A Multiscale Modeling of Triple-Heterojunction Tunneling FETs

1.1 MB·

by  Jun Z. Huang

1
A Multiscale Modeling of Triple-Heterojunction
Tunneling FETs
Jun Z. Huang, Pengyu Long, Michael Povolotskyi, Hesameddin Ilatikhameneh, Tarek Ameen, Rajib Rahman,
Mark J. W. Rodwell, and Gerhard Klimeck
7
1
0
2
Abstract—A highperformance triple-heterojunction(3HJ) de- TFETs [5]–[14]. Among these designs, the triple HJ (3HJ)
r
p sign has been previously proposed for tunneling FETs (TFETs). designs [11]–[14] significantly boost the tunnel probability of
A Compared with single heterojunction (HJ) TFETs, the 3HJ the HJ TFETs by adding two additional, properly designed,
TFETs have both shorter tunneling distance and two transmis-
3 sion resonances that significantly improve the ON-state current HJs:oneinthesourceandtheotherinthechannel.Forn-type
(ION). Coherent quantum transport simulation predicts, that 3HJ TFETs [11], atomistic quantum ballistic transport simu-
] ION = 460µA/µm can be achieved at gate length Lg = 15nm, lations have shown, that extremely high ION of 800µA/µm
ll supply voltage VDD = 0.3V, and OFF-state current IOFF = (460µA/µm) could be obtained at Lg = 30nm (15nm),
a 1nA/µm.However,strongelectron-phononandelectron-electron V =0.3V, and I =1nA/µm.
h scatteringintheheavilydopedleadsimplies,thatthe3HJdevices DD OFF
The 3HJ devices’ promisingON/OFF currentratio is likely
- operate far from the ideal coherent limit. In this study, such
s scattering effects are assessed by a newly developed multiscale tobedegradedbyvariousscatteringphenomena,asimpliedby
e
m transport model, which combines the ballistic non-equilibrium thelargespatialoverlapofconduction-andvalence-bandlocal
Green’s function method for the channel and the drift-diffusion densityofstates(LDOS)attheOFFstate[11]–[14].Theeffect
. scattering method for the leads. Simulation results show that
t of electron-phononscattering on the 3HJ design performance
a the thermalizing scattering in the leads both degrades the 3HJ
m TFET’s subthreshold swing through scattering induced leakage has been examined by the non-equilibrium Green’s function
and reduces the turn-on current through the access resistance. (NEGF) approach in the self-consistent Born approximation
-
d Assuming bulk scattering rates and carrier mobilities, the ION (SCBA) [14], considering only the diagonal components of
n is dropped from 460µA/µm down to 254µA/µm, which is still theself-energy.Itisfound,thattheelectron-phononscattering
o much larger than the single HJ TFET case.
moderately degrades the transistor’s I-V characteristics, but
c
IndexTerms—Thermalizationscattering,diffusiveleads,multi- the I at a given I and V remains much larger
[ ON OFF DD
scaletransport,heterojunction(HJ)TFETs,triple-heterojunction than that of a GaSb/InAs HJ TFET, when simulated under

2 (3HJ) TFETs.
equalintensityofphononscattering[14].Thestrongelectron-
v
electronscattering,such asthe Augergeneration[15],present
0
8 I. INTRODUCTION in the heavily doped source (and drain) lead, however, has
4 not been examined yet. Practically, this strong, close to ther-
0 TUNNELING field-effect transistor (TFET) is a steep malizing,effectofelectron-electronscatteringis verydifficult
0 subthreshold swing (SS) device that can operate at low
to model in the NEGF approach with an explicit self-energy
. supplyvoltage,soitispromisingforlow-powerlogicelectron-
1 due to its non-local nature, as explained in more detail in
0 ics application [1]. The low tunneling probability problem of Ref.[16].Therefore,wehavedevelopedanefficientempirical
7 TFETs can be mitigated by employing staggered- or broken-
scattering model, using the NEMO5 tool [17]. In this model,
1 gap heterojunction (HJ) for the tunnel junction to reduce the
the centralchannelis treated as non-equilibriumand ballistic,
:
v tunnel barrier height and tunnel distance [2]–[4]. However, whiletheleadsareassumedtobeinlocalthermalequilibrium
i even for broken-gap GaSb/InAs HJ TFETs, the tunnel prob-
X withscatteringratederivedfromexperimentalcarriermobility.
ability is low due to quantum confinement induced band gap
The local quasi-Fermi levels in the leads are determined by
r
a overlap [5]–[7]. A number of designs have been proposed solving the drift-diffusion equations in them. Note, that the
to further improve the performance of the GaSb/InAs HJ
single scattering rate takes into account multiple scattering
mechanisms present in the heavily doped leads, and the drift-
J. Z. Huang, P. Long, M. Povolotskyi, H. Ilatikhameneh, T. Ameen, R.
diffusion solver allows us to include the lead serial resistance
Rahman,andG.KlimeckarewiththeNetworkforComputationalNanotech-
nologyandBirckNanotechnologyCenter,PurdueUniversity,WestLafayette, naturally.
IN47907USA(e-mail:[email protected]). This multiscale model, originally proposed in Ref. [18] for
M. J. W. Rodwell is with the Department of Electrical and Computer
resonant tunneling diode simulation, has been generalized to
Engineering, University of California at Santa Barbara, Santa Barbara, CA
93106-9560USA. beabletosimulateotherstructures,suchastheultra-thin-body
Manuscriptreceived xxxxx,2017;revisedxxxxxx,2017.Thisworkuses (UTB) superlattice transistors [16]. In this study,the model is
nanoHUB.org computational resources operated by the Network for Com-
further extended to consider both electron and hole transport,
putational Nanotechnology funded by the U.S.National Science Foundation
underGrantEEC-0228390,GrantEEC-1227110,GrantEEC-0634750,Grant required for a band-to-bandtunneling device simulation. This
OCI-0438246, Grant OCI-0832623, and Grant OCI-0721680. This material model is then employed to systematically analyze the 3HJ
is based upon work supported by the National Science Foundation under
TFETs by varying the scattering strength, and corresponding
awards 1509394, 1639958 and Semiconductor Research Corporation under
award2694.03. mobility, of the leads. The device behaviors under channel
2
addedtwo HJs shouldbe as large as possible and they should
also balance each other, leading to optimal mole fractions
x=0.79andy =1.TheGaSbandInAsquantumwellwidths
are then adjusted to have the resonant state levels closely
aligned in the Fermi conduction window at the ON state.
Fig.1. Devicestructureandmaterialcompositions ofthen-type3HJTFET. III. THEMULTISCALESIMULATION APPROACH
The p-type doped source lead consists of a 5.6nm AlSb layer with doping
density NA = 3×1019/cm3, a 1.2nm Al0.5Ga0.5Sb grade layer and a Thedeviceisdividedintothreeregions,asshowninFig.2.
3.3nm GaSb layer, both with NA = 5×1019/cm3. The intrinsic channel
consists ofa3nmInAslayeranda12nm(InAs)0.79(AlSb)0.21 layer. The The assumption is, that in the dopedsource and drain regions
wn-ittyhpedodpoinpgeddednrasiintyleNadDc=ons2ist×s o1f01a9/1c0mnm3.(TInheAsb)o0d.y79t(hAiclkSnbe)s0s.2a1ndlaytheer tthheermstraolnegquscilaitbteriruinmg.dTrhiveerseftohree,frweee cshoalvrgeetwcaorriderrisft-indtioffulosicoanl
oxide thickness are both 1.8nm with oxide dielectric constant ǫr = 9. The
confinement (transport)crystal orientation is[1¯10]([110]). (DD)currentequationsforthethermalizedholesinthesource
and the thermalized electrons in the drain, respectively. Since
quantum confinements are critical in the leads, we obtain the
Source lead Channel Drain lead
holeandelectrondensityofstatesfromtheGreen’sfunctions.
2 The minoritycarriercurrentin the leadsis neglected,because
DD NEGF DD
both the source and the drain leads are heavily doped. In the
eV] 1 (holes) (e−h model) (electrons) intrinsic channel region, the scattering rate is much lower, so
y [ Ec the quantum-mechanical band-to-band tunneling is the major
g E
r Fd transport mechanism. Hence, in the channel region we solve
e 0 E
n Fs the ballistic NEGF equationsinvolvingboth the electronsand
E
the holes. The contact self energies and quasi-Fermi levels
−1 Ev for the quantum domain boundaries are taken from the lead
surfaceGreen’sfunctionsandDDequations,respectively.The
0 5 10 15 20 25 30 35
centralquantumdomainprovidesballisticcurrent,thatisused
X [nm]
asaboundaryconditionfortheDDequationsintheleads.The
DD equations in the leads require LDOS, that is computed
Fig. 2. Region boundaries of the multiscale model. The OFF-state band
diagramandtheFermilevelsaresuperimposed.Wecouplethedrift-diffusion from Green’s function in a recursive way, using the quantum
equations for the holes (electrons) in the source (drain) lead and the NEGF domain Green’s function as a boundary condition.
equations forboththeelectrons andtheholesinthechannel.
lengthscalingarestudiedand,finally,thedeviceperformances A. Numerical Model Detail
are benchmarked against conventionalHJ TFETs.
The device Hamiltonian is modeled using sp3d5s∗ tight
binding (TB) basis with spin-orbital interaction. The parame-
II. THETRIPLE-HETEROJUNCTION DESIGN ters are taken from Ref. [20]. The alloys are described using
We consider n-type 3HJ TFETs with double-gate UTB thevirtualcrystalapproximation(VCA)withtheirTBparam-
structures [11]. The device geometry and the optimized de- eterslinearlyinterpolatedfromtheircorrespondingbinaries.In
sign parameters are shown in Fig. 1. The added HJ in the order to utilize the efficient recursive Green’s function (RGF)
channel is InAs/(InAs) (AlSb) , while the added HJ algorithm [21], the whole device is partitioned into a set of
0.79 0.21
in the source is AlSb/GaSb with an Al Ga Sb grading layers. The layers are numbered with l = 1,2,··· ,P for the
0.5 0.5
layer. The materials are chosen so, that the channel mate- layers in the source lead, l =P+1,P+2,··· ,Q−1for the
rial ((InAs) (AlSb) in general) has a higher conduction layers in the channel, and l=Q,Q+1,··· ,N for the layers
x 1−x
band edge, than in the InAs layer, while the source material in the drain lead.
(AlyGa1−ySb in general) has a lower valence band edge, We solve ballistic NEGF equations in the central channel
than in the GaSb layer. In addition, these materials have very (betweenlayerP andlayerQ),andthecurrentpassingthrough
close lattice constants around 6.1A˚ [19], hence no significant it I is computed by the transmission T weighted by the
PQ PQ
strain is induced. As shown in Refs. [11], [13], the band Fermi function difference:
offsets greatly enhance the electric field at the GaSb/InAs
q dk dE
tunneljunctionandcreatetworesonantstatesintheGaSband y
I = ×
InAs quantum wells, improving the tunnel probability at ON PQ hZ 2π Z 2π
state. The larger band gap and transport effective mass of the TPQ(ky,E)[f(E−EF,P)−f(E−EF,Q)], (1)
(InAs) (AlSb) channel, compared with the original InAs
x 1−x
channel, also reduce the ambipolar and the source-to-drain where q is the electron charge and h is the Planck constant.
tunneling leakage in the sub-threshold region. To maximize The integration is performed over the transverse momentum
the electric field at the tunneljunction,the band offsetsof the k and energy E.
y
3
Considering both electrons and holes, the charge density in
the central channel per orbital α in layer l can be calculated
as [22]:
dk dE
y
ρ = sgn(E−E )×
l,α Z 2π Z 2π N,l
{AL (k ,E)f[sgn(E−E )(E−E )]
l,α y N,l F,P
+AR (k ,E)f[sgn(E−E )(E−E )]}, (2)
l,α y N,l F,Q
where AL and AR are the diagonal components of the
l,α l,α
left- and right-connected spectral functions in the channel,
and sgn(E) is the sign function. E is the layer dependent
N,l
threshold(chargeneutralitylevel)definedasthemiddleofthe
band gap:
E =0.5(E +E ), (3)
N,l V,l C,l
where E and E are the layer-dependent valence and
V,l C,l
conduction band edge, respectively.
We solveDD equationsforholesin the sourceleadandfor Fig.3. Theself-consistent simulation flow.
electrons in the drain lead:
Jh =µhp∇E , (4) Toaccountforabroadeningduetoscatteringintheleads,a
F
small imaginary potential−iη is added to the diagonalof the
Je =µen∇E , (5)
F lead Hamiltonian [23]. The η is constant below the confined
where, µh and µe are the hole and electron mobilities, p and valence band edge and above the confined conduction band
n are the hole and electron densities, and E is the major edge, while it is exponentially decaying in the band gap:
F
carrier quasi-Fermi level. For simplicity we assume, that the
η , E <E
Fermilevelisconstantoverasinglelayer.Therefore,wehave h V,l
(tol=de1te,r2m,·in·e· ,aPs,eQt o,Qf la+ye1r,-·d·e·p,eNnd)e.ntquasi-Fermi levels EF,l ηl(E)=ηηheexxpp(cid:16)EE−VE,El0−CE,l(cid:17),, EECV,,ll+<EVE,l <<EEC<,l+2EEV,l
For the hole transport in the source lead, current conserva- e (cid:16) E0 (cid:17) 2 C,l
tion in the transport direction requires that ηe, EC,l <E, (10)
µhp ∇E −J ≈µhp EF,l−EF,l−1 − IPQ =0, whereηe andηh aretheelectronandholescatteringconstants
l F,l PQ l
∆x Tz (rates),anddecayingconstantE0istheUrbachparameter.The
for l =1,2,··· ,P, (6) η here is related to hole momentum relaxation time τ =
h h
¯h/2η and hole mobility µh = qτ /m∗, where m∗ is the
where the backward difference is used to discretize the dif- h h h h
hole effective mass; similar expressions relate η to electron
e
ferential operator ∇. ∆x and T are the layer thickness in
z momentum relaxation time τ and electron mobility µe.
e
the x and z direction, respectively. Similarly, for the electron
transport in the drain lead:
B. Program Flow
E −E I
µenl∇EF,l−JPQ ≈µenl F,l+1 F,l − PQ =0, Given an electric potential distribution of the device V (r),
∆x T
z the special RGF algorithm in Refs. [21], [23] is employed
for l=Q,Q+1,··· ,N, (7)
to compute efficiently the transmission T , the A in the
PQ l,α
where the forward difference is used to discretize the differ- leads, as well as the AL and AR in the channel. Here, the
l,α l,α
ential operator ∇. pl and nl are averaged over layer l. RGF calculations for different transverse momentum ky and
The hole and electron orbital resolved density in the leads energyE aredistributedoverdifferentCPUcores.Then,non-
is computed by integrating the diagonals of the lead spectral linearequations(6)and(7),togetherwithboundaryconditions
functionAl,α weightedbyeitherholeorelectronFermi-Dirac EF,0 = EF,L and EF,N+1 = EF,R (EF,L and EF,R are
function with local quasi-Fermi level E : the Fermi levels of the left and right contacts), are solved
F,l
iteratively using the Newton method to find E . Note that
F,l
dky dE 1 theJacobianmatrixissparseandcanbecalculatedanalytically
p = [−sgn(E−E )+1]×
l,α Z 2π Z 2π 2 N,l (derivative of the Fermi-Dirac function). With quasi-Fermi
(cid:0)
Al,α(ky,E)f(EF,l−E) , for l =1,2,··· ,P. (8) levelsEF,l determined,thechargedensityofthewholedevice
(cid:1) is updated using (2), (8) and (9), considering both electrons
and holes in the channel (see Eq. 2) and neglecting minority
dk dE 1
n = y [sgn(E−E )+1]× carriers in the leads. The non-linear Poisson equation is then
l,α Z 2π Z 2π(cid:0)2 N,l solvedtofindanewV (r).Theself-consistentsimulationflow
A (k ,E)f(E−E ) , for l=Q,Q+1,··· ,N. (9)
l,α y F,l is summarized in Fig. 3. For the device dimensions shown in
(cid:1)
4
103 800 103 0.7 deep OFF state
(a) (b) 0.6
µµI (A/m)DS111000−−131 246000000 ηηη26((=hh39((0ee))mmm))==eeeVVV 111000−−131 Energy [eV]−000000......0123451 E(EvaFs) Ec EFd (b) ηηη=h(0em)==26e((V39))mmeeVV
−5 −5 h(e)
10 0 10 −0.2
−0.1 0 0.1 0.2 0.3 0.4 20 40 60 80 100 0 10 20 30 10−10 10−8 10−6 10−4
VGS (V) SS (mV/dec) X [nm] Current (A/eV)
0.7 OFF state
Fig. 4. (a) IDS-VGS characteristics (at VDS = 0.3V) in both logarithmic 0.6
scale and linear scale. Different η are compared. The η are associated with 0.5
3µm. ηeV=co0rrceosrproenspdotnodsµhto=µ7=24∞cmf2o/r(bVot·hs)leaadnsd.µηeh==424m92ecVma2n/d(Vηe·s=) y [eV] 00..34 Ev Ec
fcoorrrtehseposnodurtcoeµanhd=dra2i4n1clemad2s/,(rVesp·esc)tivaneldy.µηeh==164m97ecVm2an/d(Vηe·s=) f9omrethVe nerg 00..12 EFs E η=0meV
sourceanddrainleads,respectively. (b)IDS-SSextractedfromthecurvesin E 0 Fd η =2(3)meV
(a). −0.1 (c) (d) ηh(e)=6(9)meV
h(e)
−0.2
0 10 20 30 10−10 10−8 10−6 10−4
Fig. 1 and for one bias point, it usually takes around one X [nm] Current (A/eV)
hour to get a converged solution on 96 CPU cores (6 dual 8- 0.4 ON state
Ev η=0meV
coreIntelXeon-E5CPUs),whichisroughlyfourtofivetimes η =2(3)meV
slower than ballistic simulations with quantum transmitting eV]0.3 ηhh((ee))=6(9)meV
boundary method [24]. gy [ EFs Ec
r
ne0.2
IV. SIMULATION RESULTS E
(e) (f)
We use ηh = 6meV for the holes at the GaSb source, 0.1
which translates to τ = 55fs, and µh = 241cm2/(V·s) 0 5 10 15 20 0 0.2 0.4 0.6 0.8 1
h X [nm] Current (A/eV)
assuming bulk heavy hole effective mass m∗ = 0.4m .
hh 0
This mobility value is comparable to the experimental hole
mobility of bulk GaSb at 5 × 1019cm−3 doping density, FViGgS. 5=. −B0a.n1dVdi(aagaranmdsb)(,VVDGSS==00.V3V()caannddcdu),rraenndt sVpGecStr=a (0k.y3V=(e0)anadt
which is around 250cm2/(V·s) [25]. We use η = 9meV f). Different η and corresponding µ are compared. In (a), (c), and (e), the
e
quasi-Fermilevels intheleads arealsosuperimposed.
for the electrons at the (InAs) (AlSb) drain, which
0.79 0.21
translates to τ = 36.6fs, and µe = 1497cm2/(V·s) us-
e
ing bulk electron effective mass m∗ = 0.043m , obtained
e 0
from TB calculation using VCA. This mobility value is becomes bigger, as the scattering rate increases. At the deep
comparable to the experimental electron mobility of bulk OFFstate (V =−0.1V),asshowninFig. 5(a)and(b),the
GS
In Ga As at 2 × 1019cm−3 doping density, which is directsource-to-draintunnelingdominates,and, therefore,the
0.53 0.47
1,422cm2/(V·s) [26]. We use the experimental mobility total current does not increase significantly. At the OFF state
value of In Ga As as a reference, because there is no (V = 0V), as shown in Fig. 5 (c) and (d), the scattering
0.53 0.47 GS
experimental mobility data for (InAs) (AlSb) to the leakage dominates, and, therefore, the total current increases
0.79 0.21
best of our knowledge, and the electron effective mass of significantly. At the ON state (V = 0.3V), as explained in
GS
(InAs) (AlSb) is very close to that of In Ga As Fig. 5 (e) and (f), the source serial resistance induces notable
0.79 0.21 0.53 0.47
which is 0.041m . Quantum confinement may change the potentialandquasi-Fermileveldropsinthesourcelead,which
0
carrier mobility and scattering rate, that needs to be assessed become more pronounced as the mobility decreases. The po-
in future studies. We set the Urbach parameter E to be the tentialdropreducesthetransmissionandthequasi-Fermilevel
0
thermal energy at room temperature, i.e., 26meV, which has drop reduces the Fermi conduction window, both decreasing
been justified and used in Ref. [27] for studying the band tail thetotalcurrentpassingthroughthecentralchannel.Note,that
effects in TFETs. attempttoreducethesourceserialresistancebyincreasingthe
The transfer characteristics for different scattering rates, dopingdensity would result in large source Fermidegeneracy
and, hence, mobilities, are simulated and plotted in Fig. 4 that in turn degrades the SS. The potential and quasi-Fermi
(a). The extracted SS is plotted in Fig. 4 (b). They show level drop in the drain lead are less pronounced (not shown
that both the SS and the turn-ON current change in the here)duetothesmallerdrainserialresistanceasaresultofthe
presence of scattering. With fixed I = 1nA/µm and at higher electron mobility. To quantify the most relevantmech-
OFF
V = 0.3V, the I is 460µA/µm for η = 0meV. It anism among these two, i.e., the scattering induced leakage
DD ON
reduces by 23% to 352µA/µm for η =2(3)meV and by and the serial resistance, for the I reduction, we simulated
h(e) ON
45%to254µA/µmforη =6(9)meV.Inthesubthreshold µ = ∞ (keeping η = 6(9)meV) and η = 0 (keeping
h(e) h(e)
region, as explained in Fig. 5 (a)-(d), the scattering in the µh(e) =241(1497)cm2/(V·s))separately,andfoundthatthe
leads induces an additionalpeak in the currentspectra, which I (at V = 0.3V and I = 1nA/µm) drops by 29%
ON DD OFF
5
0.6ηh=0meV 10 ηh=2meV 10 110023 (a) (b)
eV]0.5 1 1 m) 1001 Ballistic Scattering
gy [0.4 0.1 0.1 µA/ 1100−1 LLgg==1250nnmm
Ener0.3 (a) 0.01 (b) 0.01 µI (DS1100−−−432 m V/dec m V/dec Lg=30nm
10 60 60
0.20 5 10 15 20 0.0010 5 10 15 20 0.001 10−5
−0.1 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4
X [nm] X [nm]
V (V) V (V)
GS GS
0.6η =6meV 10 ηh=0m eV
h ηh=2meV Fig. 7. IDS-VGS (at VDS =0.3V) for different channel length Lg=15nm,
rgy [eV]00..45 01. 1 60mV/decηh=6meV 1Lw4git9=h72c0ηmnhm2,/=a(nVd6m·Lsge)V=)3f0o(nrηmeth.e=(as)ou9BrmacleeliVs(dti)rcaaisnni)mdlueµlaahdti.o=ns,2(b4)1cscmat2te/r(inVg·ssim)u(lµaetion=s
e
n
E0.3 0.01
E
(c) (d) Fs 0.7
0.20 5 X [1n0m]15 20 0.00110 −6Elect1ro0n−4 dens1i0ty−2 [a.u.]100 eV] 000...456Ev Ec (a) (b)
y [ 0.3
g 0.2 E
akFnyigd.=η6h.0,=lVoDg6aSmri=tehVm0i.c(3cV)s.c,aTalhenedLsVDoGuOrSSce=w(ci0thhVan,tnhfeeolr)suηrephseor=inma0npto(saset)da,teηbhaisn=dm2dairmakgeerdVamw(bita)ht, Ener 0.01 Fs EFd LLgg==1250nnmm
−0.1
solid (dashed) arrows. The scattering induced LDOS in the source notch is Lg=30nm
marked withwhite circles. (d)Theelectron spectral density at (x, y, z)= −0.20 10 20 30 40 50 10−10 10−8 10−6 10−4
(6.9, 0.46, 1.1)nm. X [nm] Current (A/eV)
Fig. 8. Band diagram (a) and current spectra (b) at ky =0, VDS =0.3V
due to the scattering-induced leakage and by 24% due to the aanlldcuVrGveSs,=ηh0=for6mcheaVnne(ηlele=ngt9hmLegV=)15annmd,µLhg==202n4m1,cman2d/L(Vg=·3s0)nm(µ.eF=or
serial resistance. Therefore, the two mechanisms have similar 1497cm2/(V·s))areusedforthesource(drain)lead.
effects on the device I /I ratio.
ON OFF
To explain the additional spectral current peak in the sub-
threshold region when scattering is present, we compare the SS was also obtained, which was ascribed to the suppression
LDOS at the OFF state for different scattering rates. For of density of states (DOS) in the notch and nonequilibrium
η = 0, essentially ballistic, as shown in Fig. 6 (a), the carrier distributionbelow the thermioniclimit in the notch. In
h
channel resonant state cannot connect to the source contact our simulation, the reduced DOS in the source notch solely
due to the lack of states in the source band gap. Therefore, accounts for the sub-60mV/dec SS.
the only leakage path is the direct source-to-drain tunneling We found that the channel length scaling behaviors are
leakage, peaked at the source resonant state energy level. very different when lead scattering is included, as compared
While for η = 2meV and η = 6meV, as shown in Fig. 6 in Fig. 7. For the ballistic case, the SS improves as the
h h
(b) and (c), the source valance band states, in particular the channel length (Lg) increases, which is easily understood
source resonant state, are broadened, introducing states into because longer Lg suppresses the source-to-drain tunneling
the source band gap and into the source potential notch. leakage. For the scattering case, when Lg is increased from
As a result, the channel resonant state is connected to the 15nm to 20nm, the SS is slightly improved, but when Lg is
source, giving rise to the additional leakage path. It is worth further increased to 30nm, the SS is not improved further.
mentioning that inelastic scattering mechanisms, such as the The explanations are shown in Fig. 8 for the scattering case,
optical phonon scattering and the electron-electron scattering, where the band diagrams and current spectra at different Lg
are captured here, because in our model the −iη is also are compared. As can be seen, there are two peaks in the
h
added to the band gap (through the exponentially decaying spectra, the lower one corresponds to direct source-to-drain
function)and to the source potential notch where the ballistic tunneling through the source resonant state and the upper
LDOS is zero. The electron spectral densities for the three onecorrespondsto the scattering inducedleakagethroughthe
cases, sampled in the source quantum well, are compared channel resonant state. As Lg increases, the direct tunneling
in Fig. 6 (d). It is shown, that the slope of the spectral leakage is gradually suppressed but the scattering induced
densityincreasesasthescatteringrateincreases,andwithbulk leakageremainsunchanged.AtLg=15nm,thedirecttunneling
scattering rate η =6meV the slope is still below 60mV/dec leakage is significant and, therefore, increasing Lg helps
h
thermal limit. This explains why the SS of the scattering I- reduce the total leakage. At Lg=20nm, the scattering induced
V curves, shown in Fig. 4 (b), is still less than 60mV/dec leakage already dominates and, consequently, increasing Lg
(for 10−3µA/µm < I < 10µA/µm). For 1-D broken-gap further does not help reduce the total leakage further.
DS
TFETs featuring a similar potential notch in the source [28], To benchmark the ultimate device performances, we com-
in the presence of electron-phonon scattering, sub-60mV/dec pare I of the 3HJ TFETs with the HJ TFETs at V =
ON DD
6
3 sourceanddrainleads.However,theelectrondensitydistribu-
10
102 (a) (b) tion, especially in the source lead, is non-uniform due to the
1
m) 100 Lg=15nm Lg=30nm quantum well structure. This implies that the scattering rate
µ 10 andcarriermobilityshouldbespatiallyvarying.Moreover,the
A/ 10−1
µI (DS111000−−−432 60 m V/dec 33HHHHJJJJ bs bscacaallatlilsttiestteirtciirncingg 60 m V/dec tsshhceaotutcelodrminapglsliorcaabtteeediesnbeacrnogdnysdtaainangdtrbammeolomawnednEtuLVmDOadnSedp,etahnbedoevsnecta.EttTeChri.enrGgefiorvaretene,
10−5 a more accurate approach would need a more sophisticated
−0.1 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4
V (V) V (V) density-dependentmobilitymodel,aswellasLDOSdependent
GS GS
scattering rate. Second, the channel is assumed to be ballistic
Fig. 9. Comparison ofIDS-VGS (at VDS =0.3V)between the3HJ TFET in this model. In practice, phonon assisted tunneling would
andtheHJTFETforchannellengthLg=15nm(a)andLg=30nm(b).Forall also occur in the channel to form a third leakage path. To
s(µcaett=erin1g49c7ucrmve2s,/η(Vh =·s)6)mareeVus(eηdefo=rt9hmeseoVu)rcaen(ddrµaihn)=lea2d4.1Tchme2t/hr(eVsh·osld) model such leakage, the ballistic NEGF approach in the
voltages arealladjusted forthesameIOFF=1nA/µm. channel needs to be upgraded to include electron-phonon
scattering in the usual SCBA way. We note, however,that the
scatteringintheleadsismuchstrongerthanthatinthechannel
0.3V and I = 1nA/µm, for a short channel length case
OFF due to the high carrier concentrations in the leads. This has
(Lg=15nm) and a long channel length case (Lg=30nm), as
been observed even when only the electron-phononscattering
shown in Fig. 9. At Lg=15nm, the scattering reduces I
ON wasincluded[14].Consequently,thepresentedmodelcaptures
of the 3HJ TFET from 460µA/µm to 254µA/µm, while it
the dominant scattering leakage path.
does not change I of the HJ TFET that much, which is
ON
13µA/µm. At Lg=30nm, the scattering reduces I of the
ON
3HJTFETfrom767µA/µmdownto280µA/µmandreduces VI. CONCLUSION
I of the HJ TFET from 87µA/µm down to 75µA/µm. Wehavediscussedthattheeffectofscatteringintheleadsis
ON
Inclusionofleadscatteringis, therefore,crucialforpredicting criticalfor3HJTFETs,and,atthesametime,isverychalleng-
the performances of the 3HJ devices. The relatively small ingto modelinthe NEGFapproach.A multiscale model,that
reduction of I of the HJ TFETs is due to the band solves quantum drift-diffusion equations in the thermalizing
ON
tail in the source. Note, that Ref. [27] predicted a stronger scattering leads and NEGF equations in the ballistic channel,
band tail effect using a much lager scattering rate. Overall, is developed to assess the realistic device performances. This
the 3HJ TFETs still possess much larger I than the HJ model captures the important scattering leakage current in
ON
TFETs under equal scattering conditions. We note that the thesub-thresholdregionandserialresistanceabovethreshold.
3HJ TFETs are more sensitive than the HJ TFETs to the gate Simulationresultsshow,that,althoughthescatteringdegrades
misalignment: simulations (for Lg=15nm) show that although the SS and reduces the turn-ON current, with aligned I
OFF
the 3HJ TFET can tolerate a small amount (1nm) of gate the 3HJ TFETs still operate with <60mV/dec SS and have
underlap with the source, a 1nm gate overlap with the source muchlargerI thantheHJTFETsforboth15nmand30nm
ON
leads to a 47%decrease in I and a 140%increase in I channel lengths. The 3HJ TFETs are thus very promising
ON OFF
for the 3HJ TFET, compared with a 18% decrease in I in future fast low-power computing applications. The model
ON
and a 99% increase in I for the HJ TFET. Therefore, developed in this work can be used to study the effects of
OFF
processes with gate self-alignment are likely necessary and carrierthermalizationandserialresistanceinavarietyofhigh-
will be subject of future experimental studies. Further, the current TFETs, especially those featuring a potential notch in
3HJ TFET performance is also sensitive to the variations the source [5], [30], [31].
of the quantum well lengths, since the quantum well length
critically determines the resonant energy level. Simulations
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