In this example, we will study the performance of a hybrid silicon-photonics photodetector. The uni-traveling carrier (UTC) photodetector (PD) is fabricated from an InP/InGaAs system, and evanescently coupled to the silicon waveguide. The optical response of the PD, including input taper, is analyzed with FDTD and CHARGE is used to simulate the electrical behaviour, including the transient response.
Overview
Understand the simulation workflow and key results
Photo-detectors convert optical signals into electrical signals to recover the information encoded on the optical channel. These components can be accurately simulated and optimized using a combination of optical and electrical solvers. The optical properties of the photodetector are simulated using the finite-difference time-domain (FDTD) method; the local generation rate of electron-hole pairs can be calculated from optical absorbed power. This generation rate then appears as a source term in the continuity equations solved in the electrical simulation (more information).
For high-speed photodiodes, the uni-traveling carrier (UTC) design can be used to optimize transit time response by decoupling the absorbing layer from the collection layer [1]. In traditional PIN structures, carriers are photogenerated in the intrinsic (I) region, where a strong field separates them to generate the photocurrent. The velocity of the carriers is typically limited, and in most common material systems (e.g. Germanium) holes are slower than electrons, leading to a delayed and asymmetric response. By combining narrow and wide band-gap semiconductors, a single carrier type (typically the electrons) can be isolated, such that the photoresponse of the device is only dependent on the transport of those carriers. However, in comparison to PIN photodiodes, the band structure requirements of the UTC typically require III-V materials to implement, introducing additional processing requirements when integrating with silicon systems.
In this example, we base the design on the InP/InGaAs waveguide photodiode heterogeneously integrated on a silicon photonic integrated circuit [2]. The referenced design is comprised of a 100nm thick InP bonding/matching layer, a 250nm thick InGaAs absorber, and a 700nm thick InP intrinsic collection layer. The material stack and the associated band structure are shown in the figure below. Photodetectors with lengths of 25um, 50um, and 150um were measured [2].
Run and results
Instructions for running the model and discussion of key results
Step 1: Optical Design
- Open [[utc_pd.fsp]] and run the simulation file.
- Right click on the "generation" analysis group from the Objects Tree and select "Run analysis". The analysis group calculates the generation rate in the InGaAs absorber layer and saves the results in [[utc_pd_ogr_50.mat]] file.
The structure can be modified to include or exclude the taper – in this example, the taper is excluded (we assume an ideal mode expander) by setting the taper length to 0 um in the model properties. A mode source (λ = 1.55 um) is used as the input, and a construction group is used to adjust the layered structured of the PD. A generation rate analysis group is used to record the E field in the PD and calculate the optical generation rate. The following figures illustrate the optical generation rates in different PD planes. The minimum values of the color bars are adjusted to better highlight the variations in the generation rate.
The optical generation rate is averaged in the direction of optical propagation (y) and saved to a data file for CHARGE by the generation rate analysis object.
The generation rate analysis object also calculates the responsivity of the detector based on the input power and the total current calculated from the analysis volume. Adjusting the length of the detector, variation in the responsivity is observed. For comparison, the estimated responsivity from [2] is 0.8A/W. In the FDTD simulation, the amount of absorbed light is determined by the specified index of the InGaAs layer.
| Length (um) | Input Power (mW) | Ideal Photocurrent (mA) | Ideal Responsivity (A/W) |
|---|---|---|---|
| 25 | 10 | 5.8 | 0.58 |
| 50 | 10 | 11 | 1.1 |
Step 2: Electrical Design and Optoelectronic Response
Steady State: Dark Current and Responsivity
- Open [[utc_steady_state.ldev]] project file and run it.
- Open the script file utc_analyze_iv.lsf and run it. It runs steady-state CHARGE simulations under dark and illumination conditions and plots the dark current and photocurrent.
Nominal dark currents were measured to be less than 10nA in [2]. To simulate the steady-state behaviour of the PD, the bias is swept from -5V to 1.5V (two simulations are run: from 0 to -5V and from 0 to 1.5V). The optical generation rate is imported from the FDTD simulation for the 50um PD so running the time-consuming optical simulation can be skipped. As shown in the plot below, the responsivity is 1.07A/W, indicating negligible recombination loss. The dark current at 5V reverse bias is set to ~1nA by reducing the carrier lifetime in the InGaAs absorbing layer. Note that given the complexity of the device a very fine mesh is required which will result in a large simulation time.
Small-Signal Analysis - Capacitance Extraction and Bandwidth Calculation
- Open [[utc_ssac.ldev]] and run the simulation.
- Open the script file utc_ssac_extract.lsf and run it. It runs an SSAC CHARGE simulation and plots the magnitude of ac current, anode and cathode capacitance as a function of frequency.
The photodetector's dynamic response can be analyzed to derive an equivalent circuit model that accurately captures both the transit-time delay and the RC behavior associated with diode admittance [3]. First, to extract the diode admittance, we perform a small-signal analysis at varying bias voltages under dark condition. The small-signal model for the diode includes a series resistance RS ~ 0 and voltage dependent capacitance C(V). The conductance is negligible (e.g. VR/Idark > 1GΩ). Each of the impedances in the diode model are interpreted as densities with respect to the surface area of the PD (e.g. capacitance per unit area), and should be scaled accordingly.
To extract the impedances, we use the admittance function for the diode:
$$ Y(\omega)=\frac{I_{o}}{V_{i}}=\left(R_{S}+\frac{1}{j \omega C}\right)^{-1} \approx j \omega C $$
The project file utc_ssac.ldev is set up to sweep the bias voltage (dc) from 0 to 5 V at the cathode contact (reverse bias operation) and the perform a small-signal analysis at the end point (5 V). The small-signal analysis is performed for a frequency range of 1 GHz to 100 GHz for a small-signal ac voltage of 0.001 V. Once the simulation is run, the small-signal ac current at the contacts can be plotted as a function of frequency. Figure below (top) shows the magnitude of the small-signal current at the anode contact. Since the admittance of the photodetector increases linearly with frequency, the current versus frequency plot is a straight line. Using the utc_ssac_extract.lsf script file we can calculate the admittance of the PD and hence the value of the capacitance as a function of frequency (bottom figure).
From this response, the collection layer capacitance is determined to be 0.14 fF/um\(^2\) for the entire frequency range. Details of the additional parasitic capacitances included in the RC bandwidth calculations are shown in the last step (transient simulation section).
- Open and the script file utc_ssac_photo.lsf.
The script performs a small-signal simulation to evaluate the normalized frequency response and operational bandwidth of the photodetector under optical illumination. A small perturbation is applied to the DC optical generation rate, and a negative bias is applied to the anode to operate the photodetector under reverse bias condition. The high-field mobility model is enabled in the InP layers to account for carrier velocity saturation at high electric fields, which plays an important role in accurately determining the transit-time-limited bandwidth. The electron mobility in InP is modeled using the overshoot model, which is widely used in literature to account for electron drift velocity overshoot. In contrast, the monotonic model is employed for holes, as the valence band is characterized by a single valley (\(\Gamma\)). The normalized photocurrent of the photodetector is plotted as a function of the small-signal frequency. The 3 dB bandwidth of the photodetector under a reverse bias of 2 V is found to be around 39 GHz.
| NOTE: In 2026 R1.3, we introduced two new options for driving fields in the high-field mobility model (E and E dot J approx) to improve the convergence of CHARGE simulations that include high-field mobility effects. For more details, please visit Semiconductor Material Model Properties. |
The users can set the check_other_driving_fields variable to true to repeat the SSAC simulations using two new alternative driving-field models: “E” and “E dot J approx” (which require 2026 R1.3). They yield results that are nearly identical to the results with “E dot J” model (shown above) and usually have a higher solver convergence success rate.
Transient Response - Transit Time and Total Bandwidth
- Open [[utc_pulse.ldev]].
- Open and run the script [[utc_transient_pulse.ldev]].
The above schematic depicts the parasitic capacitances included in the total bandwidth calculations. \(C_d\) is calculated to be 0.14 dF/um\(^2\) from the SSAC simulation. Assuming a conductive substrate, there will be a parasitic capacitance between the p+ absorption layer and the substrate (insulated by the non-intentionally doped silicon wave guiding layer and buried oxide). Assuming a 2um buried oxide and 0.7um silicon layer, a simple parallel plate capacitance estimate of \(C_{\mathrm{sub}}\) = 0.013fF/um\(^2\). is obtained. Note that the absorption layer is also used to contact the device (anodes), and will have approximately twice the surface area as the PD. Additionally, a static field analysis of the metal anode and cathode contacts (excluding the fields concentrated in the PD) gives a small contact capacitance contribution of \(C_{c}\) = 0.07fF/um (note the length units). The overall capacitance is then
$$ C=\left(C_{d}+C_{s u b}\right) A+C_{c} L $$
which has a value of approximately 80 fF for a 50um x 10um PD.
To analyze the RC bandwidth, a model of the resistance that includes the load resistance and resistive density of the contact interface is used, with values from [2].
$$ R=R_{L}+\frac{\rho_{c}}{A} $$
where RL = 50Ω and ρc = 10kΩ.um\(^2\).
Note that the simulation is configured to run in a 1D vertical slice of the PD, which improves the simulation efficiency and enables the use of a fine mesh to resolve the critical junctions. To analyze the transit time response, the global shutter is used to turn the light source (generation rate) on and off to generate an optical pulse. The settings for the shutter can be found under the "Transient" tab of the "CHARGE" solver properties.
The high-field mobility model in the InP layers is also included in the transient simulation to provide a reliable estimate of the transit-time limited bandwidth. The material parameters are kept identical to those used in the final SSAC simulation step. As in the SSAC simulation, transient simulations can be performed using different driving-field options within the high-field mobility model. If check_other_driving_fields variable is set to true, the script runs three simulations sequentially with E dot J, E, and E dot J approx. as the driving fields. All three driving fields produce near identical transient results. The results presented below are obtained with the “E dot J” model.
| NOTE: In 2026 R1.3, we introduced two new options for driving fields in the high-field mobility model (E and E dot J approx) to improve the convergence of CHARGE simulations that include high-field mobility effects. For more details, please visit Semiconductor Material Model Properties. |
Three current density monitors, spaced at 0.25um intervals, are used to monitor the current traveling in the collection layer of the UTC. The image below shows the transient response at the three sample points (positions indicated in the band diagram) in the collection layer, and illustrates the propagation of the current pulse in the PD. The pulse reaches the end of the collection layer after \(\tau_{tr}\) = 9.53 ps. The dispersion in the pulse is also visible.
The transit time bandwidth can be estimated as:
$$ f_{0, t r}=\frac{0.445}{\tau_{t r}} $$
and is independent of PD area. The overall bandwidth is determined from the combination of transit time and RC limits; these quantities can also be used to populate the equivalent circuit model [3]:
$$ f_{0}=\left(\frac{1}{f_{0, R C}^{2}}+\frac{1}{f_{0, t r}^{2}}\right)^{-1 / 2} $$
Using the simulated capacitance and transit time in conjunction with the extracted resistance (load and contact), the bandwidth of the PD in relation to its area is found to be in good agreement with the measured response [2].
The transit-time limited bandwidth from the transient simulation is 46 GHz whereas the bandwidth obtained with the SSAC simulation is 39 GHz. This difference can be attributed to the fact that the SSAC simulation implicitly includes the intrinsic diode capacitance and a small diode series resistance into the bandwidth estimation. Furthermore, since the transient simulation is 1D, it does not capture non-uniformities in the electric field in the lateral direction (\(x\)) of the photodetector. These field variations can influence carrier velocities and, consequently, affect the net device bandwidth.
The total bandwidth extracted from the transient simulation accounts for both carrier transit-time effects and RC effects (intrinsic capacitance, parasitic capacitance and resistance, load resistance). Therefore, the total bandwidth is lower than the SSAC bandwidth which doesn’t include any parasitic effects or load resistance.
Additional resources
Additional documentation, examples and training material
Related publications
- Ishibashi et al., IEICE Trans. Electron., E83-C, 938 (2000)
- Beling et al., Opt. Expr., 21, 25901 (2013)
- Piels et al., Opt. Expr., 21, 15634 (2013)
See also
Related Ansys Innovation Courses