JANUARY 1987 | RICHARD A. SOREF, SENIOR MEMBER, IEEE, AND BRIAN R. BENNETT
This paper presents a numerical Kramers-Kronig analysis to predict refractive-index perturbations in crystalline silicon caused by electric fields or charge carriers. The analysis covers the 1.0-2.0 μm optical wavelength range and uses experimental electroabsorption and impurity-doping spectra from the literature. For electrorefraction at the indirect gap, a Δn of 1.3 × 10⁻⁵ is found at λ = 1.07 μm when E = 10⁵ V/cm, while the Kerr effect gives Δn = 10⁻⁶ at that field strength. Charge-carrier effects are larger, with a depletion or injection of 10¹⁸ carriers/cm³ producing an index change of ±1.5 × 10⁻³ at λ = 1.3 μm.
The paper discusses electrorefraction and carrier refraction in crystalline silicon. Electrorefraction is field-induced tunneling between valence and conduction band states, while carrier refraction is due to changes in charge carrier concentration. The Franz-Keldysh effect modifies the absorption spectrum of silicon, and electroabsorption is measured at the indirect gap. The electrorefraction results show that Δn is positive for λ > 1.05 μm and is a strong function of wavelength. At λ = 1.07 μm, Δn = +1.3 × 10⁻⁵ when E = 10⁵ V/cm.
The Kerr effect, which is present in silicon, is discussed, and its strength is estimated using the anharmonic oscillator model. The predicted Δn reaches 10⁻⁴ at E = 10⁶ V/cm. The paper also discusses charge-carrier effects, including free-carrier absorption, Burstein-Moss bandfilling, and Coulombic interaction of carriers with impurities. These effects are analyzed using experimental data from the literature.
The paper concludes that carrier refraction is the larger effect, and that the refractive index increases when carriers are depleted from doped material and decreases when carriers are injected. The paper also discusses the practical design of guided-wave modulators and 2×2 switches using electrooptic phase modulation without significant amplitude modulation. The results show that a tradeoff can be made between phase shift and loss, allowing for complete 2×2 switching with less than 1 dB of excess optical loss. The paper also discusses the response times of electrorefraction and carrier refraction, with electrorefraction having subpicosecond response times and carrier refraction having faster response times due to carrier sweep out.This paper presents a numerical Kramers-Kronig analysis to predict refractive-index perturbations in crystalline silicon caused by electric fields or charge carriers. The analysis covers the 1.0-2.0 μm optical wavelength range and uses experimental electroabsorption and impurity-doping spectra from the literature. For electrorefraction at the indirect gap, a Δn of 1.3 × 10⁻⁵ is found at λ = 1.07 μm when E = 10⁵ V/cm, while the Kerr effect gives Δn = 10⁻⁶ at that field strength. Charge-carrier effects are larger, with a depletion or injection of 10¹⁸ carriers/cm³ producing an index change of ±1.5 × 10⁻³ at λ = 1.3 μm.
The paper discusses electrorefraction and carrier refraction in crystalline silicon. Electrorefraction is field-induced tunneling between valence and conduction band states, while carrier refraction is due to changes in charge carrier concentration. The Franz-Keldysh effect modifies the absorption spectrum of silicon, and electroabsorption is measured at the indirect gap. The electrorefraction results show that Δn is positive for λ > 1.05 μm and is a strong function of wavelength. At λ = 1.07 μm, Δn = +1.3 × 10⁻⁵ when E = 10⁵ V/cm.
The Kerr effect, which is present in silicon, is discussed, and its strength is estimated using the anharmonic oscillator model. The predicted Δn reaches 10⁻⁴ at E = 10⁶ V/cm. The paper also discusses charge-carrier effects, including free-carrier absorption, Burstein-Moss bandfilling, and Coulombic interaction of carriers with impurities. These effects are analyzed using experimental data from the literature.
The paper concludes that carrier refraction is the larger effect, and that the refractive index increases when carriers are depleted from doped material and decreases when carriers are injected. The paper also discusses the practical design of guided-wave modulators and 2×2 switches using electrooptic phase modulation without significant amplitude modulation. The results show that a tradeoff can be made between phase shift and loss, allowing for complete 2×2 switching with less than 1 dB of excess optical loss. The paper also discusses the response times of electrorefraction and carrier refraction, with electrorefraction having subpicosecond response times and carrier refraction having faster response times due to carrier sweep out.