Optimizing Electric‑Field Distribution in InGaAs/InAlAs Single‑Photon Avalanche Photodiodes

Background

InGaAs/InAlAs and InGaAs/InP APDs dominate short‑wave infrared (SWIR) detection, enabling single‑photon counting at 1550 nm. Compared to photomultipliers, these devices offer high reliability, low bias, compact form factor, and excellent timing resolution [2, 3]. Recent progress in quantum key distribution has accelerated their deployment [1].

SPADs operate in Geiger mode, applying a reverse bias above breakdown to achieve avalanche gain that turns a single photon into a macroscopic pulse [6, 7]. The InAlAs material offers a higher electron‑hole ionization‑coefficient ratio than InP, yielding a lower excess‑noise factor and a higher gain‑bandwidth product [14]. Its larger bandgap also suppresses tunneling, decreasing the dark‑count rate (DCR) and improving temperature stability [15, 17].

While InGaAs/InAlAs APDs have achieved single‑photon detection efficiencies (SPDE) up to 26 % at 210 K [22], their DCRs remain higher than the <10^4 Hz typical of state‑of‑the‑art InP SPADs [23]. The excess DCR originates from band‑to‑band and trap‑assisted tunneling driven by high electric fields. Optimizing the electric‑field distribution—through charge‑layer doping and multiplication‑layer thickness—is therefore critical for SPAD performance.

Methods

We performed two‑dimensional TCAD simulations on a front‑illuminated SAGCM InGaAs/InAlAs APD structure (Fig. 1). The model incorporates the Selberherr impact‑ionization, drift‑diffusion, Poisson, and carrier‑continuity equations, as well as band‑to‑band and trap‑assisted tunneling. Fermi‑Dirac statistics, Auger recombination, Shockley‑Read‑Hall recombination, low‑field mobility, velocity saturation, and ray‑tracing were also included.

The epitaxial stack, from substrate to contact, comprises a contact layer, cladding layer, multiplication layer, charge layer, grading layer, absorption layer, grading layer, cladding layer, and contact layer. An InAlGaAs grading layer mitigates electron pile‑up at the InGaAs‑InAlAs interface.

The electric field 𝜉(x) satisfies the Poisson equation $$\frac{d\xi}{dx}=\frac{\rho}{\varepsilon}=\frac{q\,N}{\varepsilon}\,,$$ and the bias boundary condition $$V_{\text{bias}}+V_{\text{bi}}=-\int_{0}^{w}\xi(x,w)\,dx\,.$$ The tunneling generation rate for band‑to‑band tunneling is $$G_{\text{btb}}=\sqrt{\frac{2m^{\ast}}{E_g}}\frac{q^2E}{(2\pi)^3\hbar}\exp\!\left(-\frac{\pi}{4q\hbar E}\sqrt{\frac{2m^{\ast}E_g^3}{2}}\right)\,,$$ yielding a tunneling current density $$\frac{I_{\text{tunnel}}}{A}=G_{\text{btb}}\,q\,w_{\text{tunnel}}\,.$$

Figure 2 shows that tunneling becomes significant at 2.0×10^5 V cm⁻¹ in InGaAs and 6.9×10^5 V cm⁻¹ in InAlAs, matching literature thresholds [1, 9]. The simulation parameters are listed in Table 1.

Figure 1. Cross‑section of the front‑illuminated SAGCM APD.

Results and Discussion

Electric‑Field Distribution in Geiger Mode

Figure 4 and 5 illustrate the simulated field‑voltage characteristics for multiplication and absorption layers under Geiger bias. With a 50 nm charge layer and multiplication layers of 100–300 nm, the absorption field rises linearly with bias, while the multiplication field saturates as the device approaches breakdown.

Figure 4. Field in the multiplication layer versus bias.

Figure 5. Field in the absorption layer versus bias.

In Geiger mode, the absorption field exceeds 5×10^4 V cm⁻¹, sufficient for carrier transit, yet remains below the 1.8×10^5 V cm⁻¹ tunneling limit. The multiplication field peaks above 6×10^5 V cm⁻¹; thus, a thicker multiplication layer reduces the peak field and mitigates tunneling.

Design Considerations

Figure 6 demonstrates that increasing the multiplication thickness from 100 to 500 nm lowers the peak field below the tunneling threshold while preserving high gain. Accordingly, a multiplication thickness > 300 nm is recommended for Geiger‑mode SPADs.

Figure 6. Field in the multiplication layer for varying thicknesses.

Adjusting the charge‑layer doping also shapes the absorption field. Figure 7 shows that a high doping concentration (≥ 4.5×10^17 cm⁻³) keeps the absorption field below the tunneling limit even at high bias, whereas lower doping levels reach the threshold prematurely. Thus, an optimal balance of charge‑layer doping and multiplication thickness is essential.

Figure 7. Absorption‑layer field for different charge‑layer doping concentrations.

Conclusions

Our two‑dimensional simulation confirms that a multiplication‑layer thickness exceeding 300 nm and a heavily doped charge layer allow InGaAs/InAlAs SPADs to operate in Geiger mode while keeping tunneling currents below the critical thresholds. These design rules directly translate into lower DCRs and higher SPDEs for 1550‑nm single‑photon detection.

Abbreviations

2D

Two‑dimensional

APD

Avalanche photodiode

DCR

Dark count rate

SAGCMAPDs

Separate absorption, grading, charge, and multiplication avalanche photodiodes

SPAD

Single‑photon avalanche photodiode

SPDE

Single‑photon detection efficiency