# A relationship between statistical time to breakdown distributions and pre-breakdown negative differential resistance at nanometric scale

## Abstract

Using an ultra-high vacuum Conductive atomic force microscopy (C-AFM) current voltage, pre-breakdown negative differential resistance (NDR) characteristics are measured together with the time dependent dielectric breakdown (TDDB) distributions of Si/SiON (1.4 and 2.6 nm thick). Those experimental characteristics are systematically compared. The NDR effect is modelled by a conductive filament growth. It is showed that the Weibull TDDB statistic distribution scale factor is proportional to the growth rate of an individual filament and then has the same dependence on the electric field. The proportionality factor is a power law of the ratio between the surfaces of the CAFM tip and the filament's top. Moreover, it was found that, for the high fields used in those experiments, the TDDB acceleration factor as the growth rate characteristic is proportional to the Zener tunnelling probability. Those observations are discussed in the framework of possible breakdown or forming mechanism.

- Authors:

- STMicroelectronics, 850 rue Jean Monnet, 38926 Crolles Cedex (France)
- (France)
- Univ. Grenoble Alpes, LTM, F-38000 Grenoble, France and CNRS, LTM, F-38000 Grenoble (France)

- Publication Date:

- OSTI Identifier:
- 22309005

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Applied Physics; Journal Volume: 116; Journal Issue: 2; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 77 NANOSCIENCE AND NANOTECHNOLOGY; ACCELERATION; ATOMIC FORCE MICROSCOPY; BREAKDOWN; CRYSTAL GROWTH; CURRENTS; DIELECTRIC MATERIALS; DISTRIBUTION; ELECTRIC CONDUCTIVITY; ELECTRIC FIELDS; ELECTRIC POTENTIAL; FILAMENTS; NANOSTRUCTURES; NITROGEN COMPOUNDS; OXYGEN COMPOUNDS; PROBABILITY; SILICON; SILICON COMPOUNDS; SURFACES; TIME DEPENDENCE; TUNNEL EFFECT

### Citation Formats

```
Foissac, R., Univ. Grenoble Alpes, LTM, F-38000 Grenoble, France and CNRS, LTM, F-38000 Grenoble, Blonkowski, S., Delcroix, P., and Kogelschatz, M.
```*A relationship between statistical time to breakdown distributions and pre-breakdown negative differential resistance at nanometric scale*. United States: N. p., 2014.
Web. doi:10.1063/1.4888183.

```
Foissac, R., Univ. Grenoble Alpes, LTM, F-38000 Grenoble, France and CNRS, LTM, F-38000 Grenoble, Blonkowski, S., Delcroix, P., & Kogelschatz, M.
```*A relationship between statistical time to breakdown distributions and pre-breakdown negative differential resistance at nanometric scale*. United States. doi:10.1063/1.4888183.

```
Foissac, R., Univ. Grenoble Alpes, LTM, F-38000 Grenoble, France and CNRS, LTM, F-38000 Grenoble, Blonkowski, S., Delcroix, P., and Kogelschatz, M. Mon .
"A relationship between statistical time to breakdown distributions and pre-breakdown negative differential resistance at nanometric scale". United States. doi:10.1063/1.4888183.
```

```
@article{osti_22309005,
```

title = {A relationship between statistical time to breakdown distributions and pre-breakdown negative differential resistance at nanometric scale},

author = {Foissac, R. and Univ. Grenoble Alpes, LTM, F-38000 Grenoble, France and CNRS, LTM, F-38000 Grenoble and Blonkowski, S. and Delcroix, P. and Kogelschatz, M.},

abstractNote = {Using an ultra-high vacuum Conductive atomic force microscopy (C-AFM) current voltage, pre-breakdown negative differential resistance (NDR) characteristics are measured together with the time dependent dielectric breakdown (TDDB) distributions of Si/SiON (1.4 and 2.6 nm thick). Those experimental characteristics are systematically compared. The NDR effect is modelled by a conductive filament growth. It is showed that the Weibull TDDB statistic distribution scale factor is proportional to the growth rate of an individual filament and then has the same dependence on the electric field. The proportionality factor is a power law of the ratio between the surfaces of the CAFM tip and the filament's top. Moreover, it was found that, for the high fields used in those experiments, the TDDB acceleration factor as the growth rate characteristic is proportional to the Zener tunnelling probability. Those observations are discussed in the framework of possible breakdown or forming mechanism.},

doi = {10.1063/1.4888183},

journal = {Journal of Applied Physics},

number = 2,

volume = 116,

place = {United States},

year = {Mon Jul 14 00:00:00 EDT 2014},

month = {Mon Jul 14 00:00:00 EDT 2014}

}