### Abstract

In accord with the Drude model, the free-carrier contribution to the dielectric function at infrared wavelengths is proportional to the ratio of the free-carrier concentration N and the effective mass m, and the product of the optical mobility μ and m. Typical infrared optical experiments are therefore sensitive to the free-carrier mass, but determination of m from the measured dielectric function requires an independent experiment, such as an electrical Hall-effect measurement, which provides either N or μ. However, doped zincblende III-V-semiconductors exposed to a strong external magnetic field exhibit non-symmetric magneto-optical (MO) birefringence, which is inversely proportional to m. Therefore, if the spectral dependence of the MO dielectric function tensor is known, the parameters N, μ and m can be determined independently from optical measurements alone. Generalized Ellipsometry (GE) measures three complex-valued ratios of normalized Jones matrix elements, from which the individual tensor elements of the dielectric function of arbitrarily anisotropic materials in layered samples can be reconstructed. We present the application of GE at far-infrared (FIR) wavelengths for measurement of the FIR-MO-GE parameters, and determine the MO dielectric function of GaAs for wavelengths from 100 μm to 15 μm. We obtain the free electron mass and mobility results in excellent agreement with results obtained from Hall-effect and Shubnikov-de-Haas experiments. (F)IR-MO-GE may open up new avenues for non-destructive characterization of free-carrier properties in complex semiconductor heterostructures.

Original language | English (US) |
---|---|

Pages (from-to) | 90-97 |

Number of pages | 8 |

Journal | Proceedings of SPIE - The International Society for Optical Engineering |

Volume | 4779 |

DOIs | |

State | Published - Dec 1 2002 |

Event | Advanced Characterization Techniques for Optical, Semiconductor, and data Storage Components - Seattle, WA, United States Duration: Jul 9 2002 → Jul 11 2002 |

### Fingerprint

### Keywords

- Ellipsometry
- Free-carrier properties
- Magneto-optic birefringence

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Computer Science Applications
- Applied Mathematics
- Electrical and Electronic Engineering

### Cite this

*Proceedings of SPIE - The International Society for Optical Engineering*,

*4779*, 90-97. https://doi.org/10.1117/12.453722

**Far-infrared magneto-optical generalized ellipsometry determination of free-carrier parameters in semiconductor thin film structures.** / Hofmann, T.; Schubert, M.; Herzinger, C. M.

Research output: Contribution to journal › Conference article

*Proceedings of SPIE - The International Society for Optical Engineering*, vol. 4779, pp. 90-97. https://doi.org/10.1117/12.453722

}

TY - JOUR

T1 - Far-infrared magneto-optical generalized ellipsometry determination of free-carrier parameters in semiconductor thin film structures

AU - Hofmann, T.

AU - Schubert, M.

AU - Herzinger, C. M.

PY - 2002/12/1

Y1 - 2002/12/1

N2 - In accord with the Drude model, the free-carrier contribution to the dielectric function at infrared wavelengths is proportional to the ratio of the free-carrier concentration N and the effective mass m, and the product of the optical mobility μ and m. Typical infrared optical experiments are therefore sensitive to the free-carrier mass, but determination of m from the measured dielectric function requires an independent experiment, such as an electrical Hall-effect measurement, which provides either N or μ. However, doped zincblende III-V-semiconductors exposed to a strong external magnetic field exhibit non-symmetric magneto-optical (MO) birefringence, which is inversely proportional to m. Therefore, if the spectral dependence of the MO dielectric function tensor is known, the parameters N, μ and m can be determined independently from optical measurements alone. Generalized Ellipsometry (GE) measures three complex-valued ratios of normalized Jones matrix elements, from which the individual tensor elements of the dielectric function of arbitrarily anisotropic materials in layered samples can be reconstructed. We present the application of GE at far-infrared (FIR) wavelengths for measurement of the FIR-MO-GE parameters, and determine the MO dielectric function of GaAs for wavelengths from 100 μm to 15 μm. We obtain the free electron mass and mobility results in excellent agreement with results obtained from Hall-effect and Shubnikov-de-Haas experiments. (F)IR-MO-GE may open up new avenues for non-destructive characterization of free-carrier properties in complex semiconductor heterostructures.

AB - In accord with the Drude model, the free-carrier contribution to the dielectric function at infrared wavelengths is proportional to the ratio of the free-carrier concentration N and the effective mass m, and the product of the optical mobility μ and m. Typical infrared optical experiments are therefore sensitive to the free-carrier mass, but determination of m from the measured dielectric function requires an independent experiment, such as an electrical Hall-effect measurement, which provides either N or μ. However, doped zincblende III-V-semiconductors exposed to a strong external magnetic field exhibit non-symmetric magneto-optical (MO) birefringence, which is inversely proportional to m. Therefore, if the spectral dependence of the MO dielectric function tensor is known, the parameters N, μ and m can be determined independently from optical measurements alone. Generalized Ellipsometry (GE) measures three complex-valued ratios of normalized Jones matrix elements, from which the individual tensor elements of the dielectric function of arbitrarily anisotropic materials in layered samples can be reconstructed. We present the application of GE at far-infrared (FIR) wavelengths for measurement of the FIR-MO-GE parameters, and determine the MO dielectric function of GaAs for wavelengths from 100 μm to 15 μm. We obtain the free electron mass and mobility results in excellent agreement with results obtained from Hall-effect and Shubnikov-de-Haas experiments. (F)IR-MO-GE may open up new avenues for non-destructive characterization of free-carrier properties in complex semiconductor heterostructures.

KW - Ellipsometry

KW - Free-carrier properties

KW - Magneto-optic birefringence

UR - http://www.scopus.com/inward/record.url?scp=0036983888&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036983888&partnerID=8YFLogxK

U2 - 10.1117/12.453722

DO - 10.1117/12.453722

M3 - Conference article

AN - SCOPUS:0036983888

VL - 4779

SP - 90

EP - 97

JO - Proceedings of SPIE - The International Society for Optical Engineering

JF - Proceedings of SPIE - The International Society for Optical Engineering

SN - 0277-786X

ER -