The photodetector_avalanche photonic model was created to model avalanche photodetector elements. It provides the ability to model the impacts of multiplication factor and ionization ratio on the performance of avalanche photodetectors, as well as model both shot and thermal noise, and saturation effects.
The photodetector_avalanche photonic model supports statistical modeling. Users can choose an arbitrary number of statistical parameters and define their influence on the multiplication factor, responsivity, electro-optic bandwidth and dark current of the photodetector. For information on statistical CMLs, see Statistical CMLs.
Lumfoundry Templates: Avalanche Photodetector, Avalanche Photodetector (Statistical)
Quality Assurance Test: photodetector_avalanche QA
Statistical Modeling Support: multiplication factor, responsivity, bandwidth, dark current
Supported Parameters: responsivity, bandwidth, dark current, multiplication factor
Tuning Support: None.
Interoperability with Cadence Virtuoso:
- Circuit design flows using INTERCONNECT model: Yes.
- Circuit design flow using photonic Verilog-A model: Yes (no statistical modeling).
Model Information
- This model supports thermal noise, shot noise and power saturation.
- This model does not support pcells.
Electrical Equivalent Circuit for photonic Verilog-A model
The photonic Verilog-A model is compatible with Cadence Virtuoso design platform and its Spectre simulator. Electrical bandwidth and loading effect of the avalanche photodetector are described by an electrical equivalent circuit for Verilog-A model. The below figure shows a schematic of the electrical equivalent circuit for an avalanche photodetector Verilog-A model, which can be created by running CML Compiler GUI with the Verilog-A option checked.
Electrical bandwidth and loading effect of the avalanche photodetector are described by an electrical equivalent circuit for Verilog-A model. The below figure shows a schematic of the electrical equivalent circuit for an avalanche photodetector Verilog-A model, which can be created by running CML Compiler GUI with the Verilog-A option checked.
Parameter | Description | Unit | Comments |
Cp | Parasitic capacitance | F |
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Rp | Contact resistance | ohm |
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Rs | Parasitic resistance | ohm |
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Ca | Depletion capacitance | F |
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Rd | Drift resistance | ohm |
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Rl | Leakage resistance | ohm |
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Ra | Current saturation resistance | ohm |
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La | Current saturation inductance | H |
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When simulating the photonic Verilog-A APD model using Spectre, the electrical equivalent circuit and the photonic APD model are implemented inside the compiled photonic Verilog-A APD model as shown below. Spectre simulates both the electrical equivalent circuit for the APD’s electrical characteristics and the photonic APD model for its optical characteristics.
Supplementary Information
This avalanche photodetector model implements a bias-dependent multiplication factor to model bias-dependent dark current and responsivity of the photodetector. The dark current and responsivity values that are input to the model must be given at unity gain bias (i.e., the bias where the multiplication factor is equal to one). Here, we define the unity gain bias to be where the second derivative of the photocurrent with respect to the voltage is zero [1]. The figure below displays the dark and photo current as a function of bias (compared to publication data in [2]). The unity gain bias was calculated to be -3 V, and is marked in green. For more information on extracting the multiplication factor as a function of bias, please see Avalanche Photodetector, and 10-V Ge-on-Si APD with Si multiplication.
This model interpolates multiplication factor values at bias points that are not provided in the source data. The multiplication factor matrix should provide sufficient bias points to accurately model the photodetector behavior, especially near the breakdown bias where multiplication factor values may vary significantly.
Responsivity, dark current, bandwidth, and multiplication factor are statistically enabled in this model. Because multiplication factor is used to update the responsivity and dark current, enabling statistical variations in multiplication factor will result in statistical variations in responsivity and dark current, regardless of whether these are explicitly defined. Statistical variation values for responsivity and dark current should be provided at unity gain bias, and should be independent of variations from multiplication factor.
[1]. H. T. J. Meier, "Design, characterization and simulation of avalanche photodiodes," Ph.D. dissertation, ETH Zurich, no. 19519, 2011.
[2] Z. Huang, et. al. "25 Gbps low-voltage waveguide Si-Ge avalanche photodiode," Optica, vol. 3, no. 8, pp. 793-798, Aug. 2016.