With this in mind, an automated measurement system that uses the IEEE 488 standard instrumentation bus ⁽¹⁾ has been developed to characterize avalanche photodiodes (APDs). With this system we can make measurements that that would have been difficult and time-consuming had conventional equipment been used.

The IEEE 488 Bus

Before discussing the measurement system let us briefly review the basic features of the IEEE 488 bus (also commonly known as the GPIB - the General Purpose Interface Bus).

The IEEE 488 bus consists of a multiway cable containing 16 parallel signal lines; these are shared by all the instruments in the system with all the interconnections made with stackable connectors. The IEEE 488 standard ⁽²⁾ specifies a uniform digital data interface - both electrically and physically - for test equipment. This allows stand-alone laboratory equipment from different manufacturers to be interconnected to form an automatic system.

A system controller, an essential system component, oversees the system's operation. Apart from the controller (an HP-85 desk-top computer in our case), up to 14 instruments can be supported. Every instrument is defined by a unique address. This feature allows the use of a common bus structure - an instrument only responds when it is addressed by the controller. If it is not addressed, it ignores all activity on the bus and takes no part in data transfer. But instruments are designated "talkers" or "listeners". A talker originates data which are sent along the bus (for example, a paper tape reader); a listener, on the other hand, receives data from the bus. Some instruments are both talkers and listeners; for example, a digital voltmeter must be a talker to put readings on to the bus but can also be a listener if the range can be set remotely by the controller.

From the user's viewpoint, the automatic operation of the equipment via the bus is largely transparent - usually only one or two instructions are required in the controlling program to communicate with an instrument. The addressing, data transfer and associated signalling that comprise a bus transfer are taken care of by the controller hardware.

Are any drawbacks involved in using an instrumentation bus? Certainly. First, it tends to be expensive - individual instruments with the interface options are usually close to the top of the price range and, as already mentioned, a bus controller must be present. If we want a simple data logging system, say a digital voltmeter and a printer, then the need for a controller (which will form a significant proportion of the total cost) makes the "bussed" system unattractive. A home-made or proprietary link that would not require a controller will almost certainly provide a cheaper (albeit less flexible) alternative.

A second problem arises through the presence of an extended high-speed digital system close to a high sensitivity measurement system. The bus wiring will radiate electromagnetic interference that originates in the controller; the pre-amplifier picks up a significant proportion of these unwanted signals. Our solution involves removing the controller and as much of the system as possible - disc drives and plotter - to another room. This means that the bus is split into two electrically isolated parts linked by a fiber optic cable connecting a pair of bus extenders.

The Measurement System

Fig. 1 shows a simplified block diagram of our measurement system as configured at present. We are now characterizing silicon and germanium APDs. The optical system is shown in Fig 2a; a laser diode (left), of appropriate emission wavelength, provides a monochromatic source of light for the APD. The laser’s output beam is collimated using a microscope objective and passes through the optical system to a second objective. The APD lies in the focal plane of this objective; thus, the detector can be illuminated with a finely focused spot of light. (This can be used as a probe to examine small areas of the detector. Using a multimode laser we achieve a spot size of about 30 x 10 µm which is adequate for our purposes. Smaller and more symmetrical spot geometries are achievable but require the use of narrow-stripe lasers.)

A half-silvered mirror set at 45° in the collimated beam allows the APD to be viewed through the second objective. A television camera with an extended infrared response is used. Conventional tubes, such as SIT vidicons, commonly used with 850-nm junction lasers are unsuitable for use with the longer-wavelength devices.

The APD and its pre-amplifier are mounted on a motorized stage (right side of Fig. 2a). The APD can be positioned under computer control anywhere in a 16-mm square in the focal plane with an accuracy of 1 µm. The mount comprises two identical orthogonally mounted micropositioning stages. The stages contain dc motors and have incremental optical shaft encoders to provide positional information. The stage driver module, developed in the Department of Electrical Engineering Science at the University of Essex, receives commands via the bus; the driver contains a 6800 microprocessor, random-access memory and firmware. This design strategy has allowed a high degree of intelligence to be built-in; commands can either be incremental or absolute. The driver can be interrogated by the controller to ascertain the current status of the module. For example, the position of the stage can be obtained as well as the direction of movement.

The output power of junction lasers, when constant-current driven, is strongly dependent on temperature - for a typical device a rise of 15°C will result in a fall in output power of around 17%. For this reason junction lasers should operate at a constant temperature. We have mounted the laser in thermal contact with a metal block whose temperature is maintained at a predetermined level using a thermoelectric heat pump. A voltage proportional to absolute temperature is derived from a monolithic temperature-sensing integrated circuit mounted close to the laser on its block. A power differential amplifier compares this voltage with a stable reference. The output of this amplifier drives current through the thermoelectric heat pump ⁽³⁾ . The heat pump is reversible, with the direction of current flow determining the direction in which heat is pumped. Thus, we can maintain the mounting block above or below ambient temperature with long-term stability of within one Celsius degree.

We have chosen to mount and control the temperature of the APD in a similar way. Some properties of APDs such as dark current are temperature dependent, so full characterization requires temperature to be a fully controllable variable.

The heart of the data acquisition system is the Tektronix 7854 waveform processing oscilloscope, Fig. 2b. It has multiple modes of operation; it can be operated simply as a wideband oscilloscope and can also digitize an input waveform. A fast sample-and-hold circuit followed by an analog-to-digital converter performs the latter function. The digitized waveform is stored in an internal memory. ⁽⁴⁾ Once a waveform is stored it can be viewed on the oscilloscope screen and processed locally using a user-originated program. However, in most cases transferring the complete waveform data to the controller in its raw state allows us to make use of the more powerful facilities of the BASIC interpreter to analyze the data. As an example of the type of analysis achievable, consider Fig. 3a, an oscilloscope display of a digitized noise waveform from an APD. Fig. 3b is a histogram derived from Fig. 3a, approximating to the probability density function of the waveform. The histogram is found by dividing the total waveform excursion into 30 levels and then assigning each point of the waveform to one of the 30 levels. A plot of the number of points falling in each level versus the level yields the histogram.

APDs have received much attention from designers of fiber optic communication and measurement systems because they combine high sensitivity and fast response. A comprehensive description of the statistics of the noise and signal processes is required to even approach optimum receiver design; present descriptions all fall short in some way of giving a full description.

In the case of non-avalanche detectors, such as p-i-n photodiodes, the detector noise is manifest as the familiar shot noise, due to the random arrivals of photons which in turn give rise to individual free carriers. The noise spectral density of shot noise is given by:

(1)

where e is the electronic charge and I_s is the signal current. In an optical receiver, this shot noise is small and other sources of noise, such as from the amplifier and resistors, are dominant.

In the APD, the mechanism of initial carrier generation is the same. However, each primary carrier initiates an avalanche chain that ultimately results in a number of carriers. If we consider a given injected carrier this number is indeterminate, but the behaviour of a large number of chains can be described statistically. Processes of this type where one random process produces input for another are said to exhibit compound randomness.

The mean gain, G, is the most important statistic that can be attributed to the gain process in an APD. Knowing what the mean gain is doesn’t necessarily tell us anything about the range of gains operating or a probability of a given gain occurring. The spread of possible gains determines how much noise is produced by an APD - the temporal fluctuations seen at the diode output reflect the variability in the number of carriers from individual avalanches.

An often-used approximation for the APD noise spectral density is:

(2)

where x depends on the APD material: x » 0.3 for silicon and x » 1 for germanium.

This expression can be viewed as being the product of amplified shot noise (2eI_sG²) and the indeterminacy of the avalanche process or the avalanche noise, G^x.

Expression 2 is entirely empirical . A better approximation ⁽⁵⁾ based on a theoretical model is given by:

(3)

where k is a factor between 0 and 1 related directly to the behaviour of holes and electrons in the APD avalanche region. Typically, k = 0.03 in silicon and 0.5 in germanium.

Expressions 2 and 3 show that the noise is strongly dependent on G and increases rapidly for large G values. Germanium APDs and those made from other high k-value materials are inherently much noisier than their silicon counterparts.

So far the expressions have related to noise power. It is almost invariably assumed, for analytical purposes, that the noise distribution is Gaussian. This distribution, often used by designers, is chosen for convenience only. In some situations this approximation can be a poor one.

The emphasis of our research is on determining a more accurate description of the distribution. Theoretical models that predict the gain distribution ^(6,7) already exist; when combined with the statistics of carrier generation, they give an overall description of the APD. An empirical approximation ⁽⁸⁾ also gives an overall description directly; this allows us to calculate the probability density function from the mean gain, k value and the number of initial carriers. Fig. 4 compares this calculation to the Gaussian approximation. The Gaussian is in error most at low photon fluxes.

Non-Uniform Spatial Response

The preceding discussion assumed a device with uniform gain across its photosensitive surface. Practical devices often exhibit spatial non-uniformities. To show the power of the measurement system we reproduce her two high-resolution isometric plots of a typical silicon APD (Figs. 5a, 5b and 5c). Figures 5b and 5c are the result of over 5000 measurements. Data for several tens of such plots, corresponding to different gains, have been obtained. The non-uniformity results from inhomogeneities in the electric field of the avalanche region. The field is not just a function of the applied bias but rather is a complicated function of bias, device structure , doping and defects in the crystal lattice.

Fig. 5b. Isometric plot of the responsivity of the APD shown in Fig. 5a. The
gain is plotted in the vertical direction. The mean gain for this plot is 71.5.

Fig. 5c. Isometric plot of the responsivity of the APD shown in Fig. 5a.
As with Fig. 5b, the gain is plotted vertically. The mean gain for this plot
is 350. Both this plot and Fig. 5b have had their vertical scales normalised
such that the mean gain is represented by the same distance. Spacing between
adjacent points is 4 µm. The position of the bonding wire can be seen at
left where it obscures part of the active region.

The plots clearly show that the degree of non-uniformity depends on the mean gain, with high gains producing large non-uniformities. Not surprisingly, these high-gain regions contribute an excess noise so that a spatially uniform APD will, in comparison to a non-uniform APD operating at the same mean gain, have superior noise performance. Although non-uniformity is often noted in the literature, linked with an expressed desire for a high degree of uniformity, no quantitative estimate of the degree of degradation is known to us. The net performance in terms of noise power or the output distribution is calculable. In the case of noise power we can use, for example, Expression 3 in conjunction with the spatial distribution of gains such as that illustrated by Fig. 5d. The output distribution is found, although less directly, by using what amounts to multiple convolutions of the set of discrete distributions obtainable from Fig 5d.

As part of our theoretical work we are studying the influence of non-uniformity. As a consequence, the degree of uniformity that is required for a given application can be determined. A comparison of calculated output distributions and noise power with experimental measurements will allow the method's accuracy to be checked.

Acknowledgements

We would like to express our thanks to Mr. Chris Rowden who designed the stage-driver module.

References

1. "Defining the IEEE 488 interface bus," Electrotechnology, July 1982. Return to text
2. "IEEE Standard Digital Interface for Programmable Instrumentation," published by The Institute of Electrical and Electronics Engineers Inc., 345 East 47th Street, New York, November 1978. Return to text
3. L. Mayes, "Temperature stabilisation of laser diodes," Electronic Product Design, Vol. 3, Number 6, June 1982. Return to text
4. A. F. Shackil, "Digital Storage Oscilloscopes," IEEE Spectrum, Vol. 17, Number 7, July 1980. Return to text
5. R. J. McIntyre, "Multiplication Noise in Uniform Avalanche Photodiodes," IEEE Transactions on Electron Devices, Vol. ED-13, Number 1, January 1966. Return to text
6. R. J. McIntyre, "The Distribution of Gains in Avalanche Photodiodes: Theory," IEEE Transactions on Electron Devices, Vol. ED-19, Number 6, June 1972. Return to text
7. P. Balaban et al., "The Probability Distribution of Gains in Avalanche Photodiodes," IEEE Transactions on Electron Devices, Vol. ED-23, Number 10, October 1976. Return to text
8. P. P. Webb et al., "Properties of Avalanche Photodiodes," RCA Review, Vol. 35, June 1974. Return to text

1. This article was first published in Electro-Optical Systems Design, vol 14, No 12, December 1982. Apart from minor corrections, it appears here as originally published.
2. The GPIB is also known as the HPIB (Hewlett-Packard Interface Bus) since it was originally developed by that company prior to being universally adopted.
3. The software used to produce figures 5b and 5c has been published: Surface Plotting Program for the HP85.