1 Introduction

Quantum physics has been a research area of great interest and innovation (Briggs et al. 2013). A particularly interesting field is quantum information processing. For these purposes, laser radiation is frequently used as a coherent light source (Ladd et al. 2010).

One example is quantum logic gates based on ultra-cold \(^{9}\hbox {Be}^{+}\)-ions (Torun et al. 2021; Gaebler et al. 2016). To conduct experiments in this field, laser radiation at a wavelength of 313.133 nm is in high demand. Ultraviolet light blelow 313 nm has been generated directly by nitride based (Hasan et al. 2021). Nevertheless, these devices are not commercially available and have inferior properties. The use of Fabry-Pérot cavities leads to spectrally and spatially broad emission and the output power is not sufficient. Instead, 313 nm radiation needs to be generated by nonlinear second harmonic generation (SHG) of red light at 626.266 nm (Wilson et al. 2011). Based on this, the 626 nm laser source has to fulfill certain criteria to allow for efficient nonlinear conversion of the emitted beam. It should have a power as high as possible and a sufficiently small spectral linewidth around 1 MHz. Furthermore, a beam propagation factor M2 close to one is desirable. In addition to that, the whole laser device needs to have a footprint as small as possible as well as high wall plug efficiency.

The development of light sources to meet these requirements has been the focus of several research groups to date. On one hand, light in the short red spectral region below 630 nm can be generated by nonlinear frequency conversion. This can be done by SHG of near-infrared laser radiation into the target spectral range. One approach utilizes an optically pumped semiconductor laser (OPSL) to generate the needed 1252 nm radiation, resulting in 530 mW at 626 nm (Burd et al. 2020). Another approach is sum frequency generation (SFG) of laser radiation at 1550 and 1051 nm (Wilson et al. 2011). This method achieves approximately 2 W at 626 nm by using two fiber lasers as light sources. These two methods pose two major disadvantages. First, they are inefficient, due to the nonlinear nature of SHG and SFG, and in the case of the OPSL, an additional power conversion step, introducing additional losses, is needed. Second, these systems have a large footprint, making it hard to use them as laser sources for the upscaling of quantum information processing.

On the other hand, semiconductor lasers have big advantages compared to current systems. They are smaller and more efficient, as they can directly emit the target wavelength, allowing for laser systems with small footprints. Gallium-nitride-based quantum dot lasers can emit wavelengths from the yellow spectral range to wavelengths as high as 630 nm (Frost et al. 2017). Nevertheless, the available output power and spectral properties are not sufficient for SHG. 626 nm can also be covered by the AlGaInP material system grown on GaAs. The reduction of the lasing wavelength in AlGaInP is hindered by a transition from a direct to an indirect semiconductor with increasing Ga and Al mole fractions, the competition between light and heavy holes, and the poor carrier confinement in the active region due to small energetic barriers (Hatakoshi et al. 1991). Due to this, the laser threshold increases and the slope efficiency decreases significantly. Broad area lasers developed to generate laser emission at 614 and 626 nm at room temperature (Vaester et al. 1989; Bour et al. 1994; Hamada et al. 1992) used tensile or compressive strained single- and multi-quantum well (QW) active regions. Moreover, they utilized multi-quantum barriers, narrow waveguide cores (WGs) and short resonators to further reduce the threshold current and make lasing at room temperature possible. The downside of these procedures is that the usage of multi-quantum wells and barriers and narrow WGs has a negative influence on the lifetime of the device due to an increase in interfaces, crystal defects and thermal load. Current approaches use epitaxial structures optimized for emission around 635 nm, which are either tuned by hydrostatic pressure or cooled close to or below the dew point. These devices are either not spectrally stabilized, or stabilized by an external cavity configuration or have an integrated wavelength selective element (Bercha et al. 2009; Ball et al. 2013; Cozijn et al. 2013; Blume et al. 2013) to achieve narrow laser linewidths, as low as 1 MHz. These lasers can be used to seed a semiconductor optical amplifier generating powers up to 200 mW in a diffraction-limited beam with M2 values less than 2 (Ohmae and Katori 2019).

This paper focuses in detail on the theoretical development and experimental verification of epitaxial laser structures emitting at 626 nm in the AlGaInP material system as the base for devices with long lifetimes and strong amplification. In the first section, the epitaxial layer structure is introduced and the limitations of the GaInP single QW are discussed in detail. Afterward, the most promising QW configurations based on the energetic distances of the QW energy levels and their barriers are identified. Then, the calculation and evaluation of the modal gain based on k \(\cdot\) p  theory is presented. In the next section, we report on the growth of three selected QW configurations by metal-organic vapor-phase epitaxy (MOVPE) that are processed to broad-area lasers. Then the results of an experimental characterization of the devices at room temperatures are presented. This work closes with a conclusion and an outlook.

2 Design of semiconductor laser structure

This section is about the theoretical design of epitaxial structures for semiconductor lasers emitting around 626 nm at room temperature. First, the overall layer structure is described, followed by the design and theoretical investigation of the active zone (AZ). This is done by applying the improved model solid theory (Qteish and Needs 1992). The influence of the strain on the energy bands is taken into account, especially the removal of the degeneration of the X band valleys (Muñoz and Armelles 1993). Furthermore, the energy levels of the QW are determined by solving the Schrödinger equation in effective-mass approximation. The waveguide equation is solved to determine the propagating vertical mode and the confinement factor. Afterward, the modal gain of varying carrier densities is calculated utilizing the k \(\cdot\) p  theory of strained semiconductors (Enders et al. 1995; Wenzel et al. 1999). In the end, the most promising configurations are presented to enable the desired laser operation at room temperature.

2.1 Epitaxial layer structure

The layer structure is designed to minimize the aforementioned negative properties of structures used in the past. It utilizes an SQW, a medium-sized WG and no MQBs. The structure is based on previous experiments in the red spectral range (Zorn et al. 2007; Pohl et al. 2015; Paschke et al. 2022).

Fig. 1
figure 1

Profiles of conduction and valence band edges of the epitaxial structure (left) and the profile of the intensity of the fundamental waveguide mode (right). The QW has a thickness of 14 nm and a gallium mole fraction of 60%

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Figure 1 shows the energy band diagram of the structure as well as the intensity of the guided vertical laser mode. The AZ is embedded symmetrically in the epitaxial structure regarding layer thicknesses and compositions. The whole structure is nearly lattice-matched to GaAs, except the AZ. The cladding (CL) is made up of AlInP layers with thicknesses of 600 nm. The Al0.36Ga0.15In0.49P waveguide has a total thickness 1000 nm. The active InGaP QW sandwiched by 25 nm thick graded index (GRIN) AlGaInP layers is located in the center of the waveguide core. The composition is altered from Al0.36Ga0.15In0.49P to Al0.26Ga0.26In0.48P. The n-type conductivity is achieved by doping with silicon. The p-AlGaInP is doped with zinc, while the p-AlInP is doped with magnesium. Using Mg:AlInP as a cladding material instead of C:AlGaAs, as used in Paschke et al. (2022), has been shown to improve the laser performance due to the larger band gap (Zorn et al. 2007; Pohl et al. 2015; Shimada et al. 2010; Nishida et al. 2011).

From Fig. 1, one can identify two issues. The first one is that in the CL and WG, the lowest conduction band edge originates from the X valley for which the energy decreases with increasing Al mole fraction. Therefore, electrons have to overcome the energy differences between the CL and the top of the GRIN layer. It has to be noted that the electrons are injected into the QW by the GRIN layer, via a transition from the X to the \(\Gamma\) valleys in the Brillouin zone. The second issue is the low energetic difference between the X valley edge and the \(\Gamma\)-valley edge in the QW resulting in leakage of electrons into the p-doped layers (Hatakoshi et al. 1991).

This structure is the basis of subsequent investigations. The CL, WG and GRIN compositions and thicknesses are kept constant as they form an optimized laser structure for emission from 700 to 635 nm (Zorn et al. 2007; Pohl et al. 2015; Paschke et al. 2022). The WG is optimized to allow for a high carrier- and optical confinement. Increasing its aluminum content and decreasing the Indium content would lead to a decrease in refractive index. This leads ultimately to a decrease in the refractive index difference between WG and CL and a weaker guiding of the optical mode. Therefore, we kept the compositions and thickness of all layers except of the QW constant.

2.2 Constraints of GaInP quantum well design

The QW determines the emission wavelength and, most prominently, the performance of the laser. As a result, this section addresses design considerations for room temperature lasers based on \(\mathrm {Ga_xIn_{1-x}P}\) QWs at 626 nm. First, the energetic positions of the valence and conduction bands of the QW are investigated, as well as the strain in the AZ. Afterward, simulations regarding the QW thickness, gallium mole fraction (x), and resulting transition wavelengths between the electron and hole levels are performed.

Fig. 2
figure 2

Dependence of the bulk valence and conduction band edges of \(\mathrm {Ga_xIn_{1-x}P}\) on the gallium mole fraction. The energy is given with respect to the vacuum energy level (left). The resulting in-plane strain is shown on the right axis

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Fig. 3
figure 3

Calculated critical layer thickness of tensile-strained GaInP inserted between materials with a lattice constant of GaAs, according to People and Bean, as well as People and Bean (1985), Matthews and Blakeslee (1974). A Poisson ratio of 0.33 is used

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Three issues limit the gallium mole fraction usable in the GaInP QW: The energetic crossover between light and heavy holes, the transition from a direct to an indirect band gap, and a high strain due to the lattice mismatch. The conduction and valence band edges of GaInP pseudomorphically grown on GaAs as well as the corresponding in-plane strain are shown in Fig. 2 in dependence on the gallium mole fraction.

\(\mathrm {Ga_xIn_{1-x}P}\) becomes tensile-strained for \(x>\) 0.51 so that the band edge of the light holes has lower energy than that of the heavy holes. A large splitting is preferential due to a suppressed population of the heavy-hole band. However, for \(x>\) 0.73 a cross-over between the in-plane X- and \(\Gamma\)-conduction band edges can be observed which inhibits laser operation.

If a crystalline material is too heavily strained, either tensilely or compressively, dislocations evolve for thicknesses exceeding the critical layer thickness. Those crystal defects introduce non-radiative recombination centers and ultimately prevent laser operation. The calculation of the critical layer thickness for QWs is done according to People and Bean, as well as People and Bean (1985), Matthews and Blakeslee (1974). Figure 3 depicts the simulation results. There, one can extract a critical layer thickness of 15 nm for a gallium mole fraction of approximately 0.7 corresponding to a strain of 1.5%.

In conclusion, the previously mentioned constraints allow the usage of GaInP QWs with gallium concentrations between approximately 52% and 70%. The following subsection investigates the effect of the amount of gallium in the quantum-size effect in dependence on QW gallium mole fraction and thickness.

2.3 Selection of quantum well configuration

In order to achieve 626 nm laser emission at room temperature, it is necessary to define QW configurations consisting of a gallium mole fraction x in the previously defined region and a QW thickness \({\text {d}_{\text {QW}}}\). For red wavelength lasers, it was found in our labs, that the difference between the laser wavelength and the peak electroluminescence (EL) wavelength is approximately 13 nm. The EL wavelength coincides nearly with the transition wavelength between bottom most electron and top most hole levels. Therefore, QW configurations for a transition wavelength of 613 nm are targeted.

Fig. 4
figure 4

Transition wavelength in dependence to the gallium mole fraction of the QW (x-axis) and the QW thickness (set of curves). The vertical dashed line indicates the gallium mole fraction, where the QW is lattice-matched to the substrate. The kink (arrow) in the 5 nm curve is due to the change of transition between light and heavy holes

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Fig. 5
figure 5

QW thickness versus composition for a fixed transition wavelength of 613 nm. The vertical dashed line indicates the gallium mole fraction, where the QW is lattice-matched to the substrate. The kink (arrow) is due to a change in the transition between light and heavy holes

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In Fig. 4, the transition wavelength is shown versus x in the usable range and QW thicknesses from 3 to 15 nm. One can see that a transition wavelength of 613 nm is achievable for QW thicknesses at and above 4 nm. Figure 5 depicts the resulting combinations. The shown graph splits into two parts with a kink around 0.56 (black arrow in Figs. 4 and 5). The reason is anticipated from the following paragraph handling the energetic distances (Fig. 6). For \(x<\) 0.56 the first energy level of the heavy holes is above the light holes, leading to transverse electric (TE) polarized laser emission. For \(x> 0.56\) the first light hole level is above the heavy holes so that the emission is transverse-magnetic (TM) polarized. Based on the constraints, the usable gallium mole fraction is in the range 0.56–0.68 and the QW thickness is in the range 5–14 nm.

Fig. 6
figure 6

Difference between the first light and heavy hole levels (subband edges) as well the first and second electron levels for QW configurations with a transition wavelength of 613 nm. The right axis shows the energy in units of \(\textrm{k}_\textrm{BT}\). The black arrow points out where \(\text {el}_2\;\)is no longer bound in the QW

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Figure 6 shows the calculated energetic distances of the first light and heavy hole energy levels and the first to the second electron energy levels. The energetic differences between \(\text {el}_1\;\)and \(\text {el}_2\;\), decrease as the gallium mole fraction increases. At the same time, the spacing between \(\text {lh}_1\;\)and \(\text {hh}_1\;\)rises.

To minimize the threshold current, the population of other energy levels (sub bands) than the lasing ones must be as small as possible. Therefore, the spacing should be as large as possible. However, due to the opposing dependencies the optimum configuration is estimated to be around the intersection between both graphs. Hence, the ideal QW configuration has \(x \approx\) 0.64 and \({\text {d}_{\text {QW}}}\) \(\approx\) 8 nm.

2.4 Evaluation of the modal gain

The previous sections only considered material properties and solutions of the Schrödinger equation for QWs. This part utilizes the aforementioned results and calculates the carrier density-dependent dielectric function by applying an effective-mass 8-band k \(\cdot\) p  Hamiltonian of strained semiconductors (Enders et al. 1995; Wenzel et al. 1999). These results and the confinement factor are then used to determine the carrier density-dependent modal gain.

Figure 7 shows exemplarily the calculated carrier density-dependent modal gain spectra of a QW configuration with a thickness of 10 nm and a gallium mole fraction of 66%. These spectra are determined for carrier densities ranging from \(1.0 \times 10^{18}~\hbox {cm}^{-3}\) to \(4.0 \times 10^{18}\, \hbox {cm}^{-3}\) in \(0.15 \times 10^{18}~\hbox {cm}^{-3}\) steps. Below \(1.0 \times 10^{18}~\hbox {cm}^{-3}\), there is no net gain. One can see a blue shift of the peak wavelength as well as gain broadening with increasing carrier densities. Transition broadening (modeled by a sech function (Eliseev 1997) with a constant broadening of 10 Mev) and band filling (Pankove and Kiewit 1972) are responsible for this behavior. The peak wavelength shifts to approximately 626 nm for threshold modal gains of 5 cm−1, 7 cm−1 and 10 cm−1. The interval corresponds to typical threshold gains for 1–2 mm long lasers. The wavelength difference of 13 nm, between the electron–hole transition and gain peak wavelengths confirms our previous assumption regarding the EL wavelength aimed at. The red shift of the gain peak relative to the EL peak is caused by band gap narrowing, which has been phenomenologically accounted for (Zimmermann 1988).

The most promising QW configurations are sought after. For this purpose, the threshold sheet density for the aforementioned modal gain interval is determined. This is then used as a figure of merit parameter as it is an excitation measure. The lower the excitation level at the threshold of a laser device, the higher its efficiency and performance are going to be. Figure 8 shows the simulation results. There, one can see that all three different threshold modal gain curves have a minimum at approximately 64% and a \({\text {d}_{\text {QW}}}\)  of 8 nm. This confirms the findings from Fig. 6.

In summary, the model calculations of the modal gain verify all the assumptions made in the preceding sections. A wavelength shift between EL and laser operation of approximately 13 nm is predicted, as well as an optimum QW configuration at 64% gallium mole fraction and a QW thickness of 8 nm. Further steps are needed to verify those calculations through experimental data.

Fig. 7
figure 7

Carrier density-dependent modal gain spectra of a QW with a thickness of 10 nm and a gallium mole fraction of 66%. This graph is exemplary for all calculated QW configurations

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Fig. 8
figure 8

Threshold carrier density versus gallium mole fraction (bottom abscissa) and thickness (top abscissa) for a fixed transition wavelength of 613 nm for different values of the threshold modal gain of 5 cm−1, 7 cm−1 and 10 cm−1

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3 Broad area laser results

This part discusses the experimental verification of the previous assumptions and discusses the resulting laser performance. The theoretically chosen QW configurations and the respective energetic distances between the first hole levels and the first electron levels to each other are shown in Table 1. These configurations are labeled A, B and C for QW thicknesses of 8 nm, 10 nm and 12 nm and gallium mole fractions of 64%, 66% and 67%, respectively.

Table 1 The QW compositions and the figure of merit parameters, which are the energetic distance of \(\text {el}_1\;\) to \(\text {el}_2\;\) and \(\text {lh}_1\;\) and \(\text {hh}_1\)
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The epitaxial structure, which is introduced in Sect. 2.1, was grown by metal-organic vapor-phase epitaxy in an Aixtron AIX 2800G4 IC2 reactor. Three-inch n-GaAs (001) wafers are used as substrates, which were cut on an 6 °C angle towards the (111 )A direction. Figure 1 shows the energy diagram of the epitaxial laser structure.

The material parameters used in the theoretical evaluation (Sect. 2) are subject to uncertainties that are accounted for by test growth runs. The resulting EL spectra and X-ray diffraction (XRD) results are used to achieve the target peak EL wavelength of 613 nm and quantum well thickness, respectively. This correction results in gallium mole fractions that are only three percentage points off concerning the theoretical values. As a result, the \(\text {el}_1\;\)–\(\text {el}_2\;\)and \(\text {lh}_1\;\)–\(\text {hh}_1\;\)band trends are still relevant. The resulting configurations are displayed in the left part of Table 2. Based on this, three full laser structures were grown and their QW configurations were verified by additional XRD measurements. These wafers are then used to measure the EL spectra by contacting the topside of the wafer with a needle tip and the wafer bottom by the chuck. The emitted light is collected and guided to a spectrometer. The resulting spectra are shown in Fig. 9. They are recorded with currents in the mA range. The currents are altered to achieve a sufficient signal-to-noise ratio. In the spectra, one can identify two peaks. The strongest peak at 613 nm is attributed to desired electron-light hole transitions. The second peak visible at around 590 nm corresponds to electron-heavy hole transitions. The as-grown wafers show the desired EL properties and are used for further realization of laser devices.

Table 2 QW configurations are shown on the left. The measurement results are shown on the right half of the table
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Fig. 9
figure 9

Electroluminescence spectra of as-grown wafers with QW configurations A, B and C

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To characterize the laser performance, broad-area lasers with all three QW variations are fabricated. First, 100 μm separated stripes are deposited by photolithography. Afterward, the p-contact is build up, and the photoresist is lifted off. By doing so, a 100 μm wide p-contact is formed. Lateral current spreading is diminished by the implantation of He ions to prevent unwanted current flow. The p-contact acts as an implantation mask. Thereafter, the substrate is thinned down and the n-contact is attached. The cavity length of 1600 μm is defined by cleaving the wafer to laser bars. The devices have as-cleaved front and back facets. No facet coating is applied. The as cleaved laser bars are placed p-side up on a gold-plated copper heatsink with an active controlled temperature of 20 °C for the measurements. Single lasers on the bar are contacted on the p-side by pins and on the n-side by the heatsink. Measurements of laser spectra, as well as the power current characteristics, are taken under pulsed operation with pulse widths of 1 μs and a frequency of 5 kHz, resulting in a duty cycle of 0.5%, and a maximum current of 2 A. All three lasers show successful laser operation. The power current characteristics are shown in Fig. 10 and the results are summarized in Table 2. Structure A shows the best performance in threshold current density, output power, and conversion efficiency, followed by B and C, as has been expected by simulations in Sect. 2.

The emission spectra of the lasers at 2 A are shown in Fig. 11. Peak wavelengths of structures A, B and C are 625 nm, 626 nm and 628 nm, respectively. The assumption from Sect. 2 of a wavelength difference of about 13 nm between peak laser and EL emission is confirmed by these spectra. The wavelength variations can be attributed to epitaxial and process deviations. Higher internal losses, for example, induce a blue shift of the laser wavelength, whereas a red shift is observed for structures with fewer losses (compare Fig. 7).

In this section, all assumptions and findings from Sect. 2 were verified experimentally. Laser devices with three promising QW configurations were grown and fabricated. All of them show successful laser operation in the predicted spectral range. Furthermore, device A shows the best performance, followed by devices B and C, as predicted by calculations.

Fig. 10
figure 10

Power-current characteristic of laser with a cavity length of 1600 μm and a stripe width of 100 μm placed p-up on a gold-plated copper heatsink at a temperature of 20 °C under pulsed excitation with pulse widths of 1 μs and a frequency of 5 kHz

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Fig. 11
figure 11

Emission spectra obtained of laser with a cavity length of 1600 μm and a stripe width of 100 μm placed p-up on a gold-plated copper heatsink at a 20 °C under pulsed excitation with pulse widths of 1 μs and a frequency of 5 kHz at 2 A

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4 Conclusion

We have reported on the theoretical and experimental improvement of a laser structure for 626 nm room temperature emission. The usable gallium mole fraction was found to be in the range from 0.56–0.68. It is constrained by an indirect transition at the top range and a transition to the light holes at the lower range. Taking the critical layer thickness into account, the usable quantum well thickness range is 5–14 nm. Based on these intervals, the QW configurations for an EL wavelength of 613 nm were determined. These gallium mole fractions and \({\text {d}_{\text {QW}}}\) pairs were used to calculate the energetic distances of the QW energy levels with respect to each other. Due to these values, three combinations were proposed for further experimental verification. The theoretical QW configurations were used as target specs. Test growth runs were used to calibrate the growth process parameters. The following combinations were determined: A, B and C have quantum well thicknesses of 8 nm, 10 nm and 12 nm, respectively and gallium mole fractions of 67%, 69% and 70%. The combinations determined by this approach were then grown on 3 inch n-GaAs wafer. By cleaving the front and back facet and He ion implantation, 100 μm stripe wide and 1600 μm long broad-area laser bars were fabricated. These lasers were characterized by pulsed operation and did show successful laser operation. The trend predicted by the simulations was confirmed. Structure A shows the best performance. It has a threshold current density of 721 A/cm2, a slope of 0.384 mW/mA and a total maximum output power of 708 mW at 625 nm. This development is a key improvement for epitaxial laser structures in the 626 nm range and below.

This work paves the way for even more advances in lasers and optical amplifiers at 626nm, which will accelerate innovation in \(^{9}\hbox {Be}^{+}\)-ions based quantum computing. The presented devices are the base of the fabrication of externally wavelength-stabilized ridge waveguide lasers as well as ridge waveguide or tapered amplifiers to meet the requirements regarding beam quality, spectral linewidth and optical power.