Abstract

Nitride-based light-emitting diodes (LEDs) are well known to suffer from a high built-in electric field in the quantum wells (QWs). In this paper we determined to what extent the electric field is screened by injected current. In our approach we used high pressure to study this evolution. In LEDs with a narrow QW (2.6 nm) we found that even at a high injection current a large portion of built-in field remains. In LEDs with very wide QWs (15 and 25 nm) the electric field is fully screened even at the lowest currents. Furthermore, we examined LEDs with a tunnel junction in two locations – above and below the active region. This allowed us to study the cases of parallel and antiparallel fields in the well and in the barriers.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

In recent years, the wide-band-gap group III nitrides based heterostructures InxGa1-xN/GaN and AlyGa1-yN/AlN have attracted much attention due to a variety of important device applications in optoelectronics and electronics [18]. In particular, high brightness blue and green light-emitting diodes (LEDs) and laser diodes (LDs) have been demonstrated [48]. Very recently also LEDs and LDs emitting in the ultraviolet range of spectrum have been reported [914]. Performance of the nitride emitters is constantly improving due to the deeper understanding of the physical mechanisms responsible for performance limitations, which allows to increase their efficiencies. Nitride heterostructures in wurtzite symmetry exhibit spontaneous and piezoelectric polarizations [1520]. One of the effects related to the presence of the built-in electric field in polar and semipolar quantum wells or optoelectronic emitters is the quantum confined stark effect (QCSE). Piezoelectric polarization is due to the mismatch strain incorporated in the structures consisting of heterolayers with different lattice constants. Large polarization sheet charges at the interfaces lead to high internal electric field inside the heterostructures [1521]. As one of the consequences, the band profiles are tilted and the interband transition energy is reduced significantly. An additional effect caused by the presence of internal field, FQW, is the separation of electron-hole wave functions, which in turn leads to the strong decrease in the luminescence intensity.

There have been two main approaches aiming at a reduction of the negative effect of QCSE. The first idea is to use the semipolar or nonpolar substrate [2224]. It results in the full elimination of built-in piezo-field (for non-polar substrate) or its significant decrease (for semi-polar substrate). The second approach is to modify the used epistructure within the QW and/or its vicinity to alter effective polarization in the active region. A popular approach uses the concept of so-called staggered structures. In particular, a sequence of staggered quantum wells which vary in their indium compositions and quantum well widths has been proved as a successful approach to suppress a magnitude of FQW (see e.g., Ref. [25]). Doping the barriers or the well can also reduce the field but it introduces ionized dopants which negatively affect electrical and optical properties of LED [26]. However, currently, an absolute majority of commercially available InGaN/GaN light emitters are grown along the polar <0001> direction of the wurtzite structure with single or multiple QWs of rectangular, uniform shape.

Knowledge of the built-in electric field is essential in development of the high efficiency devices. However, experimental determination of FQW inside a QW is challenging. In case of emitters based on nitride polar QWs, FQW contains an additional contribution from the p-n junction electric field Fj, which can be modified by externally applied bias voltage. Furthermore, an increase in carrier density (e.g. by driving current) leads to partial screening of FQW. This results in a decrease in the emitted wavelength, equivalent to energy blue-shift. Moreover, the wave function overlap increases, which results in an increase of the intensity of emitted light in the polar InGaN/GaN QWs LEDs and LDs [2733]. The blue-shift is well pronounced in the range of low driving currents in LEDs and LDs (see e.g. [33]). Usually, after surpassing certain magnitude of the applied current the rate of EEL increase is visibly reduced or even saturated. It may suggest an entire elimination of this field. In fact, the reduction of FQW can be significant but not complete. It is difficult to determine the magnitude of this remaining field. The described blue-shift of EEL is more pronounced in InxGa1-xN/GaN QWs with higher In-content and wider QWs as predicted by QCSE.

It has been demonstrated very recently [33] that in the polar InGaN/GaN laser diodes (LDs), laser action takes place in a situation, in which the built-in electric field is still present. FQW, as deduced from a constant lasing energy, does not change above the threshold in spite of application of higher driving currents, ID. It corresponds to the well-known effect of carrier density clamping above the laser threshold. In contrast, in the superluminescent diode with the epistructure identical to that of the examined LD, screening effect deduced from the EPL blue-shift takes place for ID much higher than the laser threshold current [33]. This means that determination of the electric fields from the shift of emission energy with current may be misleading. Moreover, the transition energies in QW LEDs may be higher or lower than the bandgap of the QW material due to competing effects of confinement and QCSE.

Here we propose the alternative approach to studies of the QCSE and to the evaluation of the electric field present in the QW. It relies on using hydrostatic pressure in the examination of the dependence of the photoluminescence or electroluminescence energy (EPL or EEL) on applied magnitude of the exciting laser power or driving current, respectively [3435]. In case of an LED the variation of EEL with ID at different pressures is examined. It allows to determine the pressure coefficient of EEL, i.e., dEEL/dp for various driving currents. EEL can be approximated by [34]:

$${E_{EL}} = {E_G} + E_{conf}^e + E_{conf}^h - e{L_{QW}}|{{F_{QW}}} |- {E_{exc}}$$
where EG is the bandgap, $E_{conf}^e$ and $E_{conf}^h$ are the confinement energies of electrons and holes (measured from the lower or higher edge of the well), LQW is the well width, FQW is the electric field and Eexc is the exciton binding energy. Assuming that EG does not vary with the electric field allows us to describe the change of EEL with pressure, which we will call the pressure coefficient, as a sum of two terms [3435]:
$$\frac{{d{E_{EL}}}}{{dp}} = \frac{{d{E_G}}}{{dp}} + \frac{{d{E_{EL}}}}{{d{F_{QW}}}}\frac{{d{F_{QW}}}}{{dp}}$$

The first term reflects the pressure induced changes of the band gap of InxGa1-xN alloy, dEG/dp. This pressure coefficient has been accurately measured for quasi-bulk InxGa1-xN alloys for which F is zero [36]. dEG/dp decreases there from 40 meV/GPa for x=0 (i.e., for GaN) to 25 meV/GPa for x above 0.4 [36]. The second term is the product of the change in transition energy as a function of electric field, dEEL/dFQW, which is negative (transition energy decreases with increasing field), and the change of the electric field with pressure, dFQW/dp, which is positive and linear as was shown in Ref. [34] for InGaN/GaN QWs without the p-n junction. Therefore, this product causes a decrease of dEEL/dp with respect to dEG/dp. This decrease is more pronounced for wider QWs or for higher Indium content in the QW. In case of partial screening of the piezoelectric field in the QW, the value of dEEL/dFQW will be lower. This is because at a low built-in field the change of EEL induced by the field is lower than at a high built-in field. Finally, when the field is fully screened, the measured pressure coefficient dEEL/dp of the LED achieves the value of dEG/dp. Therefore, the measure of deviation of dEEL/dp from the value reported for bulk InGaN should be a measure of the electric field present in the QW.

In the final part of the above considerations we would like to point out the role of the confinement energies for electrons $E_{conf}^e$ and for holes $E_{conf}^h$. Both of these energies increase with the field FQW (as shown e.g. in Ref. [34]) and the resulting dependence of EEL on FQW is parabolic around FQW = 0 [37]. This has been confirmed experimentally, first for GaAs/AlGaAs quantum wells (see e.g. Reference [38] and also for InGaN/GaN quantum wells when ${\textrm{F}_{\textrm{QW}}}$ can be reduced by applying strong reverse voltage to the LED (see Ref. [39]). The derivative dEEL/dFQW is well defined and vanishes at FQW = 0.

In this work we performed studies of EEL and its hydrostatic pressure dependence, i.e., dEEL/dp in six In0.17Ga0.83N/InxGa1-xN LEDs. The studied structures contain a single QW of variable width. The gallium-polar p-n junction is combined with tunnel junction placed either above or below QW (see e.g. [4044]). These two configurations of TJ with respect to the p-i-n junction and the active region allow to change the direction of the total field in the well FQW with respect to the total field in the barrier FQB. In case of the bottom tunnel junction (BTJ) FQW is in the same direction as FQB whereas in case of the top tunnel junction (TTJ) FQW is in the opposite direction to FQB. Comparison of these two configurations is analogous to comparing diodes grown on N-polar (BTJ) and Ga-polar (TTJ) substrates.

We decided to include in our studies of QCSE, LEDs with very wide QWs. Such emitters (including laser diodes) exhibit interesting properties compared to narrow wells [45,46].

The most important questions we would like to answer in this work are: i) how efficient is the screening of the internal electric field of polar InGaN/GaN LEDs by carriers injected by driving current; ii) to what extent is the efficiency of this screening dependent on the construction of the studied LEDs, in particular on the polarity, thickness of the QWs and QBs.

2. Experiment and simulations

The LED structures were grown by plasma assisted molecular beam epitaxy technique (PAMBE) on GaN bulk substrates (Ga-polar). Our emitters contain a tunnel junction in addition to the traditional p-n junction with QW (Figs. 1(a) and 1(b)). Several advantages of using TJ are mentioned in Refs. [4044]. Part of our emitters contains the top TJ (TTJ) which is deposited after growing the main p-i-n junction. Another set of our LEDs was grown with the bottom TJ (BTJ), located below main p-i-n junction (Table 1). We also studied two samples with extremely wide quantum wells since such LED structures demonstrate low sensitivity of EEL to carrier injection [45,46].

 figure: Fig. 1.

Fig. 1. Schematic structure of In0.17Ga0.83N/InxGa1-xN light-emitting diodes with: (a) top tunnel junction (TTJ) and (b) bottom tunnel junction (BTJ). (c)-(d) Schematic images of the arrangements of the direction of fields inside QW and QB with respect to the p-n junction. The color arrows indicate electron and hole injection directions. The direction of the field in the well FQW is parallel (antiparallel) to the direction of the field in the barriers FQB in the case of BTJ (TTJ). Figures are based on Ref. [44].

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Tables Icon

Table 1. Details of light-emitting diodes with tunnel junction (TJ) studied in this work.

Doping of the studied LEDs was as follows: in TTJ LEDs the 20 nm p-type Al0.13Ga0.87N:Mg EBL layer doped to 3·1019 cm-3; then GaN:Mg cladding was doped with Mg at concentration of 1·1018 cm-3; in BTJ LED, instead of AlGaN EBL, the highly doped 20 nm GaN:Mg+ layer was deposited with Mg-concentration of 1·1019 cm-3. It was followed by 100 nm GaN:Mg (1·1018 cm-3). Tunnel junction layers were doped with Si concentration of 3·1019cm-3 and Mg concentration of 1·1020 cm-3. Background doping of oxygen in InGaN layers is in the range of 1·1017-2·1017 cm-3. GaN:Si was doped up to 5·1018 cm-3.

In this work we performed studies of EEL and its hydrostatic pressure dependence, i.e., dEEL/dp in six In0.17Ga0.83N/InxGa1-xN LEDs. The studied structures contain a single QW of variable width. The gallium-polar p-n junction is combined with tunnel junction placed either above or below QW (see e.g. [4044]). These two configurations of TJ with respect to the p-i-n junction and the active region allow to change the direction of the total field in the well FQW with respect to the total field in the barrier FQB. In case of the bottom tunnel junction (BTJ) FQW is in the same direction as FQB whereas in case of the top tunnel junction (TTJ) FQW is in the opposite direction to FQB. Comparison of these two configurations is analogous to comparing diodes grown on N-polar (BTJ) and Ga-polar (TTJ) substrates.

We decided to include in our studies of QCSE, LEDs with very wide QWs. Such emitters (including laser diodes) exhibit interesting properties compared to narrow wells [45,46].

The most important questions we would like to answer in this work are: i) how efficient is the screening of the internal electric field of polar InGaN/GaN LEDs by carriers injected by driving current; ii) to what extent is the efficiency of this screening dependent on the construction of the studied LEDs, in particular on the polarity, thickness of the QWs and QBs.

In Fig. 2, we plot the potential profiles for samples A3 and B1 obtained from the full numerical calculation [47], for the unbiased and for the forward-biased diodes. We can see that the full calculation confirms the similar values of the field in the well for the TTJ and BTJ samples in case of forward bias. In fact, the field is slightly stronger in A3 because it has a lower Indium composition in the barrier than B1. We also observe the increased field for the BTJ sample B1 in the unbiased case (compared to A3 sample with TTJ).

 figure: Fig. 2.

Fig. 2. Band profiles at zero bias (a) and (b) and at ∼1A/cm2 (c) and (d) for sample A3 TTJ (a) and (c) and B1 BTJ (b) and (d). Colored stripes are used to distinguish regions doped with Mg-acceptors and Si-donors (from left to right). Simulations performed using package presented in Ref. [47].

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3. Results

As the first set of the basic measurements we show I-V characteristics of all studied LEDs taken at atmospheric pressure (Fig. 3). One can see that all dependences demonstrate similar character, independently of the Tunnel Junction position.

 figure: Fig. 3.

Fig. 3. Measured current density vs voltage for 0.1 × 0.1 mm2 devices with (a) top-TJ structure (A1-A3) and (b) bottom-TJ structure (B1-B3)

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Further studies performed for all examined LEDs consisted of collecting electroluminescence spectra measured at atmospheric and high hydrostatic pressures. The spectra are used to determine the dependences of EEL and dEEL/dp on the driving current. As an illustration of this approach we first compare two LEDs, A3 vs. B1 (Fig. 4). The structures of LEDs A3 and B1 differ by the position of the tunnel junction with respect to the quantum well, (thus by the orientation of the p-n junction with respect to the polarization fields), parameters of the wells and barriers are similar.

 figure: Fig. 4.

Fig. 4. Comparison of electroluminescence spectra acquired for different driving currents at: atmospheric pressure for (a) LED A3 and (b) LED B1 and at the pressure of 0.6 GPa for (c) LED A3 and (d) LED B1.

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Figures 4(a) and 4(b) illustrate the evolution with ID of the electroluminescence spectra measured at atmospheric pressures in LEDs A3 and B1. With increasing ID emission moves to higher energy region which is due to the screening of the built-in electric field. Qualitatively the same behavior is observed for measurements performed at pressure of 0.6 GPa, Figs. 4(c) and 4(d).

Figures 5(a) and 5(b) show the variation of EEL measured at atmospheric pressure and different ID in LEDs A1 and A2. Figures 5(c) and 5(d) represent spectra measured at pressure of 1 GPa. Additional peaks around 3.1 eV correspond to the barrier emission (these samples have 8% InGaN in the barriers). Two conclusions can be drawn from the presented spectra. LEDs A3, B1, and A1 demonstrate a similar response to the applied driving current and pressure. In contrast, LED A2 behaves differently. The spectra collected for LED A2 are much wider. It suggests the involvement of two radiative recombination processes. We will explain the origin of this effect later.

 figure: Fig. 5.

Fig. 5. Comparison of electroluminescence spectra dependence on driving current for: (a) LED A1 and (b) LED A2 at atmospheric pressure. Lower set of spectra (c) and (d) were measured at the pressure of 1 GPa.

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To deduce dEEL/dp behavior, the EEL peak shift with pressure for constant IDs was deduced. Figures 6(a) and 6(b) represent the exemplary behavior of LEDs A1 and A3, correspondingly. One can see linear increase of EEL with pressure for each value of ID. Higher ID causes more efficient screening of the built-in electric field. Therefore, corresponding dependences move to higher energy.

 figure: Fig. 6.

Fig. 6. Shift of EEL maxima with applied pressure for different values of the driving current density (marked at the right side of diagrams). (a)-(b) illustrate a behavior of LEDs A1 and A3, correspondingly. Pressure coefficients dEEL/dp characterizing individual experimental runs are given also.

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The determined variations of EEL and dEEL/dp versus ID of all four examined above LEDs (A1, A2, A3 and B1) are shown in Figs. 7(a) and 7(b), respectively. At low driving currents the blue-shift of the peak energy EEL and an increase of dEEL/dp are observed. At higher IDs both discussed evolutions are followed by a saturation tendency, Figs. 7(a) and 7(b). The dotted violet line and the grey bar represent the band gap energy and its pressure coefficient of In0.17Ga0.83N alloy if FQW is absent.

 figure: Fig. 7.

Fig. 7. Dependence on current density of: (a) emission energy and (b) pressure coefficient; measured for LEDs A1, A2, A3, and B1. (c) Simulated dependence of emission energy on current density. (d) Simulated dependence of the average magnitude of the internal field inside single QW of each discussed LED. Dashed magenta line in (a) and (c) corresponds to the EEL value in In0.17Ga0.83N alloy. The gray bar (b) corresponds to the pressure coefficient characterizing entirely screened internal electric field in In0.17Ga0.83N alloy [36]. Error bar for determination of dEG/dp in (b) is ±1 meV/GPa.

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Concerning LEDs A3 and B1 (both contain QW of 2.6 nm width), it is worth to point out that the saturation of dEEL/dp evolution occurs at the value of 20-22 meV/GPa that is much lower than ∼31 meV/GPa (pressure coefficient of In0.17Ga0.83N alloy). This result strongly suggests that a high amount of remaining electric field is present in these diodes even at high magnitude of ID. This means that the screening process of QCSE is not effective in these LEDs with narrow QW. The main difference in the behavior of LEDs A3 and B1 shows up in their current-voltage characteristics. The opening voltage of LED with BTJ, i.e., B1 is about 0.5 V lower than LED with TTJ, i.e., A3 [44].

A1 and A2 contain QW of 2.6 and 5.2 nm width, respectively. One observes a similar character of LED A1 spectra to those belonging to LEDs A3 and B1 (both with QW of 2.6 nm), But the spectra corresponding to LED A2 look different, Fig. 5(b). Their significantly larger width and asymmetry suggest a contribution of two emission processes. The same conclusion can be drawn from the shape of spectra at pressure of 1 GPa, see Fig. 5(d). The deconvolution analysis performed in case of LED A2, supported by results of Ref. [45] showed that the < e1-h1> recombination (lower energy ground states) coexists with < e2-h1> (excited electron state and ground hole state) process. Evolutions of the corresponding EEL energies and dependence of dEEL/dp on ID – Figs. 7(a) and 7(b) – support the above interpretation of the involvement of two recombination processes. The recombination energy of < e1-h1> transition should demonstrate a higher sensitivity to the driving current (i.e. screening process) than the < e2-h1> transition. This is due to the fact that the e2 level is less sensitive (than e1) to the change of built-in field [45]. The performed measurements agree with this prediction. Variation of dEEL/dp with ID demonstrates qualitatively similar character to EEL behavior. Pressure coefficient of the lower energy transition increases weakly from 22 meV/GPa to the value of about 24 meV/GPa showing the weak screening of QCSE. However, it is clear that a small part of the built-in electric field still remains in the LED A2 at high value of ID. In case of higher energy peak its pressure coefficient exhibits a constant value about 27 meV/GPa, almost independent of the applied current.

In the next step we compare the behavior of LEDs A1, A3, and B1. All these LEDs have QW containing 17% of indium. However, quantum barrier of LED A1 comprises 8% of In. In contrast, two other diodes have barriers containing 2-3% of In. This structural difference should cause lower magnitude of built-in electric field in the QW of LED A1 with respect to A3 and B1, Fig. 7(d). Our experimental findings support this prediction. High values of EEL and dEEL/dp as well as their weak variation with ID in LED A1 (corresponding to lower field in the well) agree with this expectation – Figs. 4(a) and 4(b).

Results of the performed simulations of EEL dependence on ID by using program introduced in [47] are in qualitative agreement with the experimental findings in all studied LEDs, Figs. 7(a) and 7(c). Similar conclusion can be deduced observing variation of dEEL/dp with driving current and simulated behavior of built-in electric field, Figs. 7(b) and 7(d). Our results show that the difference dEG/dp - dEEL/dp decreases with decreasing field in the QW (for a given well width).

In the final step of our studies we applied LEDs with wide-QWs (15 and 25 nm). At the first glance using such structures as the base of efficient light emitters seems to be unreasonable. However, the results of Ref. [45] have demonstrated that this approach leads to very promising LEDs and laser diodes.

At low driving currents, low concentration of carriers is supplied, the overlap of the electron- and hole- wave functions of the ground states (<e1> and <h1>) is negligible. It is due to their large separation induced by built-in electric field. It leads on the other hand to the carriers’ accumulation in the ground states of the well. There are two consequences of this situation. First, with increasing current the built-in electric field in the QW becomes gradually screened. Second, carriers supplied by the driving current start to fill excited states and to recombine radiatively due to the large overlap of their wave functions. The quasi-continuous way of application the driving current allows to realize the above scenario. It is worth to remind that LED A2 represents the intermediate case. A sufficient overlap of the < e1> and < h1> wave-functions enables to induce the ground states electroluminescence but the involvement of the electron excited state < e2> and the hole ground state < h1> are detected also. Simulations performed in [45] confirm this interpretation.

Two LEDs with very wide QWs of 15 and 25 nm (B2 and B3) studied in this work, show spectra with the peak of EEL almost independent of the driving current (Figs. 8(a), 8(b), and 9(a). dEEL/dp demonstrate (within the experimental error) the similar behavior. Moreover, the magnitude of the emission energy and its pressure coefficient (about 31-32 meV/GPa, close to the value for bulk In0.17Ga0.83N) show independence of the radiative recombination mechanism on driving current. The performed simulations, Fig. 9(c), demonstrate very low magnitude of built-in field of 0.25-0.3 MV/cm, which is achieved already after application of very small IDs. This results in a very high wave function overlap for < e2-h2> transition (simulations performed in Ref. [45]). It shows the usefulness of such LEDs with very wide QWs in the emitter design in which the states <e2> and <h2> are responsible for the efficient light emission with energy (wavelength) independent of the driving current [45,46].

 figure: Fig. 8.

Fig. 8. Comparison of electroluminescence spectra dependence on driving current for: (a) LED B2 and (b) LED B3 at atmospheric pressure.

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 figure: Fig. 9.

Fig. 9. Measured driving-current dependence of: (a) EEL and (b) dEEL/dp of LEDs B2, and B3,. Results for LED B1, and A3 are shown for comparison. For LEDs B1 and A3 effects of FQW screening are clearly seen at low IDs (a). (b) Shows qualitatively different behavior of dEEL/dp LEDs with wide QW (B2 and B3) and narrow QW (B1 and A3). Additionally, low pressure coefficient of LEDs B1 and A3 seen in (b) illustrates the high amount of FQW remaining in these LEDs at higher magnitude of IDs. (c) Simulated dependence of average electric field in QW of LEDs B1, B2, B3 and A3 support experimental findings.

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In Fig. 9, results of examination of EEL and dEEL/dp evolution with driving current characteristic for LEDs B1, and A3 are shown for comparison. These latter LEDs contain narrow QW of 2.6 nm. Consequently radiative recombination is associated with < e1-h1> transitions. For LEDs B1 and A3 effects of FQW screening are clearly seen at low IDs, Fig. 9(a). Figure 9(b) shows qualitatively different behavior of dEEL/dp in LEDs with wide QW (B2 and B3) and narrow QW (B1 and A3). Low pressure coefficient of LEDs B1 and A3 in comparison with dEG/dp ≈31 meV/GPa, illustrates the high amount of FQW remaining in these LEDs at higher magnitude of IDs. Figure 9(c) shows the simulated dependences of average electric field in QW of LEDs B1, B2, B3, and A3 which fully support experimental findings.

There are two important results of the performed studies. The first one consists in the finding that two LEDs with tunnel junction located above QW or below it (A3 with top TJ and B1with bottom TJ) but with the same parameters of their wells and barriers behave in a similar way. (Figures 4, 7 and 9). The second outcome demonstrates that in LEDs with wide QWs, EEL and dEEL/dp are independent of the driving current, Fig. 5. It results from the efficient screening of the field in the well by carriers in the ground states and the nature of excited states involved in the radiative recombination in such LEDs [45,46].

4. Conclusions

In this work, we studied the driving current dependence of the QCSE screening effects in polar LEDs. We examined six different emitters constructed with the use of tunnel junctions and various parameters of quantum wells and quantum barriers. All studied samples have a single QW design with constant In-content of x=0.17. Tunnel junction was embedded either above or below the QW. This allowed us to change the value of the electric field arising due to the p-i-n junction with respect to the spontaneous and piezoelectric polarization in the QW.

To obtain information about the screening of QCSE, we compare the current dependence of the emission wavelength EEL (energy blue-shift) with the current dependence of the pressure coefficient dEEL/dp. In the presence of built-in electric fields in active region, this pressure coefficient is reduced with respect to the pressure coefficient characteristic for InGaN alloy band gap pressure shift (dEG/dp). This reduction increases with the amount of the built-in electric field in the QW and with the QW width (for low and intermediate widths). For large QW widths the electric field in the well becomes fully screened even by small amount of current. The emission in these wells seems to occur from higher excited states [45]. Both the transition energies and pressure coefficients do not vary with current and reach the values of EG and dEG/dp for bulk alloy. Therefore, using LEDs with wide QWs results in a stable energy/wavelength value, independent of the diode driving current. It is an important advantage of emitters with wide QWs in comparison to those with narrow QWs. Additional important feature of wide QW emitters is a decrease of carrier density for a fixed driving current density, which reduces the part of carriers lost due to the nonradiative Auger recombination. It therefore delays the onset of efficiency droop and enables to operate the LED at an increased current density. Our studies demonstrate that the value of dEEL/dp is a more reliable criterion of the field in the well than the EEL itself. The saturation of EEL and dEEL/dp does not indicate full screening of the field in well.

It is worth to point out that the LEDs with narrow QWs (2.6 nm) are characterized by small effect of QCSE screening. The amount of remaining electric field can be as high as 2 MV/cm, in spite of high density of injected carriers.

We found that LEDs with the tunnel junction embedded either above or below QW exhibit practically identical screening of the QCSE with increasing amount of injected carriers.

The performed simulations support the experimental findings.

Funding

Narodowe Centrum Nauki (2015/17/B/ST7/04091, 2019/35/D/ST3/03008, 2019/35/N/ST7/04182); Fundacja na rzecz Nauki Polskiej (HOMING POIR.04.04.00-00-5D5B/18-00, TEAM-TECH POIR.04.04.00-00-210C/16-00).

Disclosures

The authors declare no conflicts of interest.

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12. B. T. Tran and H. I. Hirayama, “Growth and Fabrication of High External Quantum Efficiency AlGaN-Based Deep Ultraviolet Light-Emitting Diode Grown on Pattern Si Substrate,” Sci. Rep. 7(1), 12176 (2017). [CrossRef]  

13. M. Kneissl, T.-Y. Seong, J. Han, and H. Amano, “The emergence and prospects of deep-ultraviolet light emitting diode technologies,” Nat. Photonics 13(4), 233–244 (2019). [CrossRef]  

14. Z. Zhang, M. Kushimoto, T. Sakai, N. Sugiyama, L. J. Schowalter, C. Sasaoka, and H. Amano, “A 271.8 nm deep-ultraviolet laser diode for room temperature operation,” Appl. Phys. Express 12(12), 124003 (2019). [CrossRef]  

15. F. Bernardini, V. Fiorentini, and D. Vanderbilt, “Spontaneous polarization and piezoelectric constants of III-V nitrides,” Phys. Rev. B 56(16), R10024 (1997). [CrossRef]  

16. T. Takeuchi, S. Sota, M. Katsuragawa, M. Komori, H. Takeuchi, H. Amano, and I. Akasaki, “Quantum Confined Stark Effect due to Piezoelectric Fields in GaInN Strained Quantum Wells,” Jpn. J. Appl. Phys. 36(Part 2, No. 4A), L382–L385 (1997). [CrossRef]  

17. O. Ambacher, J. Majewski, C. Miskys, A. Link, M. Hermann, M. Eickhoff, M. Stutzmann, F. Bernardini, V. Fiorentini, V. Tilak, B. Schaff, and L. F. Eastman, “Pyroelectric properties of Al(In)GaN/GaN hetero- and quantum well structures,” J. Phys.: Condens. Matter 14(13), 3399–3434 (2002). [CrossRef]  

18. C. Wetzel, T. Takeuchi, H. Amano, and I. Akasaki, “Electric-field strength, polarization dipole, and multiinterface band offset in piezoelectric Ga1−xInxN/GaN quantum-well structures,” Phys. Rev. B 61(3), 2159–2163 (2000). [CrossRef]  

19. P. Lefebvre, S. Kalliakos, T. Bretagnon, P. Valvin, T. Taliercio, B. Gil, N. Grandjean, and J. Massies, “Observation and modeling of the time-dependent descreening of internal electric field in a wurtzite GaN/Al0.15Ga0.85N quantum well after high photoexcitation,” Phys. Rev. B 69(3), 035307 (2004). [CrossRef]  

20. T. Takeuchi, S. Sota, M. Katsuragawa, M. Komori, H. Takeuchi, H. Amano, and I. Akasaki, “QuantumConfined Stark Effect due to Piezoelectric Fields in GaInN Strained Quantum Wells,” Jpn. J. Appl. Phys. 36(Part 2, No. 4A), L382–L385 (1997). [CrossRef]  

21. R. J. Kaplar, S. R. Kurtz, D. D. Koleske, and A. J. Fischer, “Electroreflectance studies of Stark shifts and polarization-induced electric fields in InGaN/GaN single quantum wells,” J. Appl. Phys. 95(9), 4905–4913 (2004). [CrossRef]  

22. A. E. Romanov, T. J. Baker, S. Nakamura, and J. S. Speck, “Strain-induced polarization in wurtzite III-nitride semipolar layers,” J. Appl. Phys. 100(2), 023522 (2006). [CrossRef]  

23. D. F. Feezell, J. S. Speck, S. P. DenBaars, and S. I. Nakamura, “Semipolar (2021) InGaN/GaN Light-Emitting Diodes for High-Efficiency Solid-State Lighting,” J. Disp. Technol. 9(4), 190–198 (2013). [CrossRef]  

24. M. Funato, M. Ueda, Y. Kawakami, Y. Narukawa, T. Kosugi, M. Takahashi, and T. Mukai, “Markedly distinct growth characteristics of semipolar (112-2) and (1-1-22) InGaN epitaxial layers,” Jpn. J. Appl. Phys. 45(26), L659–L662 (2006). [CrossRef]  

25. H. Zhao, G. Liu, J. Zhamg, J. Dierolf, and N. Tansu, “Approaches for high internal quantum efficiency green InGaN light-emitting diodes with large overlap quantum wells,” Opt. Express 19(S4), A991 (2011).

26. N. G. Young, R. M. Farrell, S. Oh, M. Cantore, F. Wu, S. Nakamura, S. P. DenBaars, C. Weisbuch, and J. S. Speck, “Polarization field screening in thick (0001) InGaN/GaN single quantum well light-emitting diodes,” Appl. Phys. Lett. 108(6), 061105 (2016). [CrossRef]  

27. S. Riyopoulos, “Electrostatically Shielded Quantum Confined Stark Effect Inside Polar Nanostructures,” Nanoscale Res. Lett. 4(9), 993–1003 (2009). [CrossRef]  

28. F. Fedichkin, T. Guillet, P. Valvin, B. Jouault, C. Brimont, T. Bretagnon, L. Lahourcade, N. Grandjean, P. Lefebvre, and M. Vladimirova, “Room-Temperature Transport of Indirect Excitons in (Al,Ga)N/GaN Quantum Wells,” Phys. Rev. Appl. 6(1), 014011 (2016). [CrossRef]  

29. T. Suski, G. Staszczak, K. P. Korona, P. Lefebvre, P. A. Drożdż, G. Muzioł, C. Skierbiszewski, M. Kulczykowski, M. Matuszewski, E. Grzanka, S. Grzanka, K. Pieniak, A. Khachapuridze, J. SmalcKoziorowska, E. Monroy, and P. Perlin, “Switching of exciton character in double InGaN/GaN quantum wells,” Phys. Rev. B 98(16), 165302 (2018). [CrossRef]  

30. J.-H. Ryou, P. Douglas Yoder, J. Liu, Z. Lochner, H. Kim, S. Choi, H. J. Kim, and R. D. Dupuis, “Control of Quantum-Confined Stark Effect in InGaN-Based Quantum Wells,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1080–1091 (2009). [CrossRef]  

31. F. Della Sala, A. Di Carlo, P. Lugli, F. Bernardini, V. Fiorentini, R. Scholz, and J.-M. Jancu, “Free-carrier screening of polarization fields in wurtzite GaN/InGaN laser structures,” Appl. Phys. Lett. 74(14), 2002–2004 (1999). [CrossRef]  

32. T. Suski, G. Franssen, P. Perlin, R. Bohdan, A. Bercha, P. Adamiec, F. Dybala, W. Trzeciakowski, P. Prystawko, M. Leszczyński, I. Grzegory, and S. Porowski, “A pressure-tuned blue-violet InGaN/GaN laser diode grown on bulk GaN crystal,” Appl. Phys. Lett. 84(8), 1236–1238 (2004). [CrossRef]  

33. A. Kafar, S. Stanczyk, S. Grzanka, K. Pieniak, T. Suski, and P. Perlin, “Screening of quantum-confined Stark effect in nitride laser diodes and superluminescent diodes,” Appl. Phys. Express 12(4), 044001 (2019). [CrossRef]  

34. 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]  

35. G. Staszczak, W. Trzeciakowski, E. Monroy, A. Bercha, G. Muzioł, C. Skierbiszewski, P. Perlin, and T. Suski, “Hydrostatic pressure dependence of indirect and direct excitons in InGaN/GaN quantum wells,” Phys. Rev. B 101(8), 085306 (2020). [CrossRef]  

36. G. Franssen, I. Gorczyca, T. Suski, A. Kaminska, J. Pereiro, E. Muñoz, E. Iliopoulos, A. Georgakilas, S. B. Che, Y. Ishitani, A. Yoshikawa, N. E. Christensen, and A. Svane, “Bowing of the band gap pressure coefficient in InxGa1−xN alloys,” J. Appl. Phys. 103(3), 033514 (2008). [CrossRef]  

37. The fact that EEL has a parabolic maximum around FQW= 0 is easier to see in the reference system in the middle of the well, not at its edge (like in Eq. (1)). In that case the EEL term disappears and we only deal with confinement energies measured from the center of the well. These confinement energies change parabolically with FQW (linear terms vanish) as shown e.g. in Ref. [37]. For strong fields it is convenient to use the reference system at the edge of the well, like in Eq. (1). In that case the confinement energies as a function of the field have been calculated e.g. in [34]. When the field changes sign the reference system switches to the other side of the well so for fields that can change directions it is more natural to use the reference system in the middle of the well. The resulting EEL(FQW) is of course the same for both reference systems.

38. D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Electric field dependence of optical absorption near the band gap of quantum-well structures,” Phys. Rev. B 32(2), 1043–1060 (1985). [CrossRef]  

39. 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]  

40. M. Malinverni, C. Tardy, M. Rossetti, A. Castiglia, M. Duelk, C. Vélez, D. Martin, and N. Grandjean, “InGaN laser diode with metal-free laser ridge using n+-GaN contact layers,” Appl. Phys. Express 9(6), 061004 (2016). [CrossRef]  

41. S.-R. Jeon, Y.-H. Song, H.-J. Jang, G. M. Yang, S. W. Hwang, and S. J. Son, “Lateral current spreading in GaN-based light-emitting diodes utilizing tunnel contact junctions,” Appl. Phys. Lett. 78(21), 3265–3267 (2001). [CrossRef]  

42. M. F. Schubert, “Polarization-charge tunnel junctions for ultraviolet light-emitters without p-type contact,” Appl. Phys. Lett. 96(3), 031102 (2010). [CrossRef]  

43. S. Krishnamoorthy, P. S. Park, and S. Rajan, “Demonstration of forward inter-band tunneling in GaN by polarization engineering,” Appl. Phys. Lett. 99(23), 233504 (2011). [CrossRef]  

44. H. Turski, S. Bharadwaj, H. Xing, and D. Jena, “Polarization control in nitride quantum well light emitters enabled by bottom tunnel-junctions,” J. Appl. Phys. 125(20), 203104 (2019). [CrossRef]  

45. 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]  

46. A. Bercha, W. Trzeciakowski, G. Muzioł, M. Siekacz, and C. Skierbiszewski, “Anomalous photocurrent in wide InGaN quantum wells,” Opt. Express 28(4), 4717 (2020). [CrossRef]  

47. Y.-R. Wu, C. Chiu, C.-Y. Chang, P. Yu, and H.-C. Kuo, “Size-DependentStrain Relaxation and Emission Characteristics of InGaN/GaN Nanorod Light Emitting Diodes,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1226–1233 (2009). [CrossRef]  

References

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  1. S. Nakamura and S. F. Chichibu, Introduction to Nitride Semiconductor Blue Lasers and Light Emitting Diodes (Taylor&Francis, London, 2000).
  2. B. Gil ed., Group III Nitride Semiconductor Compounds (Clarendon, Oxford, 1998).
  3. C. Wood and D. Jena eds., Polarization Effects in Semiconductors, edited by (Springer, 2008).
  4. Hadis Morkoç, Nitride Semiconductor Devices: Fundamentals and Applications (John Wiley & Sons, Weinheim, 2013).
  5. M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and Future of High-Power Light-Emitting Diodes for Solid-State Lighting,” J. Disp. Technol. 3(2), 160–175 (2007).
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  6. A. Laubsch, M. Sabathil, J. Baur, M. Peter, and B. Hahn, “High-Power and High-Efficiency InGaN-Based Light Emitters,” IEEE Trans. Electron Devices 57(1), 79–87 (2010).
    [Crossref]
  7. A. David, N. Young, C. Lund, and M. D. Craven, “Review—The Physics of Recombinations in III-Nitride Emitters,” ECS J. Solid State Sci. Technol. 9(1), 016021 (2020).
    [Crossref]
  8. T. Taki and M. Strassburg, “Review–Visible LEDs: More than Efficient Light,” ECS J. Solid State Sci. Technol. 9(1), 015017 (2020).
    [Crossref]
  9. A. E. Chernyakov, M. M. Sobolev, V. V. Ratnikov, N. M. Shmidt, and E. B. Yakimov, “Nonradiative recombination dynamics in InGaN/GaN LED defect system,” Superlattices Microstruct. 45(4-5), 301–307 (2009).
    [Crossref]
  10. Y. C. Shen, G. O. Mueller, S. Watanabe, N. F. Gardner, A. Munkholm, and M. R. Krames, “Auger recombination in InGaN measured by photoluminescence,” Appl. Phys. Lett. 91(14), 141101 (2007).
    [Crossref]
  11. A. Khan, B. Krishnan, and T. Katona, “Ultraviolet Light-Emitting Diodes Based on Group Three Nitrides,” Nat. Photonics 2(2), 77–84 (2008).
    [Crossref]
  12. B. T. Tran and H. I. Hirayama, “Growth and Fabrication of High External Quantum Efficiency AlGaN-Based Deep Ultraviolet Light-Emitting Diode Grown on Pattern Si Substrate,” Sci. Rep. 7(1), 12176 (2017).
    [Crossref]
  13. M. Kneissl, T.-Y. Seong, J. Han, and H. Amano, “The emergence and prospects of deep-ultraviolet light emitting diode technologies,” Nat. Photonics 13(4), 233–244 (2019).
    [Crossref]
  14. Z. Zhang, M. Kushimoto, T. Sakai, N. Sugiyama, L. J. Schowalter, C. Sasaoka, and H. Amano, “A 271.8 nm deep-ultraviolet laser diode for room temperature operation,” Appl. Phys. Express 12(12), 124003 (2019).
    [Crossref]
  15. F. Bernardini, V. Fiorentini, and D. Vanderbilt, “Spontaneous polarization and piezoelectric constants of III-V nitrides,” Phys. Rev. B 56(16), R10024 (1997).
    [Crossref]
  16. T. Takeuchi, S. Sota, M. Katsuragawa, M. Komori, H. Takeuchi, H. Amano, and I. Akasaki, “Quantum Confined Stark Effect due to Piezoelectric Fields in GaInN Strained Quantum Wells,” Jpn. J. Appl. Phys. 36(Part 2, No. 4A), L382–L385 (1997).
    [Crossref]
  17. O. Ambacher, J. Majewski, C. Miskys, A. Link, M. Hermann, M. Eickhoff, M. Stutzmann, F. Bernardini, V. Fiorentini, V. Tilak, B. Schaff, and L. F. Eastman, “Pyroelectric properties of Al(In)GaN/GaN hetero- and quantum well structures,” J. Phys.: Condens. Matter 14(13), 3399–3434 (2002).
    [Crossref]
  18. C. Wetzel, T. Takeuchi, H. Amano, and I. Akasaki, “Electric-field strength, polarization dipole, and multiinterface band offset in piezoelectric Ga1−xInxN/GaN quantum-well structures,” Phys. Rev. B 61(3), 2159–2163 (2000).
    [Crossref]
  19. P. Lefebvre, S. Kalliakos, T. Bretagnon, P. Valvin, T. Taliercio, B. Gil, N. Grandjean, and J. Massies, “Observation and modeling of the time-dependent descreening of internal electric field in a wurtzite GaN/Al0.15Ga0.85N quantum well after high photoexcitation,” Phys. Rev. B 69(3), 035307 (2004).
    [Crossref]
  20. T. Takeuchi, S. Sota, M. Katsuragawa, M. Komori, H. Takeuchi, H. Amano, and I. Akasaki, “QuantumConfined Stark Effect due to Piezoelectric Fields in GaInN Strained Quantum Wells,” Jpn. J. Appl. Phys. 36(Part 2, No. 4A), L382–L385 (1997).
    [Crossref]
  21. R. J. Kaplar, S. R. Kurtz, D. D. Koleske, and A. J. Fischer, “Electroreflectance studies of Stark shifts and polarization-induced electric fields in InGaN/GaN single quantum wells,” J. Appl. Phys. 95(9), 4905–4913 (2004).
    [Crossref]
  22. A. E. Romanov, T. J. Baker, S. Nakamura, and J. S. Speck, “Strain-induced polarization in wurtzite III-nitride semipolar layers,” J. Appl. Phys. 100(2), 023522 (2006).
    [Crossref]
  23. D. F. Feezell, J. S. Speck, S. P. DenBaars, and S. I. Nakamura, “Semipolar (2021) InGaN/GaN Light-Emitting Diodes for High-Efficiency Solid-State Lighting,” J. Disp. Technol. 9(4), 190–198 (2013).
    [Crossref]
  24. M. Funato, M. Ueda, Y. Kawakami, Y. Narukawa, T. Kosugi, M. Takahashi, and T. Mukai, “Markedly distinct growth characteristics of semipolar (112-2) and (1-1-22) InGaN epitaxial layers,” Jpn. J. Appl. Phys. 45(26), L659–L662 (2006).
    [Crossref]
  25. H. Zhao, G. Liu, J. Zhamg, J. Dierolf, and N. Tansu, “Approaches for high internal quantum efficiency green InGaN light-emitting diodes with large overlap quantum wells,” Opt. Express 19(S4), A991 (2011).
  26. N. G. Young, R. M. Farrell, S. Oh, M. Cantore, F. Wu, S. Nakamura, S. P. DenBaars, C. Weisbuch, and J. S. Speck, “Polarization field screening in thick (0001) InGaN/GaN single quantum well light-emitting diodes,” Appl. Phys. Lett. 108(6), 061105 (2016).
    [Crossref]
  27. S. Riyopoulos, “Electrostatically Shielded Quantum Confined Stark Effect Inside Polar Nanostructures,” Nanoscale Res. Lett. 4(9), 993–1003 (2009).
    [Crossref]
  28. F. Fedichkin, T. Guillet, P. Valvin, B. Jouault, C. Brimont, T. Bretagnon, L. Lahourcade, N. Grandjean, P. Lefebvre, and M. Vladimirova, “Room-Temperature Transport of Indirect Excitons in (Al,Ga)N/GaN Quantum Wells,” Phys. Rev. Appl. 6(1), 014011 (2016).
    [Crossref]
  29. T. Suski, G. Staszczak, K. P. Korona, P. Lefebvre, P. A. Drożdż, G. Muzioł, C. Skierbiszewski, M. Kulczykowski, M. Matuszewski, E. Grzanka, S. Grzanka, K. Pieniak, A. Khachapuridze, J. SmalcKoziorowska, E. Monroy, and P. Perlin, “Switching of exciton character in double InGaN/GaN quantum wells,” Phys. Rev. B 98(16), 165302 (2018).
    [Crossref]
  30. J.-H. Ryou, P. Douglas Yoder, J. Liu, Z. Lochner, H. Kim, S. Choi, H. J. Kim, and R. D. Dupuis, “Control of Quantum-Confined Stark Effect in InGaN-Based Quantum Wells,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1080–1091 (2009).
    [Crossref]
  31. F. Della Sala, A. Di Carlo, P. Lugli, F. Bernardini, V. Fiorentini, R. Scholz, and J.-M. Jancu, “Free-carrier screening of polarization fields in wurtzite GaN/InGaN laser structures,” Appl. Phys. Lett. 74(14), 2002–2004 (1999).
    [Crossref]
  32. T. Suski, G. Franssen, P. Perlin, R. Bohdan, A. Bercha, P. Adamiec, F. Dybala, W. Trzeciakowski, P. Prystawko, M. Leszczyński, I. Grzegory, and S. Porowski, “A pressure-tuned blue-violet InGaN/GaN laser diode grown on bulk GaN crystal,” Appl. Phys. Lett. 84(8), 1236–1238 (2004).
    [Crossref]
  33. A. Kafar, S. Stanczyk, S. Grzanka, K. Pieniak, T. Suski, and P. Perlin, “Screening of quantum-confined Stark effect in nitride laser diodes and superluminescent diodes,” Appl. Phys. Express 12(4), 044001 (2019).
    [Crossref]
  34. 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]
  35. G. Staszczak, W. Trzeciakowski, E. Monroy, A. Bercha, G. Muzioł, C. Skierbiszewski, P. Perlin, and T. Suski, “Hydrostatic pressure dependence of indirect and direct excitons in InGaN/GaN quantum wells,” Phys. Rev. B 101(8), 085306 (2020).
    [Crossref]
  36. G. Franssen, I. Gorczyca, T. Suski, A. Kaminska, J. Pereiro, E. Muñoz, E. Iliopoulos, A. Georgakilas, S. B. Che, Y. Ishitani, A. Yoshikawa, N. E. Christensen, and A. Svane, “Bowing of the band gap pressure coefficient in InxGa1−xN alloys,” J. Appl. Phys. 103(3), 033514 (2008).
    [Crossref]
  37. The fact that EEL has a parabolic maximum around FQW = 0 is easier to see in the reference system in the middle of the well, not at its edge (like in Eq. (1)). In that case the EEL term disappears and we only deal with confinement energies measured from the center of the well. These confinement energies change parabolically with FQW (linear terms vanish) as shown e.g. in Ref. [37]. For strong fields it is convenient to use the reference system at the edge of the well, like in Eq. (1). In that case the confinement energies as a function of the field have been calculated e.g. in [34]. When the field changes sign the reference system switches to the other side of the well so for fields that can change directions it is more natural to use the reference system in the middle of the well. The resulting EEL(FQW) is of course the same for both reference systems.
  38. D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Electric field dependence of optical absorption near the band gap of quantum-well structures,” Phys. Rev. B 32(2), 1043–1060 (1985).
    [Crossref]
  39. 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]
  40. M. Malinverni, C. Tardy, M. Rossetti, A. Castiglia, M. Duelk, C. Vélez, D. Martin, and N. Grandjean, “InGaN laser diode with metal-free laser ridge using n+-GaN contact layers,” Appl. Phys. Express 9(6), 061004 (2016).
    [Crossref]
  41. S.-R. Jeon, Y.-H. Song, H.-J. Jang, G. M. Yang, S. W. Hwang, and S. J. Son, “Lateral current spreading in GaN-based light-emitting diodes utilizing tunnel contact junctions,” Appl. Phys. Lett. 78(21), 3265–3267 (2001).
    [Crossref]
  42. M. F. Schubert, “Polarization-charge tunnel junctions for ultraviolet light-emitters without p-type contact,” Appl. Phys. Lett. 96(3), 031102 (2010).
    [Crossref]
  43. S. Krishnamoorthy, P. S. Park, and S. Rajan, “Demonstration of forward inter-band tunneling in GaN by polarization engineering,” Appl. Phys. Lett. 99(23), 233504 (2011).
    [Crossref]
  44. H. Turski, S. Bharadwaj, H. Xing, and D. Jena, “Polarization control in nitride quantum well light emitters enabled by bottom tunnel-junctions,” J. Appl. Phys. 125(20), 203104 (2019).
    [Crossref]
  45. 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]
  46. A. Bercha, W. Trzeciakowski, G. Muzioł, M. Siekacz, and C. Skierbiszewski, “Anomalous photocurrent in wide InGaN quantum wells,” Opt. Express 28(4), 4717 (2020).
    [Crossref]
  47. Y.-R. Wu, C. Chiu, C.-Y. Chang, P. Yu, and H.-C. Kuo, “Size-DependentStrain Relaxation and Emission Characteristics of InGaN/GaN Nanorod Light Emitting Diodes,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1226–1233 (2009).
    [Crossref]

2020 (4)

A. David, N. Young, C. Lund, and M. D. Craven, “Review—The Physics of Recombinations in III-Nitride Emitters,” ECS J. Solid State Sci. Technol. 9(1), 016021 (2020).
[Crossref]

T. Taki and M. Strassburg, “Review–Visible LEDs: More than Efficient Light,” ECS J. Solid State Sci. Technol. 9(1), 015017 (2020).
[Crossref]

G. Staszczak, W. Trzeciakowski, E. Monroy, A. Bercha, G. Muzioł, C. Skierbiszewski, P. Perlin, and T. Suski, “Hydrostatic pressure dependence of indirect and direct excitons in InGaN/GaN quantum wells,” Phys. Rev. B 101(8), 085306 (2020).
[Crossref]

A. Bercha, W. Trzeciakowski, G. Muzioł, M. Siekacz, and C. Skierbiszewski, “Anomalous photocurrent in wide InGaN quantum wells,” Opt. Express 28(4), 4717 (2020).
[Crossref]

2019 (5)

H. Turski, S. Bharadwaj, H. Xing, and D. Jena, “Polarization control in nitride quantum well light emitters enabled by bottom tunnel-junctions,” J. Appl. Phys. 125(20), 203104 (2019).
[Crossref]

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]

A. Kafar, S. Stanczyk, S. Grzanka, K. Pieniak, T. Suski, and P. Perlin, “Screening of quantum-confined Stark effect in nitride laser diodes and superluminescent diodes,” Appl. Phys. Express 12(4), 044001 (2019).
[Crossref]

M. Kneissl, T.-Y. Seong, J. Han, and H. Amano, “The emergence and prospects of deep-ultraviolet light emitting diode technologies,” Nat. Photonics 13(4), 233–244 (2019).
[Crossref]

Z. Zhang, M. Kushimoto, T. Sakai, N. Sugiyama, L. J. Schowalter, C. Sasaoka, and H. Amano, “A 271.8 nm deep-ultraviolet laser diode for room temperature operation,” Appl. Phys. Express 12(12), 124003 (2019).
[Crossref]

2018 (2)

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]

T. Suski, G. Staszczak, K. P. Korona, P. Lefebvre, P. A. Drożdż, G. Muzioł, C. Skierbiszewski, M. Kulczykowski, M. Matuszewski, E. Grzanka, S. Grzanka, K. Pieniak, A. Khachapuridze, J. SmalcKoziorowska, E. Monroy, and P. Perlin, “Switching of exciton character in double InGaN/GaN quantum wells,” Phys. Rev. B 98(16), 165302 (2018).
[Crossref]

2017 (1)

B. T. Tran and H. I. Hirayama, “Growth and Fabrication of High External Quantum Efficiency AlGaN-Based Deep Ultraviolet Light-Emitting Diode Grown on Pattern Si Substrate,” Sci. Rep. 7(1), 12176 (2017).
[Crossref]

2016 (3)

N. G. Young, R. M. Farrell, S. Oh, M. Cantore, F. Wu, S. Nakamura, S. P. DenBaars, C. Weisbuch, and J. S. Speck, “Polarization field screening in thick (0001) InGaN/GaN single quantum well light-emitting diodes,” Appl. Phys. Lett. 108(6), 061105 (2016).
[Crossref]

F. Fedichkin, T. Guillet, P. Valvin, B. Jouault, C. Brimont, T. Bretagnon, L. Lahourcade, N. Grandjean, P. Lefebvre, and M. Vladimirova, “Room-Temperature Transport of Indirect Excitons in (Al,Ga)N/GaN Quantum Wells,” Phys. Rev. Appl. 6(1), 014011 (2016).
[Crossref]

M. Malinverni, C. Tardy, M. Rossetti, A. Castiglia, M. Duelk, C. Vélez, D. Martin, and N. Grandjean, “InGaN laser diode with metal-free laser ridge using n+-GaN contact layers,” Appl. Phys. Express 9(6), 061004 (2016).
[Crossref]

2013 (1)

D. F. Feezell, J. S. Speck, S. P. DenBaars, and S. I. Nakamura, “Semipolar (2021) InGaN/GaN Light-Emitting Diodes for High-Efficiency Solid-State Lighting,” J. Disp. Technol. 9(4), 190–198 (2013).
[Crossref]

2011 (2)

H. Zhao, G. Liu, J. Zhamg, J. Dierolf, and N. Tansu, “Approaches for high internal quantum efficiency green InGaN light-emitting diodes with large overlap quantum wells,” Opt. Express 19(S4), A991 (2011).

S. Krishnamoorthy, P. S. Park, and S. Rajan, “Demonstration of forward inter-band tunneling in GaN by polarization engineering,” Appl. Phys. Lett. 99(23), 233504 (2011).
[Crossref]

2010 (2)

M. F. Schubert, “Polarization-charge tunnel junctions for ultraviolet light-emitters without p-type contact,” Appl. Phys. Lett. 96(3), 031102 (2010).
[Crossref]

A. Laubsch, M. Sabathil, J. Baur, M. Peter, and B. Hahn, “High-Power and High-Efficiency InGaN-Based Light Emitters,” IEEE Trans. Electron Devices 57(1), 79–87 (2010).
[Crossref]

2009 (4)

A. E. Chernyakov, M. M. Sobolev, V. V. Ratnikov, N. M. Shmidt, and E. B. Yakimov, “Nonradiative recombination dynamics in InGaN/GaN LED defect system,” Superlattices Microstruct. 45(4-5), 301–307 (2009).
[Crossref]

S. Riyopoulos, “Electrostatically Shielded Quantum Confined Stark Effect Inside Polar Nanostructures,” Nanoscale Res. Lett. 4(9), 993–1003 (2009).
[Crossref]

J.-H. Ryou, P. Douglas Yoder, J. Liu, Z. Lochner, H. Kim, S. Choi, H. J. Kim, and R. D. Dupuis, “Control of Quantum-Confined Stark Effect in InGaN-Based Quantum Wells,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1080–1091 (2009).
[Crossref]

Y.-R. Wu, C. Chiu, C.-Y. Chang, P. Yu, and H.-C. Kuo, “Size-DependentStrain Relaxation and Emission Characteristics of InGaN/GaN Nanorod Light Emitting Diodes,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1226–1233 (2009).
[Crossref]

2008 (2)

G. Franssen, I. Gorczyca, T. Suski, A. Kaminska, J. Pereiro, E. Muñoz, E. Iliopoulos, A. Georgakilas, S. B. Che, Y. Ishitani, A. Yoshikawa, N. E. Christensen, and A. Svane, “Bowing of the band gap pressure coefficient in InxGa1−xN alloys,” J. Appl. Phys. 103(3), 033514 (2008).
[Crossref]

A. Khan, B. Krishnan, and T. Katona, “Ultraviolet Light-Emitting Diodes Based on Group Three Nitrides,” Nat. Photonics 2(2), 77–84 (2008).
[Crossref]

2007 (2)

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and Future of High-Power Light-Emitting Diodes for Solid-State Lighting,” J. Disp. Technol. 3(2), 160–175 (2007).
[Crossref]

Y. C. Shen, G. O. Mueller, S. Watanabe, N. F. Gardner, A. Munkholm, and M. R. Krames, “Auger recombination in InGaN measured by photoluminescence,” Appl. Phys. Lett. 91(14), 141101 (2007).
[Crossref]

2006 (2)

M. Funato, M. Ueda, Y. Kawakami, Y. Narukawa, T. Kosugi, M. Takahashi, and T. Mukai, “Markedly distinct growth characteristics of semipolar (112-2) and (1-1-22) InGaN epitaxial layers,” Jpn. J. Appl. Phys. 45(26), L659–L662 (2006).
[Crossref]

A. E. Romanov, T. J. Baker, S. Nakamura, and J. S. Speck, “Strain-induced polarization in wurtzite III-nitride semipolar layers,” J. Appl. Phys. 100(2), 023522 (2006).
[Crossref]

2005 (1)

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]

2004 (3)

T. Suski, G. Franssen, P. Perlin, R. Bohdan, A. Bercha, P. Adamiec, F. Dybala, W. Trzeciakowski, P. Prystawko, M. Leszczyński, I. Grzegory, and S. Porowski, “A pressure-tuned blue-violet InGaN/GaN laser diode grown on bulk GaN crystal,” Appl. Phys. Lett. 84(8), 1236–1238 (2004).
[Crossref]

R. J. Kaplar, S. R. Kurtz, D. D. Koleske, and A. J. Fischer, “Electroreflectance studies of Stark shifts and polarization-induced electric fields in InGaN/GaN single quantum wells,” J. Appl. Phys. 95(9), 4905–4913 (2004).
[Crossref]

P. Lefebvre, S. Kalliakos, T. Bretagnon, P. Valvin, T. Taliercio, B. Gil, N. Grandjean, and J. Massies, “Observation and modeling of the time-dependent descreening of internal electric field in a wurtzite GaN/Al0.15Ga0.85N quantum well after high photoexcitation,” Phys. Rev. B 69(3), 035307 (2004).
[Crossref]

2002 (1)

O. Ambacher, J. Majewski, C. Miskys, A. Link, M. Hermann, M. Eickhoff, M. Stutzmann, F. Bernardini, V. Fiorentini, V. Tilak, B. Schaff, and L. F. Eastman, “Pyroelectric properties of Al(In)GaN/GaN hetero- and quantum well structures,” J. Phys.: Condens. Matter 14(13), 3399–3434 (2002).
[Crossref]

2001 (1)

S.-R. Jeon, Y.-H. Song, H.-J. Jang, G. M. Yang, S. W. Hwang, and S. J. Son, “Lateral current spreading in GaN-based light-emitting diodes utilizing tunnel contact junctions,” Appl. Phys. Lett. 78(21), 3265–3267 (2001).
[Crossref]

2000 (1)

C. Wetzel, T. Takeuchi, H. Amano, and I. Akasaki, “Electric-field strength, polarization dipole, and multiinterface band offset in piezoelectric Ga1−xInxN/GaN quantum-well structures,” Phys. Rev. B 61(3), 2159–2163 (2000).
[Crossref]

1999 (1)

F. Della Sala, A. Di Carlo, P. Lugli, F. Bernardini, V. Fiorentini, R. Scholz, and J.-M. Jancu, “Free-carrier screening of polarization fields in wurtzite GaN/InGaN laser structures,” Appl. Phys. Lett. 74(14), 2002–2004 (1999).
[Crossref]

1997 (3)

T. Takeuchi, S. Sota, M. Katsuragawa, M. Komori, H. Takeuchi, H. Amano, and I. Akasaki, “QuantumConfined Stark Effect due to Piezoelectric Fields in GaInN Strained Quantum Wells,” Jpn. J. Appl. Phys. 36(Part 2, No. 4A), L382–L385 (1997).
[Crossref]

F. Bernardini, V. Fiorentini, and D. Vanderbilt, “Spontaneous polarization and piezoelectric constants of III-V nitrides,” Phys. Rev. B 56(16), R10024 (1997).
[Crossref]

T. Takeuchi, S. Sota, M. Katsuragawa, M. Komori, H. Takeuchi, H. Amano, and I. Akasaki, “Quantum Confined Stark Effect due to Piezoelectric Fields in GaInN Strained Quantum Wells,” Jpn. J. Appl. Phys. 36(Part 2, No. 4A), L382–L385 (1997).
[Crossref]

1985 (1)

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Electric field dependence of optical absorption near the band gap of quantum-well structures,” Phys. Rev. B 32(2), 1043–1060 (1985).
[Crossref]

Adamiec, P.

T. Suski, G. Franssen, P. Perlin, R. Bohdan, A. Bercha, P. Adamiec, F. Dybala, W. Trzeciakowski, P. Prystawko, M. Leszczyński, I. Grzegory, and S. Porowski, “A pressure-tuned blue-violet InGaN/GaN laser diode grown on bulk GaN crystal,” Appl. Phys. Lett. 84(8), 1236–1238 (2004).
[Crossref]

Akasaki, I.

C. Wetzel, T. Takeuchi, H. Amano, and I. Akasaki, “Electric-field strength, polarization dipole, and multiinterface band offset in piezoelectric Ga1−xInxN/GaN quantum-well structures,” Phys. Rev. B 61(3), 2159–2163 (2000).
[Crossref]

T. Takeuchi, S. Sota, M. Katsuragawa, M. Komori, H. Takeuchi, H. Amano, and I. Akasaki, “QuantumConfined Stark Effect due to Piezoelectric Fields in GaInN Strained Quantum Wells,” Jpn. J. Appl. Phys. 36(Part 2, No. 4A), L382–L385 (1997).
[Crossref]

T. Takeuchi, S. Sota, M. Katsuragawa, M. Komori, H. Takeuchi, H. Amano, and I. Akasaki, “Quantum Confined Stark Effect due to Piezoelectric Fields in GaInN Strained Quantum Wells,” Jpn. J. Appl. Phys. 36(Part 2, No. 4A), L382–L385 (1997).
[Crossref]

Amano, H.

M. Kneissl, T.-Y. Seong, J. Han, and H. Amano, “The emergence and prospects of deep-ultraviolet light emitting diode technologies,” Nat. Photonics 13(4), 233–244 (2019).
[Crossref]

Z. Zhang, M. Kushimoto, T. Sakai, N. Sugiyama, L. J. Schowalter, C. Sasaoka, and H. Amano, “A 271.8 nm deep-ultraviolet laser diode for room temperature operation,” Appl. Phys. Express 12(12), 124003 (2019).
[Crossref]

C. Wetzel, T. Takeuchi, H. Amano, and I. Akasaki, “Electric-field strength, polarization dipole, and multiinterface band offset in piezoelectric Ga1−xInxN/GaN quantum-well structures,” Phys. Rev. B 61(3), 2159–2163 (2000).
[Crossref]

T. Takeuchi, S. Sota, M. Katsuragawa, M. Komori, H. Takeuchi, H. Amano, and I. Akasaki, “QuantumConfined Stark Effect due to Piezoelectric Fields in GaInN Strained Quantum Wells,” Jpn. J. Appl. Phys. 36(Part 2, No. 4A), L382–L385 (1997).
[Crossref]

T. Takeuchi, S. Sota, M. Katsuragawa, M. Komori, H. Takeuchi, H. Amano, and I. Akasaki, “Quantum Confined Stark Effect due to Piezoelectric Fields in GaInN Strained Quantum Wells,” Jpn. J. Appl. Phys. 36(Part 2, No. 4A), L382–L385 (1997).
[Crossref]

Ambacher, O.

O. Ambacher, J. Majewski, C. Miskys, A. Link, M. Hermann, M. Eickhoff, M. Stutzmann, F. Bernardini, V. Fiorentini, V. Tilak, B. Schaff, and L. F. Eastman, “Pyroelectric properties of Al(In)GaN/GaN hetero- and quantum well structures,” J. Phys.: Condens. Matter 14(13), 3399–3434 (2002).
[Crossref]

Baker, T. J.

A. E. Romanov, T. J. Baker, S. Nakamura, and J. S. Speck, “Strain-induced polarization in wurtzite III-nitride semipolar layers,” J. Appl. Phys. 100(2), 023522 (2006).
[Crossref]

Baranowski, M.

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]

Baur, J.

A. Laubsch, M. Sabathil, J. Baur, M. Peter, and B. Hahn, “High-Power and High-Efficiency InGaN-Based Light Emitters,” IEEE Trans. Electron Devices 57(1), 79–87 (2010).
[Crossref]

Bercha, A.

A. Bercha, W. Trzeciakowski, G. Muzioł, M. Siekacz, and C. Skierbiszewski, “Anomalous photocurrent in wide InGaN quantum wells,” Opt. Express 28(4), 4717 (2020).
[Crossref]

G. Staszczak, W. Trzeciakowski, E. Monroy, A. Bercha, G. Muzioł, C. Skierbiszewski, P. Perlin, and T. Suski, “Hydrostatic pressure dependence of indirect and direct excitons in InGaN/GaN quantum wells,” Phys. Rev. B 101(8), 085306 (2020).
[Crossref]

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]

T. Suski, G. Franssen, P. Perlin, R. Bohdan, A. Bercha, P. Adamiec, F. Dybala, W. Trzeciakowski, P. Prystawko, M. Leszczyński, I. Grzegory, and S. Porowski, “A pressure-tuned blue-violet InGaN/GaN laser diode grown on bulk GaN crystal,” Appl. Phys. Lett. 84(8), 1236–1238 (2004).
[Crossref]

Bernardini, F.

O. Ambacher, J. Majewski, C. Miskys, A. Link, M. Hermann, M. Eickhoff, M. Stutzmann, F. Bernardini, V. Fiorentini, V. Tilak, B. Schaff, and L. F. Eastman, “Pyroelectric properties of Al(In)GaN/GaN hetero- and quantum well structures,” J. Phys.: Condens. Matter 14(13), 3399–3434 (2002).
[Crossref]

F. Della Sala, A. Di Carlo, P. Lugli, F. Bernardini, V. Fiorentini, R. Scholz, and J.-M. Jancu, “Free-carrier screening of polarization fields in wurtzite GaN/InGaN laser structures,” Appl. Phys. Lett. 74(14), 2002–2004 (1999).
[Crossref]

F. Bernardini, V. Fiorentini, and D. Vanderbilt, “Spontaneous polarization and piezoelectric constants of III-V nitrides,” Phys. Rev. B 56(16), R10024 (1997).
[Crossref]

Bharadwaj, S.

H. Turski, S. Bharadwaj, H. Xing, and D. Jena, “Polarization control in nitride quantum well light emitters enabled by bottom tunnel-junctions,” J. Appl. Phys. 125(20), 203104 (2019).
[Crossref]

Blood, P.

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]

Bohdan, R.

T. Suski, G. Franssen, P. Perlin, R. Bohdan, A. Bercha, P. Adamiec, F. Dybala, W. Trzeciakowski, P. Prystawko, M. Leszczyński, I. Grzegory, and S. Porowski, “A pressure-tuned blue-violet InGaN/GaN laser diode grown on bulk GaN crystal,” Appl. Phys. Lett. 84(8), 1236–1238 (2004).
[Crossref]

Bour, D. P.

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]

Bretagnon, T.

F. Fedichkin, T. Guillet, P. Valvin, B. Jouault, C. Brimont, T. Bretagnon, L. Lahourcade, N. Grandjean, P. Lefebvre, and M. Vladimirova, “Room-Temperature Transport of Indirect Excitons in (Al,Ga)N/GaN Quantum Wells,” Phys. Rev. Appl. 6(1), 014011 (2016).
[Crossref]

P. Lefebvre, S. Kalliakos, T. Bretagnon, P. Valvin, T. Taliercio, B. Gil, N. Grandjean, and J. Massies, “Observation and modeling of the time-dependent descreening of internal electric field in a wurtzite GaN/Al0.15Ga0.85N quantum well after high photoexcitation,” Phys. Rev. B 69(3), 035307 (2004).
[Crossref]

Brimont, C.

F. Fedichkin, T. Guillet, P. Valvin, B. Jouault, C. Brimont, T. Bretagnon, L. Lahourcade, N. Grandjean, P. Lefebvre, and M. Vladimirova, “Room-Temperature Transport of Indirect Excitons in (Al,Ga)N/GaN Quantum Wells,” Phys. Rev. Appl. 6(1), 014011 (2016).
[Crossref]

Brown, H.

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]

Burrus, C. A.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Electric field dependence of optical absorption near the band gap of quantum-well structures,” Phys. Rev. B 32(2), 1043–1060 (1985).
[Crossref]

Cantore, M.

N. G. Young, R. M. Farrell, S. Oh, M. Cantore, F. Wu, S. Nakamura, S. P. DenBaars, C. Weisbuch, and J. S. Speck, “Polarization field screening in thick (0001) InGaN/GaN single quantum well light-emitting diodes,” Appl. Phys. Lett. 108(6), 061105 (2016).
[Crossref]

Castiglia, A.

M. Malinverni, C. Tardy, M. Rossetti, A. Castiglia, M. Duelk, C. Vélez, D. Martin, and N. Grandjean, “InGaN laser diode with metal-free laser ridge using n+-GaN contact layers,” Appl. Phys. Express 9(6), 061004 (2016).
[Crossref]

Chang, C.-Y.

Y.-R. Wu, C. Chiu, C.-Y. Chang, P. Yu, and H.-C. Kuo, “Size-DependentStrain Relaxation and Emission Characteristics of InGaN/GaN Nanorod Light Emitting Diodes,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1226–1233 (2009).
[Crossref]

Che, S. B.

G. Franssen, I. Gorczyca, T. Suski, A. Kaminska, J. Pereiro, E. Muñoz, E. Iliopoulos, A. Georgakilas, S. B. Che, Y. Ishitani, A. Yoshikawa, N. E. Christensen, and A. Svane, “Bowing of the band gap pressure coefficient in InxGa1−xN alloys,” J. Appl. Phys. 103(3), 033514 (2008).
[Crossref]

Chemla, D. S.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Electric field dependence of optical absorption near the band gap of quantum-well structures,” Phys. Rev. B 32(2), 1043–1060 (1985).
[Crossref]

Chernyakov, A. E.

A. E. Chernyakov, M. M. Sobolev, V. V. Ratnikov, N. M. Shmidt, and E. B. Yakimov, “Nonradiative recombination dynamics in InGaN/GaN LED defect system,” Superlattices Microstruct. 45(4-5), 301–307 (2009).
[Crossref]

Chichibu, S. F.

S. Nakamura and S. F. Chichibu, Introduction to Nitride Semiconductor Blue Lasers and Light Emitting Diodes (Taylor&Francis, London, 2000).

Chiu, C.

Y.-R. Wu, C. Chiu, C.-Y. Chang, P. Yu, and H.-C. Kuo, “Size-DependentStrain Relaxation and Emission Characteristics of InGaN/GaN Nanorod Light Emitting Diodes,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1226–1233 (2009).
[Crossref]

Choi, S.

J.-H. Ryou, P. Douglas Yoder, J. Liu, Z. Lochner, H. Kim, S. Choi, H. J. Kim, and R. D. Dupuis, “Control of Quantum-Confined Stark Effect in InGaN-Based Quantum Wells,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1080–1091 (2009).
[Crossref]

Chow, W. W.

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]

Christensen, N. E.

G. Franssen, I. Gorczyca, T. Suski, A. Kaminska, J. Pereiro, E. Muñoz, E. Iliopoulos, A. Georgakilas, S. B. Che, Y. Ishitani, A. Yoshikawa, N. E. Christensen, and A. Svane, “Bowing of the band gap pressure coefficient in InxGa1−xN alloys,” J. Appl. Phys. 103(3), 033514 (2008).
[Crossref]

Craford, M. G.

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and Future of High-Power Light-Emitting Diodes for Solid-State Lighting,” J. Disp. Technol. 3(2), 160–175 (2007).
[Crossref]

Craven, M. D.

A. David, N. Young, C. Lund, and M. D. Craven, “Review—The Physics of Recombinations in III-Nitride Emitters,” ECS J. Solid State Sci. Technol. 9(1), 016021 (2020).
[Crossref]

Damen, T. C.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, “Electric field dependence of optical absorption near the band gap of quantum-well structures,” Phys. Rev. B 32(2), 1043–1060 (1985).
[Crossref]

David, A.

A. David, N. Young, C. Lund, and M. D. Craven, “Review—The Physics of Recombinations in III-Nitride Emitters,” ECS J. Solid State Sci. Technol. 9(1), 016021 (2020).
[Crossref]

Della Sala, F.

F. Della Sala, A. Di Carlo, P. Lugli, F. Bernardini, V. Fiorentini, R. Scholz, and J.-M. Jancu, “Free-carrier screening of polarization fields in wurtzite GaN/InGaN laser structures,” Appl. Phys. Lett. 74(14), 2002–2004 (1999).
[Crossref]

DenBaars, S. P.

N. G. Young, R. M. Farrell, S. Oh, M. Cantore, F. Wu, S. Nakamura, S. P. DenBaars, C. Weisbuch, and J. S. Speck, “Polarization field screening in thick (0001) InGaN/GaN single quantum well light-emitting diodes,” Appl. Phys. Lett. 108(6), 061105 (2016).
[Crossref]

D. F. Feezell, J. S. Speck, S. P. DenBaars, and S. I. Nakamura, “Semipolar (2021) InGaN/GaN Light-Emitting Diodes for High-Efficiency Solid-State Lighting,” J. Disp. Technol. 9(4), 190–198 (2013).
[Crossref]

Di Carlo, A.

F. Della Sala, A. Di Carlo, P. Lugli, F. Bernardini, V. Fiorentini, R. Scholz, and J.-M. Jancu, “Free-carrier screening of polarization fields in wurtzite GaN/InGaN laser structures,” Appl. Phys. Lett. 74(14), 2002–2004 (1999).
[Crossref]

Dierolf, J.

Douglas Yoder, P.

J.-H. Ryou, P. Douglas Yoder, J. Liu, Z. Lochner, H. Kim, S. Choi, H. J. Kim, and R. D. Dupuis, “Control of Quantum-Confined Stark Effect in InGaN-Based Quantum Wells,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1080–1091 (2009).
[Crossref]

Drozdz, P. A.

T. Suski, G. Staszczak, K. P. Korona, P. Lefebvre, P. A. Drożdż, G. Muzioł, C. Skierbiszewski, M. Kulczykowski, M. Matuszewski, E. Grzanka, S. Grzanka, K. Pieniak, A. Khachapuridze, J. SmalcKoziorowska, E. Monroy, and P. Perlin, “Switching of exciton character in double InGaN/GaN quantum wells,” Phys. Rev. B 98(16), 165302 (2018).
[Crossref]

Duelk, M.

M. Malinverni, C. Tardy, M. Rossetti, A. Castiglia, M. Duelk, C. Vélez, D. Martin, and N. Grandjean, “InGaN laser diode with metal-free laser ridge using n+-GaN contact layers,” Appl. Phys. Express 9(6), 061004 (2016).
[Crossref]

Dupuis, R. D.

J.-H. Ryou, P. Douglas Yoder, J. Liu, Z. Lochner, H. Kim, S. Choi, H. J. Kim, and R. D. Dupuis, “Control of Quantum-Confined Stark Effect in InGaN-Based Quantum Wells,” IEEE J. Sel. Top. Quantum Electron. 15(4), 1080–1091 (2009).
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Dybala, F.

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A. E. Chernyakov, M. M. Sobolev, V. V. Ratnikov, N. M. Shmidt, and E. B. Yakimov, “Nonradiative recombination dynamics in InGaN/GaN LED defect system,” Superlattices Microstruct. 45(4-5), 301–307 (2009).
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ACS Photonics (1)

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).
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Appl. Phys. Express (3)

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Phys. Rev. Appl. (1)

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The fact that EEL has a parabolic maximum around FQW = 0 is easier to see in the reference system in the middle of the well, not at its edge (like in Eq. (1)). In that case the EEL term disappears and we only deal with confinement energies measured from the center of the well. These confinement energies change parabolically with FQW (linear terms vanish) as shown e.g. in Ref. [37]. For strong fields it is convenient to use the reference system at the edge of the well, like in Eq. (1). In that case the confinement energies as a function of the field have been calculated e.g. in [34]. When the field changes sign the reference system switches to the other side of the well so for fields that can change directions it is more natural to use the reference system in the middle of the well. The resulting EEL(FQW) is of course the same for both reference systems.

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Figures (9)

Fig. 1.
Fig. 1. Schematic structure of In0.17Ga0.83N/InxGa1-xN light-emitting diodes with: (a) top tunnel junction (TTJ) and (b) bottom tunnel junction (BTJ). (c)-(d) Schematic images of the arrangements of the direction of fields inside QW and QB with respect to the p-n junction. The color arrows indicate electron and hole injection directions. The direction of the field in the well FQW is parallel (antiparallel) to the direction of the field in the barriers FQB in the case of BTJ (TTJ). Figures are based on Ref. [44].
Fig. 2.
Fig. 2. Band profiles at zero bias (a) and (b) and at ∼1A/cm2 (c) and (d) for sample A3 TTJ (a) and (c) and B1 BTJ (b) and (d). Colored stripes are used to distinguish regions doped with Mg-acceptors and Si-donors (from left to right). Simulations performed using package presented in Ref. [47].
Fig. 3.
Fig. 3. Measured current density vs voltage for 0.1 × 0.1 mm2 devices with (a) top-TJ structure (A1-A3) and (b) bottom-TJ structure (B1-B3)
Fig. 4.
Fig. 4. Comparison of electroluminescence spectra acquired for different driving currents at: atmospheric pressure for (a) LED A3 and (b) LED B1 and at the pressure of 0.6 GPa for (c) LED A3 and (d) LED B1.
Fig. 5.
Fig. 5. Comparison of electroluminescence spectra dependence on driving current for: (a) LED A1 and (b) LED A2 at atmospheric pressure. Lower set of spectra (c) and (d) were measured at the pressure of 1 GPa.
Fig. 6.
Fig. 6. Shift of EEL maxima with applied pressure for different values of the driving current density (marked at the right side of diagrams). (a)-(b) illustrate a behavior of LEDs A1 and A3, correspondingly. Pressure coefficients dEEL/dp characterizing individual experimental runs are given also.
Fig. 7.
Fig. 7. Dependence on current density of: (a) emission energy and (b) pressure coefficient; measured for LEDs A1, A2, A3, and B1. (c) Simulated dependence of emission energy on current density. (d) Simulated dependence of the average magnitude of the internal field inside single QW of each discussed LED. Dashed magenta line in (a) and (c) corresponds to the EEL value in In0.17Ga0.83N alloy. The gray bar (b) corresponds to the pressure coefficient characterizing entirely screened internal electric field in In0.17Ga0.83N alloy [36]. Error bar for determination of dEG/dp in (b) is ±1 meV/GPa.
Fig. 8.
Fig. 8. Comparison of electroluminescence spectra dependence on driving current for: (a) LED B2 and (b) LED B3 at atmospheric pressure.
Fig. 9.
Fig. 9. Measured driving-current dependence of: (a) EEL and (b) dEEL/dp of LEDs B2, and B3,. Results for LED B1, and A3 are shown for comparison. For LEDs B1 and A3 effects of FQW screening are clearly seen at low IDs (a). (b) Shows qualitatively different behavior of dEEL/dp LEDs with wide QW (B2 and B3) and narrow QW (B1 and A3). Additionally, low pressure coefficient of LEDs B1 and A3 seen in (b) illustrates the high amount of FQW remaining in these LEDs at higher magnitude of IDs. (c) Simulated dependence of average electric field in QW of LEDs B1, B2, B3 and A3 support experimental findings.

Tables (1)

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Table 1. Details of light-emitting diodes with tunnel junction (TJ) studied in this work.

Equations (2)

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E E L = E G + E c o n f e + E c o n f h e L Q W | F Q W | E e x c
d E E L d p = d E G d p + d E E L d F Q W d F Q W d p

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