Performance Projection of Mono and Multi-Layer

Performance Projection of Mono and Multi-Layer Silicane FETs in the Ballistic Limit Tapas Dutta∗ , B. S. Syamalaraju∗ , Somnath Bhowmick† , Amit Agarwal‡ , and Yogesh Singh Chauhan∗ ∗ Department

of Electrical Engineering, ‡ Department of Materials Science and Engineering, † Department of Physics, Indian Institute of Technology Kanpur, Kanpur, India 208016 Email: [email protected]

Abstract—Amongst different two-dimensional semiconductor materials, silicene is fast emerging as a promising candidate for use as the channel material in field effect transistors. In this work, we first perform ab-initio calculations within density functional theory to obtain the band structure of mono- and multi-layered hydrogenated silicene, commonly known as silicane, in different stacking configurations. We then investigate the ultimate device performance of silicane FETs in the ballistic limit using the semiclassical “top of the barrier” transport model for different number of layers. Keywords—2D materials, DFT, band structure, top of the barrier, ballistic transport, silicene

I.

Gate

tox

SiO2

S

D

tch

SiO2

Gate

Lg

Fig. 1. Double gate MOSFET structure with silicane channel. Simulation settings: gate oxide: SiO2 with tox = 0.5 nm, supply voltage, VDD = 0.6 V. Perfect gate control on the channel has been assumed.

I NTRODUCTION

Starting with the demonstration of mechanical exfoliation of single layer graphene sheets [1], two-dimensional materials have been in the limelight for the last decade due to their unique properties. In particular, they have attracted attention of the semiconductor industry for their possible applications as the channel material for ultra-scaled transistors [2], as the scaling of conventional bulk semiconductors to few nanometers is very difficult. Atomically thin single or few-layered 2D materials offer the ultimate gate control and hence are inherently immune to short channel effects. Although graphene has high carrier mobility, its utility as the channel material for logic devices is severely limited due to its gapless nature [3]. This led to a spurt in the activities looking for differnt graphene derivatives and alternative materials having similar 2D structure and properties comparable to those of graphene, but without the stumbling block of zero bandgap at the Dirac point. However, most 2D materials like transition metal di-chalcogenides (TMDs) [4] (e.g. MoS2 , MoSe2 , WS2 , WSe2 ), different 2D allotropes of phosphorus [5] etc., although promising, have to overcome serious challenges with regard to compatibility with the existing silicon based CMOS platform. The possibility of existence of a graphene like material, consisting of silicon atoms instead of carbon, with buckled honeycomb lattice structure, was theoretically predicted way back in 1994 using first-principles calculations [6], and nowadays is more commonly known as silicene. More recently, epitaxial growth of silicene on metallic substrate was experimentally demonstrated [7], [8], and the first field effect transistors made up of silicene channel operating at room temperature was reported last year [9]. This has boosted the research on silicene FETs, especially driven by the prospects of seamless integration with silicon process technology. Silicene has been reported to have either zero [10] or very small [9] bandgap. Therefore various techniques have been explored to enhance or tune the bandgap, out of which

(a)

(b)

Fig. 2. (a) Band structure of monolayer silicane. The Fermi level has been set to zero. (b) Energy contours in the First Brillouin zone.

chemical functionalization e.g. hydrogenation is quite suitable for silicene due to its high reactivity and large surface area [11]. An additional advantage of hydrogenation is the removal of mid-gap states due to saturation of dangling bonds, thereby ensuring a high carrier mobility in the channel. Another way to engineer material properties is to stack multiple layers of silicene. After computational studies predicted multi-layered version of silicene [12], the existence of multilayer silicene was demonstrated [13], and was further conclusively established in a recent experimental study [14]. Although the ballistic transport performance of monolayer silicane FETs has already been reported [15], the performance evaluation of transistor with multi-layer silicane channels is still missing. In this work, for the first time, we investigate the suitability of multi-layer silicane as a channel material for MOSFETs. Fig. 1 shows the device structure considered in this work. We first calculate the electronic structure using abinitio density functional theory (DFT) calculations for single and multi-layered silicane in two different stacking arrangements. Next, using the bandstructure data with the top-of-thebarrier transport model, we explore the ballistic performance of silicane based FETs.

6

4 4

2

E n e rg y (e V )

0

E n e rg y (e V )

2 0

-2 -4

(a)

(b)

-2 -4 -6

-6

Γ

-8

Γ

M K

Γ M

(b)

2 2 0

E n e rg y (e V )

0

E n e rg y (e V )

Γ K

(a)

-2

-2 -4

-4

(c)

(d)

-6 -6

Fig. 3. (a, b) Top and side views of AA stacking. (c, d) Top and side views of ABC stacking.

Γ

-8

Γ

M K

Γ M

K

(c)

Γ

(d)

Fig. 4. Band structures of (a) two-layer (b) four-layer (c) six-layer and (d) eight-layer silicane with AA stacking.

II.

A B - INITIO BANDSTRUCTURE C ALCULATIONS

A. Computational Details 4

2 2

E n e rg y (e V )

E n e rg y (e V )

0 0

-2

-2

-4

-4 -6

Γ M

K

-6

Γ

Γ M

(b)

2

2 0

E n e rg y (e V )

0 -2 -4 -6 -8

Γ K

(a)

E n e rg y (e V )

Electronic properties of hydrogenated silicene ranging from 1 to 8 layers with two different stacking configurations are carried out using DFT calculations with the plane wave based Q UANTUM ESPRESSO [16] code. The generalized gradient approximation (GGA) parametrized by Perdew-BurkeErnzerhof (PBE) is used as the exchange correlation functional with ultrasoft pseudopotentials. Kinetic energy cutoff for wave functions and charge density are 50 Ry and 500 Ry respectively. The structures are optimized until the forces on ˚ Monkhorst-Pack mesh each atom are less than 0.001 eV/A. of 20×20×1 K-points was used to sample the Brillouin zone for the self-consistent calculations. For generating the 2D E − k bandstructure data, we used a finer rectangular grid of 100×100 K-points. Both single and multi-layer silicane are ˚ of vacuum region on the both sides to provided with 20 A avoid periodic interactions.

-2 -4 -6

Γ M

K

(c)

Γ

-8

Γ M

K

Γ

(d)

Fig. 5. Band structures of (a) two-layer (b) four-layer (c) six-layer and (d) eight-layer silicane with ABC stacking.

B. Bandstructure of Monolayer Silicane Monolayer silicane is created by hydrogenation of single layer silicene on both sides. The relaxed structure has the lat˚ with a buckling distance (∆) of 0.53 A ˚ tice constant of 3.84 A ˚ and 1.50 and intra layer Si-Si and Si-H bond lengths of 2.31 A ˚ respectively, all in close agreement with published literature A [17], [18]. Fig. 2 shows the bandstructure of monolayer silicane plotted along the Γ-M-K-Γ symmetry points. Silicane exhibits indirect band gap of 2.28 eV with conduction band minimum at the M symmetry point and valence band maximum at the Γ point, which is again in good agreement with previous works [17], [19]. The 2D E −k contour plot in the first Brillouin zone is shown in Fig. 2(b). The Γ valley is fairly isotropic while there are other six equivalent valleys with highly anisotropic dispersion.

C. Stacking Order Dependent Bandstructure of Multi-layer Silicane Hydrogenated few layer silicene can be formed in different stacking modes, e.g. AA, ABC, ABAB and so on [18], [20]– [22]. Among these, the AA and ABC configurations are the primary ones because the other sequences can be generated as a combination of these two [20], and also because the structural stability of other sequences lie between those of the AA and ABC stacking modes. Fig. 3 shows the top and side views of 4-layered silicane. Note that for bilayer there we have “AB” stacking instead of “ABC” stacking which applies to three or more layers. The formation energy of the AA stacked structures is found to be greater than that of the ABC stacked structures, in agreement with previously reported calculations

-3 G

M K

(a)

G

-2 -3

K M

G

(b)

0

2

S ILICANE FET T RANSPORT C HARACTERISTICS

We employ the semiclassical “top of the barrier” (ToB) transport model [26] for evaluating the current-voltage characteristics of double-gate MOSFETs with silicane channels shown in Fig. 1. Due to its computational efficiency, the ToB model is suitable for rapid projection of the ultimate performance of emerging devices in the ballistic limit i.e. assuming a transmission of unity for all electrons above the top of the barrier. Note that this model doesn’t capture bandto-band or intra-band source-to-drain tunneling, and hence it is applicable only when the gate length and bandgap are not too small. We assume a well-designed MOSFET where the validity of the model is assured [27]. We use the 2D E(kx , ky ) bandstructure information in the first Brillouin zone and solve for the carrier density and the potential at the top of the barrier self-consistently as a function of the applied gate and drain biases. The k-states with positive velocity are filled by the Fermi function of the source, while the k-states with negative velocity are filled by Fermi function of the drain. The ballistic current is calculated by integrating the product of

6

8

4 .5 A B S ta c k in g 4 .0 3 .5 M o n o la y e r 3 .0 A B C S ta c k in g 2 .5 2 .0 1 .5 A A S ta c k in g 1 .0 0 2 4 6 8

N u m b e r o f L a y e rs

(a)

(b) 2 .4

B a n d g a p

(e V )

III.

)

4

N u m b e r o f L a y e rs

Fig. 6. Top valence bands and bottom conduction bands for multi-layer silicane in (a) AA stacking, and (b) AB(C) stacking configurations.

[20]. It implies that silicane with ABC stacking is a more stable structure than the AA stacking. This is also reflected in the shorter inter layer Si-Si bond length for ABC stacking ˚ compared to that for AA stacking (2.4 A). ˚ The intra (2.36 A) layer bond lengths are found to be insensitive to the stacking sequence. Fig. 4 and 5 respectively show the band structures of AA and ABC stacked multi-layer silicane. The energy difference between the conduction band minima at Γ and M symmetry points increases with thickness, which can be seen more clearly in Fig. 6(a). The variation of the transverse effective mass and bandgap with number of layers for AA and ABC stacking has been shown in Fig. 7. The increase in effective mass and bandgap with thickness scaling is due to quantum confinement effect and is similar to the scaling of conventional elemental or compound semiconductor slabs [23]–[25]. Further, it can be clearly seen that the band gap is sensitive to the stacking sequence, for example, band gap of 4-layer silicane with AA stacking is 0.879 eV as compared to 0.467 eV of 4-layer silicane with ABC stacking. The weaker interactions between layers in case of AA stacking results in smaller band gaps. In contrast, the stronger inter-layer interactions in case of ABC stacking keeps the valence band maxima (VBM) at lower energy and the conduction band minima (CBM) at higher energy level. The band gap variation tends to saturate after 8-10 layers.

0

A A S ta c k in g

0 .1 4 0 .1 2

G

M o n o la y e r

0 .1 6

(m

)

0 .1 8

l

-1

8

-2

N o . o f L a y e rs 2 4 6 8

0

m

6

1

0

4

(m

2

0

A B S ta c k in g A B C S ta c k in g

0 .2 0

t

-1

N o . o f L a y e rs

m

1

0 .2 2

2

E n e rg y (e V )

E n e rg y (e V )

2

M o n o la y e r

2 .0 1 .6

A B S ta c k in g

1 .2

A B C S ta c k in g

0 .8 0 .4 0 .0 0

A A S ta c k in g

2 4 6 N u m b e r O f L a y e rs

8

(c) Fig. 7. Variation of (a) transverse effective mass, (a) longitudinal effective mass, and (c) bandgap in AA and AB(C) stacking. The corresponding values for monolayer silicane has also been shown for reference.

group velocity, h¯1 ∇k En (k) along the transport direction and the self-consistently obtained charge density over all k-states and bands [28]. The drain current-gate voltage characteristics of the device operating in the full ballistic regime has been shown in Figs. 8(a) and 8(b) for different silicane thicknesses and stacking order. Fig. 9(a) shows the output characteristics. Note that in this section, the off-state current (IOFF ) for all the devices has been set to 0.1 µA/µm. It is evident that the MOSFETs with multi-layer silicane in the AA stacking configuration offer the best drive currents, and the magnitude of the ON-current increases as we go from bilayer to a quad-layer device. The ABC stacked silicane channel transistors perform the worst with regard to drive current capability, while the performance of the monolayer device is in between the two types of multilayer devices. The average injection velocity at the top of the barrier (vinj ) also follows the same trends with gate voltage and drain voltage variation as shown in Fig. 8(c) and Fig. 9(b), respectively. These observations can be directly attributed to the bandstructure of silicane explained in detail in the previous section. It is apparent that with lower electron transverse effective mass, AA stacked multi-layer silicane performs the best in the ballistic limit. The ABC stacked silicane layers have higher electron effective masses which leads to reduced drive current in these devices. IV.

C ONCLUSION

Using rigorous density functional theory based bandstructure calculations and semiclassical full ballistic transport simulations, we investigated the performance of double gate MOSFETs with mono- and multi-layered silicane channels. We found that under iso-IOFF conditions, devices with silicane layers in the AA stacking configuration perform better than the monolayer as well as ABC stacked silicane devices on account of having a more favorable electronic structure for ballistic transport.

1 0 3

1 0 2

1 0 1

1 0 0

1 0

6 0 0 0

N L = N L = N L = N L = M o n

5 0 0 0

-1

0 .0

0 .1

0 .2 0 .3 0 .4 G a te V o lta g e (V )

A A

3 0 0 0

B

B C y e r

0 .5

A B

B C y e r

M o n o la y e r

A B (C ) S ta c k in g

2 0 0 0 1 0 0 0

0 .6

2 .0 x 1 0 5

1 .5 x 1 0 5

1 .0 x 1 0 5

N L = N L = N L = N L = M o n

2 , A 4 , A 2 , A 4 , A o la

A A B

B C y e r

in j

2 , A 4 , A 2 , A 4 , A o la

A A S ta c k in g A

V

N L = N L = N L = N L = M o n

4 0 0 0

2 , A 4 , A 2 , A 4 , A o la

(m /s )

4

D r a in C u r r e n t (m A /m m )

D r a in C u r r e n t (m A /m m )

1 0

0 .0

0 .1

0 .2 0 .3 0 .4 G a te V o lta g e (V )

(a)

(b)

0 .5

0 .6

5 .0 x 1 0 0 .0

4

0 .0

0 .1

0 .2 0 .3 0 .4 0 .5 G a te V o lta g e (V )

0 .6

(c)

Fig. 8. (a, b) Ballistic ID − VG characteristics of monolayer and AB and ABC stacked multilayer silicane in log and linear scales. (c) Injection velocity at the top of the barrier as a function of applied gate bias. “NL” stands for the number of layers. Transport direction: Γ → K. 6 0 0 0

2 0 0 0 1 0 0 0 0

0 .0

0 .1

2 , A 4 , A 2 , A 4 , A o la

0 .2 0 .3 0 .4 0 .5 D r a in V o lta g e (V )

(m /s )

N L = N L = N L = N L = M o n

3 0 0 0

A A

5

1 .5 x 1 0 5

1 .0 x 1 0 5

[13]

[14] N L = N L = N L = N L = M o n

in j

4 0 0 0

B

B C y e r

V

D r a in C u r r e n t (m A /m m )

5 0 0 0

2 .0 x 1 0

5 .0 x 1 0

0 .6

(a)

0 .0

4

0 .0

0 .1

2 , A 4 , A 2 , A 4 , A o la

0 .2 0 .3 0 .4 0 .5 D r a in V o lta g e (V )

A A

[15] B

B C y e r

0 .6

(b)

Fig. 9. (a) Output characteristics, and (b) Injection velocity at the top of the barrier as a function of drain bias.

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