This brief paper outlines the results of the first data obtained from irradiating a group of 50 APD’s. The treatise is simplified, not accounting directly for secondary effects attributing to flux values (i.e. vertical displacement), and does not establish true relationships predicted by theory. This is due to the lack of accurate data needed for such relationships to be created. However, as will be seen this paper raises some important questions and discusses briefly areas where more detailed and accurate data is obtainable or required.
Figure 1: Diagram showing relative placement of the APD’s within the irradiator.
Each position in the irradiator has a unique neutron flux, which is estimated by an inverse square law assuming a point source. For a source of 9.7e13 neutrons/hour, fluxes for each vertical row of APD’s is shown in the figure on the next page. Note in Figure 1 that the source is not vertically symmetric. For this reason, neutron flux varies within each vertical row of APD’s. However, the treatment in this report does not yet include this effect.
Below is a schematic of the neutron flux at each position in the irradiator. The values calculated were determined using the inverse square law with a source of 9.7e13 neutrons/hour. The distance from the source was calculated from the machine shop drawing. The dark circle represents ideal positioning of the source (at the crosshairs) in a symmetric position, whereas the dashed circle represents the source being displaced 1 inch upward, which is where the source is believed to be (no official data on exact position has been obtained as of late).
The numbers shown are the neutron flux for each row of APD’s on the APD carrier boards. Fluxes are in units of neutrons per hour per square centimeter. Values in parenthesis indicate fluxes for the displaced source, and values not in parenthesis represent values for the symmetrically placed source (dark circle).
Figure 2: Diagram showing neutron flux for each vertical row of APD’s for the symmetric and non-symmetric cases. Values for non-symmetric are in parenthesis. All values are given in units of hr-1 cm-2.
According to theory, the ratio of dark current (Id) to gain (M) reaches a limiting value at very high gain. This lower limit is depicted in Figure 3 below. The ratio Id/M first reaches a maximum value, and then decays to an asymptotic value at high gain. The asymptotic value of Id/M was chosen as the minimum value of Id/M that lies beyond the maximum value, which occurs at a small value of gain. This method was chosen because at very large values of gain Id/M begins to grow due to secondary effects. In the plot of Id/M versus M in Figure 3, this corresponds to Id/M = 66.2 nA at a gain of approximately 200.
Figure 3: Plot of Id/M versus M for APD # 2101003976. After achieving a maximum value, Id/M decays until reaching a lower limit, and then grows due to secondary effects.
Photocurrent at M = 1: 3.61 nA
The asymptotic value of Id/M is predicted to increase linearly with neutron flux. This theory can be tested by irradiating a number of APD’s with various neutron fluxes. Recall from Figures 1 and 2 that each vertical row of APD’s in Figure 1, or more specifically each APD, has an associated neutron flux. Thus by irradiating many APD’s at once within the irradiator, this theory can be tested. A group of 50 APD’s were all irradiated simultaneously. For the first 40 APD’s tested, the plot of Id/M vs. M had characteristics similar to Figure 3. The asymptotic values of Id/M are plotted versus the integrated neutron flux, given in units of cm-2, in Figure 4 (symmetric source model) and Figure 5 (non-symmetric source model). Figure 4 shows that the symmetric source model more closely agrees with theory, however there is also evidence that the source maybe displaced. Further studies will need to be done to determine the real position of the source.
The large variability of the data in Figure 4 and Figure 5 may be due to the variation in flux along a vertical row of APD’s. To examine the true variability in the data, Id/M is plotted vs M for only the bottom row of APD’s (in Figure 1, these correspond to positions 2, 7, 12, 17, 22), which received the largest flux. Figure 6 and Figure 7 show the results for the symmetric and non-symmetric source models, respectively. As Figure 6 shows, once again the symmetric source model more closely agrees with theory.
Figure 4: Plot of the asymptotic value of Id/M versus the integrated neutron flux for 40 APD’s using the symmetric source model. Id/M is given in units of nanoamps and integrated flux in units of cm-2.
Figure 5: Plot of the asymptotic value of Id/M versus the integrated neutron flux for 40 APD’s using the non-symmetric source model. Id/M is given in units of nanoamps and integrated flux in units of cm-2.
Figure 6: Plot of the asymptotic value of Id/M versus the integrated neutron flux for the bottom row of APD’s in Figure 1 using the symmetric source model. Id/M is given in units of nanoamps and integrated flux in units of cm-2.
Figure 7: Plot of the asymptotic value of Id/M versus the integrated neutron flux for the bottom row of APD’s in Figure 1 using the non-symmetric source model. Id/M is given in units of nanoamps and integrated flux in units of cm-2.
Although the symmetric source model more readily agrees with theory, a large variability in the data still exists. For this reason, the last 10 APD’s from the bath of 50 (which were irradiated simultaneously) were tested. When these tests were conducted, very unusual results were obtained. Instead of the expected Id/M curves, which have characteristics similar to that of Figure 3, the plots in Figure 8 through Figure 17 were found. Observing these plots suggests that these APD’s were handled differently that the first 40 that were tested.
The parameter most likely changed was the anneal time. After irradiation, the APD’s are annealed in an oven to accelerate the effects of diffusion. In this manner, the effects of 10 years of diffusion at room temperature can be studied in a much shorter time.
Figure 8: Plot of Id/M versus M for APD # 0401001460.
Figure 9: Plot of Id/M versus M for APD # 0401001461.
Figure 10: Plot of Id/M versus M for APD # 0401001462.
Figure 11: Plot of Id/M versus M for APD # 0401001463.
Figure 12: Plot of Id/M versus M for APD # 0401001464.
Figure 13: Plot of Id/M versus M for APD # 0211001238.
Figure 14: Plot of Id/M versus M for APD # 0211001241.
Figure 15: Plot of Id/M versus M for APD # 0211001242.
Figure 16: Plot of Id/M versus M for APD # 0211001244.
Figure 17: Plot of Id/M versus M for APD # 0211001245.
According to our experimental records, the first 20 APD’s tested were annealed 38 days, and the remaining 30 APD’s were annealed 40 days. Whereas the first 40 APD’s tested shows similar characteristics, this data does not support the hypothesis that anneal time had an effect. However, the accuracy of the annealing time data is questionable.
Lastly, in examining the data it was found that the photocurrents at a gain of one (M = 1) were generally much larger for the last 10 APD’s compared to the first 40 tested. Table 1 shows these data. The first 40 APD’s tested had a photocurrent at M = 1 which was less than 4.5 nA. However, the last 10 APD’s had much larger values, with the exception of APD # 0401001464. Figure 12 shows the plot of Id/M vs M for this APD. Although the plots has some features which are questionable, the Id/M does achieve an asymptotic value at large gain. From this, it may be concluded that photocurrents greater that 4.5 nA, or perhaps some slightly higher limiting value, indicate a malfunctioning APD. This result is helpful as it may be used as a simpler method of eliminating usable APD’s.
Table 1: Photocurrents at gain one for the APD’s tested.
Addendum of the APD Writeup
As was mentioned in the previous paper, the exact position of the source was unknown. In this segment the position is ESTIMATED ONLY, however this estimate will show what a drastic effect such small positional changes have on the data analysis.
To achieve the best results, the data set was first cut significantly. The data presented in the writeup consisted of APD’s from lots 02, 04, and 21. Because the data from Lots 02 and Lot 04 showed bizarre affects, only APD’s from Lot 21 were analyzed.
The data were first separated into rows. What is meant by rows can be seen in Figure 1 (All indexing of Figure and Table numbers will continue after those used in the first writeup.) In this text, Row 1 consists of positions 2, 7, 12, 17, 22; Row 2 positions 1, 6, 11, 16, 21; etc up to Row 5 positions 5, 10, 15, 20, 25.
When Id/M is plotted vs. the integrated neutron flux separately for each row, the plot in Figure 18 is obtained. It is quickly seen that the data from Lot 21 alone display a near linear relationship as predicted by the theory. Notice that Figure 18 shows the case for the symmetric source model.
Figure 18: Id/M vs. M for Lot 21 APD’s. Each row exhibits a near linear relationship, all having similar slope if extraneous data points are ignored.
As seen, the data within each row approximate linear relationships, and each row has a similar slope if the extraneous data points are ignored. The major differences between each row is the vertical shift in data. However, because the vertical distance from the source is different for each row, this is expected.
Now the non-symmetric source model is considered. First predictions suggested that the source was displaced approximately 1.0 inch as depicted in Figure 2. This may in fact be true. However, it can be shown (it has not been shown here) that if the source is displaced in a similar manner only 0.6 inches that the extraneous data points begin to lie closer to the best-fit line of the remaining data. Also, it is approximated from the magnitudes of Id/M that the source is displaced vertically, as is shown in Figure 1. A reasonable estimate is that the vertical position of the source lies directly between Row 1 and Row 2. When these dimensions are applied, the radial distance from the source can be found “exactly,” quotations used to remind the reader that the offsets are only approximate, although the exact distance from the source is calculated assuming the offsets as correct. Using this method, the plot in Figure 19 is found. As shown, the data all collapse into the same linear fit. This plot then agrees with theory, and supports the hypothesis.
Figure 19: Id/M vs. M for Lot 21 APD’s. Each row exhibits a near linear relationship, all having similar slope if extraneous data points are ignored.
Although the position of the source is only approximated here, the estimate shows much hope for fruitful results which support the theory. Once the position of the source is found, which is under progress, real results will be obtained and statistical analysis of the results can be performed.