Microwave Hall effect in germanium and silicon at 20 kmc/s

Hambleton, G. E.; Gärtner, Wolfgang W.

doi:10.1016/0022-3697(59)90353-1

Cited by 29 publications

(6 citation statements)

References 6 publications

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“…The geometric factor G H was obtained to be G H = 6.7 ± 0.7 × 10 −8 Ω −1 from Eq. (11). The result of this procedure is shown in Fig.…”

Section: Figures 5(amentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8] Thus far, several studies have investigated the microwave Hall effect meaurement. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] In these studies, the most commonly used approach is the use of a bimodal cavity, which is a resonator with two orthogonal degenerate modes. 1,2 Since the two orthogonal degenerate modes are coupled with each other through the Hall effect, the bimodal cavity can be used to measure the Hall effect.…”

Section: Introductionmentioning

confidence: 99%

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Microwave Hall effect measurement for materials in the skin depth region

Ogawa,

Okada,

Takahashi

et al. 2020

Preprint

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We developed a new microwave Hall effect measurement method for materials in the skin depth region at low temperatures using a cross-shaped bimodal cavity. We analytically calculated electromagnetic fields in the cross-shaped cavity, and the response of the cavity including the sample, whose property is represented by the surface impedance tensor; further, we constructed the method to obtain the Hall component of the surface impedance tensor in terms of the change in resonance characteristics. To confirm the validity of the new method, we applied our method to measure the Hall effect in metallic Bi single crystals at low temperatures, and we confirmed that the microwave Hall angles coincide with the DC Hall angle. Thus, it becomes clear that the Hall angle measurement under cryogenic conditions becomes possible without any complicated tuning mechanisms, and our bimodal cavity method can be used to measure the microwave Hall effect on materials in the skin depth region. The result opens a new approach to discuss the Hall effect in condensed matter physics such as the microwave flux-flow Hall effect in superconductors.

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“…The geometric factor G H was obtained to be G H = 6.7 ± 0.7 × 10 −8 Ω −1 from Eq. (11). The result of this procedure is shown in Fig.…”

Section: Figures 5(amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Microwave Hall effect measurement for materials in the skin depth region

Ogawa,

Okada,

Takahashi

et al. 2020

Preprint

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“…In this paper, we study the use of a slotted microwave series tee and a microwave bridge for making the mobility measurement. A similar technique to ours uses two crossed waveguides to separate incident microwaves from outgoing microwaves produced by the Hall effect [6].…”

Section: A Motivationmentioning

confidence: 99%

“…A useful reference for the various microwave techniques used to characterize materials is [12]. This paper discusses a third method, where the Hall signal is induced in a sample wafer in one waveguide and then couples to a second waveguide that has a polarization orthogonal to the first waveguide [6].…”

Section: B Historymentioning

confidence: 99%

The microwave Hall effect measured using a waveguide tee

Coppock

Anderson

Johnson

2016

Journal of Applied Physics

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This paper describes a simple microwave apparatus to measure the Hall effect in semiconductor wafers. The advantage of this technique is that it does not require contacts on the sample or the use of a resonant cavity. Our method consists of placing the semiconductor wafer into a slot cut in an X-band (8 -12 GHz) waveguide series tee, injecting microwave power into the two opposite arms of the tee, and measuring the microwave output at the third arm. A magnetic field applied perpendicular to the wafer gives a microwave Hall signal that is linear in the magnetic field and which reverses phase when the magnetic field is reversed. The microwave Hall signal is proportional to the semiconductor mobility, which we compare for calibration purposes with d. c. mobility measurements obtained using the van der Pauw method. We obtain the resistivity by measuring the microwave reflection coefficient of the sample. This paper presents data for silicon and germanium samples doped with boron or phosphorus. The measured mobilities ranged from 270 to 3000 cm 2 /(V-sec).2

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“…Various microwave experiments which permit the measurement analo gous to that of Hall effect have been performed as mentioned in references (10) and (11). From observation at 20 GHz Hambleton and Gartner (12) first reported the difference between the d.c. and microwave Hall mobility in germanium at low temperatures. Later, Watanabe (13) and Ho (11) also found a deviation between the microwave and d.c. Hall mobili ties for both n-type and p-type germanium at low temperatures, but the discrepancy in the p-type samples was much larger than that in the n-type samples.…”

Section: B Previous Work On Microwave Hall Effect Measurementmentioning

confidence: 99%

Microwave Hall mobilities of holes in germanium

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Hall mobilities of three p-type germanium crystals were measured at microwave frequencies of 9.5 G Hz from room temperature to near liquid helium temperatures by means of a newly designed bimodal rectangular cavity. The microwave Hall mobilities were compared with the corres ponding d.c. Hall mobilities. As the temperature was decreased, the microwave Hall mobility began to deviate from the d.c. Hall mobility at about 200°K for each of the less pure samples 439GP and GPl, but not until 150°K for the purest sample 439HGP. The difference between the microwave and d.c. Hall mobilities at low temperatures was greater in the order 439GP > GPl > 439HGP, whereas the purity of the samples followed the opposite order 439HGP > GPl > 439GP. The difference between the microwave and d.c. Hall mobilities can be explained in terms of a high frequency inertial effect in which the relaxation time depends upon scattering of the holes by impurities as well as by phonons. This inertial effect accounts for the experimental results: one, at low temperatures, the microwave Hall mobility was always lower than the corresponding d.c. Hall mobility; and two, an increase in impurity scattering always increased the difference between the microwave and d.c. mobilities of the holes.

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Microwave Hall effect in germanium and silicon at 20 kmc/s

Cited by 29 publications

References 6 publications

Microwave Hall effect measurement for materials in the skin depth region

Microwave Hall effect measurement for materials in the skin depth region

The microwave Hall effect measured using a waveguide tee

Microwave Hall mobilities of holes in germanium

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