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*f*noise in forward-biased single-walled carbon nanotube film-silicon Schottky junctions

^{1}, Hemant Rao

^{1}, Gijs Bosman

^{1}and Ant Ural

^{1,a)}

### Abstract

The electronic noise of single-walled carbon nanotube(CNT) film-Silicon Schottkyjunctions under forward bias is experimentally characterized. The superposition of a stable 1/*f*noise and a temporally unstable Lorentzian noise is observed, along with a random telegraph signal (RTS) in the time domain. The data analysis shows that the Lorentzian noise results from the RTS current fluctuations. The data agree well with theoretical descriptions of noise in Schottkyjunctions due to carrier trapping and detrapping at interface states. Understanding the noiseproperties of CNT film-Si junctions is important for the integration of CNTfilm electrodes into silicon-based devices.

This work was funded by the UF Research Opportunity Fund. The authors thank Professor A. G. Rinzler and Dr. Z. Wu for providing CNT films and Dr. A. Behnam and J. L. Johnson for help with microfabrication.

### Key Topics

- Carbon nanotubes
- 40.0
- 1/f noise
- 29.0
- Schottky barriers
- 14.0
- Random noise
- 11.0
- Thin film devices
- 11.0

## Figures

(a) The 3D schematic of the fabricated CNT film-Si MS device showing both the top and cross-sectional views. (b) I-V characteristics of the CNT film/*p*-type Si MS device in the voltage bias range from −3 V to 3 V at room temperature. Note that the polarity of the voltage bias is defined such that positive values correspond to forward bias.

(a) The 3D schematic of the fabricated CNT film-Si MS device showing both the top and cross-sectional views. (b) I-V characteristics of the CNT film/*p*-type Si MS device in the voltage bias range from −3 V to 3 V at room temperature. Note that the polarity of the voltage bias is defined such that positive values correspond to forward bias.

(a) Low frequency current noise spectral density of the CNT film-Si MS junction measured at three different forward biases (1.04, 1.97, and 2.41 V as labeled), showing a strong Lorentzian noise component on top of a 1/*f* noise component. The inset shows the time-domain current fluctuations at 1.04 V in a time frame of 500 ms, characteristic of a two-level asymmetric RTS noise. (b) The total measured current noise spectral density at 1.97 V from part (a) (red line), the Lorentzian component obtained from fitting the data (short dashed line), and the 1/*f* noise component obtained by subtracting the Lorentzian component from the total measured *S _{I} * (blue line). The dashed line is a power law fit to the extracted 1/

*f*noise component yielding an exponent of

*γ*= 1.1. The inset shows averaged over three measurements as a function of forward bias current

*I*at a frequency of 10 Hz.

(a) Low frequency current noise spectral density of the CNT film-Si MS junction measured at three different forward biases (1.04, 1.97, and 2.41 V as labeled), showing a strong Lorentzian noise component on top of a 1/*f* noise component. The inset shows the time-domain current fluctuations at 1.04 V in a time frame of 500 ms, characteristic of a two-level asymmetric RTS noise. (b) The total measured current noise spectral density at 1.97 V from part (a) (red line), the Lorentzian component obtained from fitting the data (short dashed line), and the 1/*f* noise component obtained by subtracting the Lorentzian component from the total measured *S _{I} * (blue line). The dashed line is a power law fit to the extracted 1/

*f*noise component yielding an exponent of

*γ*= 1.1. The inset shows averaged over three measurements as a function of forward bias current

*I*at a frequency of 10 Hz.

(a) Low frequency current noise spectral density of the CNT film-Si MS device at 1.97 V forward bias measured on three different days (labeled as measurements 1, 2, and 3). Note that Measurement 1 is the same as the 1.97 V curve in Fig. 2(a). The change in both the location of *f* _{c} and the value of *S* _{0} is evident, indicating temporally unstable RTS noise. The inset shows the RTS amplitude Δ*I* as a function of the forward current *I*. (b) Statistical distribution of the time durations of the up and down states for Measurement 1 recorded simultaneously as the noise spectra shown in part (a). The exponential fitting to Poisson distributions as shown in the figure gives an average lifetime of τ_{ up } = 5.81 ms and τ_{ down } = 8.55 ms. (c) A semi-log plot of τ_{ up }/τ_{ down } as a function of forward bias voltage for Measurement 1. The extrapolation of the exponential best fit as shown by the dashedline gives the zero-bias trap level with respect to the Fermi level as *E _{F} *-

*E*= 32.7 meV.

_{T}(a) Low frequency current noise spectral density of the CNT film-Si MS device at 1.97 V forward bias measured on three different days (labeled as measurements 1, 2, and 3). Note that Measurement 1 is the same as the 1.97 V curve in Fig. 2(a). The change in both the location of *f* _{c} and the value of *S* _{0} is evident, indicating temporally unstable RTS noise. The inset shows the RTS amplitude Δ*I* as a function of the forward current *I*. (b) Statistical distribution of the time durations of the up and down states for Measurement 1 recorded simultaneously as the noise spectra shown in part (a). The exponential fitting to Poisson distributions as shown in the figure gives an average lifetime of τ_{ up } = 5.81 ms and τ_{ down } = 8.55 ms. (c) A semi-log plot of τ_{ up }/τ_{ down } as a function of forward bias voltage for Measurement 1. The extrapolation of the exponential best fit as shown by the dashedline gives the zero-bias trap level with respect to the Fermi level as *E _{F} *-

*E*= 32.7 meV.

_{T}## Tables

The values of τ_{ up }, τ_{ down }, *f _{c} *, and

*S*

_{0}obtained from the time domain analysis and the values of

*f*and

_{c}*S*

_{0}obtained from the frequency domain analysis for Measurements 1, 2, and 3 shown in Fig. 3(a). The time domain

*f*and

_{c}*S*

_{0}values are calculated from τ

_{ up }, τ

_{ down }

_{,}and Δ

*I*values obtained from the measured RTS current fluctuations using Eq. (2). The frequency domain values are extracted by a Lorentzian fitting of the data in Fig. 3(a), similar to that shown in Fig.2(b).

The values of τ_{ up }, τ_{ down }, *f _{c} *, and

*S*

_{0}obtained from the time domain analysis and the values of

*f*and

_{c}*S*

_{0}obtained from the frequency domain analysis for Measurements 1, 2, and 3 shown in Fig. 3(a). The time domain

*f*and

_{c}*S*

_{0}values are calculated from τ

_{ up }, τ

_{ down }

_{,}and Δ

*I*values obtained from the measured RTS current fluctuations using Eq. (2). The frequency domain values are extracted by a Lorentzian fitting of the data in Fig. 3(a), similar to that shown in Fig.2(b).

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