Boron nitride as two dimensional dielectric: reliability and dielectric breakdown
Yanfeng Ji1, Chengbin Pan1, MeiyunZhang2, Shibing Long2, Xiaojuan Lian3, Feng Miao3,
Fei Hui1, Yuanyuan Shi1, Luca Larcher4, Ernest Wu5, , Mario Lanza1*
1
Institute of Functional Nano& Soft Materials, Soochow University, Collaborative Innovation
Center of Suzhou Nano Science & Technology, 199 Ren-Ai Road, Suzhou, 215123, China
2
Laboratory of Nanofabrication and Novel Device Integration, Institute of Microelectronics,
Chinese Academy of Sciences, Beijing 100029, China
3
National Laboratory of Solid State Microstructures, School of Physics, Collaborative
Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
4
DISMI, Università di Modena e Reggio Emilia, 42122 Reggio Emilia, Italy
5
IBM Research Division, Essex Junction, VT, USA.
* Corresponding author Email: mlanza@suda.edu.cn
Index
Table S1: Dielectric strength of BN in the literatures
Figure S1: Statistical analysis of the insulating (multilayer) areas in the CAFM current maps
Simulation of tunneling current through atomically thin BN films
1
Dielectric strength of BN in the literatures
After literature resources, different setups have been used for characterizing the dielectric
strength of BN. They are based on measuring an I-V curve and calculation of the electric field
(EBD) at which the BD is triggered or, by other words, at which the voltage VBD across the
dielectric thickness (d) induces the BD: (EBD=VBD/d) . Notably, the dielectric strength depends
on the quality of the insulator, but also on the cross sectional area between the electrodes at
which the test is performed. As the dielectric breakdown is a stochastic process that always
takes place at the weakest location of the sample, larger areas may produce a reduction on the
dielectric strength, as there are more probabilities to find a weak spot. Therefore, some values
may not be comparable. In the table below we summarize the values and setups found in the
literatures.
Fabrication
Method
Setup
Area
BN field
(MV/cm)
Reference
Mechanical
exfoliation
CAFM
~ 100nm2
7.94
Appl. Phys. Lett. 2011, 99,
243114
Mechanical
exfoliation
CAFM
~ 100nm2
~12
ACS Nano. 2015, 9(1), 916–921
Mechanical
exfoliation
CAFM
~ 100nm2
10
NanoLett. 2012, 12, 1707−1710
Mechanical
exfoliation
Probestation
Ti/Au electrodes
(1000 μm2)
6.4 - 9.0
Carbon 2013, 54, 396−402
CVD
Probestation
Au electrodes
(18 mm x 200 µm)
~9.0
Nano Res. 2013, 6(7), 602–610
CVD
Probestation
Ti/Au electrodes
(5 μm x 5 μm)
1.5 - 2.5
ACS Nano. 2012, 6, 8583–8590
Magnetron
sputtering
Probestation
Ru electrodes
(3 μm2)
*
NanoLett. 2013, 13, 276−281
Table S1: Dielectric strength of BN films reported in the literatures. The symbol "*" indicates
that the paper doesn't give a value for the dielectric strength, but it shows that the tunneling
conductance of sputtered BN is similar to that of exfoliated one, which is also a relevant
information for comparing the quality of the films.
2
Statistical analysis of the insulating (multilayer) areas in the CAFM current maps
Figure S1: Statistical analysis of the current map via CAFM software. The software provides
information on the total area covered by the hills (locations that show large currents), which is
81.97% (red dashed rectangle). The software also provides additional information such as hills
volume. The parameter "Number of Hills" is not representative in this study due to the
nucleation of different hills.
Simulation of tunneling current through atomically thin BN films
In order to understand the dielectric properties of atomically thin BN films, the current through
the tip/sample nanojunction is simulated using the charge transport model reported in [ref. S1S3]. This tunneling charge transport model across dielectric layers presented in reference
accounts for both intrinsic (e.g. direct tunneling, thermionic emission, drift and diffusion) and
defect-assisted tunneling (e.g. Trap-Assisted Tunneling, Poole-Frenkel, hopping) contributions.
3
In the case of atomically thin layer, the direct tunneling (DT) results to be the main contribution.
The electron DT current from the metal gate is computed using the Tsu-Esaki formula [ref. S5].
The tunneling probabilities are calculated using the Wentzel-Kramer-Brillouin (WKB) method.
The electric field across the stack is calculated by solving the 3D Poisson equation, which
consistently includes the defect and charge trapping contributions. The TAT current is modeled
using a multi-scale approach including for electron-phonon coupling and lattice relaxation,
which rely on the atomic description of defect properties such as thermal ionization and
relaxation energies. Contributions of conductive paths comprising more than one defects [ref.
S2]are automatically included. More details about the physics related to the model can be found
in references [ref. S1-S6].For the calculation presented in Figure 1e of the manuscript, a 10 nm
× 10 nm squared Pt/BN/Cu heterojunction is considered. The size is chosen to match the typical
tip/sample contact area for an AFM working in air environment and using similar tips, which
ranges between 50 and 100 nm2. The work function of the Pt has been selected to be 5 to match
the properties of the PtIr CAFM tip, while for Cu and BN we consider the standard work
function values of 4.9eV and 4.5eV. The current across the real system is calculated depending
on the potential difference applied between the Pt electrode and the Cu substrate. We found that,
the currents observed in the trace plot (Figure 1e in the manuscript) for each thickness, agree
with the values measured, and also with those reported in the literature. The calculations match
better the experiments when including the contribution of the capillary layer (1nm H2O between
the tip and the sample), which simulates the real system. The current values also fit the layer-bylayer progressive BD in Figure 3a.
[ref. S1] Herrmann, M. R.; Schenk, A. J. Appl. Phys. 1995, 77, 4522.
[ref. S2] Larcher, L. IEEE Trans. Electron Devices2003, 50, 1246.
[ref. S3] Padovani, A. Proc. IEEE Int. Rel. Phys. Symp.2008, 55, 616.
[ref. S4] Yang, N.; Henson, W. K.; Hauser, J. R.; Wortman, J. J. IEEE Trans. Electron
Dev.1999, 46, 1464.
[ref. S5] Duke, C. B. Academic Press, 1969.
[ref. S6] Larcher, L.; Pavan, P.; Pellizzer, F.; Ghidini, G. IEEE Trans. Electron Devices, 2001,
48, 935.
4