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I am looking to buy some new photodiodes for a project. Currently, I have been using expensive photodiodes with a picosecond level rise and fall time and a very small area to pick up light. The problem is that I am not getting much light into the photodiode so the readings are quite low and need to have more of a range.

I was just wondering what the measurement for how sensitive a photodiode is and if anyone has any good ideas for near-infrared (800-850 nm) photodiodes which are extremely sensitive so have a large range from not much light which is what I need.

This is the type of photodiode I am looking for

Any ideas?

How to tell how sensitive a photodiode is?

There's a curve in your device's datasheet that tells you exactly that:

Combined with the line in the Characteristics table that tells you the sensitivity is 0.55 A/W at 850 nm, this gives you the sensitivity at whatever wavelength you are using.

(Note: in the optical communications field, we'd call this a responsivity curve, not a sensitivity curve. For us, sensitivity is a measure of the minimum detectable signal)

if anyone has any good ideas for near-infrared (800-850 nm) photo diodes which are extremely sensitive so have a large range from not much light which is what I need.

Standard p-i-n photodiodes can't produce more than one carrier pair per photon absorbed, so you won't find any with a dramatically stronger response than this one.

If you are working at one specific wavelength, you might be able to find or custom-order one with an anti-reflective (AR) coating for that wavelength and get near a 25% improvement in responsivity (based on the 80% quantum efficiency spec for this device). This will increase the cost.

Some other solutions:

As others have said, you can use an avalanche photodiode (APD), which has an internal current gain process to effectively increase the responsivity above 1 carrier pair per photon. However these require very carefully controlled high-voltage bias, which will increase your system cost.

Or, if your problem is actually focusing your light beam onto the small device area, you could use a larger device (which will be slower and will tend to be more expensive).

Finally, a solution that hasn't been suggested yet in another answer: You could be sure your light source is chosen to match the peak responsivity wavelength of your O/E.

Another comment: The Mouser page you linked calls this a phototransistor, but the Osram datasheet just calls it a photodiode, and its responsivity is typical for photodiodes, not phototransistors. Another way you can get internal gain in the device is to use an actual phototransistor. I don't use these devices regularly, but I expect they might be relatively slow compared to ordinary photodiodes.

Depending on the speed you need, you may well be out of luck.

You state that your current diodes "with a picosecond level rise and fall time", while you link to a PD with 12 nsec rise and fall times. Furthermore, you say that your PDs are "expensive ", but the linked units are only about 6 bucks in onesies, and if you think 6 bucks is expensive for a photodiode, I suggest you need to do some research. Try Digikey or Mouser. So it's not really clear exactly what photodiodes you are talking about.

With that said, silicon photodiodes all have pretty much the same maximum sensitivity, .55 to .65 A/W. And you only get high speed by reducing the capacitance of the chip, which means low sensitivity. So you basically have 3 options.

1) Go to a bigger PD and accept the lower speed. While you have been using very fast units, you have not actually justified your need for speed, so this may be an acceptable course of action. How much speed do you really need?

2) If you really and truly need nsec rise and fall times, keep your current diode and provide a collection lens to increase the amount of light incident on the PD. Yes, this means you'll need to redesign your apparatus, and learn some optics, but that should not be an insuperable problem.

3) Go to an APD (avalanche photodiode). These will respond to lower light levels, and you can get fairly fast units. Of course, you'll also need to learn how to drive the little buggers, but think of it as a learning experience.

I was just wondering what the measurement for how sensitive a
photodiode is

The spectral sensitivity is quoted in the data sheet as 0.55 amps per watt so, if you could illuminate the sensitive area (1 sq mm) with 1 milliwatt of light at about 860 nm you'd get 0.55 milliamps produced at the output. The graphs in the data sheet show how this falls away for different light wavelengths.

anyone has any good ideas for near-infrared (800-850nm) photodiodes
which are extremely sensitive so have a large range from not much
light which is what I need

Requests for product recommendations are off-topic. However, you'll always get more signal with a bigger sensitive area but the speed will be proportionally slower.

A photomultiplier tube (PMT) can give ~10^6 gain, fast rise times (150 ps) and large sensitive areas (~10 mm dia) - all these specs at the same time!

You can use them to detect (and time the arrival time) of single photons.

Have a look at the websites of Hamamatsu, Newport & Photek.