Carrier concentration and lattice absorption in bulk and epitaxial silicon carbide determined using infrared ellipsometry

Abstract

Wetteroth, T.; Wilson, S. R.; and Powell, Adrian R., "Carrier concentration and lattice absorption in bulk and epitaxial silicon carbide determined using infrared ellipsometry" (1999 Carrier concentration and lattice absorption in bulk and epitaxial silicon carbide determined using infrared ellipsometry We have measured the dielectric function of bulk nitrogen-doped 4H and 6H SiC substrates from 700 to 4000 cm Ϫ1 using Fourier-transform infrared spectroscopic ellipsometry. Photon absorption by transverse optical phonons produces a strong reststrahlen band between 797 and 1000 cm Ϫ1 with the effects of phonon anisotropy being observed in the region of the longitudinal phonon energy ͑960 to 100 cm Ϫ1 ͒. The shape of this band is influenced by plasma oscillations of free electrons, which we describe with a classical Drude equation. For the 6H-SiC samples, we modify the Drude equation to account for the strong effective mass anisotropy. Detailed numerical regression analysis yields the free-electron concentrations, which range from 7ϫ10 17 to 10 19 cm Ϫ3 , in good agreement with electrical and secondary ion mass spectrometry measurements.Finally, we observe the Berreman effect near the longitudinal optical phonon energy in nϪ/nϩ homoepitaxial 4H SiC and hydrogen implanted samples, and we are able to determine the thickness of these surface layers.

Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons

“…At the Fröhlich resonance with Re(ε) = -2, ωdRe(ε)/dω∼10-30 for both noble metals and doped semiconductors (with values ≈20 for Ag [90]), the permittivity dispersion is enhanced in SPhP materials. For 4H-SiC at λ = 10.7 μm, ωdRe(ε)/dω≈60 [57], while for GaAs at λ = 34.6 μm, ωdRe(ε)/dω≈150 [59]. From Eqs.…”

“…2)] as a function of Re(ε) is shown for the SPhP materials 4H-SiC [57] and GaAs [59], and the plasmonic materials n-type InGaAs [29], and silver [89,90] in Figure 4A. A more comprehensive comparison of a wide range of plasmonic metals (red circles), metal alloys (pink hexagons), doped semiconductors (blue stars) and SPhP materials (green squares) are provided in Figure 4B.…”

“…(2.2). The spectral dependence of the permittivity calculated for a 4H-SiC epitaxial layer from infrared spectroscopic ellipsometry results reported by Tiwald et al [57] are presented for the entire Reststrahlen band in Figure 3A, and a magnified view covering the range of 1 ≥ Re(ε) ≥ -20 is provided in Figure 3C. For comparison, Figure 3B and D give the corresponding plots for the lowest-loss plasmonic material, silver, using optical constants from both Palik's compendium (solid lines) [89] and Johnson and Christie (dashed lines) [90].…”

“…The application of Eq. (3.2) gives maximum Q values > 600 using the optical constants reported by Tiwald et al [57], and 2)] for 4H-SiC (green trace) [57] and GaAs (blue trace) [59] SPhP and n-type In 0.3 Ga 0.7 As (red trace) [29] and Ag [using optical constants from Palik (solid gray trace) [89] and Johnson and Christy (dashed light gray trace) [90]] SPP localized resonators as a function of Re(ε). (B) Comparison of Q for a spherical particle in air for all SPP and SPhP materials listed in Tables 1 and 2, respectively.…”

“…SPhPs are the result of polar optical phonons interacting with long-wavelength incident fields from the mid-IR (e.g., hexagonal BN [52][53][54][55] and SiC [20,23,56,57]) to < 10 THz (e.g., GaAs [58,59], InP [60] and CaF 2 [61]), creating a surface excitation mediated by the atomic vibrations. Such SPhP modes can be stimulated in polar dielectric crystals between the longitudinal (LO) and transverse optic (TO) phonon frequencies, with this spectral range referred to as the "Reststrahlen" band [60,62,63].…”