We have investigated shot noise in a 6-nm-diameter, semiconducting multiwalled carbon nanotube field effect transistor at 4.2 K over the frequency range of 600–950 MHz. We find a transconductance of 3–3.5 μS
for optimal positive and negative source-drain voltages V. For the gate referred input voltage noise, we obtain 0.2 and 0.3 μV/√Hz for V > 0 and V < 0, respectively. As effective charge noise, this corresponds to (2–3) x 10−5e/√Hz.
Normalized differential conductance Gd/G0 with G0=2e2/h for our semiconducting sample measured at 4.2 K on the gate Vg vs bias voltage Vds plane: the color scale is given by the bar on the right. Lower figure is measured with larger source-drain voltage at Vg around −1 V. For the sample parameters, see text.
Transconductance gm as a function of bias Vds and gate voltage Vg. Lower figure is measured with larger source-drain voltage at Vg around −1 V.
(a) Current noise S integrated over the frequency range of 600–950 MHz vs current Ids and (b) the corresponding Fano factor. Due to lack of sensitivity, currents below 0.01 μA have been cut off from the plot. The bias voltage varies over Vds=−1.2,... ,0 V in steps of 0.2 V (from top to bottom at Vds > 0 and from bottom to top at Vds < 0
(a) Current noise S over Vg vs Vds plane. (b) Noise power of (a) converted into input voltage noise by dividing by gm2. The region of smallest noise has been denoted by an ellipsoid.
a� Ids vs Vg at bias voltage Vds = +0.135 V (squares) and Vds = −0.135 V (circles). The inset displays a set of current traces on linear scale measured when at Vds has been stepped from −0.13 to 0.13 V by 26 mV (from bottom to top). (b) Ids vs Vds (> 0) curves at Vg = const, stepped from −1.6 to 0 V by 0.2 V (from bottom to top).
Local and Non-local Shot Noise in Multiwalled Carbon Nanotubes
We have investigated shot noise in multiterminal, diffusive multiwalled carbon nanotubes (MWNTs) at 4.2 K over the frequency f = 600 − 850 MHz. Quantitative comparison of our data to semiclassical theory, based on non-equilibrium distribution functions, indicates that a major part of the noise is caused by a non-equilibrium state imposed by the contacts. Our data exhibits non-local shot noise across weakly transmitting contacts while a low-impedance contact eliminates such noise almost fully. We obtain Ftube < 0.03 for the intrinsic Fano factor of our MWNTs.
(a) 3-probe structure. The node is denoted by a circle. (b) Extended contact.
Schematics of our high frequency setup. Indices 5-8 refer to nodes with different distribution functions on the nanotube. Contacts are drawn as tunnel junctions with resistances Rij ; numbers 1-4 represent the measurement terminals. A sum of lead and bonding pad capacitance is given by Cp ~ 1 pF while the inductors represent bond wires of Ls ~ 10 nH. TJ denotes a tunnel junction for noise calibration.
a) Current noise power (arbitrary units) measured from lead 2 in sample 2 as a function of bias current. The circles are the measured data while the solid lines are theoretical fits to direction-averaged data over 0.1 < III < 2 μA. The theoretical line S2,13 corresponds to F = 0.30. b) The noise measured from terminal 3 - presentation details as above. S3,24 line corresponds to F = 0.29. The insets illustrate the differential contact resistances determined as RC2 = (R12 + R23 − R13)/2 and RC3 = (R23 + R34 − R24)/2.
Shot noise in singlewalled carbon nanotubes
We have measured shot noise in single-walled carbon nanotubes with good contacts at 4.2 K at low frequencies (f = 600–850 MHz). We find a strong modulation of shot noise over the Fabry-Perot pattern; in terms of the differential Fano factor the variation ranges over 0.4–1.2. The shot noise variation, in combination with differential conductance, is analyzed using two spin-degenerate) modes with different, energy-dependent transmission coefficients. Deviations from the predictions from Landauer-Büttiker
formalism are assigned to electron-electron interactions.
Differential conductance Gd on the plane spanned by bias voltage V and gate voltage Vg. The scale bar is given on the right in units of e2/h = G0/2.
Excess noise S(I) - S(0) vs bias voltage V > 0 (open circles) and V < 0 (closed circles) at Vg = 0.04 V. Red curve illustrates an evaluation of Eq. (4) using F = 0.65 and the experimentally determined value R(0)/(V/I). The dashed line refers to exponent Β = 1. The bottom inset displays the data on linear scale (in A2/Hz). The inset on top displays the electrical equivalent model employed to calculate the coupling of the current fluctuations as well as the corrections due to nonlinearities.
Differential Fano factor Fd on Vg vs V plane. The scale bar is given on the right.
Plots obtained using data of Figs. 1 and 3 at V = -6:2 mV. (a) Average differential Fano factor and differential Fano factor Fdd as a function of Vg. (b) Average differential Fano factor vs total conductance G = I/V plotted parametrically by varying Vg. (c) Fd vs Gd plotted parametrically by varying Vg; Fd varies in a clockwise manner with growing Vg.
Local and non-local shot noise in multiwalled carbon nanotubes
T. Tsuneta, P. Virtanen, F. Wu, T.H. Wang, T.T. Heikkilä, and P.J. Hakonen