility at different temperatures. The mobility of bulk electrons (green triangles) exhibits a power law T-2 at high temperatures, consistent a b impurity band reaches a constant value of ~ 380 cm2/Vs. 7. Figure S7| High Capacitance (a.u.) temperatures (T < 20 K), the mobility of the 9T 100 KHz 7T 40 KHz 5T 3T 0T temperature Capacitance (a.u.) with the dominant phonon scattering. At low 10 KHz 4K Hz 1K Hz 400 Hz 100 Hz T=60 K capacitance measurements 4 c 8 T=60 K 12 Gate Voltage (V) 4 d 8 12 Gate Voltage (V) 100 KHz 9T Figure S7| (a, b), Magnetic field- and f=100 measurements KHz. at (c, T=75 d), K. The same Quantum 5T 3T 0T Capacitance (a.u.) and Capacitance (a.u.) frequency-dependent capacitance at T=60 K 4K Hz 7T 1K Hz 400 Hz 100 Hz T=75 K 4 6 8 T=75 K 12 Gate Voltage (V) 4 8 12 Gate Voltage (V) oscillations completely disappear at 75 K. It is speculated that at high temperatures, the bulk carriers could be activated to reach a high enough concentration that the scattering between bulk and surfaces is no longer negligible. As a result, the mobility of the surface carriers may be degraded, in which case the capacitance oscillations are not as strong as those observed at low temperatures. 8. Figure S8| Capacitance simulations for a 2-DEG. 10 2 C2DEG (F/cm ) 8 6 4 2 0 -0.4 -0.2 0.0 Va (V) 0.2 0.4 Figure S8| Simulated quantum capacitance for a 2-DEG. The E-k relation of the 2-DEG 2 2 m k can be described by E (k ) and the DOS is g 2 DEG ( E ) 2 N ( E ) , where N ( E ) is 2m the number of contributing bands at a given energy39. From these equations, we can derive the capacitance for 2-DEG, as follows, [ p n ] 1 1 [ q v ( E )( )dE ] E EC qVa EC E qVa Va Va 1 exp( ) 1 exp( ) kT kT 1 1 q v( E ) ( )dE E E qV E E qVa Va 1 exp( C a ) 1 exp( C ) kT kT EC E qVa exp( ) 1 q q E E qVa kT Where [ ] sec h 2 [ C ] Va 1 exp( EC E qVa ) kT [1 exp( EC E qVa )]2 4kT kT kT kT C2 DEG q Finally we can get: 7 C2 DEG C2 DEG mq q 4kT 2 mq 2 Ec 2 v( E ')sec ( 2 2 kT 2 v( E )[sec ( 0 EF E qVa E E qVa ) sec 2 ( F )] 2kT 2kT E ' qVa )dE 2kT The simulated capacitance of 2-DEG is shown in Fig. S8. It is noted that the capacitance from a 2-DEG essentially saturates when the magnitude of Va is sufficiently large, exhibiting a dramatic difference compared to that from the surface states (Fig. S5). 9. Figure S9| Notes on Fe/Al contacts In our capacitor device, we used Fe/Al as source/drain contacts. It is noted from experiments that the capacitance measurements do not show significant difference when Ti/Au is used for the source/drain contacts. a b 9T 5T 3T 0T Capacitance (a.u.) Capacitance (a.u.) 7T 100 KHz 40 KHz 10 KHz 4K Hz 1K Hz 400 Hz 100 Hz T=25 K 4 8 T=25 K 12 4 Gate Voltage (V) c 8 12 Gate Voltage (V) d e 9T 5T 3T 0T 100 KHz Capacitance (a.u.) Capacitance (a.u.) 7T 40 KHz 10 KHz 4K Hz 1K Hz 400 Hz 100 Hz T=25 K 4 8 T=25 K 12 Gate Voltage (V) Figure S9. Comparison of quantum capacitance on devices with Fe/Al contacts (a and b) and Ti/Au contacts (c and d). No significant difference of quantum capacitance was observed, suggesting the minor effect from the Fe layer. (e) shows a microscope image of the new device with Ti/Au contacts. 4 8 12 Gate Voltage (V) 8 40 μm 10. Figure S10| Magnetic-field-dependent capacitance measurements To study the magnetic-field-dependent capacitance measurements, we have carried out additional experiments at 25 K using the original device (Fe as electrodes). The DC voltage during the capacitance measurements was kept constant at +8 V. The excitation ac frequency was set to be 100 KHz. Then the magnetic field was swept at a rate of 50 Oe/s, from 3 to 9 T, while the capacitance was recorded. Figure S10 shows the quantum oscillations of capacitance as a function of magnetic field (1/B) at 25 K. It suggests the formation of Landau levels. Combining Figures 3, 4 and S10, we can calculate the velocity of the surface carriers using the following equation: p mcycVF k F . From Figure S10, the periodicity of the SdH oscillations yields important parameters: the Fermi vector kF 0.029 Å-1. Therefore the Fermi velocity can be calculated by VF k F / mcyc , yielding a value of ~3.7×105 m/s (where mcyc =0.091 m0 at Vg=+8 V). This value is in a good agreement with that from the transport measurements (~3.6×105 m/s). Vg=+8 V Capacitance (a.u.) Figure R10. Capacitance measurements with a fixed DC gate voltage of +8 V and an ac frequency of 100 KHz. The magnetic field was swept from 3 to 9T at 25 K. 25 K f=100 KHz 0.1 0.2 0.3 1/B (1/T) 9 11. Figure S11| Ambipolar field effect It is a very challenging task to obtain ambipolar field effect through the capacitance measurement for the 10 nm-thick sample. The primary reason is the occurrence of the depletion capacitance when we apply negative voltages. Unlike quantum capacitance in graphene which has no bulk contributions, topological insulators always have bulk properties. When a negative gate voltage is applied, the depletion capacitance dynamically changes in accordance with the magnitude of the DC bias. Figure S11 shows preliminary results from a 6 nm-thick thin film, which suggests an ambipolar field effect. 2.60 B=0 T T=25 K f=100 KHz Figure S11. Preliminary quantum capacitance data for ~6 nm Bi2Se3 thin film. 2 CQ (F/cm ) 2.56 2.52 2.48 -10 -5 0 5 10 Vg (V) 12. More details on photolithography process A conventional photo-resist of AZ5214 is used during the photolithography process. For a standard photolithography recipe, first Bi2Se3 thin films were spin coated with a thin layer of AZ5214 (4000 rpm) immediately followed by a soft bake at 100°C for 60 s. Then we use a mask aligner to expose the wafer for 8 s and subsequently develop it in a dilute solution of AZ400K:H2O (1:5) for 40 s. Depending on the design of photomasks, sometimes an image reversal photolithography process is used. A critical process for the fabrication of a capacitor is the deposition of Al2O3 gate dielectric via an atomic layer deposition technique. A careful surface cleaning by dilute HF is employed for the removal of oxides from sample surfaces prior to the Al2O3 deposition. 10 13. Theory for frequency responses of majority carriers When an ac signal is injected into one system, the response of the inside carriers is limited by the Shockley-Read-Hall (SRH) generation/recombination rate. In our device structure, we have both high-mobility surface and low-mobility bulk channel in series. Since our capacitance measurements are conducted under accumulation region, the main response to external signal comes from the majority carriers (electrons) in both channels. Therefore, their frequency responses are determined by the different motilities transferring along each channel40-44. We can understand this kind of majority response rate by applying the Poisson’s equation in our n-type material: 2 ( qV ) q2 N D n (1 ) k BT ND (S1) Where qV is the band-bending, ND is the density of ionized donors, and n is majority electron concentration. When a small signal ac signal is added to the input dc signal, we can assume n n0 n and V V0 V . By substituting these into (S1), we thus obtain the Poisson form for the ac component: q 2n 2 ( qV ) k B T (S2) Combing this expression with the current continuity equation that I q Poisson equation finally becomes 2 (V E Fn ) n , the t n0 q (V E Fn ) (V E Fn ) 2 N D n kT t If the frequency of the ac component is, the above equation has little frequency/time-dependence only if n0 n q 1 1 n0 ( ) 0 ( ) 2 kT N D n or D ND qN D ND (S3) Here 1/D is the transfer rate of the electron in the system. In this scenario, the electrons can follow up, or equivalently speaking, they cannot be affected by the external stimulations only when their transfer rates are much faster than the applied signal frequency. Therefore, since 1/D is proportional to the mobility , the electron response in those low-mobility bulk mediums can thus be filtered out under high frequency input conditions, and leaving only the component from high-conduction surface channel. 11 14. Simplified band diagrams for the MOS capacitor and notes on SdH oscillations b. Vg < 0 a. Vg > 0 n-type EF EC n-type EF EC Ei Ei EV EV Figure S14. The MOS capacitor under positive (a) and negative biases (b). When the Fermi energy moves further away from the Dirac point, the SdH oscillations become more rapid with decreasing periods. Our experiments, however, demonstrate an opposite trend. The results suggest that the gate voltage may not have a linear relationship with the Fermi energy although CQ exhibits a quasi-linear behavior in the range of 6-12V in Figure 3a. The non-linearity could be in part attributed to the bulk states, where a certain amount of gate voltage could be shared by the bulk. As the Fermi level moves upwards, the surface becomes more conductive and the bulk may thus share a larger portion of the gate voltage. Therefore it is possible that the SdH oscillations exhibit an opposite tread in such scenarios. References 1 2 Checkelsky, J.G. et al., Quantum interference in maroscopic cystals of nonmetallic Bi2Se3. Phys. Rev. Lett. 103, 246601 (2009). Peng, H., Aharonov-Bohm interference in topological insulator nanoribbons. Nat. Mater. 9, 225-229 (2009). 12 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Analytis, J.G. et al., Bulk Fermi surface coexistence with Dirac surface state in Bi2Se3: A comparison of photoemission and Shubnikov-de Haas measurements. Phys. Rev. B 81, 205407 (2010). Analytis, J.G. et al., Two-dimensional surface state in the quantum limit of a topological insulator. Nat Phys 6, 960-964 (2010). Butch, N.P. et al., Strong surface scattering in ultrahigh-mobility Bi2Se3 topological insulator crystals. Phys. Rev. B 81, 241301 (2010). Cha, J.J. et al., Magnetic Doping and Kondo Effect in Bi2Se3 Nanoribbons. Nano Letters 10, 1076-1081 (2010). Chen, J. et al., Gate-Voltage Control of Chemical Potential and Weak Antilocalization in Bi2Se3. Phys. Rev. Lett. 105, 176602 (2010). Eto, K., Ren, Z., Taskin, A.A., Segawa, K., & Ando, Y., Angular-dependent oscillations of the magnetoresistance in Bi2Se3 due to the three-dimensional bulk Fermi surface. Phys. Rev. B 81, 195309 (2010). Lu, H.-Z., Shan, W.-Y., Yao, W., Niu, Q., & Shen, S.-Q., Massive Dirac fermions and spin physics in an ultrathin film of topological insulator. Phys. Rev. B 81, 115407 (2010). Ren, Z., Taskin, A.A., Sasaki, S., Segawa, K., & Ando, Y., Large bulk resistivity and surface quantum oscillations in the topological insulator Bi2Te2Se. Phys. Rev. B 82, 241306 (2010). Steinberg, H., Gardner, D.R., Lee, Y.S., & Jarillo-Herrero, P., Surface State Transport and Ambipolar Electric Field Effect in Bi2Se3 Nanodevices. Nano Letters 10, 5032-5036 (2010). Checkelsky, J.G., Hor, Y.S., Cava, R.J., & Ong, N.P., Bulk Band Gap and Surface State Conduction Observed in Voltage-Tuned Crystals of the Topological Insulator Bi2Se3. Phys. Rev. Lett. 106, 196801 (2011). Cho, S., Butch, N.P., Paglione, J., & Fuhrer, M.S., Insulating Behavior in Ultrathin Bismuth Selenide Field Effect Transistors. Nano Letters 11, 1925-1927 (2011). Qu, D.-X., Hor, Y.S., Xiong, J., Cava, R.J., & Ong, N.P., Quantum oscillations and Hall anomaly of surface states in the topological insulator Bi2Te3. Science 329, 821-824 (2010). Kong, D. et al., Ambipolar field effect in the ternary topological insulator (BixSb1-x)2Te3 by composition tuning. Nat Nano 6, 705-709 (2011). Zhang, J. et al., Band structure engineering in (Bi1−xSbx)2Te3 ternary topological insulators. Nat Commun 2, 574 (2011). Gusev, G.M. et al., Transport in disordered two-dimensional topological insulators. Phys. Rev. B 84, 121302 (2011). He, L. et al., Epitaxial growth of Bi2Se3 topological insulator thin films on Si (111). J. Appl. Phys. 109, 103702 (2011). Teweldebrhan, D., Goyal, V., & Balandin, A.A., Exfoliation and Characterization of Bismuth Telluride Atomic Quintuples and Quasi-Two-Dimensional Crystals. Nano Letters 10, 1209-1218 (2010). Bianchi, M. et al., Coexistence of the topological state and a two-dimensional electron gas on the surface of Bi2Se3. Nat Commun 1, 128 (2011). 13 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 Chen, Y.L. et al., Experimental realization of a three-dimensional topological insulator, Bi2Te3. Science 325, 178-181 (2009). Chen, Y.L. et al., Massive Dirac Fermion on the Surface of a Magnetically Doped Topological Insulator. Science 329, 659-662 (2010). Hasan, M.Z. & Kane, C.L., Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045 (2010). Hsieh, D. et al., Nonlinear Optical Probe of Tunable Surface Electrons on a Topological Insulator. Phys. Rev. Lett. 106, 057401 (2011). Hsieh, D. et al., A topological Dirac insulator in a quantum spin Hall phase. Nature 452, 970-974 (2008). Hsieh, D. et al., A tunable topological insulator in the spin helical Dirac transport regime. Nature 460, 1101-1105 (2009). Hsieh, D. et al., Observation of time-reversal-protected single-Dirac-cone topological-insulator states in Bi2Te3 and Sb2Te3. Phys. Rev. Lett. 103, 146401 (2009). Li, Y.Y. et al., Intrinsic topological insulator Bi2Te3 thin films on Si and their thickness limit. Adv. Mater., DOI: 10.1002/adma.201000368 (2010). Xia, Y. et al., Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nat. Phys. 5, 398-402 (2009). Xu, S.-Y. et al., Topological Phase Transition and Texture Inversion in a Tunable Topological Insulator. Science 332, 560-564 (2011). Zhang, Y. et al., Crossover of the three-dimensional topological insulator Bi2Se3 to the two-dimensional limit. Nat. Phys. 6, 584-588 (2010). Alpichshev, Z. et al., STM imaging of electronic waves on the surface of Bi2Te3:topologically protected surface states and hexagonal warping effects. Phys. Rev. Lett. 104, 016401 (2010). Cheng, P. et al., Landau Quantization of Topological Surface States in Bi2Se3. Phys. Rev. Lett. 105, 076801 (2010). Hirahara, T. et al., Topological metal at the surface of an ultrathin Bi1-xSbx alloy film. Phys. Rev. B 81, 165422 (2010). Roushan, P. et al., Topological surface states protected from backscattering by chiral spin texture. Nature 460, 1106-1109 (2009). Seo, J. et al., Transmission of topological surface states through surface barriers. Nature 466, 343-346 (2010). Fang, T., Konar, A., Xing, H., & Jena, D., Carrier statistics and quantum capacitance of graphene sheets and ribbons. Appl. Phys. Lett. 91, 092109 (2007). Ponomarenko, L.A. et al., Density of States and Zero Landau Level Probed through Capacitance of Graphene. Phys. Rev. Lett. 105, 136801 (2010). John, D.L., Castro, L.C., & Pulfrey, D.L., Quantum capacitance in nanoscale device modeling. J. Appl. Phys. 96, 5180-5184 (2004). Sze, S., Physics of Semiconductor Devices, 3rd ed. (Wiley, New York, 2007). Xuan, Y., Lin, H.C., Ye, P.D., & Wilk, G.D., Capacitance-voltage studies on enhancement-mode InGaAs metal-oxide-semiconductor field-effect transistor using atomic-layer-deposited Al[sub 2]O[sub 3] gate dielectric. Appl. Phys. Lett. 88, 263518 (2006). 14 42 43 44 Lieneweg, U., Frequency response of charge transfer in MOS inversion layers. Solid-State Electronics 23, 577-583 (1980). Lind, E., Niquet, Y.-M., Mera, H., & Wernersson, L.-E., Accumulation capacitance of narrow band gap metal-oxide-semiconductor capacitors. Appl. Phys. Lett. 96, 233507 (2010). Bülbül, M.M. & Zeyrek, S., Frequency dependent capacitance and conductance– voltage characteristics of Al/Si3N4/p-Si(100) MIS diodes. Microelectronic Engineering 83, 2522-2526 (2006). 15