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A series of the p-AlxGa1−xN/AlyGa1−yN super lattice (SL) structures has been examined as the p-contact and transparent layer for different ultra-violet light-emitting-diodes (UVLEDs) with a self-consistent 1D Poisson and Schrödinger solver. The recommended solution for designing the suitable SL structure in UVLEDs with different UV wavelength has been found. By calculating the absorption coefficient of the SL structure, we confirmed that the proper SL structure has the enormous potential of being the transparent p-contact layer in AlGaN UVLED, especially in UV-C band (< 280 nm). The suitable emission wavelengths of UVLEDs ranging from 219 nm to 353 nm are found. The influences of different well and barrier thickness on SL structures are discussed as well.
© 2015 Optical Society of America
1. Introduction
Recent years, AlGaN-based UV light-emitting-diodes (UVLEDs) have attracted extensive attention because of their special applications in industry and medicine [1–8], such as disinfection with a deep UV light source of wavelength between 260 nm and 280 nm. The wavelength of 365nm is suitable in lithography [9–11]. Morever, the UV-B radiation will lead to the formation of anti-cancerogenic substances which is good for plant growth [12, 13]. Thus, it can be expected that UVLEDs with higher efficiency could be applied in many applications.
However, currently, the external quantum efficiency (EQE) in UVLEDs is extremely low, especially in UV-C band [1,3,11]. The highest EQE ever reported only exceeds 10% [14]. One of the reasons resulting in such low EQE is due to the low internal quantum efficiency (IQE). Some earlier studies focused on improving the quality of AlGaN layer by reducing the threading dislocation density and IQE above 60% was achieved in 280 nm LEDs [15–18]. But another important issue is the low light extraction efficiency (LEE) which is due to the large absorption coefficient (> 105 cm−1) of the top p-GaN layer as the current spreading and contact layer [19]. In addition, despite the increased contact resistance, Ryu et. al. [20] demonstrated that for the vertical AlGaN UVLED without p-GaN contact layer, 45% and 72% LEE can be achieved for TM and TE modes, respectively. However, when a 25nm p-GaN layer is added, LEE reduces to 7% and 10% for TM and TE modes, respectively. The results show that although there are still 55% to 28% loss due to internal reflection even with textured surface, the issue of 38% to 62% absorption loss from p-GaN layers needs to be improved first. Therefore, the critical factor for improving the efficiency in UVLEDs is to find a new material or structure with high optical transparency as well as good conductivity to replace the p-GaN layer [1, 21].
To obtain high LEE, various methods or ideas were proposed in these years [22]. Kim et. al. [21] proposed a new method using electrical breakdown to make the AlN-based transparent conductive electrode being direct ohmic contact to the p-AlGaN layer by forming conductive filaments. This provides a p-contact with high transmittance and good conductivity in UV-C region. And in 2006, Taniyasu et. al. [23] proposed the fabrication of the AlN p-i-n LED consisting of three-periods of p-type doped AlN/AlGaN super lattice (SL) in p-type region with Mg doping. Furthermore, Allerman et. al. [24] presented a structure of Mg-doped, short-period SL consisting of AlN and Al0.23Ga0.77N epilayers grown by MOVPE, showing that such a structure with an average Al composition of 0.62 has the similar optical transparency to the Al0.62Ga0.38N alloy. It suggests that the SL structure could be used as the wide bandgap p-contact layer in AlGaN UVLEDs. However, the information about different types of AlGaN SL structure is insufficient, making it inconvenient to decide the suitable AlGaN SL structure for different emitting wavelengths. To address this issue, we focus on simulating a series of heavily doped p-AlxGa1−xN/AlyGa1−yN SL structures with different Al compositions and different barrier/well (QB/QW) thickness and try to find the optimized condition for p-type transparent contact layer in the UV region.
2. Method
To analyze the AlxGa1−xN/AlyGa1−yN SL structures, a self-consistent 1D Poisson and Schrödinger solver [25–27] is used. To obtain the potential of SL structure under zero bias, Poisson equation is solved according the equation below,
where V is the band potential while n and p are the free electron and hole carrier density, respectively. and are the activated doping density of acceptor and donor, respectively. To obtain the electron state energies Ee, hole state energies Eh and the associated wave functions ψ, Schrödinger equation is solved self consistently after solving the Poisson equation. The Schrödinger equation is shown below [28], where z is the growth direction of the SL structure while Ec and Ev present the potential of the conduction band and the valence band, respectively. After obtaining the converged eigenvalues and eigenfunctions, we can get the localized states and continuous states over the whole SL structure. And the absorption bandgap Eg,abs (corresponding to the cutoff wavelength) of a given SL structure can be defined as the energy difference between the electron localized state and the hole localized state as shown in Fig. 1(b), which leads to the absorption bandedge. The energy difference between the electron continuous resonant state and the hole continuous resonant state is defined as Eg,cont as shown in Fig. 1(b) and will be discussed as well. The best condition is that only continuous states formed in the SL structures or close to Eg,abs.
Fig. 1 Schematically views of (a) a lateral AlGaN LED structure with n pairs of AlxGa1−xN / AlyGa1−yN SL structure being used as the p-contact layer and (b) the definition of the effective bandgaps.
To describe the AlGaN SL structure, Fig. 1(a) illustrates the UVLED structure with a SL structure being used as the p-contact layer. The SL structure consists of n (n = 20) pairs of alternating AlxGa1−xN/AlyGa1−yN layers (0 < x, y < 1), each layer thickness of both QW and QB varies from 0.5 nm to 3 nm. Each layer is heavily p-doped with Mg concentration of 1×1020 cm−3. The activation energy of each layer depends on Al composition and the values we used in this work varies from 180 meV to 630 meV linearly as the Al composition increases from 0% to 100% [29]. Our simulations show that for super lattice more than 20 pairs, the result is more converged. The boundary effects of potential bending induced by polarization are minimized for n > 20 pairs. Besides, we assume that all SL structures are grown on the AlN substrate or grown on the AlN buffer layer on sapphire substrate where the AlN layer is fully relaxed. When the AlGaN layer is under strain when the substrate or buffer layer is chosen, it will induced piezoelectric polarization. The equations used for strain calculation are listed below [30]:
where aS and aL are the lattice constants of substrate and epi-layer, respectively. c13 and c33 are elastic constants while e33 and e31 are piezoelectric constants. They depend on Al content in the epi-layer and the detail values of GaN and AlN we used in this work are listed in Table 1. Except the piezoelectric polarization, the spontaneous polarization is also quite different between AlN and GaN. All the piezoelectric coefficients for AlGaN alloy are using linear interpolation depending on its alloy composition [31]. The polarization charge at the interface can be decided by:As shown by Eq. (6), the polarization difference between AlxGa1−xN/AlyGa1−yN layer will lead to the potential band bending. Although the choice of different substrates will lead to different strain and polarization charge as shown by Eqs. (3)–(5), the polarization induced charge decided by Eq. (6) is almost the same because the polarization of both AlxGa1−xN and AlyGa1−yN layers will change at the same time due to different substrates. The changes in Pez(QW) and Pez(QB) will cancel each other and the result will not change too much.
Table 1. Elastic constants and piezoelectric constants in GaN and AlN [31].
3. Results and discussion
As mentioned earlier, to measure the absorption and transportation characteristics of a given SL structure as shown in Fig. 1(b), we defined the energy difference between localized states as absorption bandgap Eg,abs, which leads to the absorption bandedge. The continuous bandgap, Eg,cont, is defined as the continuous state that carriers begin to resonate tunneling through the SL, where the subband is formed. For instance, Fig. 2 shows the calculated band diagram of a SL structure with 20 pairs of Al0.3Ga0.7N QW and Al0.6Ga0.4N QB, the thickness of each layer is 1 nm. Not only the continuous states are shown in this figure with Eg,cont of 4.52 eV, but also the lowest electron and heavy hole states are shown to be localized in several QWs. These localized states will limit carrier transport. They also lead to photon absorption, where the absorption coefficient will be affected greatly. Here we calculated the absorption coefficient of SL structures according to Eq. (7) [30]
where N2D is the 2D reduced density of states while Erf is the Error function since the inhomogeneous Gaussian broadening is considered in calculating the absorption coefficient. The deviation is about one kBT (∼ 0.026 eV). In addition, the overlap integral fnm can be expressed as: where photons will be absorbed once photon energy ħω is larger than Enm and there is a good overlap between electron states and associated hole states. As shown in Fig. 3, the calculated absorption coefficients of 3 cases of SL structures versus photon wavelength are shown. We can see that the absorption coefficient will be sharply increased as the wavelength decreases once the photon wavelength is less than the cutoff value in all three cases. For the case of Al0.3Ga0.7N/Al0.6Ga0.4N SL structure, the cutoff wavelength is 284.8 nm. The other two cutoff wavelengths of Al0.6Ga0.4N/Al0.9Ga0.1N SL structure and GaN/Al0.4Ga0.6N SL structure are 245.3 nm and 322.5 nm, respectively.Fig. 2 Band diagram of a 20 pairs AlGaN SL structure with alternating Al0.3Ga0.7N QW and Al0.6Ga0.4N QB layers, the thickness of each QW and QB layer is 1 nm.
Fig. 3 The calculated absorption coefficient of GaN / Al0.4Ga0.6N, Al0.3Ga0.7N / Al0.6Ga0.4N, and Al0.6Ga0.4N / Al0.9Ga0.1N SL structures as a function of photon wavelength.
If the effective bandgaps are all formed by continuous states where the miniband is formed, carriers will not see any barrier when transporting through the SL. Therefore, it would be the best condition for device applications. However, due to the large effective mass of hole, the localized states are easy to be formed in the valence band. Therefore, we needed to study the impact of QW and QB thickness on Eg,cont and Eg,abs in the SL structures, where Eg,abs is expressed as the cutoff wavelength as well.
To form a super lattice, the thickness of QB plays the key role. Therefore, we first investigate the influence of QB thickness. As shown in Fig. 4, a comparison among the GaN/Al0.4Ga0.6N, Al0.3Ga0.7N/Al0.6Ga0.4N and Al0.6Ga0.4N/Al0.9Ga0.1N SL structures with different QB thickness is made. The QW thickness is kept at 0.5 nm. We can find that the Eg,abs changes slightly as the QB changes. Because Eg,abs is more related to QW thickness. On the other hand, the Eg,cont is affected significantly by the QB thickness. The thicker QB makes the resonant tunneling more difficult. Therefore, the energy difference between Eg,cont and Eg,abs increases as the QB thickness increases as shown in Fig. 4(b). For the case of Al0.3Ga0.7N/Al0.6Ga0.4N SL structure, Eg,cont increases from 4.42 eV to 4.76 eV and Eg,abs increases from 4.40 eV to 4.53 eV when the QB thickness increases from 0.5 nm to 3 nm. This means that for the thinner QB in SL structures, the energy difference between Eg,cont and Eg,abs is smaller (0.02 eV for 0.5 nm and 0.36 eV for 3 nm in Al0.3Ga0.7N/Al0.6Ga0.4N SL). Therefore, for carrier to transport smoothly in SL, the thin QB thickness is recommended since the thicker QB makes it more difficult to form a continuous state.
Fig. 4 Eg,abs (a) and Eg,cont (b) versus QB thickness of GaN / Al0.4Ga0.6N, Al0.3Ga0.7N / Al0.6Ga0.4N and Al0.6Ga0.4N / Al0.9Ga0.1N SL structures with QW thickness kept at 0.5 nm.
Then we make a comparison among these cases with different QW thickness as shown in Fig. 5. These two subfigures demonstrate Eg,cont and Eg,abs of these SL structure as a function of QW thickness which ranges from 0.5 nm to 3 nm while the QB thickness is kept at 0.5 nm. As shown in Fig. 5(a), the absorption bandgap Eg,abs decreases due to a weaker quantum confinement effect when the QW thickness increases. Comparing with the QB thickness, the QW thickness seems to be a more important factor to affect Eg,abs. Therefore, to achieve a higher Eg,abs for making a transparent layer, the case with a thinner QW is recommended. Moreover, from Fig. 5(b), we can figure out the difference between Eg,cont and Eg,abs is small because QB thickness is a dominating factor rather than QW thickness as we discussed above.
Fig. 5 Eg,abs (a) and Eg,cont (b) versus QW thickness of GaN / Al0.4Ga0.6N, Al0.3Ga0.7N / Al0.6Ga0.4N and Al0.6Ga0.4N / Al0.9Ga0.1N SL structures with QB thickness kept at 0.5 nm.
If we compare our result with Allerman et. al. in Ref. [24], the calculated absorption bandgap of 0.5nm AlN/ 0.5nm Al0.23Ga0.77 super lattice is around 257nm, which is quite close to the experimental result [24] for the same structure.
Following that, we modeled a series of AlxGa1−xN/AlyGa1−yN structures with each layer thickness of 0.5 nm. The absorption bandgap Eg,abs and continuous bandgap Eg,cont with different Al compositions in QB and QW are shown in Figs. 6(a) and 6(b), respectively. The diagonal white line in these two sub figures means the Al compositions in both QW and QB are the same, which are not the SL structures. From Fig. 6(a), to achieve a same cutoff wavelength which corresponds to Eg,abs, there are several choices with different combinations of QW and QB. Although these choices result in the same cutoff wavelength, Eg,cont of these cases are different, thus we can choose the case with minimum Eg,cont from Fig. 6(b) as the best condition.
Fig. 6 Eg,abs (a) and Eg,cont (b) as a function of composition x and y in AlxGa1−xN / AlyGa1−yN SL structure with 20 periods, each QW and QB layer is 0.5 nm.
In addition, since the QB thickness is the major factor to affect the continuous state, we examine Eg,abs and Eg,cont of AlxGa1−xN/AlyGa1−yN SL structure with large QB thickness as shown in Figs. 7 and 8. Figures 7 and 8 are the SL structures with QB thickness of 1.0 nm and 1.5 nm, respectively. The QW thicknesses in both cases are kept at 0.5 nm. Comparing with these two figures, we can obviously see those cases with 1.5 nm QB thickness in Fig. 8 have a relatively high Eg,cont. Therefore, carriers are tend to fall into localized states in such structures. Besides, we can find that the cutoff wavelength depends on not only the Al composition but also the layer thickness. For example, if we set GaN as the QW layer to get the cutoff wavelength of 270 nm, the Al compositions in QB need to be 0.98, 0.86, and 0.78 with the QB thickness of 0.5 nm, 1.0 nm, and 1.5 nm, respectively. And if growing AlN/GaN SL structure is much easier to avoid random alloy leakage current [25, 32], we can find the limiting wavelength of using AlN/GaN SL structure in Figs. 7 and 8. In addition, since the transparent AlGaN layer usually results in a poor ohmic contact [33], which leads to the contact loss, we can use a thin p-GaN as the QW and the top contact layer in AlGaN SL. Therefore, not only the absorption problem but also the contact problem could be solved. Figure 9 shows the maps for SL structures with QB and QW thickness both to be 1.0 nm because it might much easier to fabricate. As mentioned in Fig. 5, the increase of QW thickness will reduce the quantized effect so that Eg,abs decreases 0.2 eV to 0.3 eV. We will need higher Al composition to reach the same cutoff wavelength. From Fig. 6 to Fig. 9, the total range of cutoff wavelength in AlGaN SL structures is from 219 nm to 353 nm. If we want to use a SL by pure AlN/GaN, the limiting wavelength is 269 nm, which is still good for UV-C wavelength. Therefore, the AlGaN SL structures have the potential of being the top p-contact layer in AlGaN UVLEDs which nearly covers the whole UV wavelength region. By improving the contact properties, the current spreading and hole injection efficiency should be improved. Therefore, these structures would be beneficial UVLED or even UV laser diode since hole injection would be quite critical for laser diode to lase.
Fig. 7 Eg,abs (a) and Eg,cont (b) as a function of composition x and y in AlxGa1−xN / AlyGa1−yN SL structure with 20 periods. QW thickness and QB thickness are 0.5 nm and 1 nm, respectively.
Fig. 8 Eg,abs (a) and Eg,cont (b) as a function of composition x and y in AlxGa1−xN / AlyGa1−yN SL structure with 20 periods. QW thickness and QB thickness are 0.5 nm and 1.5 nm, respectively.
Fig. 9 Eg,abs (a) and Eg,cont (b) as a function of composition x and y in AlxGa1−xN / AlyGa1−yN SL structure with 20 periods. QW thickness and QB thickness are 1.0 nm and 1.0 nm, respectively.
4. Conclusion
In summary, we present a complete numerical study on the AlxGa1−xN/AlyGa1−yN SL structures for using as the top p-contact transparent layer in AlGaN UVLEDs. The energy difference between Eg,cont and Eg,abs will be reduced by reducing the QB thickness. In addition, the absorption bandgap Eg,abs will be greatly affected by QW thickness. Therefore, the SL structures with thinner QW and QB are recommended in device application. The suggested combinations of alloy compositions in making the SL for different cutoff wavelength are calculated in this paper. The cutoff wavelengths of AlGaN SL structures discussed above are ranging from 219 nm to 353 nm, which covers nearly the whole UV region. Our results provide a guideline in designing the super lattice structure in different UV ranges.
Acknowledgments
The authors would like to thank the Ministry of Science and Technology in Taiwan for financial support, under Grant Nos. NSC-102-2221-E-002-194-MY3 and MOST 103-2221-E-002-133-MY3, MOST 104-2923-E-002-004-MY3, and the financial support from project of aim for top university ( 104R890957) by Ministry of Education.
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