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Abstract
We examined electroluminescence from In0.17Ga0.83N/GaN quantum wells (QW) of light-emitting diodes (LEDs) and laser diodes (LDs). For increasing QW width we observe transition from electron and hole ground-states recombination to excited states recombination. The effect is accompanied by partial (2.6 nm, 5.2 nm, 7.8 nm QW) or practically complete (10.4 nm QW) screening of the built-in electric field with increasing driving current for both types of emitters. The electric field magnitude was studied using an original high pressure method. The investigations are supported by simulations of the variation with driving current of i) electron and hole wavefunctions overlap affecting the recombination channel, ii) built-in electric field.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
InGaN/GaN semiconductor heterostructures are key materials for visible light emitters, i.e., light-emitting diodes (LEDs) and laser diodes (LDs) [1–6]. Both GaN and InN crystalize in the non-centrosymmetric wurtzite crystal structure. For this reason heterostructures based on these materials which are characterized by mismatch of the lattice constants, exhibit strong electric field induced by the piezo- and spontaneous-electric polarizations directed along hexagonal c-axis <0001> [7–11]. Electrostatic charges induced at the interfaces between quantum wells (QWs) and barriers (QBs) determine electric field present in QWs and QBs. The built-in electric field can achieve magnitude of 1-3 MV/cm. It results in the band profiles tilting and in the large reduction of the interband transition energy (energy red-shift) [12,13]. Moreover, the interrelated effect consists in the spatial separation of the electron and hole wavefunctions, which in turn induces the strong decrease in the luminescence intensity via the associated reduction of electron and hole wavefunction overlap. All the above listed phenomena are described by the Quantum Confined Stark Effect (QCSE) [8–14].
Deep understanding of the QCSE and particularly its evolution with the increasing density of carriers introduced to the emitters active region by the driving current, ID, is crucial in the design of LEDs and LDs. An increase in carrier density causes the screening of built-in electric field, Fint. Important consequences consist in the increase of electron and hole wave function overlap and related rise in the emission intensity. Another effect is a shift of the emitted light to higher energy (so called blue-shift of EEL). It is worth to mention that decay time of photo- or electro-luminescence can decrease with the current density from milli- to nano-seconds [12–15].
With increasing ID, carriers trapped in the QW start to occupy electron and hole states – first the ground states, then the excited states [16,17]. Radiative transitions occur between different energy states depending on their population and on the corresponding wave function overlaps. These two quantities depend on ID and on the well width.
It is important to point out that in LEDs and LDs, besides the built-in field induced by the spontaneous and piezoelectric polarizations there is also an additional contribution to Fint, determined by properties of the p-n junction. Increase of the polarization voltage applied in the forward direction causes first an increase of the field in the QW but then its reduction due to the screening by carriers pumped into the well. It is worth to point out that due to the complicated relation between the variety of contributions the precise determination of Fint and its evolution with driving current is very difficult.
A commonly used experimental parameter for QCSE evaluation is the blue-shift of electroluminescence (EL) energy, EEL, with driving current (see e.g. [13,15,18]). This change of EEL is significant at low magnitude of ID not exceeding 40-50 A/cm2. It is more pronounced in structures characterized by higher In-content and in wider wells (up to about 4-5 nm). With further rising of ID the rate of EEL increase is strongly reduced or almost saturated. It is tempting to interpret this saturation as due to the complete screening of Fint [19]. It turned out that such conclusion is in general incorrect (e.g., [20]). Some preliminary results obtained in LEDs have been published very recently by us [20]. In the present paper we concentrated on changes in the light emission mechanism as a function of ID in the LEDs and LDs when width of QW is increased in a systematic way. We observe a qualitative change in the origin of radiative recombination, which evolves from the involvement of electron and hole ground states to excited state [16,17].
There have been many papers studying the emission from InGaN quantum wells: i) as a functions of well width, ii) as a function of pumping (optical or electrical), or iii) as a function of hydrostatic pressure. Our present study combines all these factors in order to identify the optical transitions and describe the electric-field screening (supported by modeling). The identification of excited-state transitions has been very difficult in InGaN wells because of line broadening and shifts of transitions with the field (dependent on pumping).
The closest related work on that subject was presented by Laubsch et al. [18]. LEDs with different QW widths (2, 5, 20 nm) were studied experimentally. The LEDs with the QW width of 2 nm and 20 nm did not show any blue-shift of EEL in the wide range of the applied current density. For the LED with 2 nm QW this stable position of EEL was explained by the significant electron and hole ground states wave function overlap which did not change with driving current. In the LED with 20 nm QW the radiative recombination was attributed to excited states which (according to the authors) are less affected by QCSE. There was no identification of these excited states. In the LED containing 5 nm QW, involvement of ground states at low currents and excited states at high currents is postulated.
In [20] we proposed a new method to estimate the magnitude of Fint. It consists in utilizing hydrostatic pressure measurements of the emission energy and its dependence on ID [20]. High hydrostatic pressure increases (almost linearly [21]) the piezoelectric field in the well Fint. The pressure coefficient of the EEL, i.e., dEEL/dp, analyzed for different ID, supplies information about the evolution of Fint. There is a solid reference point related to entire elimination of Fint from the active region of the polar nitride devices. It is defined by pressure coefficient of the emission energy from InxGa1-xN alloys [22]. These alloys (in contrast to the lattice-mismatched heterostructures) have no built-in polarization induced electric field. The dependence of the emission energy EEL on external hydrostatic pressure (dEEL/dp) versus In-content is well known and varies between 40 meV/GPa for GaN decreasing almost linearly to 25-27 meV/GPa for x≥ 0.25 [22]. Thus comparing dEEL/dp in QW of the emitters with pressure coefficient of the InxGa1-xN alloy (the same x as in the QW) supplies important information difficult to obtain by other approaches. It is based on the following analysis.
The transition energy in the presence of built-in electric field in the studied emitters can be written as [20,21]:
In the present paper we concentrated on the examination of the quantum-well width dependence of the radiative recombination mechanism. All our samples had the same In content in the well (x=0.17), so that the piezoelectric field was the same. In the presence of strong field the width of the well determines the electron-hole wavefunction overlap and the redshift of emission energy. When the ground states are populated, the screening is very sensitive to the well width because the charge separation increases with well width.
After presentation of the detailed structures of the investigated LEDs and LDs, we describe the performed studies of EEL and its hydrostatic pressure dependence, dEEL/dp, in four In0.17Ga0.83N/GaN LEDs. Next we describe similar studies on two LDs. One of them contains very narrow QW (2.6 nm) and the second very wide QW (10.4 nm). Both widths of LDs QW correspond to the LED with the most narrow and the widest QW. These studies allow for the comparison of these two types of emitters.
The experimental investigations are supported by simulations [23] of the variation with driving current of i) electron and hole wavefunctions and their overlap affecting the light emission, ii) the emission energy EEL, iii) built-in electric field present in the studied emitters. Our analysis allows to identify the states involved in optical transitions.
2. Samples
Growth of LEDs and LD was carried out with plasma-assisted molecular beam epitaxy in the metal rich conditions. Details of growth can be found in Ref. [24]. Schematics of the LED and LD structures are presented in Fig. 1. The structure of LEDs consisted of 200 nm GaN:Si (Si: 2×1018 cm−3), followed by an undoped 40 nm In0.02Ga0.98N and an In0.17Ga0.83N QW. Four LEDs were grown with QW thicknesses of 2.6, 5.2, 7.8 and 10.4 nm, see Table 1. The QW is capped with an undoped 40 nm In0.02Ga0.98N and 20nm Al0.13Ga0.87N:Mg (Mg: 2×1019 cm−3), with the latter acting as an electron blocking layer (EBL). Next, a 200 nm GaN:Mg (Mg: 1×1018 cm−3) followed by a Tunnel Junction (TJ) were grown. The TJ consisted of 20 nm In0.02Ga0.98N:Mg (Mg: 2×1019 cm−3), 3 nm In0.21Ga0.79N:Mg (Mg: 1.6×1020 cm−3) 3nm In0.21Ga0.79N:Si (Si: 2×1020 cm−3) and 20 nm In0.02Ga0.98N:Si (Si: 5×1019 cm−3). A combination of piezoelectric field and heavy doping is used to decrease the depletion width and achieve efficient tunneling in this TJ. A detailed study of tunneling mechanism in these structures can be found in Ref. [25].
Fig. 1. Scheme of the epitaxial structures of the investigated devices: a) LEDs and b) LDs structure. LEDs contain the tunnel junction located above the single quantum well so the top contact is n-type. LD structure has AlGaN cladding layers to form the waveguide.
Table 1. List of the most important parameters of the studied emitters. The main difference between them was the QW width.
The LED was capped with a current spreading layer consisting of 100 nm GaN:Si (Si: 3.7×1019 cm−3), which enabled us to evaporate top metallization only on a part of the surface and collect light from the top. The LEDs were processed into 350 × 350 µm2 devices with standard Ti/Al/Ni/Au n-type metallization on both sides. The epitaxial structure of LDs was slightly modified to obtain optical mode confinement. The n-type cladding consists of a 700 nm Al0.065Ga0.935N:Si (Si: 2×1018 cm−3) and 100 nm GaN:Si (Si: 2×1018 cm−3). The waveguide is formed from an undoped 220 nm In0.03Ga0.97N, in the middle of which the QW was grown. Two LD structures were grown with QW thicknesses of 2.6 and 10.4 nm, see Table 1. The EBL was placed at the end of the waveguide. Its composition and doping were the same as in the LED structures. The p-type cladding consists of 100 nm GaN:Mg (Mg: 1×1018 cm−3) and 600 nm Al0.02Ga0.98N:Mg (Mg: ×1018 cm−3). The structure is capped with an InGaN contact layer. A standard metallization consisting of Ti/Al/Ni/Au for n-type and Ni/Au for p-type was evaporated. The ridge width was 3 µm and the resonator length was 1000 µm. The mirrors were cleaved and left uncoated. In case of LEDs, light emitted from the top surface was collected thanks to the use of TJ. In case of the LDs, light emitted through the resonator mirror was collected.
3. Experimental methods and results
Determination of the electroluminescence energy and energy of lasing vs. driving current density was performed by means of spectroscopic measurements of electroluminescence intensity vs. wavelength/energy, for constant ID. Results of LED studies were obtained under direct current (DC) conditions. Meanwhile, LDs were measured applying alternate current (AC) with 1 µsec pulses and 1% filling factor (to avoid heating of the studied emitters). For a comparison of the behavior of LEDs and LDs, results presented in subsection “Laser Diodes” were obtained applying in both cases the AC current. It is worth to point out that in order to obtain lasing (with or without pressure) higher current densities had to be applied to LD devices. This effect can be largely explained by changes of the refractive index of the pressure transmitting medium with respect to air.
To study the electroluminescence dependence on pressure and LED’s driving current we used the clamped-cell (piston-cylinder type), equipped with sapphire window and electrical leads/connection in the piston [22]. This design enabled to conduct optical and optoelectronic type of measurements including pressure tuning of laser diodes. The whole setup is shown in detail in Ref. [26]. Magnitude of the pressure generated inside of the piston-cylinder type of the cell is monitored by resistivity changes of a specially calibrated InSb semiconductor gauge. As highly transparent pressure transmitting medium (liquid) we used Plexol (bis(2-ethylhexyl) decanedioate).
3.1 Light emitting diodes
Changes of EL spectra of the studied LEDs with driving current are illustrated in Fig. 2. Results for devices from Fig. 2(a) and 2(d) show a stable shape of the spectra, implying a single transition type. Meanwhile, the spectra in Figs. 2(b) and 2(c) change their shape for different currents, implying multiple transition type. This is also illustrated in Fig. 3 showing the half-widths of the EL peaks from Fig. 2.
Fig. 2. Comparison of the evolution of electroluminescence spectra with driving current for: (a) LED1, QW=2.6 nm, (b) LED2, QW=5.2 nm, (c) LED3, QW=7.8 nm, and (d) LED4 QW=10.4 nm. Measurements were performed at atmospheric pressure.
Fig. 3. Dependence of FWHM on current density for LED’s with different QW thicknesses: a) 2.6 nm, b) 5.2 nm, c) 7.8 nm and d) 10.4 nm measured at atmospheric pressure (T=300 K).
Figure 3(b) and Fig. 3(c) demonstrate a clear reduction of FWHM with increasing ID. We interpret this behavior as corresponding to the involvement of ground and excited states in the radiative recombination. With increasing ID the excited states population becomes higher, changing the recombination process. Therefore we fit the spectra for 5.2 nm and for 7.8 nm QW samples with two Gaussians (Fig. 4). We will show later that spectra shown in Fig. 2(a) and 2(d) correspond to the light emission due to a single transition < e1-h1> and < e2-h2>, respectively. Meanwhile, in LEDs with 5.2 nm and 7.8 nm QWs contributions from both ground and excited states come into play. We will show later that this interpretation is supported by the performed simulations.
Fig. 4. Dependence of the emission energies on current density for In0.17Ga0.83N/GaN LED’s with different QW thicknesses: a) 2.6 nm, b) 5.2 nm, c) 7.8 nm and d) 10.4 nm measured at atmospheric pressure. Identification of transitions shown in the figure is based on both experimental and theoretical results.
Variation of EL energy with ID in all four LEDs is presented in Fig. 4. It is obtained from the analysis of the spectra shown in Fig. 2. Identification of transitions shown in Fig. 4 is based on both experimental and theoretical results. The light emission observed in LED with QW of 2.6 nm width we assign to < e1h1> transition between ground states. Two Gaussian contributions, related to < e1h2> and < e2h1> are used for determination of two values of EEL in case of LED with QW of 5.2 nm width.
The same (two Gaussian) procedure was applied to analyze data from Fig. 2(c) (QW=7.8 nm) for IDs below about 0.03-0.04 kA/cm2. We assumed that the associated transitions are < e2h1> (lower energies) and < e2h2> (higher energies. For higher current density one recombination channel (via < e2h2> excited states) dominated the spectrum. With increasing well width the ground-state transition energy should decrease. This is the case when we compare the energies for the 2.6 nm well (Fig. 4(a)) and for the 5.2 nm well (Fig. 4(b)). However, the lower-energy transition for the 7.8 nm well (Fig. 4(c)) is much higher than for the 5.2 nm well. This supports the above proposed assignment that both transitions shown in Fig. 4(c) are due to excited states, i.e., <e2h1> and <e2h2> for lower and higher emission energy. The single transition for the 10.4 nm well (Fig. 4(d)) is also attributed to < e2h2> excited states.
Figure 5 presents the dependencies of the electroluminescence intensity maximum on current density for four LEDs studied in this work. Comparison of these evolutions with changes of EEL (Fig. 4) shows some similarities. Blue-shift of EEL with current corresponds to the screening of internal electric field. The related effect consists in the increase of the electron-hole wavefunction overlap and thus in the corresponding rise of the electroluminescence intensity observed in Fig. 5.
Fig. 5. Dependence of Intensity on current density for LEDs with different QW thicknesses: a) 2.6 nm, b) 5.2 nm, c) 7.8 nm and d) 10.4 nm measured at atmospheric pressure and T = 300 K.
Let us now turn to the high-pressure data which we use to obtain additional information about the electric field in the well.
Figure 6 shows the evolution of EL spectra measured in In0.17Ga0.83N/GaN LED (10.4 nm QW) at ID=0.1 kA/cm2. Maxima of EL intensity shift under pressure with the rate dEEL/dp=32.5 meV/GPa, i.e., pressure coefficient characterizing InxGa1-xN alloy with x=0.17 [22]. This result indicates very efficient screening of the built-in electric field. However, we believe that there is still some amount of electric field at the interfaces of the QW. The values of dEEL/dp vs ID are collected in Fig. 7. A comparison of the data presented in Figs. 5 and 7 shows evident similarities between current dependence of EEL and dEEL/dp. An advantage of the pressure criterion consists in the existence of the upper limit of dEEL/dp corresponding to the efficient screening of the built-in field.
Fig. 6. Normalized EL spectra measured at different pressure values at fixed current density of 0.1 kA/cm2 for LED structure with QW width 10.4 nm. Inset illustrates shift of the emission energy with pressure.
Fig. 7. Dependence of pressure coefficient dEEL/dp on driving current density for LEDs with different QW thicknesses: a) 2.6 nm, b) 5.2 nm, c) 7.8 nm and d) 10.4 nm. Grey bar corresponds to the pressure coefficient characterizing entirely screened internal electric field in In0.17Ga0.83N alloy [20]. Error bar for determination of dEG/dp is ±1 meV/GPa..
The dependence of pressure coefficients on ID shown in Fig. 7 resembles the dependence of transition energies shown in Fig. 4. The behavior observed in the panels a) and d) of Fig. 7 illustrates light emission mechanism related to electron and hole ground and excited states, respectively. LED (QW=5.2 nm) represents the case where both recombination processes are present in the entire range of driving currents. LED (7.8 nm) demonstrates the switching with increasing ID from two recombination channels to the single channel at IDs higher than about 0.03 kA/cm2 (probably due to merging of two transitions into one when they approach each other). We assume that both channels in 7.8 nm well involve excited states since the ground-state transition should be much lower in Fig. 4(c). The identification of transitions shown in Fig. 7 is supported by theoretical simulations described below.
3.2 Laser diodes
Two In0.17Ga0.83N/GaN laser diodes with single QWs of 2.6 nm and 10.4 nm widths were used in the performed studies. The methods for measuring EEL and dEEL/dp were almost identical to those described earlier for LEDs. The only difference consisted in application of alternate current to drive the LDs. Figure 8 and Fig. 9 represent examples of the collected spectra used for the determination of EEL and dEEL/dp as a function of ID. Parts “a” of these figures illustrate evolution of electroluminescence/lasing spectra with ID at atmospheric pressure measured in both LDs. Parts “b” present similar data for pressures 0.6 and 0.5 GPa, respectively. A significant blue shift of the spectra with ID, corresponding to screening of the QCSE can be observed in Fig. 8. However it should not be concluded that the saturation of EEL and energy of lasing at high magnitude of IDs reflects the entire screening of the built-in electric field. This behavior is different in LD with wide QW (QW=10.4 nm). EEL and energy of lasing is weakly dependent on ID (Fig. 9). This resembles response of LED with the same width of the QW.
Fig. 8. Normalized spectra of electroluminescence/lasing at different current densities for LD structure with QW width 2.6 nm, measured at a) atmospheric pressure and b) at the pressure of 0.6 GPa.
Fig. 9. Normalized spectra of electroluminescence at different current densities for LD structure with QW width 10.4 nm measured at a) atmospheric pressure and b) at the pressure of 0.5 GPa.
Experimental data collected from series of measurements of EEL vs. pressure (for increasing values of ID) were used to determine dEEL/dp characterizing both examined laser diodes. Figure 10(a) and 10(b) illustrate a driving current dependent variation of EEL and dEEL/dp obtained for laser diode with narrow QW of 2.6 nm. At current density below about 1.5 kA/cm2 both analyzed parameters show strong increase with ID followed by much slower increase up to the threshold current. For the purpose of a comparison we performed similar analysis for the equivalent LED. In this case, similarly to LD, an alternate driving current was applied. It helped to avoid self-heating of LED. Lower values of ID with respect to LD were used. For the LD we had to apply much higher current density than for LED in order to achieve lasing. From the inspection of Fig. 10(b) one can draw an important conclusion. Namely, the saturation of dEEL/dp at about 22 meV/GPa strongly suggests that lasing in this emitter is achieved under the condition of significant built-in electric field. Simulations performed by us illustrated later in this paper show that this remaining field is of the order of 1 MV/cm. (Figs. 14 and 15).
Fig. 10. Dependence of a) emission energy and b) its pressure coefficient on current density, ID, for LED and LD with QW thickness of 2.6 nm. Yellow area determines range of IDs where lasing action occurs. Hatched area corresponds to the pressure coefficient characterizing band gap increase with pressure in In0.17Ga0.83N alloy (built-in field absent) [22]. Error bar for determination of dEG/dp is ±1 meV/GPa.
The results for the LD with 10.4 nm QW are shown in Fig. 11. Emission energy is approximately constant as shown in Fig. 11(a). Figure 11(b) demonstrates the constant value of dEEL/dp at about 32 meV/GPa. We interpret this result as the evidence that already starting from very small driving currents, the built-in field is almost entirely screened in LED and LD emitters with QW of 10.4 nm width. In addition, in the region close to the threshold current, we do not notice any anomalies in the driving current dependent variation of EEL and dEEL/dp. Simulations performed by us and presented in the next Section show that the only remaining unscreened field is located at the interfaces of the QW with barriers, while in the region of the highest wave function overlap (important for the light emission intensity), the field is close to zero.
Fig. 11. Dependence on current density of a) emission energy and b) pressure coefficient of LED and LD with QW thickness 10.4 nm. Yellow area denotes the range of lasing action. Hatched area corresponds to the pressure coefficient characterizing bandgap pressure coefficient of In0.17Ga0.83N alloy (built-in field absent) [22]. The insert shows the magnified part of Fig. 11(b) for low current densities. Error bar for determination of dEG/dp is ± 1 meV/GPa.
Discussing the possible contributions of different effects on the accuracy of our studies, it is necessary to consider contributions to the transition energy fluctuations. They are due to:(i) Indium-spatial inhomogeneities in the InGaN QWs and barriers as well as (ii) QW width fluctuations. These two effects present in different amount in InGaN quantum wells grown by both MBE and MOCVD techniques have been studied intensively. For example, Yang et al. [27] demonstrated by means of theoretical simulations the role of the indium fluctuations in the In0.17Ga0.83N quantum wells of LEDs. These fluctuations led to shifts of EL up to about 50-60 meV. Humphreys [28] has shown that thickness fluctuations in the InGaN QW of one monolayer, observed in electron microscopy, result in the variation of the transition energy of about 60 meV. It is sufficient to induce localization of the carriers at room temperature [28] and to widen and to shift emission spectra. Similar magnitude of the emission energy variation in InxGa1-xN/GaN structures with In content x=0.17 can be deduced from results presented in Refs. [13,15]. Moreover, the estimated accuracy of the pressure coefficient determination, taking into account In-content fluctuations of x= ±0.01, is equal to ±1 meV/GPa [22].
In the present work we carefully selected LEDs and LDs consisting of single QW with In-content 17% and width of QW which varied from 2.6 nm to 10.4 nm. The XRD and TEM measurements performed on our MBE-grown samples showed that, with the accuracy of 1 atomic monolayer (width of 0.26 nm) and ±1% of In-content, the structural parameters of both QWs and barriers surrounding them, agreed with the targeted values [13,15]. The above described inhomogeneities induced by the potential fluctuations correspond well with the results of Yang and Humphreys are typical for high quality InxGa1-xN/GaN heterostructures. These potential fluctuations lead to broadening of EL spectra. However, since they should not change with pressure or with the driving current, we believe that they should not change our main conclusions. We suggest that differences in the EEL values and their evolution with driving current detected for LED and LD with QW width of 2.6 nm (10.4 nm) and presented in Fig. 10(a) and Fig. 11(a,b) can to some extent result from presence of the potential fluctuations induced by (i) and (ii).
3.3 Simulations
As it was mentioned earlier, simulations were performed with SiLENS’e 5.4 package [23]. The principle of the SiLENS’e program is based on the determination of potential profiles in the simulated structure by solving the Poisson equation at a given bias voltage. The software incorporates one-dimensional drift diffusion model. In our studies we used default material parameters supplied with SiLENS’e 5.4 package. Figure 12 illustrates the profile of the conduction and valence bands, with wave functions of the ground/excited states along the c-direction in the studied In0.17Ga0.83N/GaN emitters. Upper (lower) panel corresponds to the driving current density of 0.01 A/cm2 (4 kA/cm2). The upper set of dependencies illustrates situation related to LEDs. The lower part gives information corresponding to the laser diodes. Concerning the electron and hole wave functions shape and their overlap (Fig. 13) which determines (together with the population of the levels) the intensity of light emission, one can draw the following conclusions: i) the dominant contribution to the LED luminescence evolves from < e1h1> ground state transition in the device with QW of 2.6 nm width to < e2h2> excited states transition in LED with QW of 10.4 nm, ii) in LED with 5.2 nm QW the lower transition is < e1h2> and the higher one is < e2h1>, iii) for the device with 7.8 nm wide QW the lower transition is < e2h1>and the higher one is < e2h2 > . This identification allows to extract from the experimental data in Fig. 4 the h1-h2 separation for the 7.8 nm well.
Fig. 12. Spatial distribution of the electron and hole wave functions at the driving current density of a) 0.01 A/cm2, b) 4 kA/cm2. Emitters with quantum well width of 2.6 nm, 5.2 nm, 7.8 nm, and 10.4 nm are considered. Ground states and excited states are illustrated. Direction of the polar c-axis in the examined structures is shown at the left, low corner. Simulations were performed with SiLENSe 5.4 package [23].
Fig. 13. Wave functions overlap as a function of driving current density for emitters with different width of the quantum wells. Simulations performed with SiLENS’e 5.4 package [23].
Figure 14 shows the electric field distribution in the active region of the studied emitters. Red curves correspond to LEDs (lower IDs), green curves characterize LDs (higher IDs). One can observe that in agreement with our conclusions drawn from the measurements, large amount of remaining field characterizes devices with lower width of QW. Screening of built-in electric field is much more efficient in wider quantum wells. Emitters with QWs of 7.8 and 10.4 nm show much lower Fint. Lower magnitude of Fint is predicted for LDs (due to higher ID). The differences between LEDs and LDs are reduced with increasing QW width. Results of the simulations illustrated in Fig. 14 show that the remaining unscreened field is located at the interfaces of the QW with barriers. Meanwhile, the light emission is generated in the regions of the highest electron and hole wavefunction overlap (where the field has a minimum value).
Fig. 14. Screened electric field distribution in the studied quantum wells for two values of driving current density 10 A/cm2, 100 A/cm2 and 4 kA/cm2.
Figure 15 illustrates the evolution of the minimum value of the built-in field (close to the well center) with driving current for emitters with different width of QW. The reduction of built-in field is clearly demonstrated. Concerning LEDs for which the driving current density is practically limited to 100 A/cm2 we observe the initially more efficient screening of the field, more pronounced in emitters with narrow QWs. With increasing ID the rate of screening slows down. In the emitters with QW of 10.4 nm width Fint reaches practically negligible field at very low magnitude of driving currents. Concerning LDs, the device with QW of 2.6 nm width demonstrates significant Fint remaining above threshold current. Whereas in the laser with 10.4 nm QW the internal field is negligible. It is important to point out that the results of simulations described above are in the full agreement with the experimental findings.
Fig. 15. Electric field vs. driving current density determined at the minimum Fint value in each well. Insert shows the dependence of at the minimum Fint value as a function of QW width for the driving current density 100 A/cm2.
4. Summary
In the present work we examined screening of the built-in electric field with applied current in the polar LEDs and LDs with In0.17Ga0.83N/GaN QWs of different widths.
In the examined LEDs there are three regions of QW width characterized by qualitatively different behavior of the evolution with driving current of EEL and dEEL/dp. For LED with 2.6 nm QW the blue-shift of EEL and increase of dEEL/dp with ID up to about 40 mA/cm2 are significant. For higher magnitude of ID the corresponding increase of EEL and dEEL/dp slows down. The related screening of built-in field takes place with much weaker tendency. However, large built-in field of about 0.8 MV/cm persists in the well. Radiative recombination involves the electron and hole ground states in the entire range of the applied driving current. For In0.17Ga0.83N/GaN LED with QW width of 10.4 nm, radiative recombination is governed by < e2h2> excited states in the practically entire range of IDs. This observation is in agreement with Ref. [20], where LEDs with QWs of 15 and 25 nm were used.
Screening of QCSE in case of the ground < e1h1> and excited < e2h1> states is very effective below 40-50 mA/cm2 and saturates for higher IDs. Remaining Fint is between 0.5 and 0 MV/cm. Behavior of LDs with narrow and wide QW (width of 2.6 and 10.4 nm) closely correspond to the counterpart LEDs. Radiative recombination processes involve < e1h1> ground states and < e2h2> excited states, correspondingly. In LD with 2.6 nm QW, the remaining built-in electric field, Fint, above threshold current is about 0.8 MV/cm. In LD with QW of 10.4 nm width, Fint is screened entirely in the whole range of IDs.
The identification of the transition levels was done based on numerical simulations. We compared the wave function overlaps of different ground and excited states and their evolution with ID. This allowed us to determine the dominating channels of radiative recombination. We also analyzed the magnitude and spatial distribution of electric field in the quantum wells, showing that for wide QWs the electric field is almost completely screened. Whereas, in case of the narrow QW Fint remains significant in the whole studied current range.
Funding
Narodowe Centrum Nauki (2015/17/B/ST7/04091, 2019/35/D/ST3/03008); Fundacja na rzecz Nauki Polskiej (TEAM-TECH POIR.04.04.00-00-210C/16-00).
Disclosures
The authors declare no conflicts of interest
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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