Diagnóstico de Strawberry mottle virus (SMoV)

In this thesis several AlxGax-1As/GaAs-based quantum devices were characterized

with respect to their noise spectrum. As presented in Sec. 2.5 the power spectral density (PSD) of the noise is a superposition of all noise contributions, such as thermal noise and 1/f noise. In most AlxGa1-xAs/GaAs-based devices that are in-

vestigated in this thesis the PSD is dominated by frequency-independent, i.e. white noise, SV,w. This noise is identified as thermal noise since SV,w agrees with the the-

oretically predicted value SV,Th within the measurement uncertainty. In contrast,

the contribution of 1/f noise is restricted to frequencies f < 1 kHz, which is small compared to the measurement range of up to 100 kHz. Therefore, the contribution of 1/f noise will not be further discussed in this section. As derived in Sec. 4, the theoretical value of the thermal noise is calculated with the equation

SV,Th = 4kBTeR + 2 · 4kBTamp R2 Ramp

(6.1)

with the electron temperature of the sample Te, the two-point resistance of the

sample R, the input resistance Ramp = 5 MΩ and the temperature Tamp = 300 K

of the two voltage amplifiers. The contribution of the 1D devices to the resistance, and therefore to the thermal noise, is dominant compared to the contribution of the leads. As mentioned in Sec. 4, the noise measurement setup is well-suited for temperatures in the range 4.2 K ≤ Tbath ≤ 70 K and for resistances in the

range 1 kΩ ≤ R ≤ 60 kΩ. The corresponding range of electrical conductance is 12.9 · 2e2/h ≥ G ≥ 0.2 · 2e2/h. This is found for 2D and ballistic 1D devices based

on AlxGa1-xAs/GaAs heterostructures that do not form multichannel quantum rings.

However, in quantum rings the measured noise is found to exceed SV,Th, as will be

shown later in this section.

The noise spectra of the device ConstrA, a QPC with a width of about 100 nm, are taken according to the setup shown in Fig. 6.1 a) for different gate voltages

Vg of a global top-gate. In Fig. 6.1 b) the measured two-point differential con-

ductance g is presented. From the conductance plateaus a series resistance of

Rs = g−1 − (2N e2/h)−1 ≈ 142 Ω is deduced, which stems from the leads to the

QPC and is negligible compared to the resistance of the QPC. The measured noise spectra are therefore dominated by the contribution of the QPC. From g and the bath temperature Tbath = 4.2 K the expectation value SV,Th is calculated for gate

voltages in the range from Vg = 0.3 V to Vg = 0.6 V with a step size of ∆Vg = 2 mV.

Here, Tbath is assumed to be identical to the electron temperature of the device, i.e. Tbath = Te. In this range noise measurements are performed with a step size of

∆Vg = 5 mV. The noise spectra for Vg = 348 mV and Vg = 528 mV are given as

spectrum shows a frequency-independent PSD. For Vg = 348 mV, i.e. a relatively

high resistance, the spectrum shows the behavior of a low-pass filter. As mentioned in Sec. 4, the spectrum SV(f ) is fitted with the function

SV(f ) =

SV,w

1 + (2πf RCPar)2

(6.2)

with the parasitic capacitance of the order of CPar ≈ 4 · 10−10 F, and the white part

of the noise SV,w as free parameters. In the observed range of Vg the values of the

thermal noise SV,w, derived from the fit, agree with the expected value SV,Th within

the uncertainty of the measurement, as depicted in Fig. 6.1 d).

Figure 6.1: Measurement of the noise spectra SV of the device ConstrA at Tbath =

4.2 K. a) A SEM image of the device, a QPC with a width of about 100 nm [138]. b) The measured two-point differential conductance of the QPC (dashed line) which allows to estimate the series resistance to Rs ≈ 142 Ω and to conclude that

the noise spectrum is dominated by the QPC. The solid line is calculated from the dashed line when subtracting Rs. c) Two noise spectra (solid black lines) for Vg = 348 mV and Vg = 528 mV are shown. These gate voltages are indicated with

arrows in b). Noise spectra with lower resistance have a PSD that is dominated by frequency-independent noise, whereas noise spectra of higher resistances show a low- pass behavior that is fitted to the noise spectra (red dashed line). d) A comparison between the measured thermal noise SV,w (solid squares) and the expectation value SV,Th (open squares) shows that SV,w and SV,Th agree with each other in the gate

voltage range from Vg = 0.3 V to Vg = 0.6 V. The expectation value SV,Th is

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In an ideal ballistic device a resistance R and an electron temperature Te can

not be defined locally due to the lack of scattering of the electrons. It may there- fore appear counter-intuitive to measure the noise spectrum of a ballistic device. The solution for this can be found in the Landauer-Büttiker formalism, where the properties of the ballistic electrons inherit the properties of the electron reservoirs, such as the electron temperature. In the ideal system the resistance, and therefore any fluctuation, results from the scattering of the electron wave functions at the transition from 2D leads to 1D constriction. Hence, the quantized resistance of a QPC RQPC = (2N e2/h)−1 that depends on the number of populated subbands N

produces the thermal noise SV,w = 4kBTeRQPC [74] (see Sec. 2.2 and Sec. 4).

Further 1D constrictions were investigated with respect to their noise spectrum at Tbath = 4.2 K to show that the agreement of SV,w and SV,Th is still given if an 1D

constriction is bent or has an increased length. Therefore, the two-terminal device ConstrB, a bent waveguide with a width of w = 285 nm and a length of l = 3.8 µm, and the device ConstrC, a straight waveguide with a width of w = 285 nm and a length of l = 2.8 µm, are chosen. Note that these lengths do not exceed the elastic mean free path of le≈ 18 µm. The SEM images of these devices can be seen in Figs.

6.2 c) and d). It has to be noted that the devices ConstrA, ConstrB and ConstrC were fabricated from the same wafer material. Sweeping the gate voltage Vg of the

global top-gate results in the two-point differential conductance that is depicted in Fig. 6.2 a) for ConstrB and in Fig. 6.2 b) for ConstrC. In both devices the conductance quantization is weakly pronounced, but allows an estimate of the series resistance that is found to be Rs = 580 Ω for the device ConstrB and Rs = 710 Ω for

the device ConstrC. From the two-point conductance the expectation values SV,Th

are derived and found to fit the measured values SV,w of the thermal noise in the

measured range of Vg, as shown in Fig. 6.2 c) for ConstrB and in Fig. 6.2 d) for

Figure 6.2: Measurements of the electrical conductance (dashed line) of a) the device ConstrB, a bent waveguide with a width of w = 285 nm and a length of l = 3.8 µm and b) the device ConstrC, a straight waveguide with a width of w = 285 nm and a length of l = 2.8 µm at Tbath = 4.2 K each. From the weakly pronounced conduc-

tance plateaus that are highlighted by horizontal dotted lines the series resistance can be determined to be Rs = 580 Ω for the device ConstrB and to be Rs = 710 Ω

for the device ConstrC. It is therefore concluded that the measured noise spectra are dominated by the 1D constrictions. The solid lines represent the raw data that is corrected by Rs. The results of the noise measurements are depicted in c) for the

device ConstrB and d) for the device ConstrC (black squares). White squares refer to the thermal noise calculated from the measured conductance values according to Eq. 6.1. The insets show SEM images of the samples [138].

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