A Comparative Study Of Strain Relaxation Effects On ... - IEEE Xplore

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IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 3, NO. 3, JUNE 1997

A Comparative Study of Strain Relaxation Effects on the Performance of InGaAs Quantum-Well-Based Heterojunction Phototransistors M. Ghisoni, O. Sjölund, Member, IEEE, A. Larsson, Member, IEEE, J. Thordson, T. Andersson, S. M. Wang, and L. Hart

Abstract— The performance of a GaAs based heterojunction phototransistors (HPT’s) using an n-p-i-n configuration, where the absorption is provided by InGaAs quantum wells (QW’s) have been studied. Structures with differing numbers of QW were investigated. This allowed the tradeoff between the benefits of increased light absorption and the drawbacks of increased lattice relaxation, caused by the mis-match between InGaAs and the GaAs substrate, to be examined. All the HPT’s investigated showed responsivities (A/W) far larger than unity, as well as large wavelength tolerance, for example 44 A/W 615% from 950–970 nm, for 10 W incident optical. Electrical commonemitter current gains, of up to 3000 were measured for our HPT’s and then confirmed by subsequent HBT measurements. Small relaxation levels (

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MQW region as a whole, i.e., using the average indium value. When is zero this implies pseudomorphic strain accommodation and when 100% indicates complete relaxation of the MQW region to the free-standing superlattice. Looking at Table II, we see that, unfortunately, the two growth runs were not identical. The second run (M578–580) produced a larger period and lower average indium composition in the MQW region. Importantly, however, we do have a spread of samples with different relaxation levels. M532 and M578 are pseudomorphically strained while M534 and M580 are heavily relaxed. Samples M533 and M579 on the other hand are both only partially relaxed. This spread of relaxation values, as we shall see, allow a meaningful comparison to be made of its effect on HPT performance.

Fig. 3. Absorption-length spectra for three samples under different applied biases. The voltage, CE , is applied across the collector–emitter, with no base contact as for the subsequent HPT measurements.

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III. ABSORPTION SPECTRA Prior to testing as phototransistors, absorption spectra were taken from all the processed chips as a function of applied bias. The measurements were carried out using light from a tungsten source filtered through a 0.25-m monochromator and focused onto large 500 m 500 m mesa devices. Transmission spectra were taken from the devices using a silicon photodetector and standard lock-in techniques, as well as from the substrate itself (between devices) in order to remove any contribution from the substrate. The voltage, is applied across the device, i.e., between collector and emitter, most of which will then fall as a reverse bias across the intrinsic collector region. There is no base contact used. This configuration is identical to that used for the subsequent HPT measurements. The absorption spectra, plotted as , where is the absorption and is the length of absorber, from three of the samples are shown in Fig. 3, for different values. We can see that all the samples show the typical characteristics of QW material; namely a sharply resolved heavy hole (e1hh1) exciton, which red shifts, loses oscillator strength, and broadens on application of an electric field, i.e., the quantumconfined Stark effect (QCSE) [33].

Table III shows the 0V e1-hh1 peak wavelength and absorption values and the peak HWHM for all the samples. value at a wavelength, shorter than Also shown is the e1-hh1, where the absorption is essentially bias independent. This will be used in subsequent sections. From Table III, as expected, the band-edge red shifts with increasing indium concentration in going from M578 to M580. Also these three samples are at considerably shorter wavelengths than the devices from the first growth run, again attributable to their lower indium concentration. The shift to longer wavelength from M532 to M534 may be as a result of the increase in relaxation, which would be expected to produce such an effect. This, of course, may also be a contributory cause to the shifts observed in M578–M580. Within each growth set the HWHM increases with increasing number of periods and relaxation. This increased broadening may be due to well to well inhomogeneity, i.e., well width broadening, as the number of QW’s is increased. It may also, in part, be caused by inhomogeneities across the material brought about by the relaxation. This has been observed in previous work on partially relaxed InGaAs–GaAs QW’s samples where the barrier thickness was varied [23].

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TABLE III SUMMARY OF RESULTS OBTAINED FROM ABSORPTION SPECTRA OF FIG. 3. SEE TEXT FOR DETAILS

Though the 0-V characteristics are important, since they allow the change in material quality to be observed, ultimately the HPT will be run under biased conditions. Because of this, there will inevitably be a loss of peak absorption. However, if we look at Fig. 3 we can see that we gain much in terms of spectral uniformity of the absorption in the biased spectra. For values of 0.033 (8 V spectra), 0.132 (8 V) and 0.235 (9 V) for M532, M533, and M580, respectively, the spectral range for a tolerance on of 15% is 20 nm in all three cases. Such uniformity, if translated into the responsivity of the HPT, will obviously give a large wavelength tolerance which, as mentioned in the introduction, is highly desirable. It should be noted that the absorption spectra for the other three wafers not shown here also display similar characteristics. IV. PHOTOTRANSISTOR PERFORMANCE The previous section showed the absorption characteristics of the HPT’s. In this section, the fundamental phototransistor operation is examined. The responsivity, in Amperes per Watt (A/W), of the devices was measured using a stepper motor controlled wavelength tunable Ti:Sapphire laser as the optical source. The laser light was coupled into a fiber and was then divided using a fiber coupler. One output was aligned to the transistor window and the other was incident on a calibrated Si detector for power monitoring purposes. As it is well documented that HPT’s suffer from degradation with time due to surface oxidation effects, all devices were de-oxidized in ammonia solution prior to measurement. The identical measurement procedure and, hence, time duration, was then used in all cases, so as to allow comparison. In Fig. 4, the responsivity spectra (A/W) for all six samples are shown, as a function of for an incident optical power of 10 W. Some general points can be made from the following results. 1) All the devices show responsivities significantly greater than unity, i.e., they all exhibit gain. 2) The responsivity spectra exhibit the same characteristics as the appropriate absorption spectra of Fig. 2. If we look at M532, for example, we can see a strong excitonic feature which red shifts with voltage. However, in comparing the responsivity and absorption spectra, it is clear that this excitonic feature is far stronger, relative to the continuum, in the former case. This is indicative of

the commonly observed deviation from ideal transistor behavior, whereby the gain, and, hence, responsivity in this case, increases as a function of collector current. 3) At higher biases the responsivity is uniform over a wide wavelength region, again consistent with Fig. 2. For example M533 in Fig. 3, at 7 V, has a responsivity of 44 A/W 15% from 950–970 nm. 4) A marked change occurs in the responsivity with voltage as the samples become more relaxed. We can see that, for both M534 and M580, the level of the responsivity increases dramatically with applied bias. For the unrelaxed samples, M532 and M578, the responsivity level is essentially constant. The only changes being those caused by changes in the absorption spectra. In the case of M533 and M579, the 1-V spectra is at a noticeably lower level than the other spectra. In order to further study the transistor characteristics of the devices, we measured the collector current, , versus for a number of different incident optical powers. The wavelength, in all cases, was fixed during the measurement, and chosen to be to the short side of the 0-V e1-hh1 peak, such that the absorption was as bias independent as possible. The values for each sample at these wavelengths are those given in Table III. The resultant plots are shown in Fig. 5. It should at high biases observed be noted that the rapid increase in in some of the low power curves, in particular that of M532 is simply due to the dark current of the device becoming a significant fraction of the overall current. Looking at the results of Fig. 5, we can see that in all cases, as the incident optical power is increased, so the collector current increases. This is as expected and is analogous to an HBT as the base current is raised. The samples M532, M533, M578, and M579 all display good transistor characteristics. They have both a well defined “knee” or turn-on, and very good saturation of the collector current with bias. The two weakly relaxed samples (M533 and M578), do, however, require slightly higher voltages before reaching this saturated level. When we examine the plots for the heavily relaxed samples, M534 and M580, we see a marked deviation from the ideal case. The latter does not reach a saturated level until 4 V, while the former appears never to reach this state, but shows a steady increase with voltage. These observations are consistent with the responsivity results of Fig. 4. For an ideal HPT the gain exhibited by the device would be independent of the collector current flowing through it. However this is not usually observed in practice. We have already seen evidence for this in the increased exciton strength in the responsivity, as compared to absorption, spectra. The exact nature of this effect can be seen by examining the overall phototransistor gain, , as a function of . The term is defined as [1], [29]: (2) where is the incident optical power and , and have their usual meanings. It should be noted that is often referred to as the optical gain, though this is rather misleading since the gain within the HPT is purely electrical. The results

GHISONI et al.: A COMPARATIVE STUDY OF STRAIN RELAXATION EFFECTS

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Fig. 4. Responsivity spectra at 10 W for all six wafers for various values of

VCE . The key for the different voltages is given in the plot of M580.

obtained from the plots of Fig. 5 at 6 V are shown in Fig. 6. From , we can also obtain an estimate for , the common emitter electrical current gain, for the transistor section of the HPT. It has been shown by Campbell [1] that can be approximated by

interface (see Campbell [1] for details). The linearity of the data of Fig. 5 suggests that this is the dominant term in the defect current and fits yield values of 1.49, 1.52, 1.18, 1.53, 1.55, and 1.46 for M532, M533, M534, M578, M579, and M580, respectively. The ideality factor is commonly regarded as an indication of the quality of the emitter–base junction. This would appear to suggest that sample M534 has the best such junction, with the other samples being of a similar standard. We would actually expect the opposite to be true, since M534 has a large relaxation value and, hence, defect density. The contradiction lies in an assumption inherent to the use of the ideality factor in this way, namely that the base transport factor, is very close to unity. This factor can be shown to be:

(3) where

is the external quantum efficiency: (4)

, the surface reflectance is taken to be 0.31 and the values of are those given in Table III. A number of assumptions are inherent to (3), including that the internal quantum efficiency of the detector section is unity, i.e., all photogenerated carriers are collected. The results for are displayed in Fig. 7 again . as a function of As we can see, all the samples show a linear relationship of and with respect to , when plotted on a log–log both scale. The gradient of this line can be used to calculate n, known as the ideality factor of the emitter–base junction, for the HPT’s via the relationship [1]: (5) The ideality factor stems from the generation-recombination component of the emitter defect current at the emitter-base

(6) is the effective or undepleted width of the base and where is the minority carrier diffusion length in the base. If the minority carrier diffusion length in the base is reduced such that deviates from near unity then a misleading value of will be measured. We shall return to the question of the change of in our HPT’s in later sections. Studying Fig. 7, we see that the first growth batch have lower values than those of the second batch. This is probably simply due to material differences between the two batches for example in base/emitter doping and base thickness. Concentrating on M578, M579, and M580, we see from Fig. 6

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Fig. 5. The collector current, IC as a function of collector–emitter voltage, VCE for different incident optical powers. Increasing optical powers generates increasing current. For M533, M534, M578, and M579 the powers used were 0.5, 1, 2, 5, 10, 20, and 50 W. For M580 they were, 0.5, 1, 2, 5, 10, and 20 W. For M532 they were 1, 2, 5, 10, 20, 50, and 100 W.

Fig. 6. The optical gain, G, as a function of IC . The results were obtained from the data of Fig. 5 using (2).

that increases in going from M578 to M579. This is as expected due to the increase in QW’s and, hence, absorption in the p-i-n detector section. However, we do not observe such an increase when going from the 20 QW’s of M579 to the 30

Fig. 7. The common emitter current gain, , as a function of IC , based on results from Fig. 6 and Table III, and using (3) and (4).

QW’s of M580. From Fig. 7, we see that while M578 and M579 have almost identical electrical gains, that of M580 is reduced by approximately half. The electrical gain for the three wafers should be the same since their transistor sections are


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TABLE IV COMPARISON OF PUBLISHED RC-HPT RESULTS AND THOSE OBTAINED IN THIS WORK FOR M533 AND M579 AT 6 V. THE COLLECTOR CURRENTS AND RESPONSIVITIES FOR THE FOUR RC-HPT’S QUOTED ARE THOSE AT HALF THE MAXIMUM PEAK HEIGHT, AND CORRESPOND TO THE VALUE USED TO FIND THE FWHM, , VALUE QUOTED. NOTE THAT FOR OUR NON-RESONANT STRUCTURE WE DO NOT USE THE FWHM, BUT RATHER 15% OF THE QUOTED RESPONSIBITY VALUE. MQW ABSORBER USED IN ALL CASES EXCEPT [19], WHERE A BULK InGaAs ABSORBER WAS USED

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nominally identical. Thus this result clearly indicates that there has been a degradation in the performance of the transistor section of the HPT with increased relaxation. In the following section we shall examine this in more detail, by studying the material operating as an HBT. We can conclude this section by comparing the responsivity results exhibited by our devices with some of the RC-HPT’s reported in the literature for operation at GaAs substrate transparent wavelengths. The comparison is shown in Table IV, where the collector current and responsivity at half the maximum value are given along with the bandwidth across which these values are exceeded. We can see that the responsivity values from this current work are competitive with the RC-HPT for the same given input optical power. The percentage of light absorbed in M533/M579 is low 12%–14%, as compared to the RC-HPT’s ( 30%–50%) indicating that the electrical gain is significantly larger in our devices. We should also note two more important points from this comparison. For M533, good performance has been obtained out toward common VCSEL wavelengths. Also that the nonresonant HPT’s are tolerant to fluctuations in the operating wavelength. V. HBT

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Fig. 8. Results for HBT operation. The collector current, IC as a function of collector–emitter voltage, VCE , for different base currents. The base currents used for M578 and M579 were, 0.2, 0.5, 1, 2, 5, and 10 A; for the M580, they were 0.5, 1, 2, 5, 10, and 20 A.

PHOTODETECTOR PERFORMANCE

As stated previously the wafers from the second growth batch were also processed, with the addition of a base contact, into HBT’s. This allowed separate examination of the p-i-n photodetector and transistor section. In Fig. 8 we have plotted against for different base currents, and in Fig. 9 the resultant current gain, as a function of . Fig. 8 clearly shows marked differences between the three samples. M578 has all the characteristics one would associate with a good HBT, sharp turn-on and a current which becomes rapidly and stably saturated with voltage. The heavily relaxed M580 on the other hand, while displaying a reasonable turn-on, never establishes what could be described as good saturation; the collector current shows a steady and significant increase with applied voltage. Sample M579 can be seen to reach saturation at higher biases, but it too shows strange behavior at

Fig. 9. Current gain as a function of collector current from data of Fig. 8 at VCE 3 V.

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lower biases, with a steep increase in collector current spread over the first 2–3 V. In examining Fig. 9, we can compare the results to those of Fig. 7, where we estimated the electrical gain of the HPT’s. We see that the results are perfectly consistent, M578 and M579 have similar gain characteristics while M580 shows a degradation. Interestingly, the absolute values as a function are also very similar, with gains of 3000 being obtained of 10 mA in both cases, for M578 and M579. The for results obtained for the HBT’s confirm the electrical gain

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Under steady state conditions, then the requirement for constant current density through the device requires that (7)

Fig. 10. The collection efficiency of the p-i-n detector section of the HPT, as a function of bias applied across the collector–base junction.

Fig. 11. A 1-D schematic representation of the currents flowing through the HPT. The shaded regions represent depleted areas. Note we have drawn the above such that the collector is fully depleted. See text for further details.

results obtained under HPT operation. They also show that as the relaxation increases the transistor suffers a degradation in performance, which while not catastrophic, is significant. The performance of the p-i-n photodetector section as a function of bias was also examined. The photocurrent was measured with light incident from a tunable Ti:Sapphire laser and using standard lock-in techniques. Spectra were taken at a number of voltages (applied across the collector–base contacts), and then the power was integrated over the spectral range measured. Fig. 10 shows the normalized collection efficiency for the three samples. We can see that all show sharp turn-ons at 0.5 V and saturation of the collected photocurrent by 0.5 V (remember that this is a reverse bias across the p-i-n detector). The only difference in the collection efficiency between the samples occurs in the sharpness of the turn-on. It is apparent that, as the relaxation increases, this becomes more rounded, and that saturation does not occur until slightly higher voltages. In terms of operation simply as a photodetector, the differences involved are very minor. These results are consistent with those of Bender et al., [22] who saw no significant change in photoresponse for InGaAs–GaAs p-i-n photodetectors as a function of increased relaxation. VI. MODELING In order to further understand the importance of different factors on the performance of the HPT, we have attempted to model the results obtained previously. The model used is that outlined in detail by Campbell [1], and so we will not reproduce it in this paper, except to indicate some important points and differences. Fig. 11 shows a one-dimensional (1-D) representation of the currents flowing within the device.

and represent the electron current components injected across the emitter–base and base–collector junctions, while and are the corresponding hole components. The photocurrent is denoted by , while is a defect current at the emitter–base interface, which we shall return to later. In the model used by Campbell, absorption occurred in the base-collector region of a npn HPT. In our case, we have a design where the absorption will occur predominantly in the -region, hence, we have not included any base or emitter absorption. An important difference is in our approach to transport across the collector region. From the results in Fig. 10 on the collection efficiency of the photodetector, we know that there is some carrier loss across this region at low biases. We have thus incorporated the results of Fig. 10 into the model. However, we have not only applied this as a loss mechanism to the photogenerated current, , but to all currents flowing across the collector section, hence, and as well. We have also included a defect current, at the emitter–base junction with the form (8) where is a constant, is the emitter potential, and is the ideality factor, obtained from Fig. 6 (we will continue to refer to currents, but as is apparent from the symbols, current densities are required in the equations). Values for minority carrier diffusivity and diffusion lengths for the different materials and doping types and levels were simply taken from data collated in the INSPEC series of books [34], [35]. This gave for the base section, diffusivity and diffusion lengths of 55 cm /s and 12 10 cm, respectively. The thicknesses and doping concentrations used were the nominal ones. Our approach was to take the versus data for 5 W incident power from Fig. 5, and then simply vary until the experimental and simulated currents matched at 5 V, whereupon simulation at the other incident optical powers is performed. Hence, the only fitting parameter used is . Other data, such as absorption, ideality factor, etc., were taken directly from previous measurements. The results of this simulation procedure are shown in Fig. 12, where we have replotted the relevant experimental Gummel plots of Fig. 5, along with the simulated results. Starting with M578, we see that there is excellent agreement in all respects between experiment and simulation. The turn-on, and the rapid and stable saturation of current with voltage are all well fitted. For M579 we start seeing some discrepancies occurring, notably in the position and sharpness of the current turn-on, though again the overall agreement is still good. If we look at M580, we see that the agreement has worsened. At low voltages the simulation does indeed predict a greater rounding of the current turn-on, but to a lesser extent than observed experimentally. Also at higher voltages, the simulation predicts a much stabler current saturation than that which is actually measured.


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Fig. 13. Symbols represent data for M580 at 5 W incident power. Dashed line is the fit shown in Fig. 12, while the solid line is a “best fit.” The inset shows the detector collection efficiencies upon which the two fits were based, the dashed being that measured experimentally in Fig. 10.

efficiency , which as already shown in (6) is a function of the minority carrier diffusion length in the base, . If is reduced such that , no longer applies, then saturation may not be so readily achieved. As the applied voltage across the device increases will decrease and, hence, will increase, resulting in an increase in the common emitter current gain, , since: (9)

Fig. 12. Symbols represent experimental IC versus VCE data taken from Fig. 5. Solid lines are the simulated results. See text for details.

where is the emitter injection efficiency. Such a reduction in would also account, as previously mentioned, for the surprising drop in ideality factor observed in the more relaxed samples. VII. DISCUSSION

At this point it is informative to examine in more detail the effect that the efficiency of the carrier transport across the collector region is having on the device. In Fig. 13, we have replotted the M580, 5 W experimental and simulated data from Fig. 12. We have also included a simulation based on a different collection efficiency profile than that actually measured. This latter was intentionally chosen to be a very – data. In an inset to good fit to the experimental Fig. 13 we have included both the experimental and the “best across fit” collection efficiencies, plotted as a function of the HPT. What is immediately apparent is the small difference between the collection efficiency profiles used. Thus, very small changes in the quality or efficiency of the collector region are amplified into significant performance changes within the HPT. This effect is, of course, a result of applying . The simulation the bias dependent collection efficiency to thus suggests that a loss mechanism does exists within the collector region that will also influence carrier transport across . this region and, hence, also As far as the poorer current saturation observed for M580, than expected experimentally, this may be due to a degradation of the base transport characteristics. The slope of the current versus voltage ( – ) curves is effected by the base transport

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CONCLUSION

We have observed that lattice relaxation has a detrimental effect on both the p-i-n detector and the transistor section of the HPT. The actual magnitude of the effect on the photodetector is small, and would have an insignificant effect if operated as such. It appears though that the effect which causes the degradation in the collection efficiency is also applicable to the other currents in the collector, so that this effect is amplified by the HPT. We mentioned, when discussing the HRXRD characterization, that relaxation of the MQW region causes dislocations to form in localized areas just below and just above this region [32]. The level or concentration of these will increase with increasing relaxation. Thus we have dislocation “planes” situated on either side of the MQW region, i.e., within the collector section. Such dislocations will act as nonradiative centers, carrier traps, and scattering centers. We believe that these defects account for the drop in performance of the detector and the subsequent amplification of this effect in the HPT characteristics. Obviously, there will be other factors, in particular the effect of increasing the number of QW’s which may result in an increased capture rate therein. We should note that our application, in the simulation, of the collection efficiency directly to , is undoubtedly a simplification. It did, however, allow the observation that the transport across

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the collector region could be a major problem. The above findings are consistent with work by Lin et al. [36] on similar structures. By correlating cathodoluminescence and electron beam induced current results with dark line defects, they concluded that dislocations in the collector impeded carrier transport and so affected the hole accumulation in the base. For the transistor operation, at higher biases, where there is no longer any effect from the collection efficiency, then we observed a performance drop with relaxation. This was noted as a drop in the current gain, , and also in the incomplete saturation of the collector current. As we have already stated such a problem with the saturation can be readily explained by a drop in in the base, such that deviates from unity. Since is directly related to the carrier lifetime in the base, then this implies that this lifetime is decreased. The presence of defects or dislocations within the base would cause such a reduction in the lifetime. Studies have shown that above misfit dislocations formed by MQW relaxation, point defects can form [37], and act as recombination centers reducing lifetimes. Thus, for our structures, dislocations formed in the collector region may induce point defects to occur in the base, which, by reducing the lifetime, will cause problems in achieving current saturation. Ashizawa et al. [26] in work on HBT’s with InGaAs bases, also observed incomplete current saturation, and believed this to be due to dislocation formation. In this case, however, they attributed the saturation difficulties to an increased collector hole, or leakage current, induced by the dislocations formed in the region of the base–collector junction. Such an explanation, by itself, would, in our case, not necessarily explain the observed anomaly in the ideality factor with relaxation. As we have described in the paper, dislocation and defect formation caused by lattice relaxation will degrade the HPT performance. This is not, however, catastrophic even for the large levels of relaxation present in some of our samples. All samples studied operated as HPT’s with responsivities and gains significantly greater than unity. The device performance drop was only observed for the most heavily relaxed samples and not for those that were only partially relaxed. This means that a tradeoff will exist between improvements caused by additional InGaAs absorption, and deterioration caused by the added relaxation this brings about. Interestingly, it would appear that the turning-point might occur at relaxation values of 20%, which are quite substantial. VIII. CONCLUSION We have produced nonresonant HPT’s, with high electrical gains, which result in responsivities comparable to RC-HPT’s, but with better wavelength tolerance. Relaxation is seen to effect both the detector and transistor section of the HPT’s. However, this is significant only in the case of large relaxation values. With small values an improvement in the overall device performance is observed. Further work needs to be carried out in terms of finding the optimum relaxation allowable, and also to analyze the long term stability of such relaxed devices. The results, though, clearly indicate that relaxation should not be necessarily regarded as an impediment to improving device operation.

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M. Ghisoni, photograph and biography not available at the time of publication.

O. Sjölund (S’92–M’97), photograph and biography not available at the time of publication.

A. Larsson (M’89), photograph and biography not available at the time of publication.

J. Thordson, photograph and biography not available at the time of publication.

T. Andersson, photograph and biography not available at the time of publication.

S. M. Wang, photograph and biography not available at the time of publication.

L. Hart, photograph and biography not available at the time of publication.