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^{−5}e/√Hz.
Normalized differential conductance G_{d}/G_{0} with G_{0}=2e^{2}/h for our semiconducting sample measured at 4.2 K on the gate V_{g} vs bias voltage V_{ds} plane: the color scale is given by the bar on the right. Lower figure is measured with larger source-drain voltage at V_{g} around −1 V. For the sample parameters, see text.
Transconductance gm as a function of bias V_{ds} and gate voltage V_{g}. Lower figure is measured with larger source-drain voltage at V_{g} around −1 V.
(a) Current noise S integrated over the frequency range of 600–950 MHz vs current I_{ds} 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 V_{ds}=−1.2,... ,0 V in steps of 0.2 V (from top to bottom at V_{ds} > 0 and from bottom to top at V_{ds} < 0
(a) Current noise S over V_{g} vs V_{ds} plane. (b) Noise power of (a) converted into input voltage noise by dividing by g_{m}^{2}. The region of smallest noise has been denoted by an ellipsoid.
a� I_{ds} vs V_{g} at bias voltage V_{ds} = +0.135 V (squares) and V_{ds} = −0.135 V (circles). The inset displays a set of current traces on linear scale measured when at V_{ds} has been stepped from −0.13 to 0.13 V by 26 mV (from bottom to top). (b) I_{ds} vs V_{ds} (> 0) curves at V_{g} = 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 F_{tube} < 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 R_{ij} ; numbers 1-4 represent the measurement terminals. A sum of lead and bonding pad capacitance is given by C_{p} ~ 1 pF while the inductors represent bond wires of L_{s} ~ 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 S_{2,13} corresponds to F = 0.30. b) The noise measured from terminal 3 - presentation details as above. S_{3,24} line corresponds to F = 0.29. The insets illustrate the differential contact resistances determined as R_{C2} = (R_{12} + R_{23} − R_{13})/2 and R_{C3} = (R_{23} + R_{34} − R_{24})/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 G_{d} on the plane spanned by bias voltage V and gate voltage Vg. The scale bar is given on the right in units of e^{2}/h = G_{0}/2.
Excess noise S(I) - S(0) vs bias voltage V > 0 (open circles) and V < 0 (closed circles) at V_{g} = 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 A^{2}/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 F_{d} on V_{g} 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 F_{d}d as a function of V_{g}. (b) Average differential Fano factor vs total conductance G = I/V plotted parametrically by varying V_{g}. (c) F_{d} vs G_{d} plotted parametrically by varying V_{g}; F_{d} varies in a clockwise manner with growing V_{g}.
Related publications
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