Electrooptical Effects in Silicon

Electrooptical Effects in Silicon

VOL. QE-23, NO. 1, JANUARY 1987 | RICHARD A. SOREF, SENIOR MEMBER, IEEE, AND BRIAN R. BENNETT
This paper investigates the electrooptical effects in crystalline silicon, focusing on the refractive-index changes induced by applied electric fields and charge carriers. The authors use a numerical Kramers-Kronig analysis to predict these changes over the 1.0-2.0 μm optical wavelength range, utilizing experimental electroabsorption and impurity-doping spectra. Key findings include: 1. **Electrorefraction**: At λ = 1.07 μm, an electrorefraction of Δn = +1.3 × 10^-5 is observed for E = 10^5 V/cm, attributed to indirect-gap electroabsorption. 2. **Kerr Effect**: The Kerr effect results in a Δn = +10^6 at the same field strength. 3. **Charge-Carrier Effects**: Depletion or injection of 10^10 carriers/cm^3 produces a Δn change of ±1.5 × 10^-3 at λ = 1.3 μm for free holes and ±2.1 × 10^-3 at λ = 1.55 μm for free electrons, with a carrier concentration dependence of Δn ~ (ΔN)^0.8 for holes and Δn ~ (ΔN)^1.05 for electrons. The paper also discusses the theoretical models and experimental data used to support these findings, including the Franz-Keldysh effect, the anharmonic oscillator model for the Kerr effect, and the impact of impurity doping on optical properties. The authors conclude by discussing the practical implications for guided-wave modulators and switches, emphasizing the trade-offs between phase shift and loss in electrooptical devices.This paper investigates the electrooptical effects in crystalline silicon, focusing on the refractive-index changes induced by applied electric fields and charge carriers. The authors use a numerical Kramers-Kronig analysis to predict these changes over the 1.0-2.0 μm optical wavelength range, utilizing experimental electroabsorption and impurity-doping spectra. Key findings include: 1. **Electrorefraction**: At λ = 1.07 μm, an electrorefraction of Δn = +1.3 × 10^-5 is observed for E = 10^5 V/cm, attributed to indirect-gap electroabsorption. 2. **Kerr Effect**: The Kerr effect results in a Δn = +10^6 at the same field strength. 3. **Charge-Carrier Effects**: Depletion or injection of 10^10 carriers/cm^3 produces a Δn change of ±1.5 × 10^-3 at λ = 1.3 μm for free holes and ±2.1 × 10^-3 at λ = 1.55 μm for free electrons, with a carrier concentration dependence of Δn ~ (ΔN)^0.8 for holes and Δn ~ (ΔN)^1.05 for electrons. The paper also discusses the theoretical models and experimental data used to support these findings, including the Franz-Keldysh effect, the anharmonic oscillator model for the Kerr effect, and the impact of impurity doping on optical properties. The authors conclude by discussing the practical implications for guided-wave modulators and switches, emphasizing the trade-offs between phase shift and loss in electrooptical devices.
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[slides and audio] Electrooptical effects in silicon