Far-infrared absorption of silicon crystals

Ohba, Tetsuhiko; Ikawa, Shun‐ichi

doi:10.1063/1.341325

Cited by 54 publications

(33 citation statements)

References 8 publications

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“…The dependence of the mobility on carrier density for the three theoretical fits to the data are all fit by the empirical Caughey-Thomas curve [19] with different parameters. At the lower carrier densities the C-D and Drude mobilities are much higher than previous measurements [3,19]. At carrier densities above 10 17 cm 23 these differences disappear and the theories converge.…”

mentioning

confidence: 34%

“…Compared to earlier experimental studies of doped silicon [1,3], these new results have sufficient frequency range and precision to test alternative theories [4][5][6][7][8][9][10][11][12] for the conductivity. However, for both n-and p-type silicon and over a measured range of more than 2 orders of magnitude of the carrier density we do not find agreement with any standard theory, including Drude, lattice-scattering, and impurity-scattering theories.…”

mentioning

confidence: 98%

“…We also show in Fig. 1(a) an earlier absorption measurement [3] (squares) of nonintentionally doped 9.4 V cm, n-type silicon made with a synchrotron radiation source and bolometric power detection.…”

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confidence: 99%

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Nature of Conduction in Doped Silicon

1997

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Via ultrafast optoelectronic THz techniques, we are able to test alternative theories of conduction by precisely measuring the complex conductivity of doped silicon from low frequencies to frequencies higher than the plasma frequency and the carrier damping rate. These results, obtained for both n and p-type samples, spanning a range of more than 2 orders of magnitude in the carrier density, do not fit any standard theory. We only find agreement over the full frequency range with the complex conductivity given by a Cole-Davidson type distribution applied here for the first time to a crystalline semiconductor, and thereby demonstrate that fractal conductivity is not just found in disordered material.[ S0031-9007(96) The frequency dependent complex conductivity is one of the most basic properties describing doped semiconductors. Associated with the conductivity are the key parameters characterizing the dynamics of the free carriers in semiconductors, the plasma frequency v p , and the carrier damping rate G 1͞t, where t is the carrier collision time. Characteristically, v p and G have THz frequencies. Even though the complex conductivity has been a topic of theoretical studies for several decades, complete experimental characterizations from low frequencies to beyond several THz have only started to be performed [1,2].Here we report definitive measurements of the complex conductivity from dc to 2.5 THz on doped silicon. Compared to earlier experimental studies of doped silicon [1,3], these new results have sufficient frequency range and precision to test alternative theories [4][5][6][7][8][9][10][11][12] for the conductivity. However, for both n-and p-type silicon and over a measured range of more than 2 orders of magnitude of the carrier density we do not find agreement with any standard theory, including Drude, lattice-scattering, and impurity-scattering theories. As a result, we were forced to look outside the standard theoretical approaches.Our interest in a Cole-Davidson type distribution was motivated by the close relationship between the Debye theory of dielectric insulators and Drude theory, the simplest theory of electrical conduction. For Debye theory, in response to a step-function electric field, the polarization is established exponentially with a characteristic response time. Similarly, for Drude theory, in response to a stepfunction E field, the current is established exponentially with the carrier collision time. Consequently, in the frequency domain the mathematical representations of these two theories are identical. It has been found experimentally that for relatively low frequencies the complex dielectric constants of disordered materials, such as molecular liquids [13], polymers [14], and more recently ionic glasses [15,16], show better agreement with a modified Debye spectral response, known as the Cole-Davidson (C-D) distribution. In the frequency domain, the C-D distribution corresponds to Debye theory with a fractional exponent b, limited to values between 0 and 1, and reduces to Debye th...

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Nature of Conduction in Doped Silicon

1997

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“…Its optical properties are shown in Table 1 in comparison to other common materials. A high-resistivity (>10 kΩ cm) and high-purity silicon crystal, grown by the float-zone (FZ) method, shows, below 2 THz, an absorption coefficient lower than 16,17 0.05 cm −1 and a constant index of refraction of 17 3.418±0.001. Moreover, the optical isotropy of silicon allows flexible orientation, regardless of the polarization of the incident T-rays and the crystal orientation.…”

Section: Siliconmentioning

confidence: 99%

Retrofittable T-ray antireflection coatings

et al. 2006

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Terahertz time-domain spectroscopy (THz-TDS) is able to extract optical or dielectric properties of materials, whether in the solid, liquid, or gas phase, in the T-ray frequency region. Spectroscopy of a liquid or gas often requires a receptacle to confine the sample. In order to allow T-rays to probe the sample effectively, the receptacle must have T-ray transparent windows. However, even though windows are transparent to T-rays, attenuation exists, because of multiple reflections at air-window and window-air interfaces, which accounts for a major energy loss. Due to the recent emergence of T-ray technology, there has been very little work carried out to-date on the reduction of reflection losses. This paper analyses the reduction of T-ray reflection loss by means of an antireflection coating. Because T-ray wavelengths are much larger than visible wavelengths, the antireflection layer thickness for T-rays is much larger than the usual optical case. This creates an interesting opportunity for retrofittable antireflection layers in T-ray systems. In the experiment, a coating material made from polyethylene sheets is applied onto the surfaces of a silicon window. The coated window shows enhancement of the transmittance within a range of frequencies.

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“…Silicon etalons could then be established as calibration reflection standards, based on the small uncertainties achieved in measuring their optical properties and by exploiting the low loss nature of the material. (7,8) …”

Section: Introductionmentioning

confidence: 99%

Characterization of Material Properties at Terahertz Frequencies

Giles¹

1995

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Far-infrared absorption of silicon crystals

Cited by 54 publications

References 8 publications

Nature of Conduction in Doped Silicon

Nature of Conduction in Doped Silicon

Retrofittable T-ray antireflection coatings

Characterization of Material Properties at Terahertz Frequencies

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