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Abstract
We show that in a wide In0.17Ga0.83N quantum well, placed within an undoped region of the pin diode, a photocurrent in the forward direction is observed. The photocurrent switches to reverse direction when the light intensity is increased and/or photon energy is above the bandgap of the quantum barrier. We propose a model showing that the anomalous photocurrent is due to the fact that when the carriers are pumped into the wide quantum well they cannot recombine until the built-in field is screened. For low-intensity light it takes a long time (milliseconds) for the screening to occur and during that time we observe current flowing in the forward direction. This current originates from the reorganization of carriers forming the depletion regions, rather than directly from the photogenerated carriers. The observed effects lead to the dependence of PC spectra on chopper frequency and on light power. They may also affect the operation of laser diodes and solar cells with wide InGaN quantum wells.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Photocurrent (PC) measurement is an important characterization method for diode structures containing quantum wells (QWs). For GaAs/AlGaAs based devices it can be used instead of absorption (transmission) measurements and it reveals not only the ground-state energies but many excited-state transitions [1]. It is usually assumed that the low-intensity light used for PC measurements does not change the potential profile of the diode (contrary to photolumine-scence or electroluminescence measurements). Compared to arsenide devices the PC spectra in InGaN/GaN structures are much broader due to Indium inhomogeneities and QW width fluctuations. The presence of strong piezoelectric and pyroelectric fields leads to spatial separation of electron and hole wavefunctions and, therefore, to lower oscillator strength of allowed optical transitions. This is why growers of InGaN/GaN light emitters have been using narrow (2-4 nm) QWs to make sure that the electron-hole overlap is still significant. Nevertheless, recently in [2] and [3] it has been shown that in wide wells (10-25 nm) there are transitions through excited states, which have a very high oscillator strength. However, these transitions emerge only after current flows through the diode and the ground states of electrons and holes become highly populated. The carriers occupying ground states screen the built-in electric field in the well so that the overlap between the excited states becomes significant and the diodes start to emit light and turn out to be a good material for lasers [2,3]. We studied the photocurrent from these diodes with wide QWs and we found some anomalous effects which we describe below.
These measurements are important for the following reasons. First, the idea of using wide InGaN/GaN wells for light emitting devices is relatively new and characterization of these structures by PC could bring new information about the mechanisms of transforming light into current and vice versa. Secondly, during the last decade there has been an increased interest in using InGaN/GaN QW structures for solar cells [4–7]. High efficiencies can be achieved for light in the violet-blue range and there are efforts to extend this into longer wavelengths. These solar cells perform very well at high temperatures. Therefore the possibility of using wide wells in these devices should be investigated. Finally, we found that for wide wells the shape of the PC spectra can vary significantly with the chopper frequency or with the power of light, which is unusual for interband quantum-well transitions (which are typically very fast).
2. Experimental
Two wide-well diodes were grown by plasma-assisted molecular-beam epitaxy on bulk c-plane n-GaN substrate. The claddings consisted of n-GaN:Si (Si: 2×1018 cm−3) and p-GaN:Mg (Mg: 3×1019 cm−3). The undoped region of the first (second) sample consisted of the 80 nm (110 nm) thick In0.08Ga0.92N (In0.04Ga0.96N) lower waveguide, followed by a 25 nm (10.4 nm) In0.17Ga0.83N well and the 60 nm (110 nm) In0.08Ga0.92N (In0.04Ga0.96N) upper waveguide. We also used a third sample with narrow (2.6 nm) In0.17Ga0.83N QW as a reference. This sample had identical structure to the second sample, only the well width was different. The details of growth can be found elsewhere [8]. The samples had no mirror coatings. The length of laser chips was 1 mm and the width was 0.3 mm. The width and depth of the mesa were 5 µm and 0.54 µm, respectively The lasing wavelength for the first sample was 455 nm and 453 nm for the second sample.
In case of wide wells the Stark effect is huge. However, it is difficult to study experimentally. The lasing occurs for large current densities injected into QWs. Similarly, photoluminescence signal can be measured for sufficiently strong optical injection. This is due to the fact that the optical transition probabilities (wavefunction overlaps between ground states of electrons and holes) are extremely small in wide wells with large built-in fields. Optical transitions can only be observed when the fields are screened by free carriers. Therefore, in case of strong fields only a theoretical evaluation of transition energies is possible. Using the SILENS software we performed numerical calculations of the transition energies in the two samples as a function of reverse voltage applied to the diode (which lowers the field in the QW). We obtained the energies for the first (second) sample varying from 1.16 eV (1.8 eV) at maximum field, up to 2.79 eV (2.75 eV) at zero field. These are extremely large variations, from infrared to the blue. When we illuminate the samples with monochromatic light at high (unscreened) fields, we cannot expect to observe transitions between ground states (in the infrared range). We can only expect to observe transitions between highly excited states in the well, when the wavefunction overlap becomes significant. Once the free carriers are pumped into the well, the field will be screened and the transition energies (and the wavefunction overlaps) will increase.
For PC measurements light from the Xe arc lamp (ENERGETIQ LDLS) was passed through a Jobin-Yvon microHR monochromator. The beam was chopped and we used a lock-in amplifier to detect the photocurrent generated by illumination of a short-circuited diode. For some measurements we used pulsed laser diodes as light sources (operating at 400 nm or at 430 nm) and we measured the time dependence of the photocurrent signal with the oscilloscope. In each case we illuminated the diode from the side of the facet (i.e. parallel to the epitaxial layers) because both surfaces of the diode were metallized. The sample was illuminated through a microscopic objective. The photocurrent spectra were divided by the spectrum of the Xe lamp to obtain the PC efficiency (in A/W).
The illumination from the side of the facet is superior to illuminating perpendicular to the epitaxial layers (using semi-transparent metallization) since the QW signal is enhanced. When we have a few QWs (1-3) the absorption for light perpendicular to the layers is very weak, while for light injected into the waveguide the absorption by the QWs is much stronger. In solar-cell structures 10-50 QWs have been used to increase the PC signal in the perpendicular geometry [7].
When the sample was illuminated by the laser diode the light spot was much smaller than when we used the monochromatic light from the Xe arc lamp. However, we adjusted the light power of the two sources so as to obtain similar PC signal at the wavelength of the laser diode.
It is important for the interpretation of the experiment to check whether the PC signal comes from the vicinity of the facet or from the whole length of the chip. For the tests we used our second sample with 10.4 nm QW. We measured the transmission T of the chip for monochromatic light at 430 nm wavelength. This is the wavelength that should be absorbed in the QW but not in the quantum barrier (QB). The chip was mounted in a clamp to block any scattered light (Fig. 1). When light was incident on the GaN substrate we obtained 49% transmission. This yields the absorption coefficient α=3.44 cm−1 for the substrate. This is in agreement with the results of [9] obtained for bulk crystals which we have used as substrates. For such small absorption we can expect multiple reflections of light from interfaces and metallization in the chip. The QW layer is traversed multiple times and this is why the signal is much stronger than in perpendicular geometry.
Fig. 1. Photo of the chip placed in a clamp and illuminated by 430 nm light for transmission measurements. In case of substrate illumination transmission was 49%.
In order to check if indeed the PC signal comes from the whole length of the chip we prepared a diode sample with two metallizations so that it was possible to collect the PC signal from both parts of the sample (see the inset in Fig. 2). The signal from the upper part [labeled (a)] was only 3 times stronger than from the lower part [labeled (b)]. We also measured the in-plane photocurrent between the two metallizations which shows that there is charge transfer from the regions of higher illumination to the regions of lower illumination.
Fig. 2. PC spectra for two sections of the sample with two metallizations: (a) from the upper part (illuminated directly, 0.7 mm long), (b) from the lower part (illuminated by light scattered in the chip, 1 mm long), (c) between the upper and lower part
3. Photocurrent spectra
When we used a typical chopper frequency (235 Hz) the first sample (25 nm QW) was illuminated during the time window of about 2 ms. The dependence of PC efficiency on wavelength is shown in Fig. 3. For energies below the In0.08Ga0.92N QB bandgap (about 3 eV which corresponds to 413 nm) the current was in the forward direction while for energies above the QB bandgap it was in the reverse direction. The onset of PC transitions is around 465 nm which is much higher than the calculated transition energies for unscreened (strong) electric fields. Therefore the initial absorption in the well must occur through highly excited states.
Fig. 3. PC efficiency vs wavelength (sample 1, no bias applied to the diode) for the 2 ms illumination time. Positive photocurrent values denote reverse direction, negative denote forward direction.
Next we investigated the effect of reverse bias applied to the diode on the PC spectra (Fig. 4). Such bias should reduce the field in the QW. The negative PC signal is indeed reduced with applied bias and vanishes at about -5V [Fig. 4(a)]. A similar effect can be observed when we illuminate the diode with additional dc light at 430 nm and we measure PC with chopped monochromatic light from the Xe lamp [Fig. 4(b)]. Apparently this additional illumination supplies carriers which screen the field in the well. This shows that the negative (anomalous) photocurrent is due to strong fields (in wide wells). The onset of PC transitions does not change with applied reverse bias (or with illumination) which indicates that this onset is due to higher excited transitions which are less sensitive to electric field.
Fig. 4. Photocurrent spectra for sample 1: dependence on the reverse bias (a) and on additional constant illumination by 430 nm light (b). The chopper frequency was 235 Hz.
Standard PC measurements with chopper reveal only the average current during the time of illumination. In order to obtain better insight we examined the photocurrent pulses on the oscilloscope. This time instead of the monochromator and chopper we used the laser diode with pulsed power supply. The illumination window was set to 10 ms. The laser light was attenuated so that the light intensity was varied from 30 µW up to 430 µW. The PC pulses are shown in Fig. 5 for increasing light intensity for below QB illumination [430 nm laser diode - Fig. 5(a)] and for above QB illumination [400 nm laser diode - Fig. 5(b)]. For 430 nm illumination and low light intensity the photocurrent flows in the forward direction for a few milliseconds and then almost vanishes. For increasing light intensity the region of forward current in Fig. 5(a) narrows and the current switches to normal (reverse) direction. It is clear from Fig. 5(a) that the value of photocurrent (measured with chopper) depends on the duration of the optical window (i.e. on the frequency of the chopper) and on the power of monochromatic light. It turns out that the integral of the forward current (from the beginning of the pulse to the zero-current point) is of the order of 10−11C. (This value will be compared with a simple calculation in Section 4). We can also see in Fig. 5(a) that when the light is turned off the PC signal rapidly increases and decays slowly to zero. This decay is similar to the increase of negative PC which we observe at the beginning of the pulse, only in the opposite direction and with smaller amplitude. Rectangular light pulses lead to irregular current pulses for excitation below the QB bandgap. In case of illumination with photon energy above QB [Fig. 5(b)] we can see almost rectangular PC pulses in the positive direction. This is a normal behavior expected for a pin diode.
Fig. 5. Photocurrent pulses measured on the oscilloscope (sample 1) for 10 ms light pulses in case of below-QB excitation (a) and above-QB excitation (b). Identical powers of light (in µW) have been used in both cases.
In case of sample 2 (10.4 nm QW) the negative PC pulses were very short and weak. In Fig. 6(a) we show the same measurement as in Fig. 5(a) for sample 1. 10 ms light pulses (supplied by a laser diode operating at 430 nm) lead to PC pulses that start with a small negative current and switch to positive (reverse) direction after a few tens of microseconds. For a comparison we also show PC pulses from the sample with narrow (2.6 nm) QW which do not reveal any anomalous PC signal [Fig. 6(b)]. This indicates that the anomalous PC which we observe is specific to wide QWs. Other possible contributions to below-bandgap PC (like impurity or defect transitions) would appear in samples with different well widths. All our samples have been grown under similar conditions so we can definitely attribute the anomalous effects to wide quantum wells.
Fig. 6. Photocurrent pulses measured on the oscilloscope for 10 ms light pulses at 430 nm (below-QB) excitation in sample 2 (a) and in sample 3 (b). Negative PC is very short for sample 2 and does not occur for sample 3.
4. Qualitative modeling
The modeling of the photocurrent in QW diodes has been developed in several papers, mainly for the purpose of optimizing GaAs solar cells [10–12]. The problem of strong built-in fields in QWs (opposite to the junction field) has not been addressed and all calculated components of photocurrent were in the reverse direction. Therefore these models cannot be applied to our case of wide nitride wells. The experimental papers on InGaN/GaN solar cells [4–7] concentrate on narrow QWs (2-3 nm wide) where anomalous PC does not occur.
Here we construct a qualitative picture of anomalous photocurrent, leaving the quantitative description for numerical models, combining both the classical drift-diffusion approach and quantum effects. We concentrate on sample 1 which shows more pronounced anomalous PC. The schematic potential profile of the active region of our structure is shown in Fig. 7. We can express the potential increase across the junction as
Fig. 7. Schematic potential profile of the pin junction with wide In0.17Ga0.83N well and In0.08Ga0.92N barriers before illumination. Wavefunctions of electrons and holes are shown. Radiative recombination between such states would be impossible due to vanishing wavefunction overlap. Interfaces are marked by dotted lines (together with polarization charges) and the electric fields are denoted in the well and in the barrier layers.
The polarization charge density at the interface between GaN cladding and In0.08Ga0.92N barrier plus the charge density at the interface between In0.08Ga0.92N barrier and In0.17Ga0.83N well can be estimated as 0.026 C/m2, following [14]. We must also take into account the reduction of the field in the well by the junction field (i.e. the charge density in the depletion layers). This lowers the charge density necessary for full screening of the field in the well to 0.0122 C/m2. For the area of the laser stripe 1 × 0.005 mm2 we obtain the charge equal $6.1 \times {10^{ - 11}}C$.
When we illuminate the diode with low-energy light (above the bandgap in the well but below the bandgap in the QB) electrons and holes are created only in the well. They occupy lowest levels at the opposite edges of the well. Their wavefunctions are separated in space so they cannot recombine (either radiatively or nonradiatively, as shown in [15] and [16]). The charge accumulates and screens the field in the well. When the field in the well is almost fully screened the potential profile is modified so that also the field in the QBs is reduced.
Therefore for wide InGaN QWs even a small amount of monochromatic light can cause significant changes of the potential profile. If we assume that the potential drop in the well vanishes, we can write
Fig. 8. Schematic potential profile of the pin junction with wide In0.17Ga0.83N well and In0.08Ga0.92N barriers after illumination. Wavefunctions of electrons and holes are plotted in the QW. Radiative recombination becomes possible between the excited states. Electric field is reduced in the QBs so that the depletion charge is also reduced. Interfaces are marked by dotted lines and the electric fields are denoted in the well and in the barrier layers. The field in the well is assumed to be fully screened by free carriers.
When the potential profile in the well flattens, excited states appear for electrons and for holes with overlapping wavefunctions. Therefore radiative and nonradiative recombination becomes possible. Carriers accumulated in the QW are thermally excited to the QBs and give rise to reverse photocurrent. However, during the transition from Fig. 7 to Fig. 8 the junction field is reduced so that the width of the depletion layers must be reduced as well. This means that some current must flow in the forward direction. When the light pulse is turned off, the potential profile goes back from Fig. 8 to Fig. 7 and the photocurrent pulse occurs in the positive direction. It is important to note that this “anomalous” current does not originate directly from photogenerated carriers but from depletion regions.
When we excite the diode with light energies above the bandgap in the QBs, we generate mainly reverse current which will dominate. When we pump below QB bandgap but with high power, the transition from Fig. 7 to Fig. 8 is almost instantaneous and the reverse current dominates [see Fig. 5(a)].
We can calculate the difference between the field in the QB before illumination $({{F_b} + {F_j}} )$ and the field after illumination $({{F_b} + F_j^{\prime}} )$. We obtain (neglecting the change of depletion terms)
When we illuminate the sample with below QB dc light [Fig. 4(b)] we pump electrons and holes into the well which screen (reduce) the electric field. This reduces the negative PC similarly to the application of reverse bias [Fig. 4(a)]. However, the reverse bias increases the field in the QBs while illumination reduces these fields. This is why the above-QB PC is much higher in Fig. 4(a) compared to Fig. 4(b).
The above simplified considerations assume uniform illumination in the laser stripe. This is supported by low absorption of light in the chip and the results shown in Fig. 2. We also showed in Fig. 2 that carriers generated in regions with higher illumination flow to the regions with lower illumination (i.e. we observed photocurrents parallel to the epitaxial layers). Therefore charge densities in the QW are more homogenous than the illuminating light.
6. Summary
We presented anomalous PC spectra in pin diodes with wide InGaN QWs. We observed a forward PC for low light intensity and photon energies above the bandgap of the QW but below the bandgap of the QB. When the light intensity increased and/or the photon energy increased the PC switched to reverse direction. We constructed a simple qualitative model, which explained the observed behavior by assuming a strong modification of potential profile by low intensity light with energies below the bandgap in the QB.
Funding
Narodowe Centrum Nauki (2015/17/B/ST7/03972); Fundacja na rzecz Nauki Polskiej (TEAMTECH POIR.04.04.00-00-210C/16-00); Narodowe Centrum Badań i Rozwoju (LIDER/35/0127/L-9/17/NCBR/2018).
Acknowledgments
The authors are grateful to Dr. R. Piotrzkowski for fruitful discussions.
Disclosures
The authors declare no conflicts of interest.
References
1. K. Yamanaka, T. Fukunaga, N. Tsukada, K. L. I. Kobayashi, and M. Ishii, “Photocurrent spectroscopy in GaAs/AlGaAs multiple quantum wells under a high electric field perpendicular to the heterointerface,” Appl. Phys. Lett. 48(13), 840–842 (1986). [CrossRef]
2. G. Muziol, H. Turski, M. Siekacz, K. Szkudlarek, L. Janicki, M. Baranowski, S. Zolud, R. Kudrawiec, T. Suski, and C. Skierbiszewski, “Beyond Quantum Efficiency Limitations Originating from the Piezoelectric Polarization in Light-Emitting Devices,” ACS Photonics 6(8), 1963–1971 (2019). [CrossRef]
3. G. Muziol, M. Hajdel, M. Siekacz, K. Szkudlarek, S. Stanczyk, H. Turski, and C. Skierbiszewski, “Optical properties of III-nitride laser diodes with wide InGaN quantum wells,” Appl. Phys. Express 12(7), 072003 (2019). [CrossRef]
4. R. Dahal, B. Pantha, J. Li, J. Y. Lin, and H. X. Jiang, “InGaN/GaN multiple quantum well solar cells with long operating wavelengths,” Appl. Phys. Lett. 94(6), 063505 (2009). [CrossRef]
5. R. M. Farrell, C. J. Neufeld, S. C. Cruz, J. R. Lang, M. Iza, S. Keller, S. Nakamura, S. P. DenBaars, U. K. Mishra, and J. S. Speck, “High quantum efficiency InGaN/GaN multiple quantum well solar cells with spectral response extending out to 520 nm,” Appl. Phys. Lett. 98(20), 201107 (2011). [CrossRef]
6. L. Zhao, T. Detchprohm, and C. Wetzel, “High 400 °C operation temperature blue spectrum concentration solar junction in GaInN/GaN,” Appl. Phys. Lett. 105(24), 243903 (2014). [CrossRef]
7. Y. Zhao, X. Huang, H. Fu, H. Chen, Z. Lu, J. Montes, and I. Baranowski, “InGaN-based solar cells for space applications,” 2017 IEEE 60th International Midwest Symposium on Circuits and Systems (MWSCAS) p. 954, DOI: 10.1109/MWSCAS.2017.8053083
8. C. Skierbiszewski, H. Turski, G. Muzioł, M. Siekacz, M. Sawicka, G. Cywiński, Z. R. Wasilewski, and S. Porowski, “Nitride-based laser diodes grown by plasma-assisted molecular beam epitaxy,” J. Phys. D: Appl. Phys. 47(7), 073001 (2014). [CrossRef]
9. R. Kucharski, Ł. Janicki, M. Zajac, M. Welna, M. Motyka, C. Skierbiszewski, and R. Kudrawiec, “Transparency of Semi-Insulating, n-Type, and p-Type Ammonothermal GaN Substrates in the Near-Infrared, Mid-Infrared, and THz Spectral Range,” Crystals 7(7), 187–197 (2017). [CrossRef]
10. N. G. Anderson, “Ideal theory of quantum well solar cells,” J. Appl. Phys. 78(3), 1850–1861 (1995). [CrossRef]
11. C. I. Cabrera, J. C. Rimada, M. Courel, L. Hernandez, J. P. Connolly, A. Enciso, and D. A. Contreras-Solorio, “Modeling Multiple Quantum Well and Superlattice Solar Cells,” Nat. Resour. 04(03), 235–245 (2013). [CrossRef]
12. A. Chatterjee, A. K. Biswas, and A. Sinha, “An analytical study of the various current components of an AlGaAs/GaAs multiple quantum well solar cell,” Physica 72, 128–133 (2015). [CrossRef]
13. I. H. Brown, I. A. Pope, P. M. Smowton, P. Blood, J. D. Thomson, W. W. Chow, D. P. Bour, and M. Kneissl, “Determination of the piezoelectric field in InGaN quantum wells,” Appl. Phys. Lett. 86(13), 131108 (2005). [CrossRef]
14. W. Trzeciakowski, A. Bercha, and M. Gładysiewicz-Kudrawiec, “Hydrostatic and uniaxial effects in InGaN/GaN quantum wells,” J. Appl. Phys. 124(20), 205701 (2018). [CrossRef]
15. E. Kioupakis, Q. Yan, and C. G. Van de Walle, “Interplay of polarization fields and Auger recombination in the efficiency droop of nitride light-emitting diodes,” Appl. Phys. Lett. 101(23), 231107 (2012). [CrossRef]
16. A. David, C. A. Hurni, N. G. Young, and M. D. Craven, “Field-assisted Shockley-Read-Hall recombinations in III-nitride quantum wells,” Appl. Phys. Lett. 111(23), 233501 (2017). [CrossRef]
