3.1

Mirrors

GaAs-VCSELs profit from the near lattice-matched AlGaAs-material system, which allows for growing crack-free highly reflective Distributed Bragg Reflectors (DBRs). The relatively high refractive index contrast (Δn/n_high) of 14% at 850 nm for an Al_0.12Ga_0.88As/Al_0.90 Ga_0.10As DBR, results in a broad stopband of 75 nm (full-width half-maximum) for a standard bottom DBR with 34 mirror pairs. Since both mirrors in a VCSEL need a reflectivity above 99%, an even more relevant measure would be the width of the spectrum for a reflectivity above 99%, which is 59 nm for the mentioned DBR. Besides a high reflectivity over a broad spectral range, the AlGaAs DBRs can also be electrically conductive, allowing for current injection through the DBRs and contacts can thus be placed on top of the top DBR and on bottom of the bottom DBR. Achieving broadband, high reflectivity, electrically conductive DBRs in the III-nitride-based material system is a big challenge. It is difficult to find two materials with high refractive index contrast that are lattice-matched to each other, and in addition have high electrical conductivities. High peak reflectivities (>99%) have been reached with DBRs in (Al)GaN/Al(Ga)N^50-53 as well as in AlInN/GaN^54,55. An AlN/GaN DBR has a higher refractive index contrast (about 12% at 420 nm), which is close to that of AlGaAs DBRs, and as a result the 99% stopband width is about 22 nm if 22 mirror pairs are used. However, the DBR suffers from an in-plane lattice mismatch of about 2.5%. Ternary AlGaN could be used instead of binary AlN/GaN to mitigate cracking, but a larger number of pairs is then necessary to reach high enough reflectivity due to the lower index contrast, and the stopband width will thus be narrower. To reduce stress in the DBR, short-period superlattices (SLs) have been used, below the DBR⁵⁶, and incorporated into the DBR⁵². The inserted AlN/GaN SLs can suppress the generation of cracks, but cannot reduce the number of the V-defects.⁵⁷ Another way for strain management is to use thin low-temperature AlN interlayers.⁵³ The interlayers can reduce crack-formation, but can also reduce the overall reflectivity of the DBR, which has to be taken into account when designing the DBR. Spontaneously formed interlayers have also been seen to reduce the peak mirror reflectivity and stopband.⁵⁸ Selective area growth has also been applied to grow crack-free DBRs in areas up to 150x150 μm,⁵⁹ sufficiently large for VCSELs. Instead of AlGaN, an epitaxial DBR can be realized using lattice-matched AlInN/GaN to grow strain free highly reflective mirrors⁶⁰. The composition of AlInN is very sensitive to growth conditions, but if grown correctly, it can result in a basically strain-free DBR allowing for high quality quantum wells to be grown on top. The index contrast of the layers is however lower than AlN/GaN (about 6% at 420 nm), which results in a mirror with a more narrow 99% stopband of about 12 nm if 42 mirror pairs are used. Any deviation in thickness of the DBR layers will translate into a deviation in the center position of the stopband, for example a 3% thickness deviation, results in a 3% shift of the center position of the DBR stopband, which corresponds to 12.5 nm if the mirror is designed for 420 nm. As a result, the 99% stopband could end up outside the 99% stopband of the other DBR if one mirror has 3% thicker layers. Thus, a narrow stopband DBR makes the spectral alignment between DBR reflectivities more challenging as well as their matching with gain spectrum and cavity resonance. There have been very few reports on electrically conductive DBRs^61-63 due to the low electrical conductivity of III-nitrides and the many hetero-interfaces necessary in the DBRs (due to the low refractive index contrast of the materials). Thus, intracavity contacts have so far been the only option for GaN-VCSELs.

To avoid the problem with epitaxial DBRs due to the low refractive index contrast and non-lattice-matched materials, an alternative approach is to use dielectric DBRs. Due to the higher refractive index contrast (44% if SiO2/Ti2O2 is used) only about 11 pairs are required to achieve a high reflectivity and the resulting 99% stopband width is as wide as 148nm. A double dielectric scheme does however require either substrate removal or epitaxial lateral overgrowth of the bottom dielectric DBR, making the exact control of the cavity length challenging, see Section 3.3. Substrate removal has been achieved by laser-induced lift-off, polishing and photoelectrochemical etching (PEC) of a sacrificial layer. Laser-induced lift-off is not easily applied to VCSEL structures grown on free-standing GaN, due to the lack of absorption contrast between epitaxial GaN and the GaN substrate. Insertion of light-absorbing structures is possible but might hamper the crystal quality of the VCSEL structure grown on top, since they are usually not perfectly lattice-matched to GaN. The fabrication process requires bonding to a support substrate to be able to handle the thin layer structures that are lifted-off and the layer structure has to have a certain thickness, typically above 4 μm to avoid stress fractures in the GaN film.⁶⁴ Chemical mechanical polishing (CMP) on the other hand can be applied to remove GaN substrates from epitaxial GaN structures. However, thickness control is a challenge, as is achieving low-thickness variation across a large-area substrate due to the hardness of the GaN material. This method also requires bonding to a support substrate. PEC also requires bonding, but has the advantage of providing a more accurate cavity length control. ELOG does not require bonding, but achieving short cavity lengths and an exact control of the cavity length is challenging, due to the ratio between vertical to horizontal growth rates. Besides the above-mentioned challenges with a double dielectric DBR scheme, it will in addition lead to VCSELs with increased heating thereby faster misalignment of cavity resonance and gain peak, due to the lower thermal conductivity of dielectric DBRs.

Dielectric DBRs have a high refractive index contrast, but an even higher contrast (Δn/n_high=60%) can be achieved if the DBR consists of GaN and air. In this case only a few periods would be necessary to achieve a high reflectivity, and the stopband will be very broad. In the realization of a semiconductor/air gap DBR, selective wet-etching is crucial as every second layer (sacrificial layer) in the DBR has to be removed to create the air gaps. Unfortunately, III-nitrides are chemically stable in most solutions and thus very difficult to wet etch. There have been a few demonstrations of GaN/air- DBRs, utilizing wet-chemical etching of AlInN^65,66, combined electrochemical oxidation and wet-chemical etching of AlInN⁶⁷ or photoelectrochemical etching of InGaN⁶⁸, and electrochemical etching of n-doped GaN^69,70. Most critical in the fabrication of GaN/airgap DBRs is to avoid collapse of the structure and to achieve a mechanically stable structure with no bending. The thickness of the GaN is often increased to 5λ/4 instead of λ/4 to improve mechanical stability. Another challenge is the often low selectivity in the wet-etch, which results in a non-uniform thickness of the GaN layers in the radial direction, since they are slightly etched in the removal of the sacrificial layer.

An alternative to a DBR is a high refractive index contrast grating (HCG), which is described in more detail in Section 5. HCGs are believed to offer a number of advantages⁷¹, such as transverse mode and polarization control and a broader reflectivity spectrum than epitaxially grown DBRs. An additional benefit is the possibility to set the resonance wavelength of the VCSEL by the dimensions of the grating⁷², which recently was demonstrated in a GaAs-based VCSEL⁷³. By varying the duty cycle and/or the period of the grating, while maintaining the same grating layer thickness, the phase of the reflected wave can be altered without affecting the magnitude of the reflection. A change in phase is effectively the same as changing the cavity length, i.e., by varying the lateral parameters of the grating on nearby VCSELs, individual resonance wavelengths can be achieved for devices from the same epitaxial layer structure. Thus, enabling the fabrication of a multi-wavelength VCSEL array where the emission wavelengths of the individual devices are set in one single post-growth lithography step. A main challenge in the fabrication of a III-nitride-based HCG is to find a sacrificial layer that can be selectively removed without affecting the HCG layer. There have been a few attempts, such as bandgap-selective photoelectrochemical etching of a sacrificial InGaN superlattice to form an AlGaN HCG membrane⁷⁴ however, with a limited airgap height, and focused-ion-beam etching to create an airgap underneath a GaN-based HCG⁷⁵, an impractical process for device integration on a wafer-scale. In addition, GaN membrane gratings have been fabricated from a GaN-on-Si structure^76-78 by selective etching of Si, and free-standing hafnium-oxide gratings using the same approach⁷⁹, but applying this concept to fabricate a bottom mirror in a VCSEL is not straightforward, since growth of high-quality GaN on Si for laser applications is very challenging. Due to the difficulties in realizing a III-nitride based HCG structure with an airgap, a grating reflector without an airgap could be used, which previously has been proposed for long-wavelength VCSELs where the mirror fabrication also is complex.⁸⁰ Such a reflector in GaN has been demonstrated.⁸¹ This concept offers a more mechanically rigid structure, but the lower index contrast results in a much smaller fabrication window to achieve a reflectivity above 99%. An alternative approach for an HCG for III- nitride-based light-emitters is a free-standing dielectric HCG in TiO₂ realized by a sacrificial SiO2 layer⁸². It offers approximately the same high index contrast as that of free-standing GaN HCGs, since the refractive index of TiO₂ is about 2.6 at a wavelength of 450 nm, with a negligible absorption for wavelengths above 400 nm. In addition, the TiO₂ HCG scheme allows for direct integration into many different material systems, since lattice-matching is no longer a prerequisite.

3.2

Carrier transport and optical gain

Carrier transport must be optimized along both the vertical and lateral directions in order to achieve uniform carrier distribution among the multiple QWs of the active region and within each QW defined by the current aperture. A vertically uniform carrier distribution among the QWs is a challenge in all GaN-based light-emitters^83,84 due to the large difference between the activation energy of donor and acceptor impurities⁸⁵, the strong imbalance between electron and hole mobilities⁸⁶, the large band offsets and, possibly even more critical, the spontaneous and piezoelectric polarization effects at heterointerfaces^87,88. In order to maximize the radiative recombination in the QWs, one should minimize current crowding^89,90 as well as carrier leakage beyond the active region, which can involve both electrons^91-93 and holes⁹⁴ and could be enhanced by Auger^95,96 and excited subband recombination⁹⁷. Electrons can be prevented from leaking into the p-GaN layers by inserting an energy barrier in the conduction band between QWs and p-layers, a so- called electron-blocking layer (EBL). However, an EBL will also affect hole injection into the QWs, and the EBL design is thus crucial for low-threshold operation. Many different EBLs have been proposed and their effect on VCSEL performance has been investigated such as different p-doping levels of the EBL⁹⁸, compositionally graded EBL⁹⁹, and multiple barrier EBL¹⁰⁰.

The design of the active region is very important, and Table 1 summarizes the different approaches used in electrically injected VCSELs. It is clear that there is so far no consensus on how the active region should be designed. For example, having many QWs (up to 10 have been used) may increase the optical gain per roundtrip in the cavity and the tolerances to spatial misalignment between the maximum of the standing optical wave and the QWs. One drawback is the nonuniform carrier distribution among QWs due to the above-mentioned mechanisms; as a result, it may occur that only the QWs nearest to the p-side contribute to the optical emission, as observed experimentally in InGaN/GaN LEDs¹⁰¹ and predicted by simulations of GaN-based Fabry-Pérot lasers¹⁰² and VCSELs¹⁰³. This reduces the net gain since QWs that are pumped below transparency absorb light. The use of fewer QWs can lead to a more uniform carrier distribution between QWs, but could also result in an increased electron leakage¹⁰⁴. Numerical simulations have shown that the insertion of a tunnel junction (TJ) in the middle of 10 QWs could improve the uniformity in carrier distribution and lead to higher output power¹⁰⁵. Another approach to achieve more uniform carrier distribution¹⁰⁶ and higher optical gain¹⁰⁷ is to grow on nonpolar or semipolar planes rather than along the c-plane. III-nitride-based materials have, unlike GaAs, strong built-in electric fields due to spontaneous and piezoelectric polarization. In the QWs, the large electric field perpendicular to the epitaxial layers spatially separates the hole and electron wavefunctions, which leads to a reduced wavefunction overlap and thus a reduced radiative recombination efficiency and an increased threshold current. An increased overlap between hole and electron wavefunctions can also be achieved in QWs grown on polar planes by tailoring the shape of the QW along the growth direction. These are referred to as large-overlap QWs, and both step-function compositional grading^108-109 as well as linearly grading¹¹⁰ have been proposed. However, an additional advantage with InGaN QWs on nonpolar and semipolar planes is the anisotropic optical gain leading to VCSELs with a preferred polarization state³⁵ without the use of for example surface gratings^111,112.

To achieve low threshold currents, the optical mode must overlap well with the gain region defined by the current aperture. A laterally uniform carrier distribution within the gain region is also desirable to avoid selective excitation of higher order transverse modes. However, simulations show that due to the large difference in mobility between electrons and holes in III-nitrides, the recombination will predominantly take part in the periphery of the aperture and not in the center¹¹³. In addition, III-nitride VCSELs must use intracavity contacts due to the non-conductive DBRs. Thus, current spreading layers are necessary, and the transparent conductive oxide indium-tin-oxide (ITO) is most commonly used. However, ITO has a relatively high absorption (about 1000 cm^-1), and must thus be placed in a minimum of the standing optical wave to keep the losses low. Any deviation in cavity length from design will dramatically increase the absorption losses. The surface roughness of the ITO should also be low, preferably having a root-mean-square < 1 nm to keep scattering losses low in the VCSEL¹¹⁴. Moreover, it is challenging to achieve a low contact resistivity between p-GaN and ITO, making it difficult for the contact to survive the high current densities required in VCSELs (typically tens of kA/cm²). ITO deposition, usually done by sputtering to achieve high quality¹¹⁵, can easily lead to plasma damage of the p-GaN^116,117, preventing a low-resistive contact to be formed. Remote plasma deposition or physical vapor deposition such as electron beam evaporation can be used to avoid plasma damage of the p-GaN. In addition, multilayered ITO deposition at different temperatures has been developed to optimize contact resistivity, ITO properties¹¹⁸ and surface roughness¹¹⁴.

Alternative solutions for a current spreading layer have been investigated, such as thin metal layers¹¹⁹ and graphene¹²⁰. Metals have low sheet resistance and can provide low-resistive contacts to p-GaN, but have a strong absorbance. If made thin enough and placed very accurately at an optical field node the optical absorption loss can be relatively low, but any deviation from target position will dramatically increase the absorption loss. Moreover, the resistance in very thin metals is much higher than in bulk layers¹²¹ and their reliability and degradation at high current densities needs to be investigated. A single layer of graphene has an absorption loss of 2.3%¹²² in the visible wavelength range, and if placed accurately within the cavity it would lead to a relatively low loss. However, most graphene has so far been transferred to GaN-based LEDs, and as a result of the transfer the contact resistivity is poor. There have been attempts to grow graphene directly on p-GaN^123,124. If such a technique can be developed that can provide graphene, or any other twodimensional material, with low resistance, high transparency and ohmic contact to p-GaN that can withstand high current densities, grown under conditions that do not jeopardize the underlying device structure, it may be a way forward. So far, though, the most promising approach to replace ITO is the tunnel junction (TJ). By incorporating a TJ, the topmost part of the p-GaN layer and the current spreading ITO layer can be replaced by a low-resistive n-GaN and the current spreading issue with associated high optical loss can be addressed. In long-wavelength InP-based VCSELs, which share many of the same challenges as GaN-VCSELs such as low p-type conductivity, high metal contact resistance to p-doped material, and poorly-conductive DBRs, tunnel junctions are a standard technology to achieve efficient lateral current spreading¹²⁵. In order for the TJ to be successful in III-nitride-based VCSELs, in reverse bias it should have a low resistance with low additional voltage drop, low optical absorption and be able to withstand the high current densities. This has been a challenge in III-nitrides due to the large bandgaps and low hole concentrations. In recent work, TJs with thin InGaN layers have been explored to utilize the lower bandgap and polarization fields to reduce the tunneling barrier and facilitate the carrier tunneling^126,127. However, the absorption losses, critical for VCSELs, must be investigated and will most likely be higher than if only GaN is used. GdN nanoislands have also been incorporated in the TJ interface to increase the tunneling through midgap states^128,129. Very promising are the pure GaN TJs demonstrated recently which have been incorporated into LEDs^130,131. They have shown low differential resistance for a complete device (low 10^-4 Ωcm²), and ability to withstand current densities exceeding 20 kA/cm². Buried tunnel junctions have also been demonstrated to laterally confine the current¹³⁰, and if the introduced structural step from the overgrown TJ transfers into the top DBR, it might also provide simultaneous optical guiding^132,133.

In most III-nitride-based VCSELs, the main focus has been on lateral current confinement and not on optical confinement. However, to achieve an efficient device with low threshold it is important to ensure a good lateral overlap between the optical mode and the carriers in the QWs. In fact, it has been shown that most apertures used for current confinement result in optically anti-guided structures with associated high losses^132,133, for more details see Section 4. Switching to index-guided structures instead, will contribute to lowering threshold currents and can be an effective way to reduce filamentation, something often seen in GaN-VCSELs^{27,28,30,32,39,40,46}, and also seen in early proton-implanted gain-guided GaAs-VCSELs^135,136.

3.3

Cavity length

To achieve a VCSEL with a low threshold current it is important to ensure a good spatial overlap between the optical mode and carriers. In the lateral direction this is achieved by having an aperture(s) that confines carriers and optical field to the center of the device, and in the vertical direction this is done by placing the quantum wells (QWs) in a maximum of the standing optical wave. The optically absorbing regions, such as the ITO layer, should be placed at a field minimum, see Fig. 3. Besides this spatial matching, spectral matching between the cavity resonance, gain peak, and reflectivity of the mirrors is also required. A good control of the cavity length is of utmost importance since it will affect both spatial and spectral matching. Table 2 shows that most GaN-VCSELs use a cavity length (distance between the DBRs) of about 7λ or even longer. GaAs-VCSELs, on the other hand, use a shorter cavity length, even as short as 0.5λ, to improve transport and optical confinement in order to push the high-speed performance^137-139. There are several reasons for using longer cavity lengths in GaN-VCSELs. The intracavity contacting scheme forces the use of a thick n-GaN to keep the lateral resistance from the n-contact layer low. If there is residual strain in the underlying structure, for example from epitaxial DBRs, the n-GaN must be grown to a certain thickness to allow for high quality QWs to be grown on top. If an epitaxial lateral overgrowth of the DBR is applied instead, the thickness of the n-GaN will be determined by the ratio between lateral and vertical growth rates in combination with the geometry of the overgrown DBR²⁹. If chemical mechanical polishing is used to remove the substrate, the n-GaN will also be thick due to the inaccuracy in the substrate removal process²⁸. In addition, a longer cavity length yields a decreased longitudinal mode separation, making it easier to match one longitudinal mode (or several) to the stopband of the mirrors and the gain spectrum. In a device with a 2-μm cavity length and two dielectric DBRs, the measured longitudinal mode separation was about 7 nm²⁸, while the gain spectral width for InGaN QWs is below 15 nm¹⁴⁰ for a carrier concentration of 3·10¹⁹cm^-3 and the net modal gain will be even narrower. If epitaxial DBRs are used the refractive index contrast is less, and thus the penetration depth into the DBRs will be longer, yielding a much longer effective cavity length for the same physical distance between the DBRs. Thus, devices with one epitaxial DBR usually have a shorter longitudinal mode separation, but on the other hand the reflectivity spectrum that the mode has to fit within is narrower. Moreover, the resonance wavelength (λ) is less sensitive to deviations in cavity length (ΔL) for a longer cavity, i.e. Δλ=λΔL/L.²⁸ This is an advantage since it is very difficult to control the cavity length within a few percent for a GaN-based VCSELs, no matter if epitaxial or dielectric DBRs are used. The drawbacks with a longer cavity are increased absorption loss in the cavity, reduced longitudinal confinement and decreased spontaneous emission factor.

Figure 3.

Standing optical wave inside the cavity for a GaN-VCSEL with an outcoupling DBR of 7-pairs of TiO₂/SiO₂ and a highly reflective DBR of 42-pairs of AlInN/GaN (top figure) and 11-pair TiO₂/SiO₂ (bottom figure).

The importance of an accurate cavity length is illustrated in Fig. 4 for the case of two dielectric DBRs and in Fig. 5 for and one dielectric and one epitaxial DBR. The structure and material data used are the same as in Ref.¹³², except for the bottom DBR, which in Fig. 4 consist of 11 mirror pairs of TiO₂/SiO₂ and in Fig. 5 42 mirror pairs of AlInN/GaN without any absorption losses. The calculations were performed using the one-dimensional effective index method¹⁴¹ and the deviation in cavity length corresponds to a change in the bottom n-GaN thickness that nominally is 904.4 nm thick. Negative deviation in cavity length corresponds to a shorter cavity length and positive deviation to a longer cavity length. The threshold material gain increases faster with a deviation in cavity length for the VCSEL with an epitaxial DBR, an increase of 100 cm^-1 is reached already when the cavity length deviates by less than ±10 nm, while in the double dielectric DBR VCSEL the cavity length can deviate by more than ±35 nm before the same increase of 100 cm^-1 occurs in threshold material gain. This is due to the fact that when the cavity length deviates from the optimum value, the resonance wavelength will shift, and will no longer overlap with the maximum reflectivity of the DBR. In the case of a low-refractive index DBR (as an AlInN/GaN DBR), this reduction in mirror reflectivity occurs much faster due to the narrower reflectivity spectrum. Due to the low-refractive index contrast of the epitaxial DBR, the penetration depth of the optical field into the DBR is longer, which results in a longer effective cavity length, and thus a shorter separation of the longitudinal modes. For the examples in the figures the longitudinal mode separation is about 18 nm in the case with one epitaxial DBR and 27 nm for the double dielectric scheme. The shorter longitudinal mode separation does not help much to reduce the threshold material gain required for the epitaxial DBR VCSEL, since it is dominated by the low peak reflectivity and narrow reflectivity spectrum. It can however help a bit in reducing the threshold current since the detuning between resonance wavelength of a longitudinal mode and the gain peak will be less if the longitudinal mode separation is less. On the other hand, if the longitudinal mode separation is too short, multiple longitudinal mode lasing can occur. It should be noted that the resonance wavelength shifts less with a deviation in cavity length for the epitaxial DBR VCSEL, due to the longer effective cavity length. The shift is about 7 nm for a thickness deviation of 30 nm in the epitaxial DBR VCSEL case, and 10 nm or the same thickness deviation in the double dielectric DBR VCSEL. A benefit with the epitaxial DBR is the higher thermal conductivity, which results in a smaller resonance wavelength shift with drive current due to a lower temperature rise, which also affects the overall laser performance. The increase in threshold material gain due to a deviation in cavity length will affect the laser performance, but is not big enough to totally prevent lasing in the case of a double dielectric DBR, since InGaN QWs have proven to be able to deliver a material gain above 2500 cm^-1.¹⁴⁰ However, in the case of a VCSEL with a bottom epitaxial DBR, the cavity detuning might in fact prevent the laser from reaching threshold.

Figure 4.

Threshold material gain and resonance wavelength as a function of a deviation in cavity length (n-GaN thickness) for a GaN-VCSEL with a 7-pair TiO₂/SiO₂ DBR as the outcoupling DBR and 11-pair TiO₂/SiO₂ DBR as the highly reflective DBR.

Figure 5.

Threshold material gain and resonance wavelength as a function of a deviation in cavity length (n-GaN thickness) for a GaN-VCSEL with a 7-pair TiO₂/SiO₂ DBR on top and an epitaxial 42-pair AlInN/GaN as the bottom DBR.