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Measurement of the quantum capacitance of interacting electrons in carbon nanotubes
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Ph.D. dissertation, Department of Physics, Massachusetts Institute of Technology
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G. Steele, Ph.D. dissertation, Department of Physics, Massachusetts Institute of Technology, 2006.
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Steele, G.1
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A simple low-dissipation amplifier for cryogenic scanning tunneling microscopy
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DOI 10.1063/1.1433951
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Urazhdin, S.1
Tessmer, S.H.2
Ashoori, R.C.3
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12
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79958039055
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Several other commercially available HEMTs, including the Agilent ATF 33143 and 34143, were found to be unsuitable in our measurements due to high-frequency (MHz) transport resonances
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Several other commercially available HEMTs, including the Agilent ATF 33143 and 34143, were found to be unsuitable in our measurements due to high-frequency (MHz) transport resonances.
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13
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79958063516
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Measured via an Agilent B1500A parameter analyzer and Keithley 2612
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Measured via an Agilent B1500A parameter analyzer and Keithley 2612.
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14
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79958058509
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All measurements were performed in the dark to prevent optical excitation of the exposed 2DEG in the HEMT. After cooling, HEMTs were temporarily exposed to light, to enable navigating probes to pads, so persistent photoconductivity may affect HEMT characteristics at 77 and 4 K
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All measurements were performed in the dark to prevent optical excitation of the exposed 2DEG in the HEMT. After cooling, HEMTs were temporarily exposed to light, to enable navigating probes to pads, so persistent photoconductivity may affect HEMT characteristics at 77 and 4 K.
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15
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79958027768
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Measurement time tmeas is proportional to the lock-in time constant and filter slope (Stanford Research Systems SRS830 Manual)
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Measurement time tmeas is proportional to the lock-in time constant and filter slope (Stanford Research Systems SRS830 Manual).
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16
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79958048038
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load∼ 50 S
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load∼ 50 S.
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17
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79958040237
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In such devices with a bandgap, the shunt capacitance can be measured by gating the DUT so that the Fermi level lies in the gap, thus removing the contribution of the DUT to the measured capacitance. The measured shunt capacitance for the nanotube device and bridge was 850 aF. The bond wires for the graphene device were somewhat longer, so we conservatively allow for a shunt capacitance ten times larger
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In such devices with a bandgap, the shunt capacitance can be measured by gating the DUT so that the Fermi level lies in the gap, thus removing the contribution of the DUT to the measured capacitance. The measured shunt capacitance for the nanotube device and bridge was 850 aF. The bond wires for the graphene device were somewhat longer, so we conservatively allow for a shunt capacitance ten times larger.
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18
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79958071434
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b)
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b).
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19
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79958046456
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The minimum capacitance is limited by the temperature, disorder, and DUT parallel shunt capacitances (Ref. 21)
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The minimum capacitance is limited by the temperature, disorder, and DUT parallel shunt capacitances (Ref. 21).
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20
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79958055589
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The measurements were acquired with the lock-in low pass filter set to 24 dB/oct rolloff and a 3 s time constant, corresponding to 38.4 s of acquisition per data point
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The measurements were acquired with the lock-in low pass filter set to 24 dB/oct rolloff and a 3 s time constant, corresponding to 38.4 s of acquisition per data point.
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21
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77957107491
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10.1103/PhysRevLett.105.136801
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L. A. Ponomarenka, R. Yang, R. V. Gorbachev, P. Blake, M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, Phys. Rev. Lett. 105, 136801 (2010). 10.1103/PhysRevLett.105.136801
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Ponomarenka, L.A.1
Yang, R.2
Gorbachev, R.V.3
Blake, P.4
Katsnelson, M.I.5
Novoselov, K.S.6
Geim, A.K.7
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22
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77951532253
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10.1063/1.3391670
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S. Droscher, P. Roulleau, F. Molitor, P. Studerus, C. Stampfer, T. Ihn, and K. Ensslin, Appl. Phys. Lett. 96, 152104 (2010). 10.1063/1.3391670
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Droscher, S.1
Roulleau, P.2
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Ensslin, K.7
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23
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68949175478
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10.1038/nnano.2009.177
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J. Xia, F. Chen, J. Li, and N. Tao, Nature Nanotechnol. 4, 505 (2009). 10.1038/nnano.2009.177
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, vol.4
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Xia, J.1
Chen, F.2
Li, J.3
Tao, N.4
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25
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79958061652
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Comparative measurements were made on the same graphene device using the Andeen-Hagerling AH2700A Ultra-precision Capacitance/Loss Bridge. To avoid perturbing the DUT, the integrated bridge was left bonded ufor these measurements. However, it was powered down, and probes driven by the AH2700A directly contacted pads attached to the graphene and its gate, bypassing the integrated bridge circuitry and isolating the capacitance of the graphene device. The shunt capacitance of the integrated bridge (∼10fF) should have no effect on the noise in the AH2700As capacitance measurements-indeed, the AH2700A performed to its manufacturers specifications for noise
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Comparative measurements were made on the same graphene device using the Andeen-Hagerling AH2700A Ultra-precision Capacitance/Loss Bridge. To avoid perturbing the DUT, the integrated bridge was left bonded up for these measurements. However, it was powered down, and probes driven by the AH2700A directly contacted pads attached to the graphene and its gate, bypassing the integrated bridge circuitry and isolating the capacitance of the graphene device. The shunt capacitance of the integrated bridge (∼10fF) should have no effect on the noise in the AH2700As capacitance measurements-indeed, the AH2700A performed to its manufacturers specifications for noise.
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