The capacitance-voltage characteristic of GaAs, In0.53Ga0.47As, and InAs metal-oxide-semiconductor capacitors (MOSCAPs) is calculated in three cases. First, quantization is not considered, then quantization of the C-valley is included, and finally quantization of the Gamma-, X-, and L-valleys is included. The choice of valley energy-minima is shown to determine the onset of occupation of the satellite valleys and corresponding increase in total capacitance. An equivalent-oxide-thickness correction is defined and used as a figure-of-merit to compare III-V to Si MOSCAPs and as a metric for the density-of-states bottleneck. (C) 2011 American Institute of Physics. (doi:10.1063/1.3652699

Hurley, Paul K.

O'Regan, Terrance P.

Applied Physics Letters

O\u27Regan, Terrance P.

Irish Universities

Calculation of the capacitance-voltage characteristic of GaAs, In0.53Ga0.47As, and InAs metal-oxide-semiconductor structures

Cork Open Research Archive

Title Calculation of the capacitance-voltage characteristic of GaAs,In0.53Ga0.47As, and InAs metal-oxide-semiconductor structuresAuthor(s) O'Regan, Terrance P.; Hurley, Paul K.Publication date 2011Original citation O’Regan, T. P. and Hurley, P. K. (2011) 'Calculation of the capacitance-voltage characteristic of GaAs, In0.53Ga0.47As, and InAs metal-oxide-semiconductor structures', Applied Physics Letters, 99(16), pp. 163502.doi: 10.1063/1.3652699Type of publication Article (peer-reviewed)Link to publisher'sversionhttp://aip.scitation.org/doi/abs/10.1063/1.3652699http://dx.doi.org/10.1063/1.3652699Access to the full text of the published version may require asubscription.Rights © 2011 American Institute of Physics.This article may bedownloaded for personal use only. Any other use requires priorpermission of the author and AIP Publishing. The following articleappeared in O’Regan, T. P. and Hurley, P. K. (2011) 'Calculation ofthe capacitance-voltage characteristic of GaAs, In0.53Ga0.47As, andInAs metal-oxide-semiconductor structures', Applied PhysicsLetters, 99(16), pp. 163502 and may be found athttp://aip.scitation.org/doi/abs/10.1063/1.3652699Item downloadedfromhttp://hdl.handle.net/10468/4313Downloaded on 2018-08-23T18:46:19ZCalculation of the capacitance-voltage characteristic of GaAs, In0.53Ga0.47As, andInAs metal-oxide-semiconductor structuresT. P. O’Regan,  and P. K. HurleyCitation: Appl. Phys. Lett. 99, 163502 (2011); doi: 10.1063/1.3652699View online: http://dx.doi.org/10.1063/1.3652699View Table of Contents: http://aip.scitation.org/toc/apl/99/16Published by the American Institute of PhysicsCalculation of the capacitance-voltage characteristic of GaAs, In0.53Ga0.47As,and InAs metal-oxide-semiconductor structuresa)T. P. O’Regan1,a) and P. K. Hurley21U.S. Army Research Laboratory, RDRL-SER-E, 2800 Powder Mill Road, Adelphi, Maryland 20783, USA2Tyndall National Institute, University College Cork, Lee Maltings, Prospect Row Cork, Ireland(Received 24 August 2011; accepted 23 September 2011; published online 18 October 2011)The capacitance-voltage characteristic of GaAs, In0.53Ga0.47As, and InAs metal-oxide-semiconductorcapacitors (MOSCAPs) is calculated in three cases. First, quantization is not considered, thenquantization of the C-valley is included, and finally quantization of the C-, X-, and L-valleys isincluded. The choice of valley energy-minima is shown to determine the onset of occupation of thesatellite valleys and corresponding increase in total capacitance. An equivalent-oxide-thicknesscorrection is defined and used as a figure-of-merit to compare III-V to Si MOSCAPs and as a metricfor the density-of-states bottleneck.VC 2011 American Institute of Physics. [doi:10.1063/1.3652699]High mobility III-V semiconductors are considered forscaling beyond the 22 nm node because they promise a signifi-cant electron mobility enhancement over silicon.1 The highelectron mobility of III-V semiconductors is a result of thesmall effective mass in the C-valley conduction band. Thesmall conduction-band effective-mass leads to a smallconduction-band density-of-states (DOS) and the so-calledDOS bottleneck,2 where a large gate voltage is necessary toswing the Fermi level deep into the conduction band in orderto strongly invert the III-V surface. As a consequence, theideal capacitance-voltage (CV) characteristic of III-V metal-oxide-semiconductor (MOS) structures can deviate consider-ably from the well established CV characteristic of siliconMOS structures.3–7 Knowledge of the ideal III-V MOS CVcharacteristic is essential, as it is required when assessing theimpact of interface defects on the experimental CV responsesof real III-V MOS systems.8,9 In this letter, we extend on thework reported in Ref. 10 to calculate the theoretical CV char-acteristic for the case of p-type GaAs, In0.53Ga0.47As, andInAs metal-oxide-semiconductor capacitors (MOSCAPs).This work investigates the impact of III-V satellite valleyoccupation on the ideal CV, and the DOS bottleneck is quanti-fied using the metric of an equivalent thickness of SiO2 (tcorr)as a function of the inversion charge density.The CV characteristics are modeled for a planar devicegeometry with a metallic gate, gate dielectric, and III-V semi-conducting channel. We choose Al2O3 for the gate dielectricand consider GaAs, In0.53Ga0.47As (referred to as InGaAsfrom here on), and InAs for the semiconducting channel. Weset the constant p-type doping to NA¼ 2 1017 cm3, thephysical oxide thickness to 2 nm, the metal work function to5.05 eV, and the (001) surface orientation. The effective massin the C-valley along the quantization direction, mC, is listedin Table I for the III-V semiconductors considered in thiswork. We choose a 2 nm-thick gate-dielectric to reveal thestrong asymmetry between the accumulation and inversion ca-pacitance. We show later that the strong asymmetry allowsthe occupation of the L and X valleys to be clearly observedin the ideal CV characteristic. A perfect dielectric/semicon-ductor interface is assumed, with the interface traps, bulktraps, and bulk charge all set to zero, to more clearly observethe DOS bottleneck. Reference 10 describes the calculation inmore detail.To quantify the DOS bottleneck, the reduction in totalcapacitance below the oxide capacitance (due to the finitevalue of the semiconductor capacitance, Cs) is equated to anequivalent-oxide-thickness (tcorr) of SiO2 in series with thegate dielectric. If the interface trap density is negligible, thetcorr correction is simplytcorr ¼ SiO20Cs; (1)where tcorr is an implicit function of the charge density, andSiO2 is the static dielectric constant of SiO2. This value, whilenot physically meaningful, is used here as a metric to comparethe impact of the low DOS in the C-valley and effect of satel-lite valley occupation for III-V semiconductors.Figure 1 shows the electron concentration as a functionof position for a silicon, GaAs, InGaAs, and InAs inversionlayer at an electron sheet-charge, ns¼ 4 1012 cm2. Com-paring the higher-mobility (lower mass and lower DOS)semiconductors of GaAs, InGaAs, and InAs to the higher-FIG. 1. (Color online) Electron density vs. position for Si, GaAs, InGaAs,and InAs MOSCAPs under strong inversion.a) Electronic mail: terrance.p.oregan.ctr@us.army.mil. Part of this work wascompleted while T. P. O’Regan worked at Tyndall National Institute,University College Cork, Ireland.0003-6951/2011/99(16)/163502/3/$30.00 VC 2011 American Institute of Physics99, 163502-1APPLIED PHYSICS LETTERS 99, 163502 (2011)mass silicon, the peak electron concentration is pushed fur-ther away from the dielectric interface.11 The peak of theelectron concentration moves from about 1 nm for silicon toaround 4 nm for InAs, with GaAs and InGaAs lying in-between these values.Figure 2 shows the CV characteristic for 2 nm Al2O3 onp-type (a) GaAs, (b) InGaAs, and (c) InAs. Starting fromGaAs, then InGaAs, and finally InAs, we see that the classi-cal (no quantization, but including Fermi-Dirac statistics)CV-curve becomes more asymmetric as the DOS in the con-duction band, NC, reduces with respect to the DOS in the va-lence band, NV. Table I lists NC, NV, and the ratio NC/NVfor the semiconductors considered in this work. Includingquantization of the C-valley increases the threshold voltagein all cases due to the shifting of the charge centroid awayfrom the dielectric/III-V interface.When including quantization of the C, L, and X valleys,the CV characteristic exhibits an increase in capacitance asthe satellite valleys become occupied under strong inver-sion.10 The shoulder in the capacitance occurs at differentgate voltages for the three semiconductors because theenergy separation between the valleys and 2D DOS is mate-rial dependent (as well as the differences in band gap andquantization masses, see Table I). In addition, we must relyon theoretical values of the energy minima of the satellitevalleys because they are not known experimentally. In Table I,TABLE I. Semiconductor parameters. EC, EL, and EX are energies measured from the top of the valence band to the bottom of the C, L, and X valleys, respec-tively. NC and NV are the effective DOS for the conduction band and valence band, respectively. mC is the effective mass and aC is the nonparabolicity parame-ter in the C-valley. For all semiconductors, the nonparabolicity parameters of all satellite valleys are set to 0.5/eV (see Ref. 10).Semiconductor EC (eV) ELa (eV) EXa (eV) ELb (eV) EXb (eV) NC (cm3) NV (cm3) NC/NV– mC (mo) aCc (/eV)Si 3.40 2.0 1.12 — — 3.2 1019 1.8 1019 1.78 — 0.5GaAs 1.42 1.71 1.90 1.74 1.87 4.7 1017 9.0 1018 0.052 0.067 0.61In0.53Ga0.47As 0.73 1.21 1.33 1.49 1.98 2.1 1017 7.7 1018 0.027 0.048 1.0InAs 0.35 1.08 1.37 1.43 1.96 8.7 1016 6.6 1018 0.013 0.023 1.4aReference 12.bReference 13.cReferences 10 and 17.FIG. 2. (Color online) Ideal CV characteristic of (a) GaAs, (b) InGaAs, and (C) InAs MOSCAPs with 2 nm Al2O3 gate-dielectric. Corresponding electron-sheet-density vs. gate voltage for (d) GaAs, (e) InGaAs, and (f) InAs. The solid lines are solutions to the Poisson equation only, the dotted lines include quanti-zation of the C valley, and the dashed lines include quantization of the C, L, and X valleys (using EmaxL;X from Table I). In (d)-(f), the location where the dashedline clearly deviates from the the dotted line is highlighted by a box (grey dotted lines) with the upper right corner at the onset of satellite valley occupation.163502-2 T. P. O’Regan and P. K. Hurley Appl. Phys. Lett. 99, 163502 (2011)we list two sets of values for the satellite valley minima thatrepresent the maximum and minimum values from the litera-ture, denoted EminL;X (Ref. 12) and EmaxL;X (Ref. 13), respectively.In Fig. 2, we use EmaxL;X , and discuss below the effect of thischoice in the context of tcorr. Figures 2(d)–2(f) show ns vs.gate voltage, corresponding to the CV curves in Figures2(a)–2(c). Figures 2(d)–2(f) show the approximate ns andgate voltage at which the satellite valley occupation becomessignificant. This location, where ns clearly deviates from theC-valley only case, is highlighted by a box with the upper-right corner at the onset of satellite valley occupation. Asdiscussed in Ref. 10, nonparabolic corrections strongly effectthe energy subband minima and compress the energy differ-ences between subbands in the satellite valleys and the C-valley. This effect overcomes the large satellite valley offsetsin InAs, and occupation of the satellite valleys commencesat lower ns for InAs compared to InGaAs (see Figs. 2(e) and2(f)).Figure 3 shows tcorr for the two sets of satellite-valleyenergies listed in Table I. In both Figs. 3(a) and 3(b), at midns¼ 1012 cm2, InAs has the largest tcorr, followed by InGaAs,GaAs, and finally Si. This is a direct consequence of the lowDOS in the C valley, which becomes significant as the DOSdecreases from GaAs to InGaAs to InAs (see Table I). Theeffect of quantization, as shown in Fig. 1, also contributes totcorr. For all the III-V semiconductors in Fig. 3(a), tcorr dropsto the tcorr value of Si (<0.5 nm) in the range ns¼ 5–6 1012 cm2. However, for InAs and InGaAs in Fig. 3(b), tcorrdrops to the Si tcorr value (<0.5 nm) in the range ns¼ 8–9 1012 cm2. In both cases, the drop in tcorr reflects the occu-pation of the satellite valleys.10 The shift in the drop of tcorr tolower ns is due to the choice of satellite-valley energy gaps. InFig. 3(b), the gaps are higher compared to Fig. 3(a) and theoccupation shifts to higher inversion densities. Similar valuesof tcorr versus ns for Si and GaAs has been reported by Rafhayand co-workers (Ref. 14).It is noted, that in real III-V MOS systems formed onGaAs, InGaAs, or InAs, the sharp increase in capacitance asa result of the satellite valley occupation may not beobserved, as the CV characteristic is influenced by interfacedefects. In particular, experimental evidence indicates that inthe case of high-k/InGaAs MOSCAPs, interface states existnot only in the energy gap but also with energies alignedwith the InGaAs C-valley,15,16 which can prevent the Fermilevel from reaching the satellite valley energies. If interfacedefects can be reduced to negligible levels, the CV character-istics presented in Figs. 2(a)–2(c) should be observable asthe electric field in the oxide is about 2 MV/cm for allAl2O3/III-V MOSCAPs at ns¼ 1013 cm2.In conclusion, we have shown the CV asymmetry of III-VMOSCAPs is a result of the lower conduction-band DOS rel-ative to the valence-band DOS. The CV asymmetry is largestfor InAs which has the lowest conduction band DOS com-pared to InGaAs and GaAs. The CV symmetry is partiallyrecovered when including quantization of the satellite val-leys, with the sharp increase in capacitance corresponding tothe re-population of charge into the satellite valleys. Thesharp increase in capacitance is semiconductor dependent,with the choice of satellite-valley energy gaps a key inputparameter. Finally, the capacitance of Si, GaAs, InGaAs andInAs inversion layers was related to an equivalent thicknessof SiO2 (tcorr). The values of tcorr were used to quantify thedegradation due to the low conduction-band DOS of theinversion capacitance in p-type III-V MOS systems withrespect to Si.This work was supported by Science Foundation Irelandthrough the U.S.-Ireland Research Project (08/US/I1546).T. P. O’Regan also recognizes support from the U.S. ArmyResearch Laboratory. We thank Massimo Fischetti andQuentin Rafhay for useful discussions.1W. Haensch, E. J. Nowak, R. H. Dennard, P. M. Solomon, A. Bryant, O.H. Dokumaci, A. Kumar, X. Wang, J. B. Johnson, and M. V. Fischetti,IBM J. Res. Dev. 50, 339 (2006).2M. Fischetti, T. O’Regan, S. Narayanan, C. Sachs, S. Jin, J. Kim, and Y.Zhang, IEEE Trans. Electron Devices 54, 2116 (2007).3M. Fischetti and S. Laux, IEEE Trans. Electron Devices 38, 650 (1991).4H. Pal, K. Cantley, S. Ahmed, and M. Lundstrom, IEEE Trans. ElectronDevices 55, 904 (2008).5T. Yang, Y. Liu, P. D. Ye, Y. Xuan, H. Pal, and M. S. Lundstrom, Appl.Phys. Lett. 92, 252105 (2008).6D. Jin, D. Kim, T. Kim, and J. del Alamo, Tech. Dig. – Int. Electron Devi-ces Meet. 2009, 1.7E. Lind, Y.-M. Niquet, H. Mera, and L.-E. Wernersson, Appl. Phys. Lett.96, 233507 (2010).8E. O’Connor, S. Monaghan, R. D. Long, A. O’Mahony, I. M. Povey, K.Cherkaoui, M. E. Pemble, G. Brammertz, M. Heyns, S. B. Newcomb, V.V. Afanas’ev, and P. K. Hurley, Appl. Phys. Lett. 94, 102902 (2009).9R. Engel-Herbert, Y. Hwang, and S. Stemmer, J. Appl. Phys. 108, 124101(2010).10T. P. O’Regan, P. K. Hurley, B. Sore´e, and M. V. Fischetti, Appl. Phys.Lett. 96, 213514 (2010).11A. Lubow, S. Ismail-Beigi, and T. P. Ma, Appl. Phys. Lett. 96, 122105 (2010).12W. Porod and D. K. Ferry, Phys. Rev. B 27, 2587 (1983).13J. Kim and M. V. Fischetti, J. Appl. Phys. 108, 013710 (2010).14Q. Rafhay, R. Clerc, J. Coignus, G. Pananakakis, and G. Ghibaudo, 11thInternational Conference on Ultimate Integration of Silicon, 18-19 (2010).15G. Brammertz, H.-C. Lin, M. Caymax, M. Meuris, M. Heyns, and M. Pas-slack, Appl. Phys. Lett. 95, 202109 (2009).16P. K. Hurley, E. O’Connor, S. Monaghan, R. Long, A. O’Mahony, I. M.Povey, K. Cherkaoui, J. MacHale, A. Quinn, G. Brammertz, M. M. Heyns,S. Newcomb, V. V. Afanas’ev, A. Sonnet, R. Galatage, N. Jivani, E.Vogel, R. M. Wallace, and M. Pemble, ECS Trans. 25, 113 (2009).17M. A. Littlejohn, J. R. Hauser, and T. H. Glisson, J. Appl. Phys. 48, 4587(1977).FIG. 3. (Color online) Equivalent-oxide-thickness correction vs. ns. (a) Theenergy gaps in Table I from Ref. 12 are used (here denoted EminL;X). (b) Theenergy gaps in Table I from Ref. 13 are used (here denoted EmaxL;X ).163502-3 T. P. O’Regan and P. K. Hurley Appl. Phys. Lett. 99, 163502 (2011)

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Calculation of the capacitance-voltage characteristic of GaAs, In0.53Ga0.47As, and InAs metal-oxide-semiconductor structures

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