Rigorous Analysis of Traveling Wave Photodetectors

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1 Rigorous Analysis of Traveling Wave Photodetectors Damir Pasalic Prof. Dr. Rüdiger Vahldieck Laboratory for Electromagnetic Fields and Microwave Electronics (IFH) ETH Zurich Gloriastrasse 35, CH-8092 Zurich Switzerland Workshop on Numerical Methods for Optical Nanostructures ETH Zurich, January 20, 2005

2 Outline Introduction/Motivation Theory of TWPDs Numerical Simulation Semiconductor Analysis Full-wave EM Simulation Results Conclusion 2

3 Properties of TWPDs Can be designed for broad bandwidth and high efficiency at the same time Exhibit good performance under high-power optical illumination High-power TWPDs are of key importance as optical pre-amplification is more widely used No RC bandwidth limitation Easy to integrate with planar microwave circuits 3

TWPD Application: broadband OCS Optical fibers have: Low losses Unlimited bandwidth Bottleneck in capacity on receiver s side Key importance of

4 TWPD Application: broadband OCS Optical fibers have: Low losses Unlimited bandwidth Bottleneck in capacity on receiver s side Key importance of photodetectors with: Large bandwidth High efficiency Signal in Optical transmitter Optical Fiber Signal out Optical receiver Optical communication system 4

5 TWPD Application: optical heterodyning RF out ( ) I E cos 2 f RF t f RF 1 = c

6 Analysis of TWPDs Analyses performed using equivalent circuit model This type of analysis is: Linked to a specific geometry of the structure Effects like fringing fields and optical intensity are not taken into consideration There is a need for more general and accurate analysis/design tools 6

7 Theory of TWPDs In-plane illuminated device combining optical and RF waveguides Mesa type optical waveguide Microwave waveguide defined by the metal electrodes Bandwidth and efficiency almost independent of each other 3D view of a TWPD 7

8 TWPD Bandwidth Bandwidth limitations: Carrier life/drift time Velocity mismatch between the optical and RF waveguides RF attenuation constant (lossy structure for the microwave signal) Optical absorption coefficient (power handling capability) Optical reflection at the output facet of the TWPD 8

9 Numerical Modeling of TWPDs Analysis performed in two steps Step I: Semiconductor modeling under optical input Based on Drift-Diffusion Model (DDM) Output: Currents at the cross-section (J = J n + J p ) Step II: Full wave EM modeling (TLM, FDTD, FVTD, FEM) E = j µ H H = j E+ J 9

10 Drift-Diffusion Model Semiconductor modeling: Drift-Diffusion equations in time-domain Poisson Equation Continuity Equations Transport Equations 10

11 Drift-Diffusion Model (cont.) Drift-diffusion equations in compact form: After discretization: Newton s method n, p, J n, J p 11

12 Drift-Diffusion Model (cont.) y Semiconductor cladding Absorbing core Semiconductor cladding Substrate x Optical absorption coefficient Cross-section of a TWPD Optical frequency Optical field profile 12

13 Time-Domain TLM V +yz V +yx V -zy v V -zx V -xy V +xz V -xz V +xy V +zx V +zy V-yz V -yx w u 13

14 Time-Domain TLM scattering at the transition between two nodes scattering at the node center 14

15 Time-domain TLM - Current sources V +yz V +yx V -zy v V -zx V -xy V +xz V -xz V +xy V +zx V +zy V-yz yz-plane series subnode V -yx w yz-plane shunt subnode u 15

16 Time-domain TLM Current sources Equivalent circuit V I nx nx yz-plane series subnode ( ) ( ) 2( ) i i i i ( V7 V5) + ( V4 V8) 2 V + V Y + 2 V + V Y + 2V Y V = Y + Y + Y + G i i i i i i 1 12 z 2 9 y 13 sx = 4Z + R x y z sx x x yz-plane shunt subnode V 16 i = J sx Z 0 y z 16

17 Simulated TWPD opt = 0.83 µm opt = 4182 cm -1 K. S. Giboney, M. J. Rodwell, J. E. Bowers, Traveling-wave photodetector design and measurements, IEEE J. Selec. Topics in Quantum Electronics, vol. 2, no. 3, pp , September

18 Impulse Response FWHM opt = 150 fs FWHM RF calculated: 1.54 ps measured: 1.47 ps measurement and theory in good agreement RF Current and P opt RF current Optical Signal Time (ps) 18

19 Frequency Response TWPD s bandwidth calculated: 202 GHz measured: 190 GHz Lower frequencies good agreement inaccuracy of the material parameter values Higher frequencies experimental curve oscillates around the theoretical deviation due to measurements RF Power (db) Our simulation Experiment Frequency (GHz) 19

20 Conclusion A hybrid method for rigorous analysis of TWPDs has been presented The method is a combination of 2D driftdiffusion method and full-wave EM simulator Result of the DD analysis is the photogenerated current density at crosssection The photogenerated currents are used as sources in full-wave EM analysis 20

21 Conclusion EM analysis is based on time-domain TLM method The proposed method is tested on the example of a GaAs based TWPD Good agreement with the measured data is observed 21

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