Resistor quantum

Frank S, Poncharal P, Wang ZL et al (1998) Carbon nanotube quantum resistors. Science... 

The existence of a quantum resistor with values Rg h/ie 1,2,3>...) is related to the Hall effect of a two-dimensional... 

The degree of precision of the quantized Hall effect has amaz-cd even the experts. Measured values of the Hall resistance at various integer plateaus are accurate to about one part in six million. The effect can be used to construct a laboratory standard of electrical resistance that is much more accurate than Ihe standard resistors currently in use. Authorities also observe that, if the quantized Hall effect is combined with a new calibration ol an absolute resistance standard, it should he able lo yield an improved measurement of the fundamental dimensionless constant of quantum electrodynamics. Ihe fine-structure constant or. 

Figure 3. Peak photovoltage measured across a 50n resistor as a function of applied voltage and electric field, respectively. Parameter Is the relative light Intensity. The dashed curve Is the Donovan et al. (6) result In arbitrary ordinate units. The quantum efficiency (E) for geminate dissociation used to calculate lp(E)/ (E) Is taken from reference 14.

The measuring circuit consists of a bias voltage supply ff, a pair of macroscopic electrodes, which make up the quantum contact under examination, and a serial resistor Pp of 1000 Q as illustrated in Fig. 1. The voltage drop Vp on the resistor Rp is a function of the measured conductance G ,. The piezoelectric device is used to control the backward and forward movement of the macroscopic contacts, between which the nanowires occur. A high voltage amplifier, controlled by a digital... 

FIGURE 3.20 Sketch for the apparatus measuring the quantum electrical resistance, where the electron is viewed as a traveling wave through resistor. 

Sikula, J. et al. 1998. Low frequency noise in film resistors, Proc. of 7th Quantum 1/f Noise and Other Low Frequency Fluctuations in Electronic Devices, St. Louis, MO August 1998, AIP Press, pp. 42-47. 

Kubo s linear-response theory provides the full, quantum-mechanical relation between the response of a system to external perturbations and the spontaneous decay of fluctuations in the unperturbed system. Of course, the paper had important predecessors Nyquist s [1] paper on thermal noise in resistors and Onsager s [2] seminal paper on the relation between decay of macroscopic and microscopic fluctuations, to name but the earliest. 

The anode of a photomultiplier tube is connected by a resistor of R = kQ to ground. The stray capacitance is lOpf, the current amplification 10, and the anode rise time 1.5 ns. What is the peak amplitude and the halfwidth of the anode output pulse produced by a single photoelectron What is the dc output current produced by 10 W cw radiation at A = 500nm, if the quantum efficiency of the cathode is 77 = 0.2 Estimate the necessary voltage amplification of a preamplifier (a) to produce 1V pulses for single-photon counting and (b) to read 1 V on a dc meter of the cw radiation ... 

Quantum mechanics show that the mean free path of the electrons in a metal cannot be smaller than the interatomic distance. For many concentrated alloys of transition metals this limit is approached. Near this hmit the resistivity becomes insensitive to a further increase of lattice disorder, and thus the TCR becomes low. It turns out that for these alloys the TCR is approximately zero when the resistivity is around 150 /U.S2 cm, positive when it is lower and negative when it is higher. Their low TCR makes these alloys useful for fixed resistors. 

At room temperature (300K) the second term 4kT/e is about 0.1 V. Since the Johnson noise should not be predominant, the first term 2Ri has to be larger than 0.1 V. For a maximum tolerable load resistor of 10 fl, this puts a lower limit of i > 5-10 A to the photocurrent. With a quantum efficiency = 0.1, the minimum radiation power conveniently detectable with photocells is then about 3-10 photons/s which corresponds to lO W at A = 500 nm. 

This value is based on the assumption that q 14 is correct The uncertainty arises mainly from instabilities in the value of the calibrated reference resistor necessary for the determination of a (see Fig.3). A large number of theoretical papers discuss the question whether microscopic details of the semiconductor may influence the accuracy of Eq.l4. Up to now, no corrections to the value of the quantized Hall resistance are known, and the good agreement of the a- value deduced from the quantum Hall effect (Eq.l5) with the recommended value (Eq.l) and data obtained from other experiments ( q 4, Eq.7) demonstrates that corrections to the quantized Hall resistance (if any) should be smaller than the experimental uncertainty of about lO" . We believe that Eq.l4 is correct even at a higher level of accuracy and that the QHE can be used on one hand as a standard resistor (if the value for h/e is known or defined for metrological applications) and on the other hand for the determination of the fine-structure constant with an uncertainty corresponding to the uncertainty of the reference resistor. 

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