Theoretical Analysis of InGaAs/InAlAs SAGCM Avalanche Photodiodes

Background

InGaAs (In0.53Ga0.47As) APDs are the leading detectors for short‑wave infrared (SWIR) applications such as optical‑fiber communications, remote sensing, and quantum‑key distribution. InP and In0.52Al0.48As share the same lattice spacing and excellent breakdown properties, making InAlAs a natural choice for the multiplication layer. Recent progress in single‑photon detection, time‑resolved spectroscopy, optical VLSI inspection, and 3‑D laser ranging has driven renewed interest in APDs.

Prior studies have reported single‑photon APDs with 10–30 % detection efficiency at 1550 nm, and have highlighted the role of tunneling in dark‑count generation. While InP‑based APDs have been extensively modeled, InAlAs offers a larger bandgap, higher electron‑to‑hole ionization ratio, lower excess noise, and improved breakdown characteristics. However, the interplay between charge‑layer parameters, multiplication thickness, and tunneling remains under‑explored.

In this work, we develop a theoretical framework and 2‑D simulation to quantify these effects for vertical InGaAs/InAlAs APDs operating at 1.55 µm.

Methods

We formulate the electric‑field distribution by solving the Poisson equation, depletion‑layer model, and PN‑junction equations for a simplified SACM structure that omits the grading layer. The charge density in each layer is expressed as ρ = qN, where N is the dopant concentration and ε the dielectric constant. The resulting field expressions (Eqs. 1–11) capture the dependence on layer thicknesses, dopings, and applied bias.

Using the derived field, we solve for the optimal charge‑layer doping (N2) and thickness (w2) that confine the absorption‑layer field to 50–180 kV/cm while maintaining a high avalanche field in the multiplication layer. Comparison with experimental data (Fig. 2) validates the predictive capability of Eq. 8.

Figure 3 extends the analysis to multiplication layers of 300, 500, and 700 nm, showing that thicker charge layers narrow the permissible doping range. This explains why modest doping variations can markedly affect APD performance.

Inclusion of Tunneling

When the absorption‑layer field exceeds 1.8×10^5 V/cm, band‑to‑band tunneling introduces an additional carrier generation term Gbbt (Eq. 13). This term alters the local charge density and thus the electric field in the multiplication region. Equations 14–16 capture the modified field, and the resulting change in avalanche field δE (Fig. 6) shows that tunneling reduces the multiplication field and M_n (Eq. 19).

Simulation Model

We employed a TCAD‑based 2‑D device simulator incorporating drift‑diffusion, band‑to‑band tunneling, trap‑assisted tunneling, Shockley–Read–Hall, Auger, and Selberherr impact‑ionization models. The simulated structures (Fig. 7) closely match experimental devices in Ref. 13, with two geometries: APD‑1 (800 nm multiplication, 1800 nm absorption) and APD‑2 (200 nm multiplication, 600 nm absorption).

Comparison of simulated and experimental I‑V curves (Fig. 8) demonstrates excellent agreement for both photo‑ and dark currents, validating the accuracy of the model.

Results and Discussion

Influence of Charge‑Layer Thickness

Simulations with APD‑1 (800‑nm multiplication) confirm that increasing the charge‑layer thickness narrows the acceptable doping range (Fig. 9a). The same trend holds for APD‑2 (200‑nm multiplication, Fig. 9b). Fig. 9c shows close agreement between the analytical predictions (Eq. 8) and simulation.

Figures 10a–d illustrate how a 210‑nm charge layer is highly sensitive to doping variations, while a 50‑nm layer offers broader tolerance. Consequently, thinner charge layers provide better controllability.

Tunneling Effect on Electric‑Field Distribution

Simulations (Fig. 12) reveal that when the absorption‑layer field exceeds the tunneling threshold, the avalanche field in the multiplication region decreases. This behavior is consistent across both APD geometries and confirms the analytical prediction that tunneling reduces M_n.

Figure 12c,d plot the absorption and multiplication fields versus bias. The abrupt drop in the multiplication field once the absorption field crosses the threshold illustrates the critical need to keep the absorption field below 1.8×10^5 V/cm at breakdown.

Conclusions

We have established a comprehensive theoretical and simulation framework for InGaAs/InAlAs SAGCM APDs. Key findings are:

1. The optimal charge‑layer doping and thickness for any multiplication thickness can be calculated analytically; predictions agree with experiment.
2. Thicker charge layers sharply reduce the doping tolerance, making thin charge layers preferable for robust device design.
3. Tunneling in the absorption layer lowers the avalanche field and multiplication factor; maintaining the absorption field below the tunneling threshold is essential for high‑performance APDs.

These insights enable more precise design of SWIR APDs with improved efficiency and lower dark counts.

Abbreviations

2D

Two‑dimensional

APD

Avalanche photodiode

DCR

Dark count rate

SACM APDs

Separate absorption, charge, and multiplication avalanche photodiodes

SAGCMAPDs

Separate absorption, grading, charge, and multiplication avalanche photodiodes

SPAD

Single‑photon avalanche photodiode

SPDE

Single‑photon detection efficiency

SRH

Shockley–Read–Hall