Shot noise in carbon nanotubes

Shot noise in multiwalled carbon nanotubes

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 G_d/G₀ with G₀=2e²/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_m². 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 = (R₁₂ + R₂₃ − R₁₃)/2 and R_C3 = (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 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 e²/h = G₀/2.	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 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 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_dd 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.