Modeling and optimization of p-AlGaN
super lattice structure as the p-contact
and transparent layer in AlGaN
UVLEDs
Xinhui Chen, Kuan-Ying Ho, and Yuh-Renn Wu∗
Graduate Institute of Photonics and Optoelectronics and Department of Electrical
Engineering, National Taiwan University, Taipei, 10617, Taiwan
∗ yrwu@ntu.edu.tw
Abstract:
A series of the p-Alx Ga1−x N/Aly Ga1−y N 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
OCIS codes: (230.3670) Light-emitting diodes; (260.7190) Ultraviolet.
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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
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14 Dec 2015 | Vol. 23, No. 25 | DOI:10.1364/OE.23.032367 | OPTICS EXPRESS 32368
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 Al0.23 Ga0.77 N epilayers grown by MOVPE, showing that such a
structure with an average Al composition of 0.62 has the similar optical transparency to the
Al0.62 Ga0.38 N alloy. It suggests that the SL structure could be used as the wide bandgap pcontact 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-Alx Ga1−x N/Aly Ga1−y N 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 Alx Ga1−x N/Aly Ga1−y N 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,
∇(ε ∇V ) = n − p + NA− − ND+ ,
(1)
where V is the band potential while n and p are the free electron and hole carrier density,
+
respectively. N−
A and ND 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],
2 d 1 d ψ (z)
+ Ec,v ψ (z) = E ψ (z),
(2)
∓
2 dz m∗ dz
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© 2015 OSA
Received 11 Aug 2015; revised 8 Nov 2015; accepted 9 Nov 2015; published 8 Dec 2015
14 Dec 2015 | Vol. 23, No. 25 | DOI:10.1364/OE.23.032367 | OPTICS EXPRESS 32369
Fig. 1. Schematically views of (a) a lateral AlGaN LED structure with n pairs of Alx Ga1−x N
/ Aly Ga1−y N SL structure being used as the p-contact layer and (b) the definition of the
effective bandgaps.
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 .
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 Alx Ga1−x N/Aly Ga1−y N 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]:
εxx
= εyy =
εzz
=
Pez
=
aS − aL
,
aL
c13
εxx ,
c33
e33 εzz + e31 (εxx + εyy ),
−2
(3)
(4)
(5)
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
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© 2015 OSA
Received 11 Aug 2015; revised 8 Nov 2015; accepted 9 Nov 2015; published 8 Dec 2015
14 Dec 2015 | Vol. 23, No. 25 | DOI:10.1364/OE.23.032367 | OPTICS EXPRESS 32370
Fig. 2. Band diagram of a 20 pairs AlGaN SL structure with alternating Al0.3 Ga0.7 N QW
and Al0.6 Ga0.4 N QB layers, the thickness of each QW and QB layer is 1 nm.
depending on its alloy composition [31]. The polarization charge at the interface can be decided
by:
ΔP
=
Psp (QW ) + Pez (QW ) − Psp (QB) − Pez (QB),
(6)
As shown by Eq. (6), the polarization difference between Alx Ga1−x N/Aly Ga1−y N 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 Alx Ga1−x N and Aly Ga1−y N
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].
Material
C13 (N/m2 )
C33 (N/m2 )
e31 (C/m2 )
e33 (C/m2 )
Psp (1/cm2 )
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© 2015 OSA
GaN
10.3 × 1011
40.5 × 1011
-0.49
0.73
−2.125 × 1013
AlN
10.8 × 1011
37.5 × 1011
-0.5361
1.5606
−5.625 × 1013
Received 11 Aug 2015; revised 8 Nov 2015; accepted 9 Nov 2015; published 8 Dec 2015
14 Dec 2015 | Vol. 23, No. 25 | DOI:10.1364/OE.23.032367 | OPTICS EXPRESS 32371
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 Al0.3 Ga0.7 N QW and Al0.6 Ga0.4 N 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]
α (ω ) =
π e2 1
N2D (ω )
|a · pi f |2
∑ fnm Erf(Enm − ω ),
2
ω
W
m0 cnr ε0
n,m
(7)
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 kB T (∼ 0.026 eV). In addition, the overlap integral f nm can be expressed
as:
2
vm n (8)
fnm = ∑gv |gc ,
v
where photons will be absorbed once photon energy ω 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
Al0.3 Ga0.7 N/Al0.6 Ga0.4 N SL structure, the cutoff wavelength is 284.8 nm. The other two cutoff
wavelengths of Al0.6 Ga0.4 N/Al0.9 Ga0.1 N SL structure and GaN/Al0.4 Ga0.6 N SL structure are
245.3 nm and 322.5 nm, respectively.
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/Al0.4 Ga0.6 N,
Al0.3 Ga0.7 N/Al0.6 Ga0.4 N and Al0.6 Ga0.4 N/Al0.9 Ga0.1 N 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 Al0.3 Ga0.7 N/Al0.6 Ga0.4 N 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 Al0.3 Ga0.7 N/Al0.6 Ga0.4 N SL). Therefore, for carrier to transport
#247616
© 2015 OSA
Received 11 Aug 2015; revised 8 Nov 2015; accepted 9 Nov 2015; published 8 Dec 2015
14 Dec 2015 | Vol. 23, No. 25 | DOI:10.1364/OE.23.032367 | OPTICS EXPRESS 32372
Fig. 3. The calculated absorption coefficient of GaN / Al0.4 Ga0.6 N, Al0.3 Ga0.7 N /
Al0.6 Ga0.4 N, and Al0.6 Ga0.4 N / Al0.9 Ga0.1 N SL structures as a function of photon wavelength.
Fig. 4. Eg,abs (a) and Eg,cont (b) versus QB thickness of GaN / Al0.4 Ga0.6 N, Al0.3 Ga0.7 N /
Al0.6 Ga0.4 N and Al0.6 Ga0.4 N / Al0.9 Ga0.1 N SL structures with QW thickness kept at 0.5
nm.
smoothly in SL, the thin QB thickness is recommended since the thicker QB makes it more
difficult to form a continuous state.
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.
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© 2015 OSA
Received 11 Aug 2015; revised 8 Nov 2015; accepted 9 Nov 2015; published 8 Dec 2015
14 Dec 2015 | Vol. 23, No. 25 | DOI:10.1364/OE.23.032367 | OPTICS EXPRESS 32373
Fig. 5. Eg,abs (a) and Eg,cont (b) versus QW thickness of GaN / Al0.4 Ga0.6 N, Al0.3 Ga0.7 N
/ Al0.6 Ga0.4 N and Al0.6 Ga0.4 N / Al0.9 Ga0.1 N SL structures with QB thickness kept at 0.5
nm.
Fig. 6. Eg,abs (a) and Eg,cont (b) as a function of composition x and y in Alx Ga1−x N /
Aly Ga1−y N SL structure with 20 periods, each QW and QB layer is 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 Al0.23 Ga0.77 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 Alx Ga1−x N/Aly Ga1−y N 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.
In addition, since the QB thickness is the major factor to affect the continuous state, we
examine Eg,abs and Eg,cont of Alx Ga1−x N/Aly Ga1−y N 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
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© 2015 OSA
Received 11 Aug 2015; revised 8 Nov 2015; accepted 9 Nov 2015; published 8 Dec 2015
14 Dec 2015 | Vol. 23, No. 25 | DOI:10.1364/OE.23.032367 | OPTICS EXPRESS 32374
Fig. 7. Eg,abs (a) and Eg,cont (b) as a function of composition x and y in Alx Ga1−x N /
Aly Ga1−y N 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 Alx Ga1−x N /
Aly Ga1−y N SL structure with 20 periods. QW thickness and QB thickness are 0.5 nm and
1.5 nm, respectively.
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
#247616
© 2015 OSA
Received 11 Aug 2015; revised 8 Nov 2015; accepted 9 Nov 2015; published 8 Dec 2015
14 Dec 2015 | Vol. 23, No. 25 | DOI:10.1364/OE.23.032367 | OPTICS EXPRESS 32375
Fig. 9. Eg,abs (a) and Eg,cont (b) as a function of composition x and y in Alx Ga1−x N /
Aly Ga1−y N SL structure with 20 periods. QW thickness and QB thickness are 1.0 nm and
1.0 nm, respectively.
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.
4.
Conclusion
In summary, we present a complete numerical study on the Alx Ga1−x N/Aly Ga1−y N 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-002-133MY3, MOST 104-2923-E-002-004-MY3, and the financial support from project of aim for top
university (104R890957) by Ministry of Education.
#247616
© 2015 OSA
Received 11 Aug 2015; revised 8 Nov 2015; accepted 9 Nov 2015; published 8 Dec 2015
14 Dec 2015 | Vol. 23, No. 25 | DOI:10.1364/OE.23.032367 | OPTICS EXPRESS 32376