# The Avalanche Photodiode Blog

Part 2: DC Characteristics

- Posted by Hektor Meier
- Jul, 05, 2013
- Comments Off on The Avalanche Photodiode Blog

Part 2: DC Characteristics

In this post I give an introduction to the typical DC characteristics of an avalanche photodiode. This includes the dark and photo current characteristics as well as the defintion of the multiplication gain.

# Dark and photo current characteristics

The figure below shows a typical DC characteristic of our 10G APD. The origin of the dark current (I_{d}) in APDs is similar to PIN diodes. The dark current is mainly created by diffusion, generation-recombination and tunneling [1]. In the APD as well as in the PIN diode the initial dark current increases for higher reverse bias voltage (V). However, in case of an APD some part of the initial dark current is multiplied (I_{dm}) by the avalanche multiplication gain (M) while some of the dark current is unmultiplied (I_{dum}). The total dark current can be written as I_{d}(V) = I_{dum}(V)+ M(V) x I_{dm}(V). The reverse bias dependence as well as the existence of a multiplied and unmultiplied component makes I_{d} unsuited for the measurement of multiplication gain versus reverse bias characteristic of the APD (M(V)).

Extracting the M(V) from the photo current (I_{p}) is much more accurate than using I_{d }because the entire initial photo current is multiplied. For this kind of measurement we recommend an optical input power (P_{in}) of few µW. This input power leads to a photo current which is sufficient to neglect the impact of I_{d} on the total current and it is low enough to allow ramping up to high M without reaching the damage threshold of the APD.

# Low breakdown voltage

The dark-current (I_{d}) increases exponentially at high reverse bias voltage. This is due to the exponential dependence of the impact ionization rate on the electric field inside the APD which dramatically amplifies the multiplied part of the dark current.

The dark current versus reverse bias voltage is an easy and fast measurement. This makes the dark current characteristic well suited for the measurement of the APD breakdown voltage (V_{br}). Avalanche breakdown and the corresponding breakdown voltage describe the point for which the multiplication gain (M) goes towards infinity. In a real world application, infinite M and therefore infinite current is neither realistic nor a practical definition. Therefore, we define V_{br} as the reverse bias voltage for which I_{d} reaches 20 µA.

One of the main advantage of our APDs is their low V_{br} which is between 22 V and 32 V in comparison with other commercially available APDs which can have a V_{br} of 40V or more. This allows a low operation bias voltage which simplifies biasing and reduces power consumption of the APD receiver.

# Low dark-current operation

In our datasheet, we specify the dark current (I_{d}) at 90 % of the breakdown voltage (V_{br}). This makes sense because a bias of 90% V_{br} is around the optimal operation point in terms of sensitivity. At this bias our APD exhibits a low I_{d} of typically ten nA. Such a low dark current ensures a high sensitivity operation.

# Unity gain

The photo current (I_{p}) strongly increases for a bias voltage around 12 V to 15 V. This turn-on of the APD is followed by a plateau for which I_{p} remains nearly constant for increasing reverse bias. We define the corresponding reverse bias voltage as the unity gain voltage (V_{M1}). The ratio between I_{p}(V_{M1}) and the incoming light power (P_{in}) corresponds to the responsivity, R = I_{p}(V_{M1}) / P_{in} (in units of A/W).

# Multiplication gain

The multiplication gain (M) is the ratio between the photo-current (I_{p}) and the photo current at the unity gain voltage (V_{M1}). For a measurement with an optical input power of few µW the error due to the contribution of the dark current on the total current can be neglected. The multiplication gain can be written as M = I_{p}(V) / I_{p}(V_{M1}). Typically, our 10G APD is operated around M = 8 to M = 15 for which the optimal receiver sensitivity is achieved. The gain-voltage characteristic is shown below.

# Low temperature dependence of V_{br}

The temperature coefficient of the breakdown voltage (V_{br}) is defined as ρ = ΔV_{br} / ΔT (in units of mV/ K). Our APDs show an exceptionally low temperature dependence with values around ρ = 25 mV / K. The operation point for optimal sensitivity shows a very similar temperature dependence. A low temperature dependence offers a significant simplicification in terms of temperature control of the bias voltage in the receiver design.

The shift in the breakdown voltage for changing temperature can be explained by semiconductor physics: The increased temperature will cause the charge carriers to interact more often with the semiconductor crystal lattice. Due to that interaction the mean carrier energy decreases which reduces the probability of an impact ionization event for a given electric field. Therefore, a higher electric field and hence a higher bias voltage is required to achieve the same impact ionization rate and to reach the avalanche breakdown condition.

# Summary

Dark and photo currents are both multiplied by the avalanche multiplication process at high reverse bias. The measurement of the dark current versus the reverse bias voltage is a simple way to determine the breakdown voltage of the APD. For the measurement of the multiplication gain it is recommended to measure the photo current characteristics for moderate optical input power of a few µW.

Our 10G APD offers low dark current at low operation bias voltage with a small temperature dependence. This allows high sensitivity operation and enables simplified biasing with lower power consumption.

# Literature

[1] Forrest S.R., “Performance of In_{x}Ga_{1-x}As_{y}P_{1-y} Photodiodes with Dark Current Limited by Diffusion, Generation Recombination, and Tunneling”, IEEE J. Quantum Electron., vol. 17, no. 2, pp. 217-226, Feb. 1981

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