# The Avalanche Photodiode Blog

Part 1: Avalanche Multiplication

- Posted by Hektor Meier
- Mar, 01, 2013
- Comments Off on The Avalanche Photodiode Blog

Part 1: Avalanche Multiplication

The major benefit of an avalanche photodiode (APD) compared to a PIN photodiode is an internal signal amplification by means of avalanche multiplication. This makes APDs suited for high sensitivity receivers where amount of incoming light is very limited.

In the following I will give a short introduction in the physics behind the multiplication process and the impact ionization rate. I will explain the k-ratio which is a figure of merit for the avalanche multiplication process.

# Avalanche multiplication

The reverse operation voltage of our APDs is around of 27V. Under this conditions the electric fields in the APD are in the orders of hundreds of kV/cm. In presence of this high electric fields the free charge carriers, electrons and holes, are accelerated and their energy is strongly increased. Above a a threshold energy, which is larger than the material bandgap, these carriers may initiate an impact ionization (II) event. In this process, a new pair of charge carriers is created. The number of carriers increases from initally one to three. The newly generated carriers are accelerated again by the electric field and may induce another impact ionization event on their own. A subsequent series of impact ionization events is called avalanche multiplication. The avalanche multiplication process multiplies the amount of initial, optically generated charge carriers. This increases the photo-current which results in a signal amplification. Due to the randomness of the impact ionization process an additional noise source is added, the so called multiplication excess noise.

# Impact ionization rate

The rate at which new carriers are generated is called electron and hole impact ionization rate, α and β. This rate strongly increases for a higher electric field which is shown in the grafic below (Okuto-Crowell model impact ionization parameters from Ref. [1]). A material with β>α is called a hole multiplying material (InP, Ge), a material with α>β is called an electron multiplying material (Si, InGaAs). Materials with smaller bandgap such as Ge and InGaAs require a smaller electric field for the same impact ionization rate compared to a higher bandgap material such as InP and Si.

# The effective k-ratio

The k-ratio describes the avalanche multiplication characteristic of a semiconductor material. For a a hole multiplying material, the k-ratio is given by k=α/β. In case of a electron multiplying material it is common to define the k-ratio as the inverse k=β/α.

An important characteristic of real world APD is the effective k-ratio. The effective k-ratio does not only depend on α and β of the bulk semiconductor material. It also includes modifications on the avalanche multiplication process which are the result of intentional sophisticated design features of the APD. Such engineered, effective k-ratios may be significantly lower than the corresponding k-ratio of the bulk semiconductor material.

# The benefit of a low effective k-ratio

A low effective k-ratio has two main benefits. First, an APD with a low k-ratio will have a smaller excess noise factor at high gain (see grafic below). This improves the sensitivity of an APD receiver.

Second, a low k-ratio results in a better speed of response at high gain. To build-up high avalanche gain, several subsequent impact ionization events are required. This is a time consuming process which limits the speed of response of an APD at high gain. In this avalanche build-up time limited regime, the rise and fall time of the APD response are in first approximation proportional to the k-ratio times the multiplication gain M, τm ~ M * k. This fundamental relationship gives rise to the defintion of the so called APD gain-bandwidth (GB) product. A lower k-ratio will result in a higher GB-product. I will come back to this topic in a future post.

For our 10G APD we measure a sensitivity of -28 dBm in combination with an appropriate TIA. Based on the TIA characteristic and the gain dependence of the sensitivity we can estimate a k-ratio of approximately 0.3. The corresponding gain-bandwidth product of our 10G APD is approximately 100 GHz.

A good introduction to the k-ratio and its effect on excess noise and speed of response is given by Ref. [2].

# Summary

In contrast to PIN photodiodes, APDs provide an internal signal gain. Therefore, they are suited for high sensitivity applications where the incoming light power is very low. The internal signal gain is the result of the avalanche multiplication process which amplifies the number of the optically generated carriers.

The effective k-ratio describes avalanche multiplication process in the APD. A low k-ratio results in a reduced excess multiplication noise and a faster speed of response at high gain.

# Literature

[1] H.-F. Chau and D. Pavlidis, “A physics-based fitting and extrapolation method for measured impact ionization coefficients in III-V semiconductors”, J. Appl. Phys., Vol. 72, No. 2, pp. 531-538, July 1992.

[2] R. McIntyre, “The distribution of gains in uniformly multiplying avalanche photodiodes: Theory”, IEEE Trans. Electron Devices, Vol. 19, No. 6, pp. 703-713, June 1972.

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