Growth and Optical Properties of GaN-Based Non- and Semipolar LEDs

Michael Kneissl; Jens Rass; Lukas Schade; Ulrich T. Schwarz

doi:10.1007/978-94-007-5863-6_5

III-Nitride Based Light Emitting Diodes and Applications pp 83-119 | Cite as

Growth and Optical Properties of GaN-Based Non- and Semipolar LEDs

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Michael Kneissl
Jens Rass
Lukas Schade
Ulrich T. Schwarz

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Part of the Topics in Applied Physics book series (TAP, volume 126)

Abstract

Light emitting diodes (LEDs) based on the (In,Al,Ga)N material system offer the possibility to generate light in the entire visible wavelength range, extending into the ultraviolet and the infrared regions. The widely tunable bandgap makes nitride based LEDs suitable devices for applications such as general energy efficient lighting, water purification, UV curing and medical applications. Conventionally, all group III-nitride based devices have been grown epitaxially on the polar (0001) c-plane of the wurtzite crystal structure. This leads to the formation of strong polarization fields pointing along the [0001] c-axis. These fields reduce the device efficiency through the quantum confined Stark effect (QCSE) and also cause other detrimental effects like wavelength-shifts and efficiency droop with increasing current densities. By growing InAlGaN heterostructures on non- and semipolar growth planes, these fields can be significantly reduced or even eliminated. In addition, due to the reduction of in-plane symmetry, a number of new heterostructure design options emerge to control the optoelectronic properties of non- and semipolar light emitters. Among these are the occurrence of anisotropic strain with the consequence of an anisotropic valence band structure and the possibility to generate strongly polarized light emission from LEDs. In this chapter we will discuss the origin of the polarization fields in III-nitrides and their control by growth on non- and semipolar crystal planes. Different approaches for the homo- and heteroepitaxial growth of non- and semipolar nitride heterostructures as well as structural properties, such as surface morphologies and indium incorporation efficiencies will be discussed. The influence of the crystal plane and the indium content on the valence band structure and the polarization state of the emitted light will be presented and the state-of-the-art device characteristics of non- and semipolar LEDs will be reviewed.

Keywords

Quantum Well External Quantum Efficiency Polarization Switching Indium Content Thread Dislocation Density

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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5.1 Introduction

The development of smooth (0001) GaN films on c-plane sapphire [1] and the activation of p-dopants in GaN [2] led very quickly to the realization of high brightness InGaN LEDs on c-plane sapphire substrates [3, 4]. Already at the end of the last century blue and green LEDs with tens and hundreds of milli-Watt output power levels were demonstrated. Today, blue InGaN LEDs boast record external quantum efficiencies exceeding 80 % and the emission wavelength of c-plane InGaN quantum well (QW) LEDs has been pushed into the yellow and even red spectral range. Although the performance characteristics of c-plane LEDs seem excellent, the strong polarization fields at InGaN/GaN heterointerfaces can lead to a significant deterioration of the device performance. This polarization field is suppressed or reduced in LEDs with InGaN/GaN heterointerfaces of nonpolar or semipolar orientation, respectively. Triggered by the first demonstration of nonpolar GaN quantum wells grown on LiAlO₂ by Waltereit and colleagues in 2000 [5], impressive advancements in the field of non- and semipolar nitride semiconductors and devices have been achieved. Today, a large variety of heterostructures free of polarization fields exhibiting exceptional optical properties have been demonstrated, and the fundamental understanding of polar, semipolar, and nonpolar nitrides has made significant leaps forward. This chapter is intended to provide an overview on the epitaxial growth and optical properties of group III-nitride LEDs on non- and semipolar surface orientations [6]. After introducing the physical origins of piezoelectric and spontaneous polarization effects in group-III nitrides, different approaches for the heteroepitaxial growth of low defect density non- and semipolar (Al,In)GaN layers and (Al,In)GaN/GaN heterointerfaces are presented, followed by a discussion of the effect of surface orientation on the indium incorporation efficiency in InGaN layers and quantum wells. In the third section the polarized light emission characteristics and the optical properties of non- and semipolar InGaN QWs are discussed and finally the performance characteristics of non- and semipolar LEDs are presented including the effects on droop, wavelength shift and external quantum efficiencies of state-of-the-art devices.

5.2 Piezoelectric and Spontaneous Polarization in Group-III Nitrides

The stable crystal structure of the group-III nitrides AlN, GaN, and InN and their ternary compounds AlGaN, InGaN, and AlInN is the hexagonal wurtzite structure. The high electronegativity of the nitrogen atom creates a strong dipole in the metal–nitrogen bond which is the origin of the strong polar character of the group-III nitrides. In their real crystal structure the bond lengths and bond angles deviate slightly from the ideal tetrahedral configuration of the wurtzite structure, without loosing the hexagonal crystal symmetry C_6v. This is the point group of highest symmetry without a center of inversion [7]. Because of this distinction between “up” and “down”, the crystal has two polar surfaces, one terminated with metal atoms Al, Ga, or In, the other N-face. By convention, the [0001] direction points from a metal atom to the nearest-neighbor nitrogen atom in the direction of highest symmetry, which is also the optical axis of the uniaxial crystal, or the c-axis.

Because of the missing inversion symmetry, the material is pyroelectric and consequently exhibits spontaneous and piezoelectric polarization [8]. This leads to sheet charge layers at surfaces and interfaces. Surface charges screen most of the fields in thick layers or bulk material. However, at internal interfaces the spontaneous and piezoelectric polarization causes strong band bending and can induce two-dimensional electron gases (2DEG) of high charge carrier density. These are the basic mechanisms enabling GaN-based high electron mobility transistors (HEMT) [9]. In InGaN quantum wells (QW) of optoelectronic devices, the polarization field has a strong influence on radiative recombination. In standard c-plane LEDs or laser structures, the active region consists of several few nanometer thick InGaN QWs between GaN or InGaN barriers. Because of the increasing in-plane lattice constants of InGaN with indium content, the QW experiences biaxial compressive strain. The thickness of the QWs must remain below the critical thickness to suppress the formation of new dislocations. In this regime of pseudomorphic growth, the in-plane strain ε _xx for the QW is given by the difference of the a-lattice constant a of the QW and a ₀ of the barrier:

$$ \varepsilon_{xx} = \frac{a-a_0}{a_0}. $$

(5.1)

Stress and strain are related through the elastic tensor with elastic constants c _ij. For the polar QW with biaxial strain the stress component σ ₁ in the basal plane can be calculated by

$$ \sigma_1 = \varepsilon_{xx} \biggl( c_{11}+c_{12}-2 \frac {c_{13}^2}{c_{33}} \biggr). $$

(5.2)

Strain and piezoelectric polarization are related through the piezoelectric coefficients d _ij. For the hexagonal crystal of C_6v symmetry the piezoelectric polarization P _i in i direction is given by

$$ P_i = \sum_j d_{ij} \sigma_{j}, \quad i=1,2,3, \ j=1,\ldots,6. $$

(5.3)

For the polar QW the piezoelectric polarization in the direction z perpendicular to the QW resulting from biaxial in-plane strain ε _xx is then given by [8]

$$ P_z = 2 d_{31} \varepsilon_{xx} \biggl(c_{11}+c_{12}-2\frac {c_{13}^2}{c_{33}} \biggr). $$

(5.4)

The resulting internal field in an InGaN QW is of the order of 0.5 MV/cm to 3 MV/cm for a standard LED structure. This large internal field causes a strong bending of the band edge in the active region. It severely affects recombination rates, wavelength of emission, and transport.

Radiative recombination is proportional to the absolute square of the overlap integral of electron and hole wave functions. The field inside the QW causes a spatial separation of the electron and hole wave function, resulting in a spatial indirect transition which reduces the radiative recombination rate. This shifts the balance from radiative to non-radiative recombination, which is less affected by the internal field, and therefore reduces the internal quantum efficiency of the LED.

The wavelength of emission is shifted due to the so-called quantum confined Stark effect (QCSE): Band bending in the active region shifts the transition between bound states of the QW to longer wavelengths. Because the internal fields are partially screened with increasing carrier density, the wavelength of a polar InGaN LED is shifting towards shorter wavelength with increasing current density. This effect is most pronounced for LEDs emitting in the green spectral region where the strain and consequently the field inside the QW is largest. Carrier transport is affected because the polarization field causes additional barriers in the active region which affect forward voltage and current injection efficiency [10, 11].

A way to avoid these limitations is to use different lattice orientations than the polar c-plane. For planes perpendicular to the c-plane the spontaneous and piezoelectric field perpendicular to the QW is zero because of crystal symmetry. These planes are therefore called nonpolar planes. In other planes with an inclination between polar and nonpolar plane the polarization fields can be expected to be reduced. Prominent polar, semipolar and nonpolar planes which are being used for LED growth are shown in Fig. 5.1. Each plane is associated with a specific angle θ between the axis perpendicular to the QW and the c-axis of GaN. This angle ranges from θ=0^∘ for the polar QW to θ=90^∘ for the nonpolar case.

Fig. 5.1
Orientations of c-plane, semipolar $(11\bar{2}2)$- and $(20\bar{2}1)$-planes and nonpolar $(10\bar{1}0)$-plane (*shaded polygons*) with inclination angle θ to the c-plane [12] (Color figure online)

A simple projection of the piezoelectric field pointing in c-direction as described by Eq. (5.3) on the respective plane will not give correct results for the internal field. Instead, one has to first calculate the strain for the QW under the assumption of pseudomorphic growth in the respective orientation. From the strain components the piezoelectric polarization is then calculated with the piezoelectric coefficients. A semipolar QW has non-vanishing strain components ε _xx, ε _yy, ε _zz, and ε _xz. In a strain model developed by Park and Chuang, the strain components as function of the inclination θ are given by

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(5.5)

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(5.6)

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(5.7)

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(5.8)

where $\epsilon_{xx}^{(0)} = (a_{s} - a_{e})/a_{e}$ and $\epsilon_{zz}^{(0)} = (c_{s} - c_{e})/c_{e}$ and a _s,c _s,a _e,c _e are the lattice constants of the substrate [13]. The fact that the shear strain ε _xz is non-vanishing in a semipolar QW has major consequences for the band structure and polarization of the optical emission, as will be discussed in Sect. 5.4. The dependency of the different components of the strain tensor on θ is shown in Fig. 5.2.

Fig. 5.2
Strain tensor components as function of crystal angle for a fully strained In_0.25Ga_0.75N layer grown on free-standing GaN substrate. The *dashed lines* mark the semipolar $(11\bar{2}2)$- and the $(20\bar{2}1)$-planes [12]

The polarization discontinuity ΔP _z′ between QW and barrier is then given through the strain tensor and piezoelectric coefficients d _ij:

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(5.9)

Here, z′ points in growth direction and perpendicular to the QW. $P_{sp}^{ (QW)}$ and $P_{sp}^{ (b)}$ are the spontaneous polarization in the quantum well and in the barrier, respectively. Equation (5.9) holds for all angles θ. The resulting polarization discontinuity is plotted in Fig. 5.3 together with the wave function overlap for a $3 \,\rm nm$ wide In_0.25Ga_0.75N QW. The polarization discontinuity can be implemented as sheet charge layers at the interfaces between QWs and barriers in a drift-diffusion model. This allows the calculation of the internal field as well as carrier transport as function of external applied bias voltage within the accuracy of the drift-diffusion model. An estimation for the internal field can be given by assuming appropriate boundary conditions and employing Gauss’ law $\vec{\nabla} \cdot(\varepsilon\varepsilon_{0} \vec {E} + \vec{P}) = 0$, resulting in [12]:

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(5.10)

Here, ε ₀ is the permittivity of vacuum, ε ^(b) and ε ^(QW) are the static dielectric constants for the barrier layers and the quantum well, respectively.

Fig. 5.3
Polarization discontinuity ΔP _z′ along growth direction and wave function overlap as function of crystal angle for a $3\,\rm nm$ wide In_0.25Ga_0.75N quantum well. The *dashed lines* mark the semipolar $(11\bar{2}2)$- and the $(20\bar{2}1)$-planes [12]

For an inclination of about θ=50^∘ the different components of the piezoelectric field compensate each other, resulting in a zero polarization discontinuity. For some time the existence of this zero transition of the polarization field was heavily discussed, as it depends critically on the parameters used in the strain model on the theoretical side and on the strain in a real QW when the internal field is determined experimentally [14, 15, 16]. However, currently the parameters determining strain and piezoelectric field are converging and there is a general agreement on the existence of the zero crossing for the internal field. Because this zero crossing is close to the angle corresponding to the $(11\bar{2}2)$ lattice plane, this plane, which also shows stable growth, is preferred for semipolar LEDs. However, considering also optical properties and transport, other planes may be better candidates for semipolar LEDs and laser diodes. We will later see that the effect of polarization switching is most prominent for the $(11\bar{2}2)$ orientation, which is relevant for semipolar optoelectronic devices emitting in the green spectral region.

5.3 Growth of GaN and InGaN on Different Non- and Semipolar Surface Orientations

The synthesis of GaN layers with non- or semipolar surface orientations can be achieved by different means. The most straightforward approach is the growth of single crystal GaN boules, from which GaN wafer slabs can be cut out at basically any angle and therefore crystal orientation of choice. Another advantage of this approach is that the defect densities in the semi- and nonpolar bulk GaN substrates are similar to the defect densities of the original GaN boule. Since GaN boules can be realized with very low defect densities the resulting semi- and nonpolar bulk GaN provide an excellent growth substrate with very low defect densities. This type of approach has already been successfully demonstrated by a number of research groups [17, 18, 19, 20, 21]. In most cases the bulk GaN crystal boules have been grown by hydride vapor phase epitaxy (HVPE) or ammonothermal growth along the (0001) direction. In order to obtain GaN wafers with non- or semipolar surface orientations the GaN boules have to be cut perpendicular to the c-plane surface for nonpolar orientations or at the appropriate off-axis angle corresponding to the respective semipolar surface plane. The challenge with this approach is, that in order to obtain larger non- and semipolar substrate sizes, the c-plane GaN boules have to be large in height as well as in diameter. This is still a significant challenge, since the GaN growth rates, even with HVPE, are relatively low and the built-up of strain and parasitic deposits during growth limits the maximum heights that can be achieved without fracturing the boule. In addition the fabrication costs for bulk GaN boules are relatively high, which also translates into high costs for the semi- and nonpolar bulk GaN substrates. Therefore the heteroepitaxial growth of non- and semipolar GaN layers on readily available sapphire, silicon, SiC and other substrates is still of great interest and importance. All of the heteroepitaxial substrates are available with large diameters (e.g. 6″ is already standard for sapphire substrates and 8″ and 12″ sapphire are under development) and the costs of these substrate are low to moderate. In the past decade a large number of substrate materials and surface orientations have been explored in order to realize heteroepitaxial GaN layers with different non- and semipolar surface orientations. A detailed discussion of the different approaches is given in the following paragraph.

5.3.1 Heteroepitaxial Growth of Non- and Semipolar GaN on Sapphire, Silicon, Spinel, and LiAlO₂ Substrates

Growth of non- and semipolar GaN layers has been demonstrated on sapphire, silicon, SiC, spinel, as well as LiAlO₂ substrates and on a number of different substrate orientations. Initially most of the experiments have focused on heteroepitaxial growth on planar substrates [5, 22, 23, 24, 25, 26, 27]. In these instances the orientation of the grown GaN layers is strongly correlated with the crystal orientation of the host substrate, although in some cases several semipolar orientations can be obtained for the same growth substrates (e.g. growth on $(10\overline{1}0)$ m-plane sapphire can yield $(11\overline {2}2)$ and $(10\overline{1}3)$ GaN layers). An overview of the different heteroepitaxial substrates and the orientations of the resulting non- and semipolar GaN layers is provided in Fig. 5.4. Although the figure does not attempt to provide a complete list, all of the main approaches are included newline.

Fig. 5.4
Overview showing the relationship between different substrate orientations and materials and the orientation of the resulting GaN layer. The examples include heteroepitaxial growth of GaN layers on planar substrates as well as growth of non- and semipolar GaN on patterned sapphire and silicon substrates

In addition the heteroepitaxial growth of non- and semipolar GaN has also been demonstrated on patterned host substrates. Growth of GaN on stripe-patterned substrates allows access to different surface orientations depending on the angle of the exposed growth facet and simultaneously is a method to reduce the defect density in the overgrown GaN layers. Figure 5.5 shows schematically the heteroepitaxial growth on planar host substrate and on a stripe patterned sapphire substrate. In order to prepare the stripe pattern several micron wide mesa stripes oriented along the a-direction are dry-etched into the r-plane sapphire substrate. To prevent GaN growth on the $(11\overline{2}3)$ n-plane mesa terraces a 100 nm thin SiO₂ layer is deposited on top of the mesa. The subsequent GaN growth is nucleated at the inclined etched mesa facet, which is close to parallel to the sapphire and GaN c-planes. The GaN growth from these facets continues along the c-direction and a planar $(10\overline{1}1)$ GaN surface is formed when the adjacent GaN growth stripes coalesce. This method has been pioneered by Tadatomo et al. [28, 29] and Sawaki et al. [30, 31] and has since been demonstrated for a number of different patterned sapphire as well as silicon substrates as can be seen from the genealogy displayed in Fig. 5.4. The patterned substrate approach provides access to a number of GaN surface orientation, e.g. by adjusting the angle of the mesa facets or by utilizing different crystal orientations. Using the patterned sapphire substrate approach m-plane GaN layers on patterned a-plane sapphire, a-plane GaN on m-plane or c-plane sapphire, $(10\overline{1}1)$ GaN on n-plane sapphire, and $(20\overline{2}1)$ and $(10\overline{1}3)$ GaN on r-plane sapphire have been demonstrated. Similarly $(10\overline {1}1)$ GaN layers have been realized on patterned (001) silicon substrates and $(11\overline{2}2)$ GaN on patterned (311) silicon substrates. Most recently the group of Krost et al. have shown the growth of $(1\overline{1}06)$ oriented GaN films on (112) Si as well as $(1\overline{1}05)$ and $(1\overline{1}04)$ GaN layers on (113) Si substrates [32]. Again, this list is certainly not complete and the number of possible orientations is expected to grow as more and more substrate materials, stripe patterns, and orientations are being explored.

Fig. 5.5
Schematic illustration of (a) heteroepitaxial growth of semipolar $(11\overline{2}2)$ GaN on planar $(10\overline{1}0)$ m-plane sapphire substrate, (b) defect reduction by epitaxial lateral overgrowth (ELO) for $(11\overline{2}0)$ GaN layers on $(10\overline{1}2)$ r-plane sapphire, (c) $(10\overline{1}1)$ GaN facet on 3-dimensional stripes on c-plane sapphire and (d) heteroepitaxial growth of semipolar $(11\overline{2}2)$ GaN on a stripe patterned $(10\overline{1}2)$ r-plane sapphire substrate

5.3.2 Surface Morphologies and Strutural Defects of Non- and Semipolar GaN Films

The control of the surface morphology and defect densities of heteroepitaxially grown semipolar and nonpolar GaN layers on planar substrates is very challenging. Wernicke et al. have investigated $(11\overline{2}0)$ GaN on r-plane sapphire, $(10\overline{1}0)$ GaN on LiAlO₂, and $(11\overline{2}2)$ GaN on $(10\overline{1}0)$ sapphire substrates [34] and found strongly varying surface morphologies. For example, one problem with the growth of a-plane GaN was the creation of surface pits that are formed by $(10\overline {1}0)$, $(10\overline{1}1)$ and $(000\overline{1})$ facets, whereas semipolar $(11\overline{2}2)$ GaN layers exhibited a strong tendency to roughen and show arrowhead like features as depicted in Fig. 5.6(a) [33, 35].

Distinct surface morphologies develop even for non- and semipolar GaN layers grown on low defect density bulk GaN substrates as shown in Fig. 5.6(b). The scanning white light interferometry (SWLI) images of homoepitaxially grown m-plane, $(10\overline{1}1)$, $(10\overline{1}2)$, and $(11\overline{2}2)$ GaN layers show very distinct short range surface features for each surface orientation. While the $(11\overline{2}2)$ surface seems relatively smooth, the m-plane and the $(10\overline{1}1)$ exhibit very distinct microscopic features, which are partly due to faceting. The surface morphologies are affected by the growth conditions, in particular growth temperature and reactor pressure. Figure 5.7 shows a series of Normarski contrast microscope images of semipolar $(10\overline {1}1)$, $(10\overline{1}2)$, and $(11\overline{2}2)$ GaN layers grown homoepitaxially with different MOVPE reactor pressures on bulk GaN substrates. While under optimized growth conditions the $(10\overline {1}2)$ and $(11\overline{2}2)$ GaN layers showed a relatively smooth surface morphology, the $(10\overline{1}0)$ and $(10\overline{1}1)$ GaN surfaces exhibited macroscopic pyramids, which originated from screw dislocations [36].

Fig. 5.7
Normarski contrast microscope images of semipolar $(10\overline{1}1)$, $(10\overline{1}2)$, and $(11\overline{2}2)$ GaN layers grown homoepitaxially with different reactor pressures on bulk GaN [34]. The growth temperature was kept constant at 980 ^∘C

Even though the surface morphologies of non- and semipolar GaN layers can be significantly improved by optimization of the growth parameters, the reduction of the defect densities, especially for heteroepitaxially grown layers is much more challenging. Despite refined growth processes, the edge dislocation densities of heteroepitaxially grown non- and semi-polar GaN layers range typically from 10⁹ to 10¹⁰ cm⁻² and the basal plane stacking faults (BSF) density is about 10⁶ cm⁻¹. This poses serious limitations to the device performance, since extended defects act as non-radiative recombination centers and are thus detrimental to the internal quantum efficiencies of light emitting diodes. In order to reduce the dislocation densities a number of different techniques have been explored. The most intensively explored is lateral epitaxial overgrowth (ELOG) [37]. Originally the ELOG method has been applied to reduce the defect density in planar semi- and nonpolar GaN layers. For example, thin silicon dioxide stripes were patterned on nonpolar $(11\overline{2}0)$ GaN layers on sapphire which enabled a selective re-growth of a-plane GaN in the mask openings [38]. By aligning the 100 nm thick SiO₂ stripe mask parallel to the $[10\overline{1}0]$ direction, TEM investigations and other studies have shown that the BSF and threading dislocation densities can be reduced by several orders of magnitudes in the laterally overgrown GaN areas [39, 40, 41]. The improved structural quality also translates into much improved optical properties of the nonpolar GaN films. For example, cathodoluminescence (CL) investigations of ELOG GaN films show sharp donor bound excitonic emission from the defect-reduced laterally overgrown areas whereas without defect reduction the CL is dominated by BSF luminescence [40]. An alternative approach to defect reduction is the growth on patterned substrates, as already described in Sect. 5.3.1. Since the semi- and nonpolar layers are selectively nucleated on c-plane like facets very few basal plane stacking faults are generated in the grown GaN layers and the threading dislocations are mostly concentrated in the coalesced regions [28, 29]. Depending on the semipolar orientation of the overgrown GaN layer and the patterned sapphire substrate, the threading dislocation densities and BSF densities can vary significantly. Table 5.1 summarizes some of the recent results. As can be seen from Table 5.1, very low CL dark spot densities in the 10⁶ cm⁻² range can be achieved. These values are close to numbers obtained from growth of non- and semipolar layers on bulk GaN substrates, indicating that heteroepitaxial growth has the potential to provide low defect density templates for high efficiency non- and semipolar light emitters.

Table 5.1

Cathodoluminescence (CL) dark spot density of different semipolar GaN layers grown on patterned sapphire substrates

GaN orientation	Patterned sapphire orientation	Dark spot density [cm⁻²]	Reference
$(11\overline{2}2)$	$(10\overline{1}2)$	2⋅10⁸	[28]
$(10\overline{1}1)$	$(11\overline{2}3)$	1.2⋅10⁸	[28]
$(20\overline{2}1)$	$(22\overline{4}3)$	5.6⋅10⁶	[29]
$(10\overline{1}0)$	$(11\overline{2}0)$	not specified	[42]

Table 5.2

Overview over performance of nonpolar and semipolar LEDs at 20 mA dc current

Growth plane	Substrate	Wavelength [nm]	Power [mW]	EQE [%]	Reference
$(11\overline{2}2)$	GaN	425	1.76	3.0	[94]
$(11\overline{2}2)$	GaN	525	1.91	4.1	[94]
$(11\overline{2}2)$	GaN	585	0.54	1.3	[94]
$(11\overline{2}2)$	GaN	516	5.0	10.5	[95]
$(11\overline{2}2)$	GaN	562.7	5.9 (pulsed)	13.4	[96]
$(11\overline{2}2)$	Patterned Si	439			[93]
$(10\overline{1}1)$	Patterned Si	419			[93]
$(10\overline{11})$	GaN	455	31.1	54.7	[97]
$(10\overline{11})$	GaN	444	16.21 (pulsed)	29	[98]
$(20\overline{2}1)$	GaN	516.3	9.2	19.1	[99]
$(20\overline{2}1)$	GaN	552.3	5.2	11.6	[99]
$(11\overline{2}0)$	PLOG-sapphire	460	7.5		[90]
$(11\overline{2}0)$	HVPE-LEO	413	0.24		[91]
$(10\overline{1}0)$	GaN	435	1.79	3.1	[100]
$(10\overline{1}0)$	GaN	407	23.7	38.9	[69]
$(10\overline{1}0)$	GaN	457	0.24		[101]
$(10\overline{1}0)$	GaN	452	0.6	1.09	[102]
$(10\overline{1}0)$	GaN	402	28 (pulsed)	45.4	[103]
$(20\overline{21})$	GaN	423	30.6	52	[70]
$(10\overline{11})$	MgAl₂O₄	439	0.01	0.02	[92]
$(10\overline{13})$	MgAl₂O₄	439	0.19	0.35	[92]

Recently Ravash et al. have shown that high silicon doping [32] can lead to a significant reduction of threading dislocation density and BSF density in $(1\overline{1}06)$ and $(1\overline{1}04)$ GaN layers grown on (112) and (113) Si substrates, respectively. Similarly the insertion of low-temperature (LT) AlN interlayers [43] has also led to a significant reduction of threading dislocation and BSF density in $(1\overline{1}06)$ and $(1\overline {1}04)$ GaN. In both cases the reduction of BSFs is most likely due to the generation of a- and c-type misfit dislocations at the LT-AlN/GaN interface, which are preferential to the generation of new stacking faults, especially for semipolar GaN with a low-inclination angle.

A third approach to realize InGaN light emitters on semipolar GaN surfaces is the selective growth of three-dimensional (3D) triangular-shaped GaN structures on stripe patterned c-plane GaN/sapphire substrates [44]. A schematic of this approach is shown in Fig. 5.5(c). Depending on the growth conditions, the resulting triangular-shaped GaN stripes can either exhibit $\{1\overline{1}01\}$ or $\{11\overline{2}2\}$ facets. One advantage of this approach is that it can be realized on large area and low cost (0001) sapphire substrates. Since the growth originates from the c-plane, the semipolar surfaces are mostly free of stacking faults and exhibit fairly low threading dislocation densities. The downside is that the 3-dimensional growth makes the device fabrication and electrical contacting more difficult. In addition indium incorporation efficiency depends strongly on the position on the pyramid leading to large scale fluctuations of the emission wavelength.

5.3.3 Indium Incorporation in InGaN Layers and Quantum Wells on Different Semipolar and Nonpolar Surfaces

For the realization of high efficiency blue, green, and yellow LEDs indium incorporation efficiency in InGaN layers and quantum wells is very critical. Theoretical studies based on first principles calculations by Northrup et al. [45] have already shown that the indium incorporation efficiency on $(11\overline{2}2)$ surfaces is expected to be higher than for $(10\overline{1}0)$ surfaces. For the $(11\overline{2}2)$ and $(10\overline{1}0)$ surfaces this was explained by the strain-induced repulsive interaction between the relatively large indium atoms at the surface. Recently a systematic experimental study by Wernicke et al. [46] has shown that the indium incorporation in InGaN multiple quantum well structures varies indeed significantly for the different semi- and nonpolar surfaces. A fundamental aspect of these experiments was to compare the growth of InGaN QWs on low defect density bulk GaN substrates with different surface orientations, in particular $(10\overline{1}0)$, $(10\overline{1}1)$, $(10\overline{1}2)$, $(11\overline{2}2)$, and $(20\overline{2}1)$ GaN surfaces for a series of growth temperatures. The experiments showed that the indium incorporation efficiency in InGaN QWs was consistently highest on the $(10\overline{1}1)$ surfaces and very similar to (0001) GaN surfaces for growth on $(11\overline {2}2)$ and $(20\overline{2}1)$ oriented surfaces. In contrast, InGaN QWs grown on the $(10\overline{1}2)$ and $(10\overline{1}0)$ surfaces showed much lower indium mole fractions than QWs grown on the conventional (0001) GaN surfaces. Figure 5.8 summarizes these results for a number of different non- and semipolar orientations as well as different growth temperatures. These results indicate that growth on $(11\overline{2}2)$ and $(20\overline{2}1)$ oriented GaN may be preferable, especially for long-wavelength light emitters that require high In mole fraction InGaN QWs. Overall these investigations demonstrates that the growth on semipolar GaN constitutes a very interesting approach for high efficiency green, yellow, and even longer wavelength light emitting diodes.

Fig. 5.8
Emission wavelength and indium incorporation efficiency of InGaN quantum well structures grown on c-plane and different semipolar and nonpolar GaN substrates [46]

5.4 Polarization of the Light Emission from Non- and Semipolar InGaN QWs

In contrast to LEDs with c-plane QWs which emit unpolarized light in the direction perpendicular to the surface, a planar LED structure with QWs of semipolar or nonpolar growth direction emits light which is partially polarized. This polarization is a direct consequence of the lower symmetry of the system. While a polar QW is symmetric within the QW plane, a semipolar or nonpolar QW has two distinct directions, parallel and perpendicular to the projection of the c-axis of the crystal onto the plane of the QW. Standard notation is to introduce a Cartesian coordinate system (x′,y′,z′) with z′ perpendicular to the QW, x′ and y′ within the QW plane; x′ and y′ are parallel and perpendicular to the projection of the c-axis onto the QW plane, respectively. x′ is also called c′. The degree of polarization is then defined as

$$ P=\frac{I_{y^{\prime}} - I_{x^{\prime}}}{I_{y^{\prime}} + I_{x^{\prime}}} $$

(5.11)

and determined from intensities I _y′ and I _x′ measured using linear polarizers oriented in y′- and x′-direction. P=±1 corresponds to fully linear polarized light, P=0 to unpolarized light. Positive and negative P stands for a dominant polarization perpendicular (y′) and parallel (x′) to the projection of the c-axis onto the QW plane, respectively. One has to be aware that this definition of the degree of polarization does not distinguish between partially linear polarized light and elliptically or circular polarized light. The latter may arise in InGaN LEDs due to birefringence or reflection from tilted surfaces. The full state of polarization in that case can be described with Stokes parameters.

Emission of polarized light was observed in electroluminescence [47, 48] and photoluminescence [49]. For nonpolar QWs in m-direction polarization ratios as high as 0.91 [48, 50] have been observed by electroluminescence at room temperature. Light emitted from nonpolar QWs is linearly polarized, perpendicular to the c-axis. Semipolar QWs generally emit light with a lower degree of polarization. Ueda et al. observed that the direction of the predominant polarization changes from perpendicular to the c-axis to parallel to the c-axis with increasing indium content for QWs of $(11\overline{2}2)$ orientation [51]. This phenomenon was termed “polarization switching” and was reproduced in semipolar InGaN QWs of different lattice orientations [49].

Generally, the degree of polarization and the dominant direction of the linearly polarized light depend both on the structure of the LED, which is determined during growth, and on measurement conditions. During growth, QW inclination, composition (In or Al content), thickness, and strain are fixed. Upon observation, temperature and excitation density are free parameters. The first set of parameters determines the band structure. The symmetry of the band structure and consequently the selection rules for intraband transitions are the physical origin of the emission of polarized light. The second set of parameters determines the occupation of the subbands, such selecting those states which contribute to light emission. The situation is complicated by the inhomogeneities of the ternary InGaN or AlGaN QWs. Composition, thickness, and strain vary within the QW plane. As discussed in the previous section, semipolar QWs tend to form micro-facets of different lattice orientations with different physical properties. Dislocations—in particular stacking faults intersecting nonpolar QWs—modify strain and are a competing source of polarized light. Last but not least, a precise measurement of the degree of polarization is complex. The experimental setup may either scramble polarization (e.g. with a microscope objective of high numerical aperture), leading to the observation of a lower degree of polarization, or artificially polarize the emitted light by reflection from a tilted surface of an optical component (e.g. a beam splitter). Still, the main effect causing polarized light emission is the band structure. Therefore in the following the band structure of polar, nonpolar and semipolar InGaN QWs will be discussed, proceeding from the simplest to the most complex situation.

The crystal and band structure of bulk GaN around the Γ-point (k _x′=k _y′=k _z′=0) are shown in Fig. 5.9. The spin degenerate heavy-hole (HH), light-hole (LH), and crystal-field split-off (CH) bands form the valence band. They are composed from wave functions of p-character with angular momentum l=1. The angular momentum eigenfunctions of heavy-hole and light-hole bands are $\frac{1}{\sqrt{2}} | X - i Y\rangle$ and $-\frac {1}{\sqrt{2}} |X + i Y\rangle$ at the Γ-point. For the crystal-field split-off band the eigenfunction is |Z〉. Here, we neglect the spin degree of freedom. A full description of the 6×6 Hamiltonian in k⋅p approximation can be found e.g. in Refs. [13, 52, 53]. The eigenfunction of the conduction band has s-character with angular momentum l=0 and is spherical symmetric. The angular momentum eigenfunction for all bands are shown as insets in Fig. 5.9. As the intensity of an optical transition is proportional to the transition matrix element, the degree of polarization for an individual subband m can be written in the following way [54]:

$$ P_{m}=\frac{|M_{y^{\prime}}^m|^2 - |M_{x^{\prime}}^m|^2}{|M_{y^{\prime}}^m|^2 + |M_{x^{\prime}}^m|^2}. $$

(5.12)

The transitions matrix elements $M_{x^{\prime}}^{m}$ and $M_{y^{\prime}}^{m}$ between conduction and valence band states are calculated in dipole approximation from the wavefunctions of the individual subband as calculated in k⋅p approximation. Technical details of these calculations are discussed e.g. in [53, 54, 55].

Fig. 5.9
*Left*: Orientation of the polar (0001) lattice plane with respect to the GaN lattice structure. *Right*: Band structure of a bulk GaN. The *insets* show the angular momentum eigenfunctions of the individual bands. The *arrow* marks one possible optical transition [12]

For light emitted in c-direction, the polarization vector is perpendicular to the c-axis of the crystal. The transition matrix element is large and independent of the in-plane direction for transitions between conduction band and both heavy-hole and light-hole bands. Therefore light emitted from both bands in c-direction is unpolarized. This can be seen from the shape of the angular momentum eigenfunctions as shown in Fig. 5.9. The crystal-field split-off band does not contribute to emission in c-direction, because its angular momentum eigenfunction has neither |X〉 nor |Y〉 component. The situation changes for light emitted in a direction perpendicular to the c-axis. From the orientation of the angular momentum eigenfunctions it follows that photons stemming from the transition between conduction band and heavy-hole or light-hole bands are polarized perpendicular to the c-axis, while the transition from conduction band to crystal-field split-off band is polarized parallel to the c-axis. The energy splitting between heavy-hole and light-hole band is smaller than k _B T at room temperature, therefore the thermal occupation of both states is similar. In unstrained bulk GaN, the crystal-field split-off band is separated by about 22 meV from the band edge, therefore contributing to a lesser extend to light emission. Therefore light emitted perpendicular to the c-axis in a bulk GaN crystal is partial linearly polarized. This is also the reason for the higher gain of the TE mode when compared to the TM mode in an in-plane (Al,In)GaN laser diode.

The bound states in an InGaN QW result in subbands of the band structure. Anti-crossing between these bands results in a modification of the transition matrix elements. For a c-plane QW, however, the in-plane symmetry is conserved. Therefore the polarization characteristics are those of the bulk GaN crystal, i.e. unpolarized light is emitted perpendicular to the QW. Light propagating along the QW plane remains linearly polarized, resulting in a larger TE gain.

In addition, the separation of the crystal-field split-off band is increased in an InGaN QW by strain and reaches several k _B T. Therefore the discussion of the electroluminescence and photoluminescence can be limited to heavy hole and light hole bands.

5.4.1 Light Emission from Nonpolar InGaN QWs

This symmetry is broken in a nonpolar QW. Even in an unstrained thick InGaN or GaN layer, light emitted in a direction perpendicular to the c-axis is polarized because of the symmetry of the crystal structure, as discussed above. In addition to this effect, the band structure is strongly modified in a nonpolar QW by anisotropic strain. This anisotropic strain is a consequence of the different lattice constants in the direction parallel and perpendicular to the c-axis. It modifies the band structure through the deformation potential, which is described in k⋅p approximation by six parameters D ₁ to D ₆. The resulting band structure for a 3 nm thick nonpolar In_0.2Ga_0.8N QW at a carrier density of 1×10¹⁸ cm⁻³ is shown in Fig. 5.10. The bands are labeled with capital letters A, B for the valence bands and a number m for the respective subband corresponding to the bound states of the QW. For the nonpolar QW the eigenstates are fully polarized at the Γ-point. For the A and B bands the angular momentum eigenfunctions are approximately |Y′〉=|Y〉, |X′〉=|Z〉 respectively.

Fig. 5.10
Topmost valence bands of a 3 nm thick nonpolar In_0.2Ga_0.8N QW at a carrier density of 1×10¹⁸ cm⁻³ [53]

In contrast to the polar case (cf. Fig. 5.9), the band structure in a nonpolar QW is different in $k_{x}^{\prime}$ and $k_{y}^{\prime}$ directions, resulting in an anisotropy of the effective mass and density of states [56]. The energy distance between A1 and B1 band in a nonpolar QW is considerably larger than the splitting between heavy-hole and light-hole band in a polar QW. The band structure in Fig. 5.10 was calculated with standard parameters and strain model, resulting in an A1–B1 splitting of approximately k _B T. Experiments usually report a wider splitting, which is probably caused by a higher strain in the QW. The large energy difference results in a small occupation of the B1 band and consequently in a high degree of polarization even at room temperature.

For a typical QW thickness of a few nanometers, the confinement energy is similar to the splitting between A and B subbands. This results in anti-crossing of the B1 and A2 bands close to the Γ-point, as shown in Fig. 5.10. Transitions from conduction band to the A2 band are forbidden by symmetry in the nonpolar QW. However, the A2 band contributes to the density of states. Also, the subbands exchange their dominant polarization at these anti-crossings. This means that transitions from the conduction band to the B1 band are x′-polarized at the Γ-point. However, for $k_{x}^{\prime}>200~\mathrm{cm}^{-1}$ and for $k_{y}^{\prime}>600~\mathrm{cm}^{-1}$ the emitted photon will be y′-polarized.

The strain model used in the k⋅p Hamiltonian is symmetric with respect to a tilt of the QW towards m- or a-direction. So from the theoretical point of view no difference between a-plane and m-plane nonpolar QWs would be expected. However, the microscopic growth conditions are different on the individual lattice plane, as was discussed above. Therefore a-plane and m-plane QWs grown in a single growth run may be different not only in terms of indium incorporation and thickness but also with respect to their microstructure and anisotropic strain within the QW, modifying both band structure and optical properties.

The measured photoluminescence spectra of a nonpolar $(10\overline {1}0)$ QW sample are shown in Fig. 5.11. The spectra were taken with a linear polarizer, rotated by 5^∘ between each spectrum. The emitted light is strongly polarized in y′-direction, i.e. perpendicular to the c-axis. This is the emission from the transition from conduction band to the A1 valence band. With the polarizer rotated by 90^∘, the emission of the B1 band can be measured. It is much weaker and blue shifted by 78 meV. The spectrally integrated degree of polarization is P=0.68. This high value at room temperature is in quantitative agreement with the large energetic spacing of the A1 and B1 band [57].

5.4.2 Light Emission from Semipolar InGaN QWs

For semipolar orientation, the eigenstates of each of the valence bands are composed of all three angular momentum eigenfunctions |Y〉, |X〉, and |Z〉 even at the Γ-point. Therefore, partially polarized light is emitted from the transition of the conduction band to the uppermost valence band already at low temperature. Still, one of the angular momentum eigenfunctions dominates at the Γ-point. This predominant component of the hole wave function is indicated for the semipolar planes $(11\overline{2}2)$ and $(20\overline{2}1)$ in Fig. 5.12. In the example of 3 nm thick In_0.35Ga_0.65N QWs, the polarization of the transition to the uppermost valence band changes from parallel to the projection of the c-axis for the $(11\overline {2}2)$ plane to perpendicular polarization for the $(20\overline{2}1)$ plane. The band ordering depends on the inclination of the lattice plane, and a crossing of the A1 and B1 bands occurs between θ=58^∘ and θ=75^∘. It is worth noting that the band structure of the $(20\overline{2}1)$ plane is very similar to that of the nonpolar plane, indicating little change of the band structure between θ=75^∘ and θ=90^∘.

Fig. 5.12
*Top left*: Orientation of the $(11\overline{2}2)$ lattice plane (*light blue rectangle*) with respect to the GaN lattice structure. Indicated are the crystal coordinate system x, y, z, and the growth coordinate system x′, y′, z′. The angle between the surface normal and the crystal c-axis is θ=58^∘. *Top right*: Orientation of the $(20\overline{2}1)$ crystal plane; this image has to be compared to the one on the *top left*. *Below* are the valence band structures for a 3 nm In_0.35Ga_0.65N QW (n=10¹⁸ cm⁻³) of the respective orientation. The angular momentum of the in-plane component of the hole wave function at the Γ-point is indicated for the two topmost valence bands [12]

For the $(11\overline{2}2)$ band structure the energy spacing of the uppermost bands A1 and B1 is relatively small, and anti-crossing occurs close to the Γ-point. Both effects reduce the degree of polarization. The small energy shift results in a similar thermal occupation of both bands. The anti-crossing indicates a strong mixing of the angular momentum eigenfunctions.

Ueda et al. first observed a dependency of the polarization on the indium content of the semipolar $(11\overline{2}2)$ In_xGa_1−xN QW [51]. For an indium content x≤0.22 the polarization degree was positive, for x≥0.3 it was negative (see Fig. 5.13). Also the energy difference between the two uppermost valence bands changed accordingly. They termed this behavior “polarization switching” and interpreted it in terms of band ordering. This behavior was confirmed by electroluminescence measurements for $(11\overline{2}2)$ LEDs [58] as well as for other lattice planes [49].

Fig. 5.13
Polarization resolved electroluminescence spectra of a $(11\overline{2}2)$ blue and red LED with indium content of 17 % and 48 %, respectively. The *solid blue* and *broken red line* correspond to y′ and x′ polarization, respectively. The LED was driven at 0.5 mA [51]

The mechanism causing polarization switching is illustrated by the band structure for $(11\overline{2}2)$ In_xGa_1−xN QW with increasing indium content x=0.15, 0.25 and 0.35 in Fig. 5.14. As the indium mole fraction increases, the point of anti-crossing moves from k _y′ direction to k _x′ direction, changing the symmetry at the Γ-point and shifting the dominant contribution to the hole wave function from |Y′〉 to |X′〉 [59]. The polarization P _m of the A1 and B1 subbands is plotted in Fig. 5.14 below the respective band structure. Going from k _x′ to k _y′, the polarization of the A1 subband changes from P _m=+1 to P _m=−1. The k-value where the optical polarization becomes zero is a function of indium content. For an indium content of about 20–25 %, polarization P _m is zero at the Γ-point. This corresponds to the situation where polarization switches from y′ to x′. Looking at Fig. 5.14 it becomes obvious that this is a smooth transition, which also depends on the occupation of states in k-space and therefore on carrier density. Quantum confinement has only slight effect on ordering and cannot explain the observed polarization switching [60].

Fig. 5.14
Band structure and polarization of the two topmost valence bands A1 (*continuous line*) and B1 (*dashed line*) for an $(11\overline{2}2)$ QW (n=10¹⁸ cm⁻³). The indium content is 15 %, 25 %, and 35 %, as indicated. The polarization P _m corresponding to the A1 and B1 subbands is plotted below the respective band structure plots. Higher order valence bands are drawn for reasons of clarity

The main cause for the switching of the uppermost valence bands is the anisotropic strain in the semipolar InGaN QW. Ueda et al. pointed out that a high value of the deformation potential D ₆ for InN is necessary to explain the observed polarization switching. From his measurements he derived a value D ₆=−8.8 eV [51]. To calculate the band structure shown in Fig. 5.14 we used the value D ₆=−7.1 eV [59] and the strain model as proposed by Park and Chuang [13]. Other models for the strain in semipolar InGaN QWs have been developed [61, 62], but lead to similar results regarding strain and band structure. The large value of D ₆ is however in contradiction to first-principles calculations which predict D ₆=−3.95 eV for GaN and D ₆=−3.02 eV for InN [63]. Using the standard strain models, these lower values of D ₆ would not be able to explain the observed polarization switching. Yan et al. proposed that a partial strain relaxation would cause polarization switching of a semipolar InGaN QW even for these low values of D ₆. The morphology of semipolar InGaN QWs supports this idea of an anisotropic strain relaxation [58]. Yet, XRD and TEM measurements demonstrate pseudomorphic growth of an $(11\overline{2}2)$ InGaN QW between GaN barriers [62].

Polarization switching is not a phenomenon of the individual $(11\overline{2}2)$ lattice plane, but rather a general property of InGaN QWs which can be explained for all lattice orientations and indium compositions in a unified picture [49]. This can be seen from the plot of polarization for transitions to the two uppermost valence bands, as shown in Fig. 5.15. For this figure the band structures for 3.5 nm wide QWs with indium contents between x=0.05 and x=0.35 have been calculated in k⋅p approximation. The family of curves shows the degree of polarization for the A1 subband. For semipolar QW orientation θ<30^∘, the polarization is negative, i.e. the polarization is parallel to the projection of the c-axis on the QW, the x′-direction. For large angles θ>70^∘ up to nonpolar case θ=90^∘ the emission is y′ polarized, perpendicular to the c-axis. For intermediate planes, the direction of polarization switches from negative to positive. The switching point therefore depends on the indium content. The yellow crosses mark the critical angle θ _c where polarization switching occurs for a given indium concentration. The maximum critical angle is θ _c,max=69.4^∘ for InN and the chosen set of parameters [49]. For angles smaller than θ _c,max the degree of polarization P _m decreases with increasing indium content, for angles larger than θ _c,max it increases.

Fig. 5.15
Degree of polarization P _m for transitions from the conduction band to the A1 band at the Γ-point. The indium content was varied between 5 % and 35 % in steps of 5 %. QW thickness was 3.5 nm and carrier density was n=10¹⁸ cm⁻³. The numbered markers (1) to (3) represent measured polarizations at T=10 K. (1): photoluminescence from violet light emitting QW structures; (2): electroluminescence from violet $(20\overline{2}1)$ LED; (3): photoluminescence from blue-green light emitting QW structures. The *crosses mark* the critical angle θ _c for the different indium contents [49]

Electroluminescence and photoluminescence measurements of LED structures on different polar, semipolar and nonpolar orientations are indicated as markers in Fig. 5.15. Also the polarization switching as observed by Ueda et al. [51] and the decreasing P _m with increasing indium content observed by Masui et al. for $(11\overline{2}2)$ LEDs [58] are in agreement with this unified picture of polarization switching. However, the values measured for the $(20\overline{2}1)$ orientation by several groups [49, 58, 64] are consistently lower than predicted by Fig. 5.15. Still, the increase of the polarization ratio with increasing indium content was confirmed by experiments for the $(11\overline{2}2)$ plane [58].

Zhao et al. studied the polarization ratio of semipolar LEDs in the blue and green wavelength region grown on the $(20\overline{2}1)$- and $(20\overline{21})$-facet. Both of these planes are tilted by ±15^∘ from the m-plane and differ in their surface configuration [65]. The experimental work showed that the LEDs on $(20\overline{21})$ have a higher degree of polarization and a larger band splitting than the $(20\overline{2}1)$-devices. This was attributed to indium interdiffusion in $(20\overline{2}1)$ QWs and consequently a modification of the valence sub band structure.

As pointed out above, the polarization is not only important at the Γ-point, but has to be considered in k-space, as band mixing occurs in semipolar QWs in the valence band close to the Γ-point. Therefore the degree of polarization is plotted in Fig. 5.16 for the A1 and B1 band of a 3.5 nm thick In_0.3Ga_0.7N QW as function of substrate inclination θ and hole momentum k _x′ and k _y′. Horizontal and vertical lines (red and blue shading, color online) indicate the sign of P _m. In the red shaded area the polarization is perpendicular to the c-axis. For nonpolar orientation (θ=90^∘) the range of positive P _m extends from the Γ-point both in k _x′ and k _y′ direction. The dotted line and white shading indicates the unpolarized case P _m=0. The polar QW with θ=0^∘ is unpolarized. The dotted line crosses the k=0 axis again between the black vertical lines marking the lattice planes of $(11\overline{2}2)$ and $(10\overline{1}1)$ orientation. This is the signature of polarization switching of the $(11\overline{2}2)$ QW at the indium composition of about x=0.20–0.25. The polarization map of the B1 band is complementary to that of the A1 band in the center of the Brillouin zone. At higher k-values mixing with higher bands modifies the polarization of the B1 band.

Fig. 5.16
Degree of polarization P _m for transitions from the conduction band to the A1 (*left*) and the B1 (*right*) valence bands as function of substrate inclination θ in $k_{x}^{\prime}$–$k_{y}^{\prime}$ space for a 3.5 nm wide $\rm In_{0.3}Ga_{0.7}N$ QW. The *dotted line* represents unpolarized emission (P _m=0). The *vertical lines* a to d mark the lattice planes $(10\overline{1}2)$, $(11\overline{2}2)$, $(10\overline{1}1)$, and $(20\overline{2}1)$ [49] (Color figure online)

The map of P _m shows clearly that polarization switching is not an abrupt phenomenon, but rather a transition of a QW through a range of low degree of polarization as function of either inclination θ or indium content. The map also tells that high degrees of polarization can only be expected far from regions of polarization switching. This explains why large values of P _m are observed for nonpolar QWs. The experimental fact that $(20\overline{2}1)$ QWs up to now do not show the expected high polarization ratios may either suggest some strain relaxation mechanisms or faceting during the growth of these QWs, or that the deformation potential parameters are still not correct.

Masui et al. observed a decrease of polarization with current injection in a nonpolar LED [66]. They suggested that the filling of states according to Fermi statistics is responsible for this reduction of P _m. With increasing carrier density the quasi-Fermi level comes close to the top of the valence band, resulting in a similar occupation probability of the A1 and B1 bands. Because of the complementary polarization of both bands, the ratio of polarization decreases. Another effect is that states further away from the Γ-point are occupied, which also decreases the overall polarization ratio (see Fig. 5.16). It should be noted that Kyono et al. did not observe a decreasing polarization ratio with increasing current for a semipolar QW [64]. However, for a nonpolar LED structure the decrease of the polarization ratio with increasing carrier density was confirmed by Schade et al. [57] and could be explained quantitatively by state filling using the Fermi-Dirac distribution.

5.5 Performance Characteristics of Non- and Semipolar InGaN QW Light Emitting Diodes

5.5.1 Wavelength Shift

Light emitting diodes based on the (Al,In,Ga)N material system show a strong dependency of the emission wavelength λ on the carrier concentration n in the quantum well (QW) active region and hence on the injected current I. This behaviour is undesired since this means a dependency of spectral characteristic on the light output power, which is unacceptable for many applications such as lighting, sensing and consumer electronics systems. There are four main effects that influence the emission wavelength.

Due to ohmic heating at high operation currents, the bandgap E _g decreases and hence the wavelength is red-shifted to longer values. This effect is present in all semiconductor materials and cannot be avoided completely. Thermal management, heat sinking and the reduction of the current density by increasing the device area can reduce the effect. The dependency of the bandgap on the temperature T is phenomenologically described by the Varshni model:
$$ E_g (T ) = E_g (T=0 ) - \frac{\alpha T^2 }{T+ \beta} $$

(5.13)
where α and β are the Varshni parameters (e.g. [67]).
At high injection currents I the increased carrier density n leads to the so called band-filling where lower energy states are filled and the emission moves to higher excited states in the quantum well. The consequence is a blue-shift in emission wavelength. In order to avoid this the volume of the active region can be increased, thus reducing the carrier density n. This can be done either by an increase in the number of quantum wells or by an increase of the thickness and volume of each quantum well. The reduction of the carrier density also reduces the droop (see Sect. 5.5.2).
If the active region exhibits fluctuations in the thickness of the quantum well or the indium content, the emission spectra broaden. Especially the indium fluctuations are an important technological challenge and the strength of the fluctuation increases with the total amount of indium in the active region, making the growth of green and yellow emitters more challenging. Upon carrier injection the so-called band-tail states are filled first since they have the lowest band gap energy. When the injection current increases, emission from material regions with lower indium content and hence shorter emission wavelength occurs, shifting the emission wavelength to the blue.
If polarization fields are present in the active region, the emission wavelength is originally red-shifted by the QCSE (see Sect. 5.2). This effect is reduced in semipolar emitters and vanishes for nonpolar emitters. If carriers are injected into the active region then the polarization charges at the interfaces of the quantum well are partially screened by the free carriers, compensating the initial red-shift. The consequence is a strong blue shift of the emission wavelength which is stronger in c-plane devices than in semipolar or nonpolar devices. This effect therefore dominates the emission characteristics in c-plane devices while it is not present in nonpolar devices and reduced in semipolar devices.

All of the above mentioned effects occur at the same time. The design of the active region, the crystal orientation and the material quality determine which effect is the dominating part. If the crystal quality is low and the indium fluctuations are large, the filling of band-tail states dominates.

In Fig 5.17 a spectrum of an m-plane MQW-LED in cw-mode is shown and only a very small shift is observed. The blueshift in pulsed mode is compared to an LED with the same epitaxial structure on (0001) c-plane. At low current densities j the initial shift of the m-plane LED is stronger than for the c-plane LED which is attributed to filling of states caused by indium fluctuations. When j is increased, the shift of the m-plane LED is smaller than that of the c-plane LED, since here no polarization fields occur and hence the only cause is band filling, while strong polarization fields in the c-plane LED are partially screened, causing a stronger blue shift.

Similar results have been found by Kuokstis et al. [68]. Schmidt et al. reported a very small wavelength shift of less than 1 nm for a 407 nm m-plane LED on bulk GaN in the range of 1 mA to 20 mA [69]. LEDs on $(20\overline{21})$ GaN that have been reported by Zhao et al. also show a very small wavelength shift, caused by the strongly reduced polarization fields [70].

5.5.2 Droop

The term “droop” describes the fact that the external quantum efficiency EQE which is defined as the ratio of extracted photons divided by the injected carriers is not a constant, but is influenced by the carrier concentration n in the active region and therefore the injected current I. The easiest way to describe this phenomenon is to treat the recombination mechanism by a third order polynomial model, the ABC-model. Since the different contributions to the overall recombination rate are proportional to n (non-radiative Shockley Read Hall SRH recombination, e.g. at defects), to n ² (radiative recombination) and to n ³ (Auger-like recombination), the overall efficiency can be described as

$$ \mathit{EQE}= \frac{r_{\mathrm{rad}}}{r_{\mathrm{nrad}}+r_{\mathrm{rad}}+r_{\mathrm{Aug}}} =\frac{Bn^2}{An+Bn^2+Cn^3} $$

(5.14)

A, B and C are the corresponding recombination parameters. The consequence of this droop model is that the maximum EQE is found at a carrier concentration $n_{\max}=\sqrt{A/C}$. Beyond this density, the efficiency decreases, making it favorable to drive the LED at low currents. There has been a strong debate regarding the actual cause for the droop [71], since theory predicts a C-coefficient that is so low for nitrides, that droop shouldn’t occur at normal carrier concentrations. The fact that many groups observed strong droop was explained by higher than expected C-coefficients [72], electron leakage [73], non-constant ABC-coefficients [74], density-activated defect recombination (DADR) [75] or indirect Auger recombination which was mediated by electron-phonon coupling and alloy scattering [76].

In order to reduce the unfavorable droop, the carrier concentration in the active region of the LED should be small, and as close as possible to n _max. This however contradicts the demand for high-power devices and requires an increase in the device area, which in turn increases the device costs. In semipolar and nonpolar LEDs the droop in principle should be smaller than in c-plane devices due to the absence of polarization fields. Since the QCSE is reduced or eliminated, the radiative recombination rate and the B-coefficient are much larger, increasing the device efficiency.

Recent studies on the droop give hints for fundamental advantages of QWs with reduced fields [77, 78]. According to them, Auger recombination has the same linear connection with the absolute squared overlap integral of the wave functions in the conduction and the valence bands as the radiative recombination has. Consequently, there is a lower charge carrier density in a semipolar compared to a similar polar QW for a given current density. The droop maximum is shifted effectively to a higher current density.

In c-plane devices the quantum wells are very thin in order to limit the effect of spatial separation of the electron- and hole wavefunctions and thus the reduction in oscillator strength. This limitation in the design of the active region is lifted for non- and semipolar LEDs and hence the quantum wells can be made much thicker, thus reducing the carrier concentration n at a given injection current I.

Pan and Zhao et al. studied the droop in blue LEDs on $(20\overline{21})$ GaN for multiple 3 nm thin quantum wells (MQW) [70] and one 12 nm thick single quantum well (SQW) [79]. The EQE reduced from 52.6 % at 35 A cm⁻² current density to 45.3 % at 200 A cm⁻² for the MQW LED which is very low compared to c-plane devices [80, 81]. Similar results were found for the SQW-LEDs.

5.5.3 Polarization and Light Extraction

It is important to note that the optical polarization of the emitted light is a crucial factor for the light extraction. Only photons which are emitted within a narrow angle ϑ with respect to the surface normal can escape due to total internal reflection. The refractive index n _r of the GaN and the surrounding air together define the escape cone. Only photons with a $\vec{k}$-vector within this cone can escape. Since $\vec{E} \perp\vec{k}$, this means that mostly TE-polarized light is emitted. A change in the optical polarization for semipolar and nonpolar emitters, as discussed in Sect. 5.4, therefore strongly affects the light extraction efficiency.

There has been much work on the increase in light extraction efficiency by surface roughening techniques and attempts to increase the angle ϑ of the escape cone. The mechanisms behind this is the random and multiple reflection of photons at the rough surface which changes the propagation direction and hence allows the photons to escape from the semiconductor. The drawback of this method is that the linear polarization, which is desirable for many applications such as liquid crystal display (LCD) back lighting, is lost during the scattering process.

In order to increase the extraction rate and maintain the polarization, Matioli et al. employed photonic crystals (PhC) tailored to the wavelength and dominant polarization direction of m-plane oriented blue LEDs [82]. By using one-dimensional air-gap PhCs, the extraction rate was significantly increased compared to planar devices.

Regarding optical properties, one should also be aware that InN, GaN, and AlN are birefringent. This is of particular importance to semipolar (Al,In)GaN laser diodes, where waveguide modes have to be categorized as TE/TM or ordinary/extraordinary, depending on the waveguide orientation [53, 83, 84, 85, 86]. In an LED the effect of birefringence is of lesser importance, as light usually passes only through a thin layer of semiconductor. Still, one has to be aware that the thickness of a λ/4 plate at 470 nm made of a-plane GaN would be of about 4.5 μm which is of the order of the n-GaN layer of a typical thin-film LED. For a standard planar nonpolar LED the polarization is perpendicular to the c-axis which is the optical axis of the crystal. Therefore the layer does not convert the emitted linearly polarized light to circular polarized light. However, in any structure with out-of-plane geometry or photonic structures, one needs to consider birefringence also in GaN based LEDs.

5.5.4 3D-Semipolar LEDs on c-Plane Sapphire

One of the main obstacles in the realization of nonpolar and semipolar LEDs is the challenge of supplying large area and cheap substrates of high quality. While many groups experimented with heteroepitaxial growth on various crystal planes on sapphire, spinel or silicon (see Sect. 5.3.1), another approach is to use high quality semipolar surfaces on conventional planar c-plane GaN-on-sapphire substrates. Selective area growth of stripes along the $[11\overline {2}0]$-direction results in triangular pyramidal stripes with $\{ 10\overline{1}1\}$ side facets. The quality of these samples exceeds the one known from other methods since the growth starts from a high quality c-plane GaN template [44]. Although the surface of the overgrown wafer is not planar anymore, devices have been processed using this technique (layout depicted in Fig. 5.18). First LEDs with continuous wave emission at 425 nm with 0.7 mW at 20 mA have been shown in 2008 by Wunderer et al. [87]. In 2010 Scholz et al. demonstrated 495 nm LEDs on these stripes with an output power of 0.24 mW at 20 mA driving current [88].

Fig. 5.18
The selective growth of triangular stripes with semipolar side facets allows the realization of semipolar LEDs on high quality (0001) GaN templates [89]

5.5.5 State-of-the-Art of Non- and Semipolar Blue, Green, and White LEDs

During the past ten years several groups worldwide have investigated the properties of nonpolar and semipolar LEDs, and tremendous progress has been achieved. In the beginning, the limiting factor was the availability of large area and high quality substrates, and hence most LEDs were grown heteroepitaxially on foreign substrates with a high density of threading dislocations (TDD) and basal plane stacking faults (BSF). Among the most favored substrates were sapphire overgrown by HVPE-GaN, and in 2012 Jung et al. demonstrated a violet LED on $(11\overline{2}0)$-GaN with 0.24 mW output power at a dc current of 20 mA [90]. By using epitaxial lateral overgrowth (ELO or LEO) for defect reduction, Chakraborty et al. realized a blue nonpolar LED on a sapphire substrate with 7.5 mW emission power [91]. Furthermore, LEDs with 439 nm emission wavelength were demonstrated on semipolar $(10\overline{13})$- and $(10\overline {11})$-GaN orientations grown on (100) and (110) spinel $\mathrm {MgAl_{2}O_{4}}$ substrates [92]. Due to its large available size, low cost and the compatibility to existing processing procedures silicon has attracted high interest. In 2008 Hikosaka et al. realized LEDs with blue-violet emission on patterned Si on the semipolar $(11\overline{2}2)$ and $(10\overline {1}1)$ orientation [93].

Due to the large defect densities present in all heteroepitaxially grown LEDs, many groups focused on homoepitaxial growth on quasi-bulk substrates cut from HVPE-grown boules. Although the size and price of these substrates is a limiting factor, LEDs with emission from the violet, blue and green up the yellow wavelength region have been demonstrated. For a long time the most commonly used orientations were the nonpolar a- and m-planes and the semipolar $(11\overline {2}2)$-plane. In 2009 impressive progress was shown based on the newly studied $(20\overline{2}1)$-plane [112, 113], and many groups have explored LEDs on this plane since then [46, 49, 65, 114, 115, 116, 117, 118]. Other planes such as the $(30\overline{3}1)$-plane have also been investigated for the use in LEDs and laser diodes [119].

In the blue region external quantum efficiencies (EQE) of more than 50 % have been reported on the $(10\overline{11})$-plane [97] and on the $(20\overline{21})$-plane by Zhao et al. [70]. Green emitters with high EQE values were realized on the semipolar $(20\overline{2}1)$-plane with 516 and 552 nm wavelength and 19.1 and 11.6 % external quantum efficiency, respectively [99]. Furthermore, on the $(11\overline {2}2)$-plane a 562.7 nm LED was shown with 13.4 % EQE under pulsed conditions [96].

Figure 5.19 shows the emission power P and the external quantum efficiency (EQE) of semipolar and nonpolar LEDs. For blue and green emitters EQE-values of more than 50 % and 20 % have been achieved, respectively.

Fig. 5.19
Emission power P (*left*) and external quantum efficiency *EQE* (*right*) of polar, nonpolar and semipolar InGaN based LEDs and AlInGaP showing the “green gap”. For reference see Table 5.2 and [80, 104, 105, 106, 107, 108, 109, 110, 111]

5.5.6 Towards Yellow LEDs and Beyond

The initial driving force behind the increase in wavelength of nitride-based light emitting diodes was the aim to close the “green gap”, thus making the realization of emitters for the green wavelength region the most profitable and also most challenging goal. Since the InGaN-system covers the whole visible spectrum from UV to IR, even longer wavelength such as yellow and orange seem possible. This is even more challenging due to the higher indium content of the longer wavelength active region resulting in problems such as material decomposition, indium inhomogeneities and strain due to the increased lattice mismatch. The increased strain also increases the polarization fields, making semipolar and nonpolar crystal orientations the natural choice for this application.

The interest for the realization of GaN-based yellow light emitters is not as strong as for green, though, since the AlInGaP-system covers this wavelength range and the wavelength is on the long-wavelength edge of the “green gap’’’. In 2008 Sato et al. reported on yellow semipolar $(11\overline{2}2)$ LEDs and compared them to AlInGaP-based devices [96]. They showed that for nitride-based LEDs the dependency of output power and EQE onto the ambient temperature was lower than for the phosphide-based devices. This behaviour was attributed to carrier overflow due to the smaller energy offset between quantum well and barriers in the AlInGaP-LEDs.

5.6 Summary and Outlook

Despite the short time period in which the growth of light emitters on non- and semipolar surfaces has been explored, non- and semipolar InGaN QW LEDs already show great promise. This is impressively demonstrated by a number of performance indicators. For example, external quantum efficiencies of blue, green and yellow non- and semipolar light emitters are close or already exceeding those of conventional c-plane InGaN LEDs. Other important parameters like droop and wavelength stability with drive current are also showing great advances compared to LEDs grown on polar surfaces. However, many of these improvements and records have been realized on the relatively costly bulk GaN substrates. Therefore the questions remains whether non- and semipolar InGaN QW LEDs can also be produced cost-effectively, e.g. on sapphire or silicon substrates. Some of the possible approaches have been outlined in the previous chapter and indicate a number of pathways to realize low-cost and large volume production of high-efficiency non- and semipolar LEDs. Young start-up companies, like Soraa Inc. (Fremont, USA) are already trying to seize these opportunities and have introduced the first LED lamps based on non- and semipolar technology that generate more than 2300 candela of white light with only 12 Watt of electric input power [120]. Of course this is just the start. Only time will tell whether non- and semipolar LEDs will have a lasting impact on future lighting technology. Considering the short time span in which non- and semipolar light emitters have been explored and the astonishing advances that have already been demonstrated, non- and semipolar LEDs are certainly serious contenders.

Notes

Acknowledgements

This work was partially supported by the Deutsche Forschungsgemeinschaft (DFG) within the Collaborative Research Center (SFB 787) “Semiconductor Nanophotonics” and the Research Group (FOR 957) “PolarCoN”.

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Authors and Affiliations

Michael Kneissl
- 1
- 2
Email author
Jens Rass
- 1
Lukas Schade
- 3
Ulrich T. Schwarz
- 3
- 4

1.Institute of Solid State PhysicsTechnische Universität BerlinBerlinGermany
2.Ferdinand-Braun-InstitutLeibniz Institut für HöchstfrequenztechnikBerlinGermany
3.Department of Microsystems EngineeringUniversity of FreiburgFreiburgGermany
4.Fraunhofer Institute for Applied Solid State Physics (IAF)FreiburgGermany

Growth and Optical Properties of GaN-Based Non- and Semipolar LEDs

Abstract

Keywords

5.1 Introduction

5.2 Piezoelectric and Spontaneous Polarization in Group-III Nitrides

5.3 Growth of GaN and InGaN on Different Non- and Semipolar Surface Orientations

5.3.1 Heteroepitaxial Growth of Non- and Semipolar GaN on Sapphire, Silicon, Spinel, and LiAlO₂ Substrates

5.3.2 Surface Morphologies and Strutural Defects of Non- and Semipolar GaN Films

5.3.3 Indium Incorporation in InGaN Layers and Quantum Wells on Different Semipolar and Nonpolar Surfaces

5.4 Polarization of the Light Emission from Non- and Semipolar InGaN QWs

5.4.1 Light Emission from Nonpolar InGaN QWs

5.4.2 Light Emission from Semipolar InGaN QWs