Monte-Carlo simulation of MOSFETs with band offsets in the source and drain

Available online at www.sciencedirect.com

Solid-State Electronics 52 (2008) 506–513 www.elsevier.com/locate/sse

Monte-Carlo simulation of MOSFETs with band offsets in the source and drain M. Braccioli a

a,b,c,*

, P. Palestri d, M. Mouis c, T. Poiroux b, M. Vinet b, G. Le Carval b, C. Fiegna a, E. Sangiorgi a, S. Deleonibus b

ARCES-DEIS, Cesena Laboratory, University of Bologna-IUNET, Via Venezia 52, 47023 Cesena, Italy b CEA LETI-MINATEC, 17 Rue des Martyrs, 38054 Grenoble Cedex 9, France c IMEP-LAHC, INPG/MINATEC, 3 Parvis Louis Neel, BP 257, 38016 Grenoble Cedex 1, France d DIEGM, University of Udine-IUNET, Via delle Scienze 208, 33100 Udine, Italy Available online 4 December 2007

The review of this paper was arranged by Youri V. Ponomarev

Abstract Full-band Monte-Carlo simulations of short channel double-gate SOI nMOSFETs were used to assess possible enhancement of drain current in devices featuring a conduction band offset between the source and the channel as those obtained using non-conventional source/drain materials. We found that the coupling between carrier transport and device electrostatics tends to balance the enhancement of charge injection provided by the band discontinuity, so that the largest contribution to the current enhancement given by alternative S/D materials is due to the strain that they induce in the channel. Ó 2007 Elsevier Ltd. All rights reserved.

1. Introduction Technology options such as silicon–carbon source/drain (S/D) regions [1,2] are used to produce uniaxial tensile stress in the Si or SiGe channel [3] of nanoscale nMOSFETs. Hole transport is enhanced in pMOSFETs by the adoption of SiGe S/D (embedded SiGe) [4] introducing compressive stress in the channel. Beside their influence on the channel material properties, these options produce conduction (valence) band offsets that influence carrier injection into the channel [5]. In particular, source and drain regions with smaller electron affinity (and thus larger electron band gap than in the channel) are expected to provide a larger ONcurrent thanks to enhanced injection velocity [6,7]. In this work, we use full-band Monte-Carlo simulations in order to study the effect of conduction band offsets *

Corresponding author. Address: ARCES-DEIS, Cesena Laboratory, University of Bologna-IUNET, Via Venezia 52, 47023 Cesena, Italy. E-mail address: [email protected] (M. Braccioli). 0038-1101/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.sse.2007.10.038

(CBO) on injection velocity and back-scattering coefficient in n-type SOI MOSFETs, and to provide a new insight into the impact of alternative S/D regions on the device performance. Many cases are considered: a channel affinity larger than the S/D one and vice versa, and abrupt as well as graded hetero-junctions (HJ). We show that the coupling between electrostatic and carrier transport washes out most of the possible improvements that can be expected due to S/D regions with larger gaps than the channel one. The paper proceeds as follows. The simulation code is described in Section 2; the model verification is discussed in Section 3; the simulated devices are presented in Section 4, and results for double-gate SOI nMOSFETs are shown in Section 5. Finally, conclusions are drawn in Section 6. 2. Simulation approach The simulations have been performed using the fullband self-consistent Monte-Carlo (MC) simulator that has been described in [8,9]. The code treats electrons in

M. Braccioli et al. / Solid-State Electronics 52 (2008) 506–513

the device as a free-carrier gas and implements the coupling between the Monte-Carlo transport and the Poisson equation through a linear coupling scheme [10,11]. Corrections to the potential, based on the effective potential approach [12,13], can be applied to mimic the effects of carrier quantization, although they have not been used in this work. A subset of simulations has been repeated introducing quantum-corrections: the drain current is reduced due to the lower inversion charge in the channel, but the changes in current are the same as in the simulations without quantum-corrections. Acoustic and optical phonon scattering, as well as ionized impurities, are included; the surface roughness is treated as an additional scattering mechanism, whose scattering rate is a function of the vertical effective field [8]. The parameters of these scattering mechanisms have been adjusted in order to reproduce the universal mobility curves in unstrained silicon inversion layers [14]. When the composition of the source and drain is changed, the mismatch produces strain in the channel that changes its transport properties. In this work, we focus on the effects of the band gap discontinuity itself on the device performance, i.e., on the effects of the conduction band offset on the injection velocity, inversion charge in the channel and electrostatic potential profile, without considering the fact that the discontinuity is obtained by using materials with transport properties different than those of pure Silicon. In order to separate these effects from the ones produced by strain, we assume the transport properties of pure unstrained silicon within the whole device. In order to handle hetero-junctions, appropriate models are needed to describe a carrier crossing them. We have considered two cases: graded and abrupt HJ. In the first case, the conduction band (CB) profile varies gradually from the source to the channel; the presence of the HJ is treated by using a quasi-field, added during the electron free-flight to the electric field determined by the Poisson equation. In other words, the carriers are moved based on the conduction band edge, instead of using only the electrostatic potential (the driving force is thus F = qdEC/dx) [15]. When considering abrupt HJs, the CB profile has a stepwise shape. This case is more complicated and requires different procedures depending on the energy of the carriers involved. Let us start by assuming small CBOs and small carrier energy (below 75 meV). At such small energies we can use parabolic bands, so that it is possible to separate the total carrier kinetic energy into components associated with the different transport directions. Assuming that a CBO occurs along the x direction, three possible cases exist (see Fig. 1): (a) the electron enters a region with lower affinity and its kinetic energy EL ¼  h2 k 2xL =ð2mx Þ in the x direction is larger than DE; in this case the particle can enter in the lower affinity region, and the kinetic energy (x direction) decreases ffi by DE, i.e., we set qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k xR ¼

k 2xL  2mx DE= h2 ; ky and kz, that is the com-

(a)

507 (c)

ER y

(b)

ΔE

ΔE x

EL

z

Fig. 1. Possible cases of electrons crossing an abrupt conduction band discontinuity.

ponents in the plane normal to the direction of the motion, are not modified; (b) the electron enters a region with lower affinity, but EL < DE; in this case the carrier can not overcome the barrier, therefore it is reflected (kx is inverted); the reflection is perfectly elastic; (c) the electron enters a region with higher affinity; in this case it can cross the barrier regardless of its energy, and the energy component in the x direction increases qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi by DE, i.e., k xR ¼ k 2xL þ 2mx DE=h2 . For higher energies, detailed full-band effects are considered as follows: the total kinetic energy is increased/ decreased by DE (depending on the different electron affinities and on the direction of the motion, as described above); the wavevector on the plane normal to the motion is conserved; kxR is found by searching states in the fullband structure having kyR = kyL, kzR = kzL, total energy ER = EL ± DE and conserving the direction of the group velocity of the incoming electron (vG). All possible states in the first Brillouin zone (FBZ) are considered. Due to the symmetry of the FBZ, sets consisting of either two or four values of kxR are found. Only the ones with the direction of the vG equal to the one of the incoming electron are considered, and one of them is selected randomly. Different approaches for this latter selection have been tried, but the choice of selection methodology is found to be inconsequential. Finally, when such states do not exist (e.g., case (b) in Fig. 1) the electron is reflected (elastic process). At very large energies the CB features many branches making the selection of the final state extremely complicated. For this reason, we relax the conservation of ky and kz at energies above 500 meV (only a negligible number of electrons is concerned): the total kinetic energy is increased/decreased by DE, and the ~ k-state is randomly selected, with the only constraint of conserving the direction of the group velocity of the incoming electron. Tunneling through the energy barrier that arises in presence of hetero-structures [16] is neglected, thus we consider the worst case in terms of the provided current. 3. Model verification In order to validate our model for HJs, we have carried out simulations of a simplified, unidimensional template structure, featuring uniform doping N = 1019 cm3 and

M. Braccioli et al. / Solid-State Electronics 52 (2008) 506–513

10

nR /nL

10 10 10 10

EC [meV]

50

0

ΔV1 –50 4.0 3.0

–3

2.0

exp(ΔE/kBT) abrupt graded (steps) graded (quasi-field)

4

19

–3

N=10 cm 1.0 0.0 0

20

40

60

x [nm] Fig. 3. Electron concentration and conduction band profile along a structure featuring uniform doping and two abrupt HJs of amplitude DE and DE (i.e., the affinity in the center is larger than at the sides). The simulation is self-consistent.

300

ΔV=ΔE abrupt graded (steps) graded (quasi–field)

6

5

ΔE

ΔV2

200

ΔV [mV]

10

100

19

two symmetric CBOs with the same DE (the affinity in the center is DE higher than at the two ends). First, we have run non-self-consistent simulations with a null electric field and neglecting the Pauli exclusion principle. In the absence of any electric field, at the two sides of the CBO on the left of the structure we should have carriers concentrations nL (low affinity) and nR (high affinity) verifying the equation nR/nL = exp(DE/kBT), where kB is the Boltzmann constant and T the lattice temperature. When the simulation starts, electrons are uniformly distributed inside the structure. During the simulation they diffuse and interact with the CBO. When the simulation stops we collect nL and nR. Results are shown in Fig. 2, considering abrupt and graded discontinuities. The latter have been implemented either as a series of small abrupt HJs (four steps for each discontinuity) or as a quasi-field. In all cases nR/nL follows what is expected from the theory. On the other hand, when performing a self-consistent simulation, the electron concentration tends to become equal to the doping at all points. A depletion layer forms close to each CBO, producing an electrostatic potential drop that compensates the CBO. Typical EC and carrier profiles are reported in Fig. 3.

n [10 cm ]

508

3

100 2

1

0 10

0

0

0

50

100

150

200

250

50

150

200

250

300

ΔE [mV]

300

ΔE [mV]

100

Fig. 4. Comparison between the built-in voltage DV = DV1 + DV2 (see top graph in Fig. 3) and the CB offset DE. Same structure of Fig. 3, but featuring abrupt as well as graded HJs.

100

Fig. 4 shows that the built-in voltage produced by the depletion regions exactly compensates the DE of the CBO.

10

18

–3

n [10 cm ]

nR

1

4. Simulated devices

nL

nL 19

–3

N=10 cm 0

0

20

40

60

x [nm] Fig. 2. Plot (a): ratio between the electron concentration at the right and left sides of a CBO with height DE (affinity in the right side of the structure is higher than in the left side). Plot (b): carrier concentration profile for the case DE = 100 meV, abrupt HJ.

We have considered as reference device a double-gate SOI nMOSFET. The main device characteristics are (see Fig. 5): gate length LG = 34 nm, TSi = 10 nm, abrupt junctions, pure SiO2 dielectric with tox = 1 nm. The gate workfunction /G = 4.346 eV and the channel doping Nch = 1016 cm3 have been selected in order to have IOFF = 100 nA/lm and a small DIBL = 40 mV/V in the absence of HJs. The threshold voltage is VT = 0.2 V. The supply

M. Braccioli et al. / Solid-State Electronics 52 (2008) 506–513 x y Ld=Ls=50 nm

Lg= 34 nm channel = 32 nm

Nd=1e+20

Na=1e+16

Nd=1e+20

Tsi=10 nm

Ec ΔE Lgrad

509

the VS, and vx(xinj) is the carrier velocity, averaged over the vertical direction y, at the same point. However, also þ the average velocity vþ x of the I inj flux is relevant, since it is the velocity of the injected carriers. It can be demonþ 1r strated [9,18] that vx ðxinj Þ  vþ inj ð1þrÞ, therefore r and vinj are two quantities that are important in order to understand the magnitude of the average velocity vx at the VS. Thus we will focus on the effects of the CBO on NINV, vþ x and r at the virtual source.

Abrupt HJ Graded HJ

5.1. Abrupt hetero-junction

voltage is VDD = 1 V. The overlap length between the gate and the source/drain regions is set to 1 nm for all the considered devices. Both abrupt and graded HJ will be considered. In all cases we have assumed that the same offset is present at the source and at the drain. The positions of these discontinuities are symmetric with respect to the center of the channel (x = 0). For devices featuring HJs, /G has been modified in order to keep the same IOFF. This task has been performed by using drift–diffusion simulations [17]. If /G is kept constant, the introduction of the HJ shifts the IDS (VGS) characteristic. This shift strongly depends on D E and only weakly on the position of the HJ. When /G is modified in order to keep IOFF constant, the threshold voltage VT remains the same, since the subthreshold slope remains constant as well. We have also verified that the drain-induced barrier lowering (DIBL) remains constant, around 40 mV/V, in all the considered structures. 5. Results Before showing the results, we briefly review the approach (based on the theory in [18–20]) used here to understand and explain the obtained drain current improvements. In this approach, the drain current can be understood in terms of current injected from the source into the channel I þ inj , and current back-scattered to the source I  , both evaluated at the abscissa xinj, that is the inj position of the maximum of the potential energy, also referred as virtual source (VS). Positive and negative fluxes are related by means of a back-scattering coefficient, þ r ¼ I inj =I inj . The theory in [18–20] assumes that the back-scattering coefficient r is determined by the electric field profile near the VS: approximately, scattering contributes to I  inj only by events taking place within the distance LkT from the VS that it takes for a potential drop equal to kBT/q, where kB is the Boltzmann constant and T the lattice temperature. The drain current can be written as IDS = qNINV (xinj)vx(xinj) where NINV(xinj) is the inversion charge at

Fig. 6 shows the ON-current (VGS = VDS = VDD) as a function of DE. The source-to-channel CBO is placed at the abscissa xinj corresponding to the position of the VS of the reference device (DE = 0), i.e., the MOSFET without any discontinuity. In this figure, DE > 0 (DE < 0) represent MOSFETs featuring a larger (smaller) affinity in the channel than in the S/D. In all cases the introduction of the CBO reduces ION. The result is not peculiar to the MC simulations and it is predicted also by DD simulations [17]. Differences between DD and MC are small for positive DE. In the case of negative DE the disagreement is large, mostly because the current is mainly controlled by thermionic emission above the CBO of electrons featuring large energies in the source and drain (minimum kinetic energy equal to DE) and at such large energies the density-of-states of the full-band MC significantly differs from the DD one. In Fig. 7, we have chosen two DE values (50 and 100 mV) and we moved the position of the discontinuity, starting from the gate edge (x = 17 nm) and gradually moving inside the channel. The further current reduction with respect to the reference case, when the CBO is moved, is evident. In order to understand the origin of the degradation of drain current induced by the CBO, we have analyzed the profile along the channel of some relevant quantities. An example of results is reported in Fig. 8 for DE = 100 mV.

2.2

ION [mA/μm]

Fig. 5. Sketch of the simulated device. The CBO is positive (i.e., DE > 0) when the affinity in the channel is higher than in the S/D regions, as when using Si1xCx S/D. When using graded HJs, the grading starts on the gate edges.

1.7

DD DD (ref.) MC MC(ref.)

1.2

0.7

–200

–100

0

100

200

ΔE [mV] Fig. 6. Simulated drain current for VGS = VDS = VDD in devices featuring abrupt CBOs with different DE. Results obtained with the MC simulator of this work are compared with DD simulations [17]. The discontinuities are place at x = 15.2 nm (position of the VS in the reference device) and x = 15.2 nm. The horizontal lines are the currents in the reference device. The current includes both front and back channels.

510

M. Braccioli et al. / Solid-State Electronics 52 (2008) 506–513 Table 1 Values of the inversion charge NINV, the average velocity vx, the positive velocity vþ x and the back-scattering coefficient r at the VS, for the two cases presented in Fig. 8

2.5

ION [mA/μm]

2.4 2.3 2.2

ref. ΔE=100 mV ΔE=50 mV

2.1 2 –17

–16

–15

–14

XHJ [nm] Fig. 7. Simulated drain current (including both front and back channels) for VGS = VDS = VDD in devices featuring abrupt CBOs for different positions of the CBO at the source (in all the cases the one at the drain is symmetric with respect to the center of the channel, x = 0). DE = 50 mV, 100 mV.

EC [V]

–0.25

vel. 7 [10 cm/s]

2.0 +

vx 1.0

vx 0.0 5.0

NINV 13 –2 [10 cm ]

vx (107 cm/s)

7 vþ x (10 cm/s)

r

Ref DE = 100 meV

3.3 2.3

0.5 0.66

1.20 1.17

0.4 0.24

device featuring the CBOs (see again the middle plot). However, the back-scattered electrons hitting the barrier create an accumulation of charge next to the discontinuity (right side), that tend to prevent further injection from the source. As a result the charge at the VS is lower in the device with DE 5 0 than in the reference (compare the NINV in Table 1). This effect overcompensates the enhancement in average velocity, thus reducing ION.

We now consider linearly graded HJs. As explained in Section 2, in this case the HJ is treated as an additional electric field, added during the free-flight to the field given by the Poisson equation. In the following we will assume an higher affinity in the channel than in the S/D region (i.e., the quasi-field accelerates the electrons entering the channel) and a symmetric structure (i.e., even at the drain side we have the same discontinuity, see Fig. 5). In this first set of simulations, the graded region begins at the gate edge (i.e., at x = 17 nm). It is useful to remember that the gate work-function has been modified in order to have the same IOFF = 100 nA/ lm, similarly to the case of abrupt HJ. Fig. 9 shows ION as a function of the extension Lgrad of the HJ, for different DE. With respect to the abrupt case shown in the previous section, we now see a slight current

–0.15

4.0

2.0

NINV (1013 cm2)

5.2. Graded hetero-junction

–0.05

3.0

@VS

ref. ΔE=100 mV

1.0 –20

–15

x [nm]

2.5

Fig. 8. Conduction band profile averaged over y (top), velocity profiles averaged over y (middle) and inversion charge density (bottom, including both front and back channels) as a function of the position along the channel. The reference device (solid line) is compared to a case with abrupt HJs at x = ±15.2 nm (dashed line). VGS = VDS = VDD.

ION [mA/μm]

The CBO at the source side is placed at the VS of the reference case (see top graph). The discontinuity acts as a launcher for the electrons injected into the channel, as demonstrated by the profile of vþ x . This latter quantity (middle graph) is much larger than in the reference case, in the channel region beyond the VS. However, vþ x is essentially the same at the position x = 15.2 nm (the VS in both cases). The device with the CBO features a lower back-scattering (r in Table 1), since the electrons moving with negative velocity see an energy barrier, and therefore, only a fraction of them can go back to the source. As a result the average velocity vx before the CBO is larger in the

2.4

ref. ΔE=100mV ΔE=50 mV

2.3

2.2 0

1

2

3

4

5

6

7

8

Lgrad. [nm] Fig. 9. ON-current (front and back channels) in devices featuring graded HJs (see Fig. 5) as a function of the extension of the graded region. Dashed line: reference device (no HJ).

M. Braccioli et al. / Solid-State Electronics 52 (2008) 506–513

to an accumulation of charge at the end of the graded region (lower graph), the electric field after the VS is slightly lower in the graded case, compensating the advantages related to the presence of the quasi-field at the VS, since the average velocities are essentially the same in the two cases. In particular (see middle plot) we have a slightly higher vþ x (due to the quasi-field at the VS), but the same vx, since back-scattering is enhanced by the lower field next to the VS (i.e., LkT is larger [9,18]). In the second set of simulations, we vary the relative position of the graded region with respect to the virtual source (see Fig. 11), considering three possible cases: the VS can either correspond to the end, the middle or the beginning of the graded region. As previously, higher electron affinity in the channel than in the S/D regions is

improvement in particular when the region with grading includes the position of the VS in the reference case (that is xinj = 15.2 nm, requiring Lgrad P 2 nm, since the grading starts at the gate edge, 17 nm). The improvement is however modest and decreases for large Lgrad as the quasi-field is reduced. As reported in the previous section, we can understand this behavior by plotting some internal quantities, see Fig. 10. The VS has essentially the same position in the reference and in the graded devices (top graph). However, due

–0.13

EC [V]

511

–0.15

graded 2.5

–0.17

+

vx 1

2.4

vx

ION [mA/μm]

vel. 7 [10 cm/s]

2

0

NINV 13 —2 [10 cm ]

5

ref. ΔE=100 mV

3

2.3

end middle

1 –20

beginning –15

–10 2.2

x [nm]

0

Fig. 10. Conduction band profile averaged over y (top), velocity profiles averaged over y (middle) and inversion charge density (bottom, including both front and back channels) as a function of the position along the channel. The reference device (solid line) is compared to a case with graded HJs from 17 to 14 nm and from 14 to 17 nm, corresponding to Lgrad = 3 nm (dashed line). VGS = VDS = VDD.

1

2

3

4

5

6

Lgrad [nm] Fig. 12. Simulated drain current for VGS = VDS = VDD as a function of the extension of the graded region. The three different situations, presented in Fig. 11, are considered. DE = 100 meV. Dashed line: reference device (no HJ). The current includes both front and back channels.

Virtual Source x=–15.2 nm

end

middle

ΔΕ

beginning

Ec

Lgrad

Fig. 11. Sketch of the different positions of the graded region with respect to the virtual source (VS) of the reference transistor, to be considered in Figs. 12–15 and Table 2.

512

M. Braccioli et al. / Solid-State Electronics 52 (2008) 506–513 –0.12

EC [V]

EC [V]

–0.12

–0.15

–0.15

graded

graded

–0.18

–0.18 2

V

+ x

+

Vx

vel. 7 [10 cm/s]

vel. 7 [10 cm/s]

2

1

Vx

1

Vx 0

ref.

5

end 3

1 –20

–15

ref.

5

NINV 13 –2 [10 cm ]

NINV 13 –2 [10 cm ]

0

middle 3

1 –20

–10

x [nm]

–15

–10

x [nm]

Fig. 13. Conduction band profile averaged over y (top), velocity profiles averaged over y (middle) and inversion charge density (bottom, including both front and back channels) as a function of the position along the channel. The reference device (solid line) is compared with the device where the VS corresponds to the end of the graded region (see Fig. 11). Lgrad = 3 nm, DE = 100 meV.

assumed, and a symmetric structure is considered. Fig. 12 shows ION as a function of Lgrad for DE = 100 meV. Even in these situations, as in Fig. 9, the current improvement is modest, and it decreases rapidly when the graded region is moved towards the channel. When the virtual source is at the end of the graded region (see Fig. 13), the position of the VS is slightly moved towards the channel (xinj = 14.5 nm instead of xinj = 15.2 nm). vþ x ðxinj Þ, r and thus vx(xinj) are essentially the same (see Table 2). On the other hand, the inversion charge at the VS is larger than in the reference case, and this effect is responsible for the small current improvement in Fig. 12. When the VS is in the middle of the graded region (see Fig. 14), the position of the VS does not change (xinj = 15.2 nm) with respect to the reference, as well as the inversion charge at the injection point (see Table 2). Even the conduction band profiles are identical, as well

Fig. 14. Same as Fig. 13 but the reference device (solid line) is compared with the device where the VS corresponds to the middle of the graded region (see Fig. 11). Lgrad = 3 nm, DE = 100 meV.

as the back-scattering coefficient r. On the other hand, the positive velocity vþ x is slightly larger than in the reference device, and it is responsible for the small current improvement. Finally, when the graded region starts at the VS (see Fig. 15), it acts as a launcher for electrons. Similarly to the latter case, the position of the VS does not change with respect to the reference device, but now the conduction band profile is steeper. The kT-layer is shorter, and the back-scattering coefficient decreases with respect to the previous devices (see Table 2), i.e., the graded region acts as a barrier for the back-scattered carriers. However, the inversion charge at the VS is now lower than in the reference case (see Fig. 15 and Table 2), so most of advantages due to the higher velocity are lost. This behavior is similar to the one considered for abrupt hetero-junctions (see Section 5.1), but now the effects are ‘‘spread’’ over the graded region. In summary, there is an evident trade-off between the inversion charge at the VS and the injection velocity, tradeoff that is detrimental and limits the current improvement.

Table 2 Values of the inversion charge NINV, the average velocity vx, the positive velocity vþ x and the back-scattering coefficient r at the VS, for the four cases presented in Figs. 13–15 @VS

NINV (1013 cm2)

vx (107 cm/s)

7 vþ x (10 cm/s)

r

Ref DE = 100 meV, Lgrad = 3 nm, end DE = 100 meV, Lgrad = 3 nm, middle DE = 100 meV, Lgrad = 3 nm, beginning

3.3 3.6 3.3 2.4

0.5 0.49 0.53 0.7

1.20 1.26 1.25 1.25

0.4 0.43 0.4 0.28

M. Braccioli et al. / Solid-State Electronics 52 (2008) 506–513

References

EC [V]

–0.12

–0.15

–0.18

vel. 7 [10 cm/s]

2

Vx

+

1

Vx

NINV 13 –2 [10 cm ]

0

5

3

graded

ref. beginning

1 –20

513

–15

–10

x [nm] Fig. 15. Same as Figs. 13 and 14 but the reference device (solid line) is compared with the device where the VS corresponds to the beginning of the graded region (see Fig. 11). Lgrad = 3 nm, DE = 100 meV.

6. Conclusions We performed Monte-Carlo simulations of nMOSFETs featuring hetero-junctions, as those obtained using alternative materials for the S/D regions. Although abrupt CBOs between the source and the channel are expected to enhance the injection velocity and thus the current, simulations of nanoscale DG SOI transistors point out that carrier accumulation next to the CBO influences the device electrostatics reducing the charge available for transport, overcompensating the velocity improvement. Due to the same mechanism, only small current improvement are obtained for graded HJs. It should be noticed that these comparisons were made at given IOFF = 100 nA/lm, i.e., at given gate overdrive VGS  VT. We have focused on the effect of the band offsets alone. In many practical cases, the source/drain material induces strain in the channel, that is the main responsible of the ION improvement, whereas, according to our simulations, the effect to the offset alone seems to be modest. Acknowledgements Work partially funded by the UE: SINANO Network of Excellence (FP6, IST-1-506844-NE), PULLNANO project (FP6, IST-026828-IP) and Marie-Curie action EDITH (MEST-CT-2004-504195).

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