# Two-Dimensional Device Simulation of the InGaAs/InP Avalanche Photodiodes

**1. Introduction**

The high gain, and high gain-bandwidth product of the avalanche photodiodes is one of the key device for the long distance optical communication systems. For the 0.92-1.65um wavelength range, the narrow bandgap materials, like InGaAs(0.77eV), are used as the absorption medium. And the breakdown location is a major issue to design of the APD’s. In order for the device to operate with high gain and low noise[1], the design of the guard ring to suppress edge breakdown is important.

The object of this article is to get the multiplication[2],
the leakage current under the dark and the illuminated current[3] was simulated.
And the other important factor of the cut-off frequency calculated by the numerical
device simulator * ATLAS*.

**2. Device Structure and Models**

In order to simulate of the APD’s, the thickness and doping level used conventional APD device. The dark current and illuminated current is very depend on the absorbed layer and the doping profile. And the multiplication layer thickness is the very key parameter of the breakdown voltage and position of the avalanche. Here the simple APD’s structure showed with guard ring as Figure 1.

Figure 1. Cross-sectional view
of the simulated APD. |

A thick InGaAs absorption layer with very low donor type is on the InP substrate with the InP buffered layer. The speed of the APD is very depend on the thickness of the absorption layer. This is due to the reduction in transit time when this absorption layer is reduced. And in order to reduce the charge build-up at the heterojunction interface a graded layer is introduced between the InP and InGaAs absorption layer.

To simulate the avalanche photodiodes, the generation rate due to impact ionization must be calculated.

The general impact ionization process is described by

here, G is the local generation rate of electron-hole pairs,
_{n
p} are the ionization coefficient for the electron and hole, *J _{n}J_{p}*
are their current density.

In* Blaze/ATLAS*, the impact ionization
rate included with the self-consistantly in basic equation and material parameters[4].
For the purpose of numerical simulation, the parameters for the InP and InGaAs
was given in Table I. And the other basical material parameters are integrated
in

**depend on the mole fraction. Figure 2 shows the Band structure of this APD.**

*Blaze/ATLAS*Figure 2. The Band structure
of the APD. |

And the influence of the applied bias with illuminated condition,
the opto-generation rate must be calculated. The Luminous is a general purpose
of ray tracing and light absorption program integrated into the ** ATLAS**.

here, the _{0}
is the internal quantum efficiency, *P** contains the cumulative effects
of reflection, transmission, and loss due to absorption,
is the wavelength of the illuminated light, h is Planck’s constant, c
is the speed of light,
is the absorption coefficient.

The light into the APD can set the gaussian form as like the beam from the optical fiber. And the C-Interpreter could make sure the user’s unique absorption model depend on the illuminated wavelength. In Figure 3 under the metal has high absorption coeff, so the photogeneration rate close to be zero.

Figure 3. The gaussian beam form
like outcoupling from optical fiber. |

**3. Simulation Results and Discussion**

The dark current and illuminated current versus bias voltage is shown in Figure 4. As the Figure 4, there are 3 phase of operation.

In phase I, the current is due to thermally excited carriers in the InP, and for the illuminated case, the collection of generated is zero.

In Phase II, the charge sheet has been fully depleted and the device operates like to p-i-n photodetector. Under this condition, the carriers are not transported to multiplication layers in the high field. And for the illuminated case, the depletion layer still under the Graded layers, so the absorption effect is very low.

In phase III, the device operates as an APD. The carriers generated within the InGaAs absorption layer with photogeneration can drift into the high field multiplication region, so an internal gain mechanism was provided with the impact ionization. In Figure 5, the distribution of the impact ionization rate shows where the maximum electric field is high on the multiplication layer.

Finally, the AC response of the APD was calculated with small
signal analysis of the illuminated light. The Figure 6 shows the 3 GHz cut-off
frequency by the ** Luminous/ATLAS**. The plot of the 3dB
bandwidth could make the collect the cut-off frequency each Anode bias point.

Figure 4. Typical I-V plot of the
dark and illuminated current. |

Figure 5. Impact Ionization rate
distribution due to the Electric field. |

Figure 6. Frequency vs Normalized
modulated output. |

**4. Conclusion**

The InGaAs Avalanche Photodiodes has been successfully simulated
within the ** Luminous/ATLAS** for the DC analysis and
AC analysis in this article. And the dark current and illuminated current was
shown under the reverse voltage. The

**is linked seamless the drift diffusion to impact ionization and photogeneration.**

*ATLAS*

Reference

- Mohammad A. Saleh et al, “Impact-Ionization and Noise Characteristics of Thin III-V Avalanche Photodiodes”, IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 48, NO. 12, DECEMBER 2001, pp.2722-2731
- V.Chandramouli, Christine M. Maziar, Joe C. Campbell, “Design Considerations for High Performance Avalanche Photodiode Multiplication Layers”, IEEE Transactions on Electron Devices, Vol.41, No.5, May 1994, pp.648-654
- C.L.F.Ma, M.J.Deen , L.E.Tarof, “Multiplication in Separate Absorption, Grading, Charge, and Multiplication InP-InGaAs Avalanche Photodiodes”, IEEE Journal of Quantum Electronics, Vol.31, No.11 November 1995, pp.2078-2088
- Joseph W. Parks, et al,”Theoritical Study of Device Sensitivity and Gain Saturation of Separate Absorption, Grading Charge, and Multiplication InP/InGaAs Avalanche Photodiodes”, IEEE Transactions on Electron Devices, Vol.43, No.12, December 1996, pp.2113-2121