PSI - Issue 23

Gour P. Das et al. / Procedia Structural Integrity 23 (2019) 334–341 G. P. Das / Structural Integrity Procedia 00 (2019) 000–000

340

7

(a) Graphene

(b) Silicene

60

2000

30

Nika et al.

4000

LB

40

25

DB

2000

)

1500

Graphene

20

-1

Graphene

20

K

0

0

-1

15

(c) Germanene

1000

(d) Stanene

DB-Silicene

LB-Silicene

12

6

L (Wm

D (K)

10

LB

κ

LB-Silicene

LB

s (Km/s)

4

8

θ

DB

500

v

DB-Silicene

LB-Germanene

DB-Stanene DB-Germanene

LB-Germanene

5

LB-Stanene

2

4

DB-Germanene DB-Stanene

DB

LB-Stanene

100 200 300 400 0

100 200 300 400 0

0

0 1 2 3 4 0

1 2 3 4

T (K)

(Å)

∆

Fig. 4. (Left panel) The average velocity of the acoustic phonons v s (Km / s) and the average Debye temperature θ D (K) of LB and DB sheets as function of buckling height ∆ . (Right panel) The lattice thermal conductivity κ L calculated using the Debye Callaway formalism for (a) graphene compared with result of (Nika et al., 2009), (b) LB and DB silicene, (c) LB and DB germanene, and (d) LB and DB stanene.

1 K − 1 ) at 300 K for graphene ( ∗ ) and of LB and DB silicene germanene, stanene. Comparison

Table 3. Lattice Thermal conductivities κ L (Wm −

with the results of Peng et al. (2016). System Graphene

LB-Si

LB-Ge

LB-Sn

DB-Si

DB-Ge

DB-Sn

Present work

∼ 3000 (*) 3716

33

3.1 2.4

6.7 5.8

3.5

0.9

0.4

Peng et al. (2016)

28.3

-

-

-

4. Conclusions

To summarize, we use density functional theory to explore the phonon dynamics of the members of the graphene family. We model the phonon lifetimes of the sheets from the Debye temperature, group velocity, and Gru¨neisen parameter of the acoustic phonon modes in their harmonic phonon spectrum. We use the Asen-Palmer modified version of Debye-Callaway theory to calculate the lattice thermal conductivity of graphene, low and double buckled silicene, germanene, and stanene. The lattice thermal conductivity of the low buckled sheets is found to be orders of magnitude lower than graphene. DB germanene and stanene have ultralow lattice thermal conductivity that are estimated to be even lower than unity. The main di ff erence in the vibrational dynamics of the sheets down the group arises from the buckling in their structure that lowers the group velocity and Debye temperature of the acoustic phonons drastically. We use the di ff erence in the geometry of graphene, LB, and DB sheets to investigate the e ff ect of buckling on the phonon group velocity and Debye temperature. The maximum lowering in the zone boundary frequency and group velocity is observed from graphene to LB-silicene i.e. as soon as buckling is introduced. Increase in buckling from LB to DB structure does not lead to any major changes in the given parameters. This implies that although buckling height leads to the lowering of the lattice thermal conductivity of the sheets down the group, but it’s e ff ect on these parameters saturates beyond a point.

References

Asen-Palmer, M., Bartkowski, K., Gmelin, E., Cardona, M., Zhernov, A P, Inyushkin, A.V., Taldenkov, A., Ozhogin, V.I., Itoh, K.M. Haller, E.E., 1997. Thermal conductivity of germanium crystals with di ff erent isotopic compositions. Physical Review B - Condensed Matter and Materials Physics 56, 9431-9447. Bhattacharya A., Bhattacharya, S., Das, G. P., 2011. Strain-induced band-gap deformation of H / F passivated graphene and h-BN sheet. Physical Review B - Condensed Matter and Materials Physics 84 1-5. Bhattacharya, A., Bhattacharya, S., Majumder, C., Das, G. P., 2010. First principles prediction of the third conformer of hydrogenated BN sheet. Physica Status Solidi - Rapid Research Letters 4, 368-370. Bhattacharya, A., Bhattacharya, S., Das, G. P., 2013. Exploring semiconductor substrates for silicene epitaxy. Applied Physics Letters103, 123113.