Calibrated Photodiodes

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Figure 1. Overview of the Photodiode's Response Curve,
Highlighting the Saturation Limit and the Noise Floor

We present laboratory measurements of the saturation limit and noise floor of a Thorlabs silicon photodiode. While all photodiodes function similarly, there are a number of parameters that affect the noise floor and saturation limit of a photodiode including the sensor temperature, resistivity, reverse bias voltage, responsivity, and system bandwidth. Here we investigated the effect of reverse bias voltage and load resistance within a silicon-based photodiode detection system. Increasing the reverse bias increased the saturation limit and had minimal effect on the noise floor. Decreasing the load resistance decreased the noise floor until reaching the noise of the measurement system, but also decreased the saturation limit. These results demonstrate some of the considerations necessary for choosing the reverse bias voltage and load resistance, and emphasize that noise sources within all of the components must be considered when creating a detection system.

For our experiment we used the FDS100 Si Photodiode as the photodiode under investigation. The collimated output of a fiber-pigtailed laser diode was used as the light source with output power from 0 to 50 mW. The collimated beam was incident upon a beamsplitter that transmitted the majority of the light to the photodiode under investigation and reflected the rest towards a reference power sensor. The photodiode response was then evaluated under various resistive loads and with different reverse bias voltages.

Click for Full Lab Facts Summary

The plots to the right and below summarize the measured results for the various tested configurations. From these graphs the changes to the photodiode's linear response, noise floor, and saturation limit can be observed under different reverse voltage biases and load resistances. Figure 1 provides an overview of the photodiode response with a reverse voltage bias of 5 V and resistive load of 10 kΩ. The photodiode saturated at the upper limit of the response when the output photovoltage approached the reverse bias voltage. The noise floor at the lower limit of the response was a result of dark current and the thermal noise from the resistive load (Johnson noise). Figure 2 summarizes the results obtained using the photodiode with a 1 kΩ resistive load and various reverse bias voltages. It illustrates that the saturation limit can be raised by increasing the reverse bias voltage (within specification). Figure 3 summarizes the results from using the photodiode with a 5 V reverse bias voltage and various resistive loads. It illustrates that the slope of the photovoltage response increased as the load resistance was increased. Figure 4 summarizes the noise floor results obtained using a 0 V reverse bias voltage and various resistive loads. The noise floor increased when larger load resistances were used. It is important to note that the 1 kΩ data was measured above the theoretical Johnson noise due to the voltage noise within the measurement system. Minimal change in the overall noise floor was seen when using a 5 V reverse bias voltage. For details on the experimental setup employed and these summarized results, please click here.

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Figure 2. Photovoltage Dependence on Reverse Bias Voltage

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Figure 4. Noise Floor with Various Resistive Loads

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Figure 3. Response with Various Resistive Loads

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Figure 1: Responsivity, which describes the relationship between the strength of the photocurrent output by the photodetector and the optical power in the incident beam, is dependent on the wavelength of the incident light.

Do all regions of a photodiode's active area have the same responsivity? 

The output signal strength from a photodetector is significantly affected by the optical power and wavelength of the incident light. A measure of this relationship is responsivity, which is the magnitude of the output photocurrent divided by the optical power of the incident light. While responsivity has units of ampere per watt, it also varies with wavelength. Often overlooked is that responsivity can also vary as different regions of the photodiode's active area are illuminated.

This work investigated the change in photodetector response as a light beam, with a diameter that was small in comparison to the active area of the photodiode, was scanned across the active area. A selection photodetectors, based on mounted gallium phosphide (GaP), silicon (Si), indium gallium arsenide (InGaAs), or germanium (Ge) photodiodes, were tested.

Responsivity is Wavelength Dependent^1,2
One reason responsivity varies with respect to wavelength is the relationship among optical power, wavelength, and photo-generated electrons. A light beam illuminating a surface provides an optical power equal to the energy in the beam divided by the time the surface was illuminated. The energy in a single-wavelength beam equals the number of incident photons times the energy of a single photon. Decreasing the wavelength of the light increases the energy of the photons. If the wavelength is decreased, but the optical power is kept the same, there are fewer incident photons.

A single photon can generate no more than a single electron of photocurrent in these photodetectors. Due to this, reducing the wavelength of the incident light while holding its optical power constant results in a reduced photocurrent. Since responsivity relates the output photocurrent to the incident optical power, instead of to the number of incident photons per unit time, responsivity is lower at lower wavelengths. The responsivity curves plotted in Figure 1 are examples showing responsivity increasing with wavelength.

The upper wavelength of a photodetector's responsivity is limited by inherent properties of the semiconductor material. In order for an incident photon to contribute to the photocurrent, the photon must have enough energy to free an electron from its bonds to its host atom. Photons with wavelengths above the upper wavelength limit do not have enough energy. The semiconductor material composing the photodiode determines the wavelength of this limit. 

Response May Vary as Different Regions of the Photodiode's Active Area are Illuminated^1,2
An electron that has escaped the bonds of its host atom by absorbing the energy of a photon is a photo-generated electron. A photo-generated electron contributes to the photocurrent only if the electron is able to successfully travel from where it was generated, across the semiconductor material, and to an electrical contact. A photo-generated electron does not contribute to the photocurrent if it is re-absorbed by the semiconductor material before reaching a contact, which is a more likely outcome if the electron encounters a defect.

Defects are places where the semiconductor's crystal lattice is not perfect. These locations include dislocations, impurities, and voids in the crystal lattice. The external surfaces of a real crystal with finite dimensions are also imperfections, since a perfect crystal is infinite in length, height, and width. Defects in the semiconductor crystal absorb photo-generated electrons at a high rate and turn their kinetic energy into heat, rather than allow the electrons to contribute to the photocurrent.

Electrons generated near defects are more likely to be re-absorbed and less likely to contribute to the photocurrent. While the density of defects in a semiconductor can be minimized, the semiconductor crystals used in photodiodes are not perfect. It is also not unusual for the density of defects to vary throughout the volume of the semiconductor crystal, as well as for the growth of some semiconductor materials to be more prone to forming defects than others. 

If the density of defects varies throughout the volume of the semiconductor material, the magnitude of the photocurrent generated within each region would be expected to be different. Since the photodetector's responsivity depends on the magnitude of photocurrent, a varying density of defects would result in the responsivity changing as different locations on the photodetector are illuminated. This effect was investigated using the procedure described in the following section.

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Figure 2: The setup used to measure the change in response across the active area of each photodiode included: a reflective collimator (A), an achromatic doublet lens (B) , vertically-mounted linear translation stage (C), the photodetector under test (D), and two horizontally-mounted translation stages (E) of which one is visible.

Experimental Setup and Results

Measurement Objectives
Several photodetectors were tested to investigate the uniformity of the responsivity across their active areas. The spatially dependent responsivities of one GaP-based, four Si-based, two InGaAs-based, and two Ge-based photodetectors were measured at selected wavelengths. Testing was conducted to investigate the spatial uniformity of the responsivity of:

• All nine photodetector models at a wavelength close to the wavelength of peak responsivity. (Results contained in the first expandable table below.)
• A Si-based, an InGaAs-based, and a Ge-based photodetector at three different wavelengths. (Results contained in the second expandable table below.)
• Eight different units of a single Si-based photodetector model at a wavelength close to the wavelength of peak responsivity. (Results contained in the third expandable table below.)

Experimental Setup (Components Labeled in Figure 2 are Labeled in the Following)
The experimental setup consisted of a light source (not shown) that was fiber-coupled to an RC12APC-P01 collimator (A), which was installed in a KM100T kinematic mount. An AC254-150-A achromatic doublet lens with a 150 mm focal length (B), which was installed in a ST1XY-D mount, focused the light on the active area of the photodetector (D), which was mounted with the help of a KB1P magnetic quick-release carriage set. Other components in the vertical arm included an LTS150 motorized linear translation stage (C), an XT66P1 vertical mounting plate, an XT66-500 66 mm construction rail, and four XT66C4 clamping platforms. The components in the horizontal arm included two LNR50S motorized linear translation stages (E), an LNR50P3 XY adapter plate, an LNR50P1 baseplate, and two BSC201 closed-loop stepper motor controllers (not shown), which scanned the beam across the active area of the photodetector (D). Most light sources were products from our Superluminescent Diode series. The exception was the 405 nm light source, which was an S3FC405 benchtop laser source.

Procedure
The diameter of the beam was scaled according to the active area of the photodetector, so that approximately 3600 measurements were taken in a 60 x 60 grid across the surface of each photodiode. The beam diameter used for each photodiode was between 50 µm and 500 µm, and the size used to make a particular measurement is included in the notes that accompany each plot in the following expandable tables. To view this information, click on the plot of interest.

During the scan, the position of the beam remained stationary, and the two LNR50S motorized stages were used to translate the photodetector in the two directions perpendicular to the optic axis. To ensure that the entire active area of the photodetector was tested, the dimensions of the scan area exceeded the dimensions of the active area.  

No reverse bias voltage was applied to any of the photodiodes during this investigation.

Results (Click More [+] to Expand the Following Tables, and Click Less [-] to Hide Them)
The measurement data were normalized and then plotted with respect to the measurement position. The data in each measurement set were normalized with respect to the value at the center of the active area, which resulted in plots that show the variation of the responsivity across each photodetector's active area and allow the results from these nine different photodetector models to be compared. The plotted data were also processed to remove data points with values indistinguishable from noise. This was done to eliminate data points corresponding to measurements made outside of the active area of each photodetector. However, this approach also removed some measurements made within, but close to, the outer edges of the active areas. The lower photocurrent generated by these regions may have been due to the beam spot partially illuminating regions outside of the active area, as well as photocurrent suppressed by a higher density of defects near the edges.

The plots can be revealed by expanding the following tables. Each plot includes a dashed outline surrounding the central 90% of the active area of the photodiode. Under general use, the light beam should remain within this central 90% region to avoid edge effects. Click on each plot to reveal information about the active area of the photodiode and the size of the beam scanned across the active area.

Since these photodetectors represent a small sample size, these measurements are representative of the other photodetectors of its model, but results obtained using other units of the same model may vary. The measurements acquired for these photodetector units were repeatable, but no two semiconductor crystals are identical and unit-to-unit variations should be expected. The following tables show that:

• First Table: The variations of the responsivities across the active areas of the Ge-based and GaP-based photodetectors are greater than the variations of the responsivities across the active areas of the Si-based and InGaAs-based photodetectors. This suggests the defect densities of the Si-based and InGaAs-based semiconductor materials are more uniform than the defect densities of the Ge-based and GaP-based semiconductor materials. 
• Second Table: The variations of the responsivities across the active areas of a Si-based, an InGaAs-based, and a Ge-based photodetector change with wavelength. For each photodetector, the minimum spatial variations of the responsivity occurred when the wavelength of light was near the wavelength of the peak value of responsivity.
• Third Table: Eight units of a single Si-based photodetector model had similar variations of spatial uniformity across their active areas. 

Photodetector Measured	Plot of Response Across the Sensor Area to Light of the Indicated Wavelength		Typical Responsivity Plots Measurement Wavelength Indicated
GaP-Based Photodetector SM05PD7A: Mounted Photodiode FGAP71	Click for Details		Click to Enlarge
Si-Based Photodetectors SM05PD2A: Mounted Photodiode FDS010 and SM1PD2A	Click for Details	Click for Details	Click to Enlarge
Si-Based Photodetectors SM05PD1A: Mounted Photodiode FDS100 and SM1PD1A: Mounted Photodiode FDS1010	Click for Details	Click for Details	Click to Enlarge
InGaAs-Based Photodetectors SM05PD5A: Mounted Photodiode FGA21 and SM05PD4A: Mounted Photodiode FGA10	Click for Details	Click for Details	Click to Enlarge
Ge-Based Photodetectors SM05PD6A: Mounted Photodiode FDG1010 and SM1PD5A: Mounted Photodiode FDG03	Click for Details	Click for Details	Click to Enlarge

2) Selected Si-, InGaAs-, and Ge-Based Photodetectors: Uniformity of Response of Each to Three Different Wavelengths of Light

Photodetector	Plots of Response Across the Sensor Area to Light of the Indicated Wavelengths			Typical Responsivity Plots Measurement Wavelengths Indicated
Si-Based Photodetector SM1PD1A: Mounted Photodiode FDS1010	Click for Details	Click for Details	Click for Details	Click to Enlarge
InGaAs-Based Photodetector SM05PD5A: Mounted Photodiode FGA21	Click for Details	Click for Details	Click for Details	Click to Enlarge
Ge-Based Photodetector  SM1PD5A: Mounted Photodiode FDG1010	Click for Details	Click for Details	Click for Details	Click to Enlarge

Eight different Si-based SM1PD2A photodetectors were measured to compare the unit-to-unit variation of the response across the active area. Measurements were performed using 830 nm light, which is close to the wavelength of peak responsivity, as is indicted on the plot on the left.		Click to Enlarge
Click for Details	Click for Details	Click for Details	Click for Details
Click for Details	Click for Details	Click for Details	Click for Details

References

[1] G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed., John Wiley & Sons, Inc., New York, 1997. (Particularly Chapter 4)
[2] A. Rogalski, K. Adamiec, and J. Rutkowski, Narrow-Gap Semiconductor Photodiodes, SPIE Press, Bellingham, WA, 2000.

Measurements of dark current as a function of temperature were acquired for several unmounted photodetectors. As is described in the following section, dark current is a relatively small electrical current that flows in p-n junction photodetectors when no light is incident on the detector. Measurements were taken for silicon (Si), germanium (Ge), gallium phosphide (GaP), and indium gallium arsenide (InGaAs) reverse-biased photodiodes over temperatures from 25 °C to approximately 55 °C. 

Figure 1: Current-Voltage Characteristic of a P-N Junction

Current-Voltage Characteristics of p-n Junction Photodiodes

The characteristic current-voltage relationship of p-n junction photodiodes, as diagrammed in Figure 1, possesses forward-biased and reverse-biased voltage regimes. In the reverse-biased voltage regime, in which p-n junction photodiodes are operated, a potential difference applied across the diode resists the flow of current.  Ideally, if no light is incident on a reverse-biased photodiode, no current flows.   

Under real-world conditions, random processes in the semiconductor material of the photodiode always generates current carriers (electrons and holes) that produce current. These current generation processes are not driven by the photogeneration of electrons and holes. Instead, they are largely driven by the thermal energy contained in the semiconductor material.[1] This dark current is generally small, but it is present when the photodiode is reverse biased and not illuminated. Dark current magnitudes vary for photodiodes of different material compositions; the efficiencies of the thermal generation processes depend on the type and crystal quality of the semiconductor used in the detector's sensing head. The magnitude of the dark current can be expected to increase as the temperature of the photodiode increases. 

When a photodiode is illuminated, the current generated by the incident light adds to the dark current. The carriers in the photocurrent are generated by the energy contained in the photons of the incident light. Above a certain illumination threshold intensity, the magnitude of the photocurrent exceeds the magnitude of the dark current. When the photocurrent is larger than the dark current, the magnitude of the photocurrent can be calculated by measuring the total current and then subtracting the contribution of the dark current. When the photocurrent is smaller than the dark current, the photocurrent is undetectable. Because of this, it is desirable to minimize the levels of dark current in photodiodes.

For convenience, both dark current and photocurrent are discussed as being independent of voltage over a range of voltages when the photodiode is reverse biased; however, the current flowing in real-world reverse-biased photodetectors is not completely independent of voltage over any voltage range. Regardless of whether the diode is illuminated, the current will increase as the magnitude of the reverse-bias voltage increases. In addition, if the reverse-bias voltage is increased beyond a certain threshold, the photodiode will suffer reverse breakdown, in which the magnitude of the current increases exponentially and permanent damage to the diode is likely.

Experiment: Dark Currents Measured for Packaged Photodiodes

Dark currents were measured over temperatures of 25 °C to approximately 55 °C for four representative unpackaged photodiodes: the Si-based FDS1010, the Ge-based FDG50, the GaP-based FGAP71, and the InGaAs-based FGA10.

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Figure 2: The Nested Metal Box Test Fixture with Covers Removed and FGA10 Installed
Black insulating foam lines the interiors of both boxes.  
A: Thermistor; B: FGA10; C: BNC-to-BNC Feedthrough; D: Outer Box; E: Inner Box; F: BNC-to-Triax Feedthrough; G: BNC-to-BNC Feedthrough 

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Figure 4: An electrical circuit that included a resistive foil heater, TED8040 temperature controller, and two rectifying diodes controlled current flow through the resistive current heater as described in the text.   

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Figure 3: The Test Setup
The custom-built temperature chamber is on the top of the cart, and the temperature control instrumentation that includes the PRO8000 and TED8040 cards is on the cart's lower shelf.

Experimental Setup
The experimental setup was designed to ensure a constant reverse-bias voltage across the photodiode, control the temperature of the detector, block light from reaching the detector, and establish an electrical path between the detector and the Keithley 6487 ammeter that isolated the measured current from extraneous electromagnetic interference (EMI) noise sources. Dark currents for these detectors can be on the order of nA, which made it important to control these conditions to ensure accurate measurements.

The detector enclosure consisted of a pair of nested aluminum metal boxes, which are shown with their covers off in Figure 2. Only one box would be required to create a light-tight environment for the photodiode, but an outer box was included in the setup to shield the inner box from EMI. The detector was placed inside the inner box, and it was electrically connected to the Keithley 6487 ammeter. The ammeter provided the required 5 V reverse-bias and received the output current signal. The electrical signals between the ammeter and the photodiode were routed through the two boxes using a combination of cables and feedthroughs. The 5 V bias voltage was connected to the photodiode using coax cables and BNC-to-BNC feedthroughs in the walls of both metal boxes. The current signal from the photodiode was connected to the BNC end of a BNC-to-Triax feedthrough integrated into the wall of the inner box. The signal was then routed through the outer box and to the Keithley 6487 using triax cables and a Triax-to-Triax feedthrough in the outer box. Triax cables were used because coax cables are poorly shielded, and using a coax cable to route the signal to the ammeter could introduce noise from EMI sources to the signal read from the detector. As the outer box shields the inner box from EMI, the noise introduced on the signal as it travels from the detector to the BNC-to-Triax feedthrough is mitigated.

Thermistors were used to monitor the temperatures of each photodiode continuously during the experiment. A piece of thermal tape was used to hold the thermistor flush against the TO cans of the FDG50, FGAP71, and the FGA10 during testing. The photosensor of the FDS1010 is mounted on a ceramic substrate, and when it was tested the thermistor was taped to the back of the substrate. The electrical connection between the thermistor and TSP01 temperature logger was performed using BNC cables, BNC-to-BNC bulkhead feedthroughs to route the signal out of the nested boxes, and a custom BNC-to-phono jack cable to connect to the temperature logger.

A custom temperature chamber based on a XE25C9 standard enclosure was used to conduct these tests. It is shown on top of the cart in Figure 3. The enclosure had a floor and four walls, and insulation was attached to all inner and outer surfaces. A lid for the enclosure was fashioned from a sheet of hardboard bordered with XE25 rails, and insulation was attached to the inner surface of the hardboard. Six resistive foil heaters were affixed to the walls of the XE25C9 enclosure, and they were driven using the PRO8000 fitted with six TED8040 thermoelectric cooler (TEC) controller cards placed on the bottom shelf of the cart in Figure 3. Each TED8040 was interfaced with a heater and a thermistor installed in the chamber. The reading from the thermistor determined the current sent to drive the heater. The chamber was not actively cooled; cooling was instead performed by withdrawing the current driving the heaters and, as an option, opening the lid of the chamber. 

The TED8040 units are designed to be interfaced with TECs, which produce heat when current flows in one direction, and which provide cooling when the current flows in the opposite direction. Because of this, when the enclosure exceeded the setpoint temperature, the TED8040 units in this experimental setup did not cut off the driving current. They instead reversed the current flow in an effort to produce cooling. In contrast to TECs, resistive foil heaters generate heat regardless of the direction of current flowing through them. In order to divert the driving current from the heaters, an electrical circuit, diagrammed in Figure 4, that included two rectifying diodes was designed and implemented. Rectifying diodes allow current to flow only in one direction. When the temperature reading from the thermistor was lower than the setpoint temperature, current flowed in the direction of the red arrows and through the resistive heater, and heat was generated. When the temperature of the enclosure exceeded the setpoint temperature, the TED8040 controllers reversed the direction of the current, so that it flowed in the direction of the blue arrows. Under this condition, the circuit diverted the current from the heaters and the chamber was allowed to cool.

Experimental Results
The data curves plotted in Figure 5 are the dark currents measured for the Si-based FDS1010, the Ge-based FDG50, the GaP-based FGAP71, and the InGaAs-based FGA10. Data were acquired continuously while the temperature was between 25 °C and 55 °C (shaded region of Figure 6). Figure 6 is representative of the temperature measured at the photodiode during the experiment. The temperature profile included an initial segment of increasing temperature, followed by a soak that allowed the photodiode to reach the maximum temperature, and concluded with a cool-down. The data plotted in Figure 5 include all dark current measurements measured between 25 °C and 55 °C; current measurements taken at the same temperature, but at different times, overlay one another for each diode. 

The data curves plotted in Figure 5 show that the measured dark current magnitudes differed depending on the material composing the photodiode. From lowest to highest:

• GaP-Based Detector FGAP71 (Lowest Dark Current) 
• InGaAs-Based Detector FGA10
• Si-Based Detector FDS1010
• Ge-Based Detector FDG50 (Highest Dark Current)

These span approximately 6 orders of magnitude. In all cases, the dark current increased with the temperature of the photodiode, as expected. The individual points on this graph, plotted as diamonds, are the values of the dark current specified for each detector at 25 °C. These points specify a maximum value of dark current at 25 °C; each diode's dark current must be equal to or less than this value at 25 °C, but the dark current may exceed this specification at higher temperatures, as is the case for all but the measured FDS1010 detector.

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Figure 5: Dark Current Data Measured for Four Unmounted Photodiodes
The discrete data points, plotted as diamonds, are values of the dark current specified for each detector at 25 °C.

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Figure 6: Temperature of a Representative Photodiode Controlled by the Conditions in the Environmental Chamber
Dark current measurements were acquired between 25 °C and 55 °C (indicated by the shaded region) and are plotted in Figure 5 .

Experimental Limitations
Measurements were performed using a single representative of each detector type, as these data were intended to illustrate overall trends. These data should not be taken as specific for a particular diode. The measured dark current is a function of voltage bias, temperature dependence of resistive loads, and other effects. Efforts were made to suppress their influence on these measurements, including using the Keithley 6487 ammeter to provide the required 5 V reverse bias.  Using the ammeter removed the need to use a load resisitor, which may exhibit its own temperature dependence. The thermistor was placed as close to the semiconductor sensor as was possible, but it was not placed in direct contact with the sensor. Because of this, there may have been a difference between the measured temperature and the temperature of the semiconductor material. The dark current was measured while the temperature of the environmental chamber was continuously varied. Humidity was not controlled during this experiment.

 [1] J. Liu, Photonic Devices. Cambridge University Press, Cambridge, UK, 2005

Noise Equivalent Power (NEP) was determined as a function of temperature for several unmounted photodetectors. As is described in the following section, NEP is a common metric used to describe the minimum sensitivity of a photodetector. Measurements were taken for silicon (Si), germanium (Ge), gallium phosphide (GaP), and indium gallium arsenide (InGaAs) reverse-biased photodiodes over temperatures from 25 °C to approximately 55 °C. 

Noise Equivalent Power

The most general definition of NEP is "the input signal power that results in a signal-to-noise ratio (SNR) of 1 in a 1 Hz output bandwidth." [1] Therefore, in order to determine the NEP, the minimum noise of the photodiode must be determined. When the optical signal is blocked, noise is still present, which is generated by the detector itself. There are two main contributors to photodiode noise: the shot noise due to dark current and thermal noise due to the shunt resistance.

Dark current is a relatively small electric current present in photosensitive devices that flows through the device, including when there is no incident light. More information on the dark current can be found in the "Dark Current as a Function of Temperature" section above. Shot noise is due to the quantized nature of the charge carriers. For the case where there is no light incident on the detector, it can be calculated from the dark current of the detector using the equation [2]

where i_s is the shot noise, I_d is the dark current, q is the electron charge, and f_BW is the bandwidth, which will be set to 1 Hz to allow for comparison between different photodiodes.

Thermal, or Johnson, noise is due to the random thermal motion of the charge carriers. Thermal noise will be generated only by the resistive elements of the system. For the photodiode detector, the shunt resistance needs to be considered. Shunt resistance is the resistance of the zero-biased photodiode p-n junction; put another way, it is the inverse of the slope of the I-V curve at the zero-voltage point. Since it is difficult to correctly calculate the slope at the zero crossing, the generally accepted industry practice is to measure the current at V = ±10 mV and then calculate the slope. Then the thermal noise due to the shunt resistance, R_SH, can be expressed as:

where i_t is the thermal noise (expressed as a current), k_B is Boltzmann's constant, T is temperature, R_SH is shunt resistance, and f_BW is the bandwidth.

The total noise, i_total, is the quadrature sum of all noise sources:

Note that this result is the total noise expressed for the current output of the photodiode, while the NEP is expressed in terms of incident optical power. Thus, to compare with the NEP specifications a typical responsivity value,,  is chosen for the specified wavelength:

Also, to allow for comparison between different diodes, we set the bandwidth to 1 Hz for the calculation.

Experiment: Dark Current and Shunt Resistance Measurements

NEP was determined over 25 to 55 °C for four representative unpackaged photodiodes: the Si-based FDS1010, the Ge-based FDG50, the GaP-based FGAP71, and the InGaAs-based FGA10. 

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Figure 1: The nested metal box test fixture with covers removed and FGA10 installed.
Black insulating foam lines the interiors of both boxes.  
A: Thermistor; B: FGA10; C: BNC-to-BNC Feedthrough; D: Outer Box; E: Inner Box; F: BNC-to-Triax Feedthrough; G: BNC-to-BNC Feedthrough 

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Figure 3: An electrical circuit that included a resistive foil heater, TED8040 temperature controller, and two rectifying diodes controlled current flow through the resistive current heater as described in the text.   

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Figure 2: The Test Setup
The custom-built temperature chamber is on the top of the cart, and the temperature control instrumentation that includes the PRO8000 and TED8040 cards is on the cart's lower shelf.

Experimental Setup
The experimental setup was designed to ensure a constant reverse-bias voltage across the photodiode, control the temperature of the detector, block light from reaching the detector, and establish an electrical path between the detector and the Keithley 6487 ammeter that isolated the measured current from extraneous electromagnetic interference (EMI) noise sources. Dark currents for these detectors can be on the order of nA, which made it important to control these conditions to ensure accurate measurements.

The detector enclosure consisted of a pair of nested aluminum metal boxes, which are shown with their covers off in Figure 1. Only one box would be required to create a light-tight environment for the photodiode, but an outer box was included in the setup to shield the inner box from EMI. The detector was placed inside the inner box, and it was electrically connected to the Keithley 6487 ammeter. The ammeter provided the required reverse-bias voltage and received the output current signal. The electrical signals between the ammeter and the photodiode were routed through the two boxes using a combination of cables and feedthroughs. The bias voltage was connected to the photodiode using coax cables and BNC-to-BNC feedthroughs in the walls of both metal boxes. The current signal from the photodiode was connected to the BNC end of a BNC-to-Triax feedthrough integrated into the wall of the inner box. The signal was then routed through the outer box and to the Keithley 6487 using triax cables and a Triax-to-Triax feedthrough in the outer box. Triax cables were used because coax cables are poorly shielded, and using a coax cable to route the signal to the ammeter could introduce noise from EMI sources to the signal read from the detector. As the outer box shields the inner box from EMI, the noise introduced on the signal as it travels from the detector to the BNC-to-Triax feedthrough is mitigated.

For dark current measurements, the bias voltage was set to 5 V. In order to calculate the shunt resistance, measurements of the current were made with the bias voltage set to +10 mV and -10 mV.

Thermistors were used to monitor the temperatures of each photodiode continuously during the experiment. A piece of thermal tape was used to hold the thermistor flush against the TO cans of the FDG50, FGAP71, and the FGA10 during testing. The photosensor of the FDS1010 is mounted on a ceramic substrate, and when it was tested the thermistor was taped to the back of the substrate. The electrical connection between the thermistor and TSP01 temperature logger was performed using BNC cables, BNC-to-BNC bulkhead feedthroughs to route the signal out of the nested boxes, and a custom BNC-to-phono jack cable to connect to the temperature logger.

A custom temperature chamber based on a XE25C9 standard enclosure was used to conduct these tests. It is shown on top of the cart in Figure 3. The enclosure had a floor and four walls, and insulation was attached to all inner and outer surfaces. A lid for the enclosure was fashioned from a sheet of hardboard bordered with XE25 rails, and insulation was attached to the inner surface of the hardboard. Six resistive foil heaters were affixed to the walls of the XE25C9 enclosure, and they were driven using the PRO8000 chassis fitted with six TED8040 thermoelectric cooler (TEC) controller cards placed on the bottom shelf of the cart in Figure 2. Each TED8040 was interfaced with a heater and a thermistor installed in the chamber. The reading from the thermistor determined the current sent to drive the heater. The chamber was not actively cooled; cooling was instead performed by withdrawing the current driving the heaters and, as an option, opening the lid of the chamber.

The TED8040 units are designed to be interfaced with TECs, which produce heat when current flows in one direction, and which provide cooling when the current flows in the opposite direction. Because of this, when the enclosure exceeded the setpoint temperature, the TED8040 units in this experimental setup did not cut off the driving current. They instead reversed the current flow in an effort to produce cooling. In contrast to TECs, resistive foil heaters generate heat regardless of the direction of current flowing through them. In order to divert the driving current from the heaters, an electrical circuit, diagrammed in Figure 3, that included two rectifying diodes was designed and implemented. Rectifying diodes allow current to flow only in one direction. When the temperature reading from the thermistor was lower than the setpoint temperature, current flowed in the direction of the red arrows and through the resistive heater, and heat was generated. When the temperature of the enclosure exceeded the setpoint temperature, the TED8040 controllers reversed the direction of the current, so that it flowed in the direction of the blue arrows. Under this condition, the circuit diverted the current from the heaters and the chamber was allowed to cool.

Experimental Results
The data curves plotted in Figure 4 are the dark currents measured for the Si-based FDS1010, the Ge-based FDG50, the GaP-based FGAP71, and the InGaAs-based FGA10. Figure 5 shows the calculated shunt resistance values for the same diodes as Figure 4. Data were acquired continuously while the temperature was between 25 °C and 55 °C (shaded region of Figure 7). Figure 7 is representative of the temperature measured at the photodiode during the experiment. The temperature profile included an initial segment of increasing temperature, followed by a soak that allowed the photodiode to reach the maximum temperature, and concluded with a cool-down. The data plotted in Figures 4 and 5 include all dark current measurements measured between approximately 25 °C and 55 °C; current measurements taken at the same temperature, but at different times, overlay one another for each diode. 

As shown in Figure 5, the shunt resistance for the measured GaP, InGaAs, and Si detectors is relatively large; therefore in many situations it can be ignored. For the Ge-based FDG50 the shunt resistance is relatively low, especially at higher temperatures. For this diode the shunt resistance might need to be considered if there is a high load involved.

Figure 6 shows the calculated NEP vs. temperature for each diode. Since the NEP is a function of responsivity, which varies with wavelength, the NEP values are calculated at the peak responsivity value as given in the table to the right.

The data curves plotted in Figure 6 show that the calculated NEP magnitudes differed depending on the material composing the photodiode. From lowest to highest:

• GaP-Based Detector FGAP71 (Lowest NEP) 
• InGaAs-Based Detector FGA10
• Si-Based Detector FDS1010
• Ge-Based Detector FDG50 (Highest NEP)

These span approximately 6 orders of magnitude. In all cases, the dark current increased with the temperature of the photodiode, as expected. The individual points on this graph, plotted as diamonds, are the values of the dark current specified for each detector at 25 °C. These points specify a maximum value of dark current at 25 °C; each diode's dark current and NEP must be equal to or less than this value at 25 °C, but the dark current and NEP may exceed this specification at higher temperatures.

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Figure 4: Dark Current Data Measured for Four Unmounted Photodiodes
The discrete data points, plotted as diamonds, are values of the dark current specified for each detector at 25 °C.

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Figure 5: Shunt Resistance Calculated as Described in the Text for Four Unmounted Photodiodes

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Figure 6: NEP Calculated from the Quadrature Sum of Shot Noise and Thermal Noise for Four Unmounted Photodiodes
The discrete data points, plotted as diamonds, are values of the NEP specified for each detector at 25 °C. There is no point for FGA10 since the NEP is not specified at the peak responsivity wavelength.

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Figure 7: Temperature of a Representative Photodiode Controlled by the Conditions in the Environmental Chamber
Dark current measurements were acquired between 25 °C and 55 °C (indicated by the shaded region) and are plotted in Figure 5 .

Experimental Limitations
Measurements were performed using a single representative of each detector type, as these data were intended to illustrate overall trends. These data should not be taken as specific for a particular diode. The measured currents were functions of voltage bias, temperature dependence of resistive loads, and other effects. Efforts were made to suppress their influence on these measurements, including using the Keithley 6487 ammeter to provide the required 5 V reverse bias. Using the ammeter removed the need to use a load resistor, which may exhibit its own temperature dependence. The thermistor was placed as close to the semiconductor sensor as was possible, but it was not placed in direct contact with the sensor. Because of this, there may have been a difference between the measured temperature and the temperature of the semiconductor material. The currents were measured while the temperature of the environmental chamber was continuously varied. Humidity was not controlled during this experiment.

[1] Thorlabs' Noise Equivalent Power White Paper.

[2] Quimby, Richard S. Photonics and Lasers: An Introduction. Wiley-Interscience, Hoboken, NJ, 2006, pp 241-244.

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Figure 1: Normalized change in output current for a fixed incident power as the photodiode Device Under Test (DUT), FDS1010, was translated through the focus of a lens.

We present laboratory measurements showing the effect of beam size on the saturation point of a Thorlabs silicon photodiode. As defined here, saturation is a 1% deviation from the linear response region. As illustrated in Figure 1, the photodiode saturated at lower incident power levels as the beam size decreased. Several additional calculations and experiments were performed to verify the cause of the change in saturation was not a function of the power density. These results suggest that users should be cognizant of the beam size when attempting to measure absolute power with a power sensor, such as our S130C photodiode power sensor.

For our experiment, we used the SM1PD1A mounted photodiode, which consists of an FDS1010 photodiode in an SM1-threaded housing. An 830 nm superluminescent diode was used as the light source. A beamsplitter directed 20% of the light to a monitor photodiode while the remainder was transmitted through a focusing lens. Power values were calibrated using an integrating sphere, while the beam size of the focusing beam was calibrated with a beam profiler mounted to a translation stage. After calibration, the beam profiler was replaced with the device under test (DUT), an SM1PD1A at a 0 V bias. The output current was measured with an ammeter to remove the need for a load resistor. We then recorded datasets as the beam diameter was continuously scanned from 0.06 mm to 5 mm while power was held constant, as well as measurements for beam diameters ranging from 1 mm to 5 mm (measured to the 5% clip level) as the incident power was continuously scanned from 0.12 mW to 5 mW.

The figures show the results from the measurements. Figure 1 (right) and Figure 2 (below) show the deviation from linear response for continuously varying beam diameter at a fixed 1 mW incident power (Figure 1) and continuously varying incident power for several beam diameters (Figure 2).  Figure 1 shows that for a 1 mW input, the photodiode saturated at beam sizes less than 300 µm. Figure 2 shows that beam diameters ≥2 mm did not saturate at the power levels investigated.

Click for Full Lab Facts Summary

One hypothesis for these results was that local saturation due to a large power density locally depleted or reduced the population of available carriers. In Figure 3, we calculated the power density by taking the quotient of the measured power and beam diameter presented in Figure 2 and plotted the current output as a function of that power density. If the results were due to local saturation, we would have expected that all of the beam diameters would saturate at a single power density; however, this was not the case.

Since the results presented in Figure 3 coupled the beam size change with a change in optical power density, we performed another experiment to increase the power density incident on the sensor within the same envelope of beam area to see if there was a change in the saturation point. This was done by segmenting the Gaussian beam into an array of beamlets with a microlens array, concentrating the overall optical power into smaller spots within the same Gaussian envelope. This created larger power densities while maintaining a similar electrical path to the sensor leads. Figure 4 shows the same results as Figure 2 with the results from the microlens array overlaid as dashed lines. Since the results are nearly identical to the original Gaussian beam for all diameters, the saturation appears to be dependent on the overall beam diameter and independent of the power density. In the complete Lab Facts presentation, we discuss how these results support the theory of Scholze et al. that the change in saturation with beam size is due to a change in the series resistance of the photodiode  [1].

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Figure 2: Percent Deviation from the linear response with increasing power for 1 mm - 5 mm beam diameters. The 1% deviation level is indicated with a dashed horizontal line.

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Figure 3: Normalized output current versus power density for 1 mm - 5 mm beam diameters. This shows the saturation effects do not appear to be based on a single power density.

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Figure 4: Normalized output current versus optical power for 2 mm - 5 mm beam diameter with (Dashed Line) and without (Solid Line) the microlens array (MLA) prior to the photodiode.

[1] F. Scholze, R. Klein, R. Muller, Linearity of silicon photodiodes for EUV radiation. 2004 Proc. SPIE 5374 926–34.