Response Time and Linearity of Photo-diodes


 

Many of the Instruments manufactured by Delta Developments use photo-diodes to measure the pulsed power or pulsed energy of a laser.   For most of our instruments we have to calibrate at about 1mW CW because that is the only reliable power standard available with a reasonable choice of wavelengths.   At the same time, we want the system to work on short pulses at perhaps 100W or even 10MW.   Our target absolute accuracy is about 2% or better.   To get measurements of this accuracy several questions arise:-

This web page describes the details of the working of these photodiodes both from a computer model and experimentally.   The computer model was originally developed by Edwards and Jefferies (1973) at the UK National Physical Laboratory.   At Delta Developments we have now updated the model, making it more accurate, analysing both PIN and NIP photodiodes and including a non-fully depleted diode.   This last was not previously possible because of limitations set by the then speed of computers.
We give the limitations on response time and linearity at various wavelengths and bias voltages.   The web page Accuracy of Pulsed Laser Measurements describes how we use these diodes to achieve the required accuracy and traceability in our Laser Peak Power measuring systems.

 

Photo-diode Structure

The lower diagram on Figure 1 shows the structure of a typical Silicon Photo-diode with the internal fields which are created when the bias voltage is applied.   The field reduces as we go towards the N layer at the back of the device because of the charge trapped in the intrinsic or "I" layer which forms the central part of the device.   The I layer is quite thick (perhaps 200m) to give good absorption at wavelengths out to 1.1m.   Notice that the field reaches right through to the back of the device (called "fully depleted").

 

Figure 1.   Structure of typical PIN Photo-diode
Electrodes and Fields in a typical PIN Photo-diode

The upper part of Figure 1 shows the new field we would get if it were possible to create a small isolated packet of holes (P) and electrons (N) deep inside the device.   Under the influence of the applied field the electrons separate from the holes.   As soon as these carriers separate the field between them is reduced.   But the total area under the line must remain constant (constant bias voltage).   So the field rises slightly along the rest of the line.   The rise of field at the two electrodes causes a charge to flow into one electrode and out of the other.   This is the photo-current.   Notice that a photo-current flows even though the carriers themselves have not yet reached the electrodes.   Thus the device may actually be a lot quicker than you would expect from the carrier transit time.

Of course, in real life the light creating the electron/hole pairs decays exponentially through the depth of the Intrinsic layer.   Our computer model simulates the real situation.   It takes into account the thickness and doping levels of all the layers including the absorption of the light through the depth of the device (in silicon the 1/e depth is 30m at 900nm and 300m at 1064nm).   We also take into account the slight drop in bias voltage when a current flows through the external load (usually 25Ω or 50Ω).

 

Device Parameters

The manufacturers of photo-diodes are very secretive about the dimensions and doping levels of their devices.   Fortunately, their "secrets" can be uncovered by measuring the capacitance at various bias voltages.   We have done this for a lot of devices to find the doping level of the "I" layer and its thickness.   A certain amount of innocent fun can then be had by publishing the "secrets" in the open literature!

The parameter that can't be measured easily in an assembled device is the absorption depth of the light at various wavelengths.   The literature is full of measurements of the absorption of Silicon with good claimed accuracy - several with claimed accuracies of just a few percent.   Unfortunately, these different "accurate" measurements often differ by factors of 2 or 3!   We have therefore been forced to run our simulation with a variety of values (corresponding to different wavelengths and different opinions as to the value of the absorption depth).

 

Figure 2.   Predicted effect of absorption depth in a PIN photodiode
Effect of absorption depth on pulse shape

These curves are for a very short input pulse.   For this hypothetical PIN device the first peak in the photo-current is due to the movement of the holes and the second one due to the electrons.   The vertical scale is given as a percentage where a perfect very fast diode would give 100% response in the peak.

Taking a consensus of values for absorption depths in silicon we have:- A=10m @ 850nm, A=30m @ 904nm, A=300m @ 1064nm.

 

Is the Computer Simulation Accurate?

Obviously, we need to be sure that the computer simulation is giving us essentially the right results.

 

Figure 3.   Predicted and measured currents
Predicted and measured currents for a PIN Photo-diode

Figure 3 shows the predicted and measured currents plotted against time for a very short input pulse at 904nm.   Considering the difficulty in matching the exact conditions, there is very reasonable agreement between the shapes of the predicted and measured currents.   The parameters on the computer were:- an "I" layer 200m deep with 5000Ω-cm resistivity, an absorption depth of 30m (probably corresponding to 904nm).   Bias voltage = 54V.   These parameters are our best estimate for the diode FND100 made by Excelitas/EGG.

 

Linearity

For the measurement of high power lasers it is vital to know the maximum linear current.   At high currents the electron/hole pairs in the "I" region are trapped in a region of low field that they themselves are creating.   So, the carriers move out very slowly - giving a reduced current over a longer time.

 

Figure 4.   Output pulse shapes for various light levels (PIN photo diode)
Output distorted by high level of light

FND100, Bias=54V, W=200m, R=5000Ω-cm, 1/e depth=300m (1064nm).

 

Figure 4 shows the distortions than can occur if the light level is too high.   The three curves have been scaled so that they would have the same peak height if no distortion had occurred (the area under each curve is the same).   The optical input pulse is a half sine pulse of 20ns total duration (FWHM = 13.3ns).   Wavelength = 1064nm (1/e depth =300m).   You can see that compared to the 1mA shape, the curve is badly distorted at what should be 30mA and even worse at 100mA.   With a sensitivity at 1064nm of about 0.12A/W these levels correspond to about 8.3mW, 250mW and 830mW pulsed power reaching the diode itself.

Annoyingly, the maximum current that is still linear depends on every other parameter.   The pulse duration affects it because a short pulse only needs to be stretched slightly by the excess carriers to give a reduction in the peak output current.   It also depends on the bias voltage, the doping of the "I" layer and the wavelength (via the different absorption depth).   Our computer simulation takes all these factors into account.

 

Figure 5.   Maximum linear current against bias voltage in a PIN photo-diode
Maximum linear currents against bias voltage at different wavelengths

FND100. Pulse = 20ns FWHM. 1/e depths = 10m (850nm), 30m (904nm), 1000m (1100nm)

 

Fig 5 shows some of our predictions of the maximum linear current for a 30ns half sine pulse (FWHM = 20ns).   We have taken a 3% drop in peak height as the maximum current allowed to be called "linear".

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Notice the large effect of the bias voltage on the maximum linear current.   The 1/e absorption depth is also important but not so dramatically.

 

Partially Depleted Device

Figure 6 shows the fields inside a device where the bias is insufficient for the field to reach right through to the back ("partially depleted").   In this case the electrons take just a few ns to reach the region of zero field but then take a few s to diffuse through to the very back.   This gives a long tail on the response which typically can contain half the charge.   So if we calibrate a partially depleted diode by using a CW beam we would collect all the carriers - both fast and slow - during the calibration.   But when that same device is used to measure the power of a pulse perhaps only 80ns long we only see the fast component and we underestimate the pulsed power - possibly by a factor of x2.

 

Figure 6.   Fields in a partially depleted PIN photo-diode
Fields inside a partially depleted photo diode

In a partially depleted diode some further slowing down occurs because the section of the I layer with no field also acts as a resistance in series with the high field section.   This resistance can be 1kΩ-5kΩ and acts with the device capacitance (perhaps 100pF) to slow it down even further (R*C=100ns).   So for ease of calibration and best speed we should always use a fully depleted device.

The very fast devices used at GHz speeds in telecommunications have a narrow depth of just a few m and are not usually fully depleted.   This does not matter - it is the fast part of the response that they want.

 


      PIN versus NIP

It is possible to make basically the same photo-diode with the P and N layers interchanged so that the P layer is at the back.   We call this an NIP device.  

 

Figure 7.   Structure and fields for an NIP photo diode
Fields and Charges inside an NIP photodiode

 

But, I hear you ask, which of these systems is the better?

 

Figure 8.   Pulse shapes from NIP photo-diode at various wavelengths (1ns input)
Pulse shapes for NIP Photo diode

Figure 8 shows predicted pulse shapes in response to a 1ns duration pulse for a diode which is the NIP twin of the FND100 diode.   The bias voltage has to be 200V to correspond to 54V in the PIN version (that is 2x the voltage for full depletion).

 

High Bias Voltages

The curves above show that for both PIN and NIP devices higher bias voltages are always to be preferred - they are faster and have higher linear currents.   However, experience shows that if the bias is too high the diode will almost certainly become very leaky after sufficient time.   One particular FND100 was held at 100V essentially continuously for a few months after which it had a 30A leakage as opposed to <1nA at the begriming of the test.   However, to be fair, most of these diodes can withstand 150V indefinitely.

To avoid this potential problem we usually use a bias of 54V in our Peak Power Meters.   Typically, for 30ns pulses the sensitivity is only 2-3% lower than at 150V.   The CW sensitivity appears to be identical.   So we do the CW calibration at 150V and then measure the ratio for pulses at 150V versus 54V.   The final calibration given to the customer is that slightly reduced figure for 54V.

 

Speed of Response

The various graphs show that the sort of photo-diode we use is easily fast enough for measurements on laser range finders, target markers, speed cameras etc.   These all have pulses around 5-50ns duration.   Our customers need an accurate value for peak power or pulsed energy which these diodes can provide.   Most users also need sufficient speed of response to be able to see the pulse shape that they are generating and possibly study echoes etc.   However, the diodes we use are nothing like fast enough for fibre-optic communications which work at many GHz.  

But what about the strange response to very short pulses giving two peaks about 5ns apart?  Well, it turns out that for our usual diode (FND100) if the optical pulse is more than 9ns long the double peak disappears and the output pulse is a reasonable representation of the input pulse - although a bit slower.

One can correct for the difference in observed and true pulse lengths by adding all the response times in quadrature:-

[DOBS]2 = [DTRUE]2 + [DDIODE]2 + [DSCOPE]2

Where DSCOPE etc are the Full Width Half Maximum response of that component to a very short impulse (FWHM).   For the FND 100 and pulses longer than 13ns the value of DDIODE is about 4.0ns.   So for example, an observed FWHM of 16ns might come from a 4ns diode and a 'Scope with FWHM of 3.5ns (150MHz).   Hence the true pulse duration is close to 15ns FWHM.   The formula above is not proveable analytically but in practice allows one to make pretty good estimates of the true pulse duration as long as the correction is no more than 20%. 

 

Noise

It is extremely rare for the noise from the photo-diode to be the limiting factor in the overall system performance.   If we are detecting the very low level pulses returning from a distant target it is usually the amplifier noise that dominates.   If the light level is really low (giving a current of less than perhaps 200A) then the "Shot" noise (caused by the statistical nature of the photons) begins to be noticeable over the amplifier noise.

A fairly common source of noise is sudden fluctuations in the dark current from the diode.   This is caused by microplasmas on the edge of the silicon slice and occurs at higher bias voltages.   Typically they are in the range 100nA to 10A in contrast to the usual dark current of about 1-3nA.   Once some weak sites have been created they tend to persist even if we return to a low bias and they may make the diode unuseable.

Then there is the mysterious noise traditionally called D* which is widely quoted in most data sheets.   It is related to the square root of the detector area and the bandwidth.   After almost 50 years working in light detection I have never once found a situation in which D* was relevant.

 


Last Update: 6 March 2018