Electrical Modeling of Long-Wavelength VCSELs for Intrinsic Parameters Extraction

• Published in: IEEE journal of quantum electronics Vol. 46; no. 3; pp. 313 - 322
• Main Authors: Bacou, A., Hayat, A., Iakovlev, V., Syrbu, A., Rissons, A., Mollier, J.-C., Kapon, E.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-03-2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Chips; Circuits; Coplanar transmission lines; Delay; Devices; Distributed parameter circuits; Electric circuits; Electrical modeling; Equations; Exact sciences and technology; Extraction; Frequency response; Fundamental areas of phenomenology (including applications); Holes; intrinsic parameters; Lasers; long-wavelength VCSELs; Mathematical models; Modulation; Optical modulation; Optics; Parameter extraction; Physics; Semiconductor device measurement; Semiconductor lasers; laser diodes; Transmission line measurements; turn-on delay; Vertical cavity surface emitting lasers; wafer-fusion; {\rm S} -parameters; Electrical modeling; Optimization method; S-parameters; turn-on delay; Vertical cavity laser; Semiconductor lasers; Dynamic measurement; long-wavelength VCSELs; Surface emitting lasers; Optical resonators; Rate equation; intrinsic parameters; wafer-fusion; T matrix; Frequency response; Equivalent circuits
• ISSN: 0018-9197; 1558-1713
• DOI: 10.1109/JQE.2009.2031312

We present an efficient method to model the small- signal modulation response of a long-wavelength VCSEL chip using an equivalent electrical circuit. This circuit serves two distinct purposes. Based on T-matrix formalism, it is used to remove the parasitics contribution originating from the electrical access of the chip in order to obtain the optical cavity intrinsic frequency response as defined by the rate equations. The same circuit is also used to extract the intrinsic cavity parameters since every circuit element represents a physical optical cavity entity. The extraction of reliable intrinsic parameters requires that the circuit element values be representative of the device under test. To achieve this, we have developed a new methodology based on static and dynamic measurements such as the S-parameters and the turn-on delay time. In accordance with this procedure, each element of the cavity is fixed without numerical optimization. The good agreement between measured and simulated curves confirm the validity of the technique used.