2754 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 60, NO. 9, SEPTEMBER 2013

Quantum Mechanical Study of the GermaniumElectron–Hole Bilayer Tunnel FET

Cem Alper, Student Member, IEEE, Livio Lattanzio, Luca De Michielis, Student Member, IEEE,Pierpaolo Palestri, Member, IEEE, Luca Selmi, Senior Member, IEEE, and

Adrian Mihai Ionescu, Senior Member, IEEE

Abstract— The electron–hole bilayer tunnel field-effect tran-sistor (EHBTFET) is an electronic switch that uses 2-D-2-Dsub-band-to-sub-band tunneling (BTBT) between electron andhole inversion layers and shows significant subthermal swingover several decades of current due to the step-like 2-D densityof states behavior. In this paper, EHBTFET has been simu-lated using a quantum mechanical model. The model resultsare compared against transactions on computer-aided designsimulations and remarkable differences show the importance ofquantum effects and dimensionality in this device. Ge EHBTFETwith channel thickness of 10 nm results as a promising devicefor low supply voltage, subthreshold logic applications, with asuper steep switching behavior featuring SSavg ∼ 40 mV/decup to VDD. Furthermore, it has been demonstrated that highON current levels (∼40 µA/µm) can be achieved due to thetransition from phonon-assisted BTBT to direct BTBT at higherbiases.

Index Terms— 2-D-2-D tunneling, band-to-band tunneling(BTBT), density of states (DOS), electron–hole bilayertunnel field-effect transistor (EHBTFET), germanium, quantummechanical (QM) simulation, subthreshold slope, tunnelfield-effect transistor (TFET).

I. INTRODUCTION

TUNNEL field-effect transistors (TFETs) have started togain significant attention in the recent years among

the scientific community dealing with simulation, modeling,and fabrication aspects [1]–[4]. This interest can be mostlyattributed to the subthermal subthreshold swing (SS) that

Manuscript received January 25, 2013; revised June 19, 2013; acceptedJuly 17, 2013. Date of publication August 6, 2013; date of current versionAugust 19, 2013. This work was supported by the European Community’sSeventh Framework Program (FP7/2007–2013) under Grant 257267. Thework of P. Palestri and L. Selmi was supported by the EU project STEEPERvia the IUNET consortium and by the MIUR FIRB Futuro in Ricerca project.The review of this paper was arranged by Editor J. Knoch.

C. Alper, L. Lattanzio, and A. M. Ionescu are with the NanoelectronicDevices Laboratory, Ecole Polytechnique Federale de Lausanne, LausanneCH-1015, Switzerland (e-mail: cem.alper@epfl.ch; livio.lattanzio@epfl.ch;adrian.ionescu@epfl.ch).

L. De Michielis was with the Nanoelectronic Devices Laboratory, EcolePolytechnique Federale de Lausanne, Lausanne CH-1015, Switzerland. Heis now with the Integrated Systems Laboratory, ETH Zurich, Zurich 8092,Switzerland (e-mail: luca.demichielis@epfl.ch).

P. Palestri and L. Selmi are with the Dipartimento di Ingegneria Elettrica,Gestionale e Meccanica, University of Udine, Udine 33100, Italy (e-mail:palestri@uniud.it; luca.selmi@uniud.it).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TED.2013.2274198

can be attained at room temperature. Unlike MOSFET, thecarrier injection mechanism in TFETs relies on band-to-band tunneling (BTBT) of carriers. Hence, for TFETs, thesubthreshold conduction is not limited by thermionic emissionof carriers, which would result in SS > 60 mV/dec at roomtemperature.

Although it can be argued that there is no unique TFETstructure, the vast majority of the devices that have beenfabricated and simulated are asymmetrically doped gatedp-i-n structures [2]. A serious drawback of such devices isthe low ON current level. One of the reasons for this isthe inefficiency of the gate, in the sense that very little ofthe gate-induced electric field contributes to tunneling, sincethe tunneling direction and the gate electric field are notparallel in those structures as explained in [5].

To overcome this drawback, a second class of TFETdevices has been proposed, for which the gate electric fieldis aligned with tunneling direction [3]–[6]. In these devices,the ON current is proportional to the gate length, and itcan be much higher compared with previous generation ofTFETs. Even if various geometries have been proposed,the common working principle of these devices is BTBTbetween a bulk (3-D) source and a 2-D carrier gas formedin the semiconductor by gate-induced quantization. As anatural extrapolation to this concept, the electron–hole bilayerTFET (EHBTFET) has been proposed, which exploits BTBTbetween a 2-D electron gas (2-DEG) and a 2-D hole gas(2-DHG) [7].

In line with this trend, the impact of carrier dimensionalityon tunneling junctions has been extensively studied in [8] ina direct bandgap material using the transfer-matrix approach.Among all possible combinations, their study points out thatedge tunneling between two 2-D regions stands out as the mostpromising in terms of the switching behavior and predicts astep-like turn-on characteristic. Similarly, Teherani et al. [9]did an optimization study concerning different channel mate-rials and assessed the impact of quantization and gate leakage.

In this paper, EHBTFET is studied through simulationsusing a state-of-the-art full quantum mechanical (QM) model.The results are compared against semiclassical transactions oncomputer-aided design (TCAD) simulations. It is found thatquantization, which cannot be adequately treated in semiclas-sical simulations, plays an important role in EHBTFET deviceoperation.

0018-9383 © 2013 IEEE

ALPER et al.: QUANTUM MECHANICAL STUDY OF THE GERMANIUM EHBTFET 2755

Fig. 1. (a) Cross-sectional view of EHBTFET. (b) Formation of inducedelectron/hole bilayer by the application of appropriate gate biases. Arrows:BTBT direction.

II. DEVICE WORKING PRINCIPLE

The EHBTFET is a thin double-gated p-i-n diode (Fig. 1),similar to a conventional TFET. The i-region is gated fromboth sides to induce electron and hole inversion layers usingthe field effect. The only architectural difference between aconventional density gradient (DG)-TFET and the EHBTFETis the asymmetric placement and biasing of the gates. Thisis required to create gate-source (-drain) underlaps to preventlateral tunneling [10].

The asymmetrically biased gates induce quantized energylevels in both electron and hole inversion layers in the thinchannel. The exact configuration of sub-bands in terms ofquantization energy and occupancy depends on the semicon-ductor band structure and quantization direction. The basicdevice operation can be summarized as follows: in the OFF

state, the minimum sub-band energy of electrons Ee1 is abovethe maximum sub-band energy of the holes Eh1, therefore noBTBT can take place. When the device enters into the ON state,the sub-band energies for electrons and holes align and, owingto the step-like behavior of the 2-D density of states (DOS),a significant amount of states are available to contribute fortunneling even at low voltages, and thus a steep switchingbehavior can be obtained.

Albeit EHBTFET is intended mostly for low supply voltageapplications, since germanium is used as the channel materialin this paper, it is important to consider the fact that at highbiases, both direct and phonon-assisted BTBT can play a rolein the tunneling current [11]. Hence, a model that includesboth contributions has been implemented and will be detailedin the following section.

III. SIMULATION APPROACH

Our simulation scheme is based on the QM phonon-assistedBTBT model developed in [12] and on the direct BTBT modeldeveloped in [13]. Our implementation solves the effectivemass Schrödinger and Poisson equation self-consistently in a1-D slice for both electrons and holes. In the quantizationdirection z, the envelope equation for the kth wavefunctionresiding in the band and valley α reads (assuming a uniform

structure with a constant effective mass)[∓ h̄2

2mz,α∇2 + E(c,v)(z)

]ψkα(z) = Ekαψkα(z) (1)

where mz,α is the effective mass in the quantization direc-tion, E(c,v)(z) are the conduction and valence band profiles,respectively. The effective mass Schrödinger equation is solvedfor each electron valley, heavy hole, and light hole bands.Dirichlet boundary conditions (ψkα = 0) are assumed at theoxide–semiconductor interface thus neglecting wavefunctionpenetration into the oxide, which is a reasonable assumptionfor SiO2 and most high-k dielectrics. The wavefunctionsψkα(z) and sub-band energies Ekα are then used to obtainthe carrier concentrations as [14]

n(z) =∑α∈c

∑k

ψ∗kα(z)ψkα(z)nkα

p(z) =∑α∈v

∑k

ψ∗kα(z)ψkα(z)pkα (2)

where nkα and pkα are the electron and hole occupation termsof their respective kth wavefunctions, which can be calculatedas a zeroth-order Fermi integral

nkα = gαmxy,α

π h̄2

∫ ∞

Ekα

1

1 + eE−EFn

kB T

· d E

= gαmxy,αkB T

π h̄2 ln(1 + eEFn−Ekα

kB T )

pkα = gαmxy,αkB T

π h̄2 ln(1 + eEkα−EFp

kB T ). (3)

In the above equation, mxy,α is the DOS effective massin the transverse direction (xy-plane) and gα is the valleydegeneracy factor. To consider the nonparabolicity of the� electron valleys, the sub-band energy correction schemeproposed in [15] has been implemented. This method correctsboth the sub-band energy and the DOS. However, due to thelow occupation of the � valleys, we have considered only thesub-band energy modification (which has an effect on sub-band alignment and thus on the tunneling current) and keepthe DOS as in the parabolic case.

Once self-consistency is reached, the total current is eval-uated by summing up the calculated direct and phonon-assisted BTBT current components in a postprocessing step.For the phonon-assisted model, the diagonal elements of thespectral functions [12], which are used for evaluation of thetransmission terms, are calculated for each of the bands. Forinstance, the diagonal elements for the spectral function ofany valley α1 in conductance and valence bands, respectively,reads

Acα(z, E) = gαmxy,α

h̄2

∑k

ψ∗kα(z)ψkα(z)�(E − Ekα)

Avα(z, E) = gαmxy,α

h̄2

∑k

ψ∗kα(z)ψkα(z)�(Ekα − E) (4)

where �(E) is the step function given by the step-like 2-DDOS. Since quantization in only one direction is assumed,

1Only L valleys are considered for phonon-assisted BTBT.

2756 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 60, NO. 9, SEPTEMBER 2013

the spectral functions essentially reduce into summationsof various sub-band 2-D DOS functions weighted by theprobability distribution of carriers. The total phonon-assistedtunneling current is evaluated by first calculating thetransmission terms

T abs,emv (E)

= �|M ′k0

|2∑α,α′

∫Avα′(z, E)Acα(z, E ± h̄ωk0 )dz (5)

where �|M ′k0

|2 is the phonon-assisted coupling term2 andh̄ωk0 is the phonon energy corresponding to the crystalmomentum offset of conduction and valence bands [12], [16].Then, the phonon-assisted BTBT current is calculated as

Iph− = −2eLG W

h̄

×∫

d E

2π· ({ fv (E)[1 − fc(E − h̄ωk0 )][ν(h̄ωk0 )+ 1]

− fc(E − h̄ωk0 )[1 − fv (E)]ν(h̄ωk0 )}T emv (E)

+{ fv (E)[1 − fc(E + h̄ωk0 )]ν(h̄ωk0 )− fc(E + h̄ωk0 )

×[1 − fv (E)][ν(h̄ωk0 )+ 1]}T absv (E)) (6)

where fc,v are the Fermi–Dirac distributions of the conductionand valence bands, respectively, ν(h̄ωk0 ) is the Bose–Einsteindistribution, LG is the gate length, and W is the width of thedevice.

The direct tunneling current is given in [13]

Idir = −eEG LG W

2h̄

∑k

∑α′,k′∈v

ψ2k�ψ

2k′α′C0,α′(θ)( fv (ET )

− fc(ET ))�(Ek′α′ − Ek�) (7)

where EG is the direct bandgap of the semiconductor, C0,α′(θ)is a form factor with θ being the angle between the wavevectorcomponent in z (tunneling) direction and the total wavevector.The wavefunction magnitude-squared (ψ2

k�,ψ2k′α′) values are

calculated at the maximum overlap point. ET is the singletunneling energy dictated by the simultaneous conservation ofenergy and in-plane momentum [13].

Since the current is computed in a postprocessing step andnot included in the self-consistent loop, it is implicitly assumedthat electron and hole distributions are at equilibrium with then- and p-region contacts, respectively, which translates intoEFn = −qVD and EFp = −qVS. It is thus safely assumedthat, due to the low current levels inside the device, tunnelinggeneration does not appreciably alter the charge distributionin the low voltage regime. It has to be mentioned that themodel assumes tunneling only in vertical direction; therefore,the lateral tunneling component is not considered. However, inthis paper, only germanium EHBTFET structures with gate-source/drain underlaps of 50 nm are studied. This underlaplength is long enough to suppress the lateral tunneling [17].In addition, we note that the gate leakage, which is neglectedin our simulations, is an important issue to be investigated infuture works. An accurate estimate strongly depends on the

2The volume � does not affect the final result since a 1� term is present

inside |M ′k0

|2.

gate-stack parameters (electron affinity, tunneling mass, anddielectric constant) and it is beyond the scope of this paper,and we rather suggest the work in [9] concerning gate leakagein EHBTFET.

Sentaurus device with the nonlocal BTBT model has beenused for comparison purposes and also for the calculation ofthe current contribution due to Shockley–Read–Hall (SRH)recombination/generation mechanism, not accounted for bythe QM model presented above. QM effects on the electro-statics are included in Sentaurus device via the DG correctionmethod [18].

IV. SIMULATION PARAMETERS AND RESULTS

A Ge EHBTFET with a gate length LG = 50 nm is con-sidered in the simulations (Fig. 1). Both gate stacks feature agate oxide with an equivalent oxide thickness of 0.53 nm. Thei-region is lightly n-doped with ND = 1015cm−3 (arsenic).Unless otherwise stated, a device with channel thicknessTch = 10 nm is considered, and top and bottom gate work-functions�TG = 3.408 eV and�BG = 5.642 eV, respectively.The quantization direction is aligned with the [100] crystaldirection of Ge. In this direction, the L electron valleys ofgermanium are fourfold degenerate with quantization effectivemasses calculated as mz,α = 0.117m0 and transverse effectivemass mxy,α = 0.29m0 [19]. For the � valley, the effectivemasses of heavy, light holes, and electrons are mhh = 0.33m0,mlh = 0.043m0, and me = 0.043m0, respectively, [11]. Theelectron–phonon interaction term �|M ′

k0|2 and the phonon

energy h̄ωk0 for Ge are calculated and given as: 4.85 ×10−32 eV2m3 and 8.6 meV, respectively, using the parametersfrom [11]. The Sentaurus simulations for the calculation of theSRH recombination contribution used the following carrierlifetime parameters: τmax,n = 4 · 10−5 s and τmax,p =4·10−5 s [20]. The nonparabolicity factor for the � conductionband of germanium is taken as 0.85 eV−1 [21].

For this paper, we only vary the top gate bias (whichcontrols the electron inversion layer) and keep the bottomgate bias at a constant value. Consequently, the bottom gateworkfunction is adjusted so that the hole inversion layer isalready formed in equilibrium.

The transfer characteristics are, shown in Fig. 2, in conjunc-tion with the evolution of the sub-band energies. The resultsconfirm the working principle described in Section II: an OFF

region is seen until VGS ≈ 0.05 V due to the lack of alignmentbetween any electron and hole bands. As the top gate biasincreases, the electrostatic potential in the channel regioncontrolled by the top gate increases as well, therefore pushingdown the sub-band energies of the electrons (in a linear fashionin weak inversion). The onset of strong inversion is seen whenthe lowest sub-band reaches the vicinity of the drain quasi-Fermi level EFn = −qVDS. A slight effect on the hole energylevels is also observed, since the top gate voltage influencesthe portion of the channel populated by the holes as well.

The switching behavior is caused by the alignment of theground states in electron and heavy hole energy levels, whichare denoted in the plot as e1 and hh1, respectively. Themost striking feature of this characteristic is the super steep

ALPER et al.: QUANTUM MECHANICAL STUDY OF THE GERMANIUM EHBTFET 2757

EFp

EFn

(a)

(b)

Fig. 2. (a) Transfer characteristics (ID–VGS) for the EHBTFET with separatecontributions from phonon-assisted and direct BTBT shown. Results showsteep switch-on behavior at low VGS and smeared out contributions due to thealignment of higher energy sub-bands. (b) Evolution of the sub-band energiesfor L-valley (e), �-valley (�) electrons, heavy (hh), and light (lh) holes withrespect to the top gate voltage VGS.

Fig. 3. Impact of the gate voltage on the wavefunctions overlap. Black lines:energy band diagrams with probability density overlaps. A sizable decrease inthe overlap is evident stemming from the wavefunctions being pushed towardthe oxide.

switching slope, allowing for SSavg ≈ 10 mV/dec over threedecades at VDS = 0.5 V. However, above a certain VGS(∼0.3 V), a plateau of relatively constant current is seen untila second alignment is achieved, resulting in an ON currentof ∼12 nA/μm at VGS = VDS = 0.5 V. The reason forthat is the decrease of the wavefunction overlaps of e1 andhh1 levels (Fig. 3), which is caused by the increased slope ofthe potential profile, pushing electron, and hole wavefunctionstoward the semiconductor/oxide interfaces. Although the ener-getic window allowing for tunneling is constantly increasingwith increasing gate voltage, the reduction in wavefunctionoverlap can actually counterbalance this gain and may causea decrease of the drain current for increasing VGS. Further

increasing the gate voltage eventually results in overlap ofthe heavy hole and � valley sub-bands, hence allowing directBTBT to occur. Since direct BTBT rate is much higher thanphonon-assisted one, a sharp increase in current is observed,which also results in high drain current levels (∼40 μA/μm)at VGS = 1 V, VDS = 0.5 V.

Since we have a bandgap difference of EG = 0.14 eVbetween L and � valleys in Ge, the onset of direct tunnelingis expected at a relatively lower voltages compared with otherindirect bandgap materials such as silicon. While this onset isclose to EG in unquantized structures such as bulk diodes[22], the onset in a quantized structure such as the EHBTFETwill be shifted to higher voltages. Indeed, we observe a shiftof VGS ∼ 0.6 V between the onset of phonon-assisted anddirect BTBT for the EHBTFET under study (Fig. 2).

It is helpful to underline the main determinants of thetunneling current in relation to the discussion above. A closerlook at (4)–(7) reveals that the tunneling current is mainlydependent on: 1) the energetic position of the quantized levels;2) the DOS of both electrons and holes; and 3) the overlapbetween the electron and hole wavefunctions. The currentspectra shown in Fig. 4 show that light hole contribution ishigher than that of the heavy holes. However, low effectivemass of the light holes results in considerably higher quanti-zation energies compared with heavy holes; therefore, the lighthole contribution does not play any role at low voltage levelsin the region of switching. By the same token, it is evident thatdirect BTBT does not occur in lower voltages in the presenceof quantization.

Also, we can note a spike in the current spectrum inFig. 4(c) inset corresponding to the only allowed tunnelingenergy [ET in (7)] that preserves momentum and energyof the tunneling electron. We do not observe such behaviorfor phonon-assisted BTBT, since the phonons compensate forthe momentum difference between the initial and destinationbands, therefore resulting in a continuum of tunneling energyvalues available between aligned hole and electron sub-bandenergies.

One point worth noting with respect to the simulation toolsis the difference between the semiclassical Sentaurus deviceand the QM model simulations (Fig. 5). It can be observed thatalthough Sentaurus assumes a bulk, continuous band structurerather than quantized sub-bands, the semiclassical model isstill able to capture an important part of the basic deviceprinciple. The reason is that, even in the continuous band case,there is no current conduction if the conduction and valencebands are not aligned. Once the alignment is achieved, tunnel-ing is eventually allowed and a step-like switching behavior isseen. The step-like behavior is caused by the switching froman OFF-state to an ON-state with a relatively short tunnelingdistance. However, since the energy bands are not quantized inSentaurus, the alignment voltage is drastically different, whichis consistent with the results in [12]. The model parametersfor direct and phonon-assisted BTBT in the semiclassicalsimulations have been taken from [11]. Compared with thedefault calibration of Sentaurus for Ge (where phonon-assistedBTBT is dominant at all biases and direct BTBT is null), theset proposed in [11] is based on an accurate analysis and

2758 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 60, NO. 9, SEPTEMBER 2013

Fig. 4. Quantized energy levels for various gate biases. The current densityspectra are given as insets for each case. Various subband energies for heavyhole (hh), light hole (lh), L (e) and � (�) valley electrons are denoted.Spectra reveal that phonon-assisted tunneling between e-lh occurs at a higherrate per energy slice. Note the spike (Dirac-delta) in the current spectrumfor VGS = 0.9 V corresponding to the single tunneling energy in direct2D–2D tunneling as a result of simultaneous energy and in-plane momentumconservation.

feature high BTBT rates when direct tunneling enters intoplay. In fact, from Fig. 5, we can observe that the onsetsof phonon-assisted and direct BTBT are roughly separatedby VGS EG for Sentaurus results (since there is noquantization in the semiclassical model) and that the currentin the direct tunneling regime is significantly larger than inthe phonon-assisted one.

Fig. 5. Transfer characteristics comparison between the QM model andSentaurus. Sentaurus curve has been rigidly shifted to match the turn-onpotential calculated by the QM model. Both models predict steep switchingbehavior, although Sentaurus significantly overestimates the ON current. Theworkfunctions used for Sentaurus are �TG = 3.945 eV and �BG = 4.875 eV.The workfunctions used for QM model are the same as Fig. 2 (�TG =3.408 eV and �BG = 5.642 eV).

Fig. 6. EHBTFET transfer characteristics for different VDS in linear and logscale. A negative transconductance region is visible for high VGS voltages.

Fig. 6 shows the transfer characteristics for different VDSvoltages. What is most striking is the almost overlap of thecurves for VDS ≥ 0.2 V. Up to 0.2 V, the increase in VDSeffectively increases the DOS that can contribute to tunneling.However, increasing VDS further does not result in an increasein the tunneling current, unless the increase allows for anotheralignment between energy sub-bands. This can be explained bythe previously mentioned wavefunction repulsion mechanism,which decreases the tunneling probability albeit the increase inthe allowed energy window, resulting in negative transconduc-tance at high VGS. In the case of VDS = 0.2 V, we observe animpressive ION/IOFF ratio of 105 and an average subthresholdslope of 40 mV/dec up to VDD.

The output characteristics are shown in Fig. 7 for differentVGS voltages. In line with Fig. 6, we observe a smallersaturation current for VGS = 0.5 V than for VGS = 0.4 V,due to the negative transconductance effect. The quasi-idealsaturation characteristic is a limitation of the model, since itcalculates the current using 1-D vertical slices of the deviceand 2-D effects are not considered. Nevertheless, full 2-DSentaurus simulations have already shown that an extremely

ALPER et al.: QUANTUM MECHANICAL STUDY OF THE GERMANIUM EHBTFET 2759

Fig. 7. EHBTFET output characteristics for different VGS. Note the absenceof the superlinear region at low VDS region, which is commonly seen in TFEToutput characteristics.

Fig. 8. Transfer characteristics of the EHBTFET for different channelthicknesses (Tch). For increased Tch, the quantization effects get relativelyweaker, and the energetic spacing between quantized levels decreases. Thecases Tch = 9 nm and Tch = 11 nm have the same gate metal workfunctionas Tch = 10 nm. The top gate metal workfunction �TG for Tch = 15 nm andTch = 20 nm are 3.808 eV and 3.868 eV, respectively.

good saturation behavior can be achieved [17] and there is noreason to think that the vertical quantization would change thisproperty. Therefore, a high output resistance is expected fromthe EHBTFET in the saturation region. Also, the absence ofa superlinear onset [23], [24] at low VDS is a result of sub-band alignment occurring at energies sufficiently larger thanthe source Fermi level EFp.

Finally, by inspecting the transfer characteristics in Fig. 8,it is seen that increasing the channel thickness drasticallyreduces the tunneling current as the transmission probabilityis reduced. We see that the first alignments (e1–hh1) forthe 15- and 20-nm cases are unable to produce a significantamount of current and they are in the order of the SRHcurrent contribution (corresponding to the almost flat part ofthe curves around VGS = 0 V). Indeed, the extremely sensitivedependence of the current over the tunneling length is alreadyknown as a major issue in TFETs and we see that a similardependence persists also in this device. Nevertheless, from theplots for Tch = 9 nm and Tch = 11 nm, it is evident that steepswitching behavior is retained, albeit the shift in the alignmentvoltage. This finding is consistent with the results in [25] on

Si EHBTFETs, where a shift in the tunneling onset voltageand a decrease in the ON current are reported with increasingchannel thickness.

Furthermore, for all the cases investigated, we see that whenthe � sub-bands align with the hole sub-bands, a large IONis observed, because direct BTBT is allowed, which occursat a much higher rate compared with phonon-assisted BTBT.Especially for the Tch = 20 nm case, we observe a very steepincrease around VGS = 0.7 V where the � valley sub-bandand the light hole sub-bands align. This presents an interestingtradeoff as an optimum can be reached between the tunnelingdistance (which is ∝ Tch) and the carrier types involved intunneling, which depend on the strength of quantization insidethe channel.

V. CONCLUSION

In this paper, it was shown via QM self-consistent simula-tions that the EHBTFET behaves quite differently comparedwith a conventional TFET, due to the strong quantization atboth sides of the tunneling path. Exploitation of both 2-DEGand 2-DHG results in a steep switching behavior caused bythe staircase-like 2-D DOS. Comparison with the semiclassicalTCAD simulations shows that TCAD models overestimate thecurrent and also underestimate the alignment voltage since itdoes not account for the quantized nature of the electron andhole inversion layers.

Although reduced ON current levels are obtained comparedwith CMOS, the EHBTFET is still shown to be a promis-ing candidate for low supply voltage applications due toits super steep switching resulting in SSavg ∼ 40 mV/decand ION/IOFF ≈ 105 (VDD ≈ 0.2 V). Furthermore, it hasbeen demonstrated that, due to the direct (�) bandgap beingcomparable energetically to the indirect (L) bandgap, a tran-sition between phonon-assisted BTBT and direct BTBT canbe observed. This transition allows EHBTFET to achievehigh current levels (∼40 μA/μm) at a relatively larger sup-ply voltages (∼1 V) compared with a conventional TFET.The impact of the channel thickness on the device char-acteristics was investigated and it has been shown thatchannel thickness has a strong influence on the tunnelingcurrent.

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Cem Alper (S’08) is currently pursuing the Ph.D.degree with the Nanoelectronic Devices Labora-tory, Ecole Polytechnique Federale de Lausanne,Lausanne, Switzerland. His work focuses on noveltunneling devices.

Livio Lattanzio received the Ph.D. degree fromEcole Polytechnique Federale de Lausanne, Lau-sanne, Switzerland.

He is currently a Post-Doctoral Fellow with theNanoelectronic Devices Laboratory, Ecole Polytech-nique Federale de Lausanne.

Luca De Michielis (S’11) received the Ph.D. degreefrom Ecole Polytechnique Federale de Lausanne,Lausanne, Switzerland, in 2012.

He is currently a Post-Doctoral Fellow with theComputational Nanoelectronics Group, Swiss Fed-eral Institute of Technology Zurich, Zurich, Switzer-land.

Pierpaolo Palestri (M’05) received the Ph.D. degreein electronic engineering from the University ofUdine, Udine, Italy, in 2003.

He has been an Associate Professor with theUniversity of Udine since 2005.

Luca Selmi (SM’10) received the Ph.D. degree inelectronics from the University of Bologna, Bologna,Italy, in 1992.

He is currently with the Department of Electrical,Managerial and Mechanized Engineering, Universityof Udine, Udine, Italy.

Adrian Mihai Ionescu (SM’06) received the Ph.D.degree from the National Polytechnic Institute ofGrenoble, Grenoble, France, in 1997.

He is a Full Professor and the Director of theNanoelectronic Devices Laboratory, Ecole Polytech-nique Federale de Lausanne, Lausanne, Switzerland.