The design and experimental realization of a type-II “W”-multiple quantum well heterostructure for emission in the λ > 1.2 *μ*m range is presented. The experimental photoluminescence spectra for different excitation intensities are analyzed using microscopic quantum theory. On the basis of the good theory–experiment agreement, the gain properties of the system are computed using the semiconductor Bloch equations. Gain values comparable to those of type-I systems are obtained.

Semiconductor laser systems in the near-infrared regime have a wide range of applications, especially in optical data transfer and telecommunication.^{1,2} Due to the absorption properties of optical fibers, wavelengths greater than 1.2 *μ*m are particularly important. More recently, vertical-external-cavity surface-emitting lasers (VECSELs) with high output power, the possibility of intra cavity frequency conversion via nonlinear crystals, and their ability of short-pulse generation have become increasingly important for a wide range of applications.^{3–5}

While the flexibility of using different semiconductor alloys, quantum confinement and/or strain allows the sample designers to access a wide variety of emission wavelengths, it is often difficult to optimize the gain and simultaneously reduce the intrinsic losses. Especially for longer wavelength applications, Auger losses lead to prominent non-radiative carrier recombination and introduce significant heating in the structures.^{6,7} Therefore, it can become desirable to utilize a somewhat more complex design, which combines two materials with relatively large band gaps in a type-II setup, where electrons and holes are spatially separated in neighboring quantum wells and the optical recombination occurs across the interfaces.^{8} In such type-II systems, more degrees of freedom are available in the design process than in a traditional type-I configuration. Thus, the gain can be optimized while, at the same time, Auger losses can be controlled.^{9}

Pioneering work in this field has been presented by Meyer et al., Kudo et al., and Vurgaftman et al. who introduced type-II “W”-material systems as active region of a laser setup.^{10–12} These structures consist of a sandwich configuration involving two different materials (see Fig. 1) whose composition and well width can be adjusted independently to achieve the desired type-II transition energy. Making use of the possibilities to independently adjust the individual band gaps and to some degree also the band alignment the resulting type-II energy difference can be tailored.

In this paper, we report on the experimental realization, the luminescence properties and the theoretical modeling of a gain structure that can be used in an optically pumped VECSEL with an emission wavelength of λ > 1.2 *μ*m. For this purpose, we construct a type-II “W”-design for a material system consisting of (Ga_{1−x}In_{x})As and Ga(As_{1−y}Sb_{y}) quantum wells. The growth of these samples is analyzed by high resolution X-ray diffraction (HR-XRD) measurements. Their experimentally obtained photoluminescence (PL) spectra for various optical excitation densities are compared to those predicted by a fully microscopic theory. This many-body theory is based on the multi-band semiconductor luminescence^{13,14} and Bloch^{14,15} equations as implemented in the software SimuLase.^{16} The predictive abilities of this theory allow us to present absorption spectra by utilizing independently determined material parameters only.

Samples of the type-II “W”-multiple quantum well heterostructure (MQWH) were grown by metal organic vapor phase epitaxy (MOVPE) using a commercial Aixtron horizontal Aix 200-gas foil rotation (GFR) reactor system. We held the reactor pressure at 50 mbar under H_{2}-carrier gas. The standard group-III precursors triethylgallium (TEGa) and trimethylindium (TMIn) in combination with tertiarybutylarsine (TBAs), tertiarybutylphosphine (TBP), and triethylantimony (TESb) were applied. Typical growth rates were chosen at 0.4 nm/s. All structures were grown on semi-insulating GaAs substrates with exact (001) (±0.1^{∘}) orientation. Prior to epitaxial growth we prepared the substrates in a TBAs-stabilized bake-out step to remove the oxide layer. The 250 nm thick GaAs buffer layer was grown at 600 ^{∘}C, while the highly strained type-II “W”-layer stack was deposited at 550 ^{∘}C. To allow for strain compensation of the active compressively strained “W”-MQWH stack, additional tensile-strained Ga(AsP)-barrier layers with small P contents were incorporated in the layer stack.

The HR-XRD pattern ((004)-reflection) of two samples with different active type-II “W”-MQWH are shown in Fig. 2. We obtained the simulated HR-XRD pattern by applying a full dynamical description as detailed in Ref. 17. The evaluated sample parameters (thicknesses and respective compositions) are indicated in the inset of Fig. 2 for the sample A and B, respectively.

In order to record spectrally resolved photoluminescence measurements, we used a germanium detector in combination with a monochromator. A continuous-wave argon ion laser was employed for optical excitation at 514 nm. The spot size on the sample was approximately 160 *μ*m (full width at half maximum) in diameter. All our measurements were performed with excitation powers varying over several orders of magnitude. Their respective spectra are shown in Fig. 3 (a) (sample A) and 3 (b) (sample B). Sample A exhibits its peak intensity at about 1.06 eV corresponding to a wavelength of 1170 nm. Due to the higher Sb content in the Ga(As_{1−y}Sb_{y}) hole-confining wells, sample B exhibits its peak intensity at about 1.01 eV corresponding to a wavelength of 1228 nm. A slight blue shift is observed for intermediate excitation densities until a red shift occurs due to saturation, which involves excessive heating of the sample.

To analyze the experimental results, we use the fully microscopic semiconductor luminescence and Bloch equations. The single-particle properties are obtained by evaluating an 8 × 8 Luttinger **k** ⋅ **p** model for the designed heterostructure to determine the band structure and the electron and hole wave-functions.^{18,19} Strain effects between the different layers of the semiconductor heterostructure are treated as described in Ref. 20.

In the next step, we calculate the dipole matrix elements *d*_{λ,ν}(**k**) between different sub bands λ and *ν* and the Coulomb matrix elements,^{21}

where *ϵ*_{0} is the background refractive index. Changes in the confinement potential due to local charge inhomogeneities are included by solving the microscopic Schrödinger–Poisson equation.^{22}

Using these results, we calculate the PL via the semiconductor luminescence equations,^{13,14} assuming thermal equilibrium for the carrier distributions $ f \lambda , k e/h $ of electrons and holes in their respective bands. Since the spontaneous emission is a purely quantum-optical effect, we have to quantize the light field and introduce the creation and annihilation operator for photons of light mode with frequency *ω _{q}* =

*cq*as $ B \u02c6 q \u2020 $ and $ B \u02c6 q $.

^{14}We now examine the dynamics of the following quantities: The photon-assisted polarization $ \Pi \lambda , \nu , k , q \u2261\u3008 B \u02c6 q \u2020 p \lambda , \nu , k \u3009$, where

*p*

_{λ,ν,k}is the microscopic polarization, and the photon-number-like correlations $ N q \u2032 , q \u2261\u3008 B \u02c6 q \u2020 B \u02c6 q \u2032 \u3009$,

with the Coulomb renormalized energies $ E \lambda , \lambda , k e/h $. The photon-assisted polarization is driven by two source terms representing the spontaneous emission $ \Omega \lambda , \nu , k , q sp $ and the stimulated emission $ \Omega \lambda , \nu , k , q st $, respectively. The electrons and holes in the structure are assumed to be in a quasi-equilibrium Fermi-Dirac configuration with the density $ n e/h = \u2211 \lambda , k f \lambda , k e/h $.

While the microscopic modeling is based on the assumption that the structures are perfect, the real systems have unavoidable growth-related impurities and imperfections, e.g. thickness fluctuations of layers and/or small changes in the material composition. We model these effects phenomenologically by convolving our computed spectra with a Gaussian distribution of a fitted width.^{23} In a way, we can interpret the resulting inhomogeneous broadening as a measure for the experimentally realized sample quality.

Figures 3(c) and 3(d) present the computed PL calculations for both samples assuming carrier densities of 0.1 − 1 × 10^{12}/cm^{2} at room temperature. Using an inhomogeneous broadening of 25 meV for both samples, we obtain very good agreement with the experimental results. In particular, the main peaks have the same shape and also the shoulder around 1.2 eV with its relative decrease for increasing Sb content agrees well with the experiments. Looking at the theory–experiment comparison for sample A with an Sb content of 17.3 % in Figs. 3(a) and 3(c), we notice a slight difference in the energetic position of the main peak. This difference could be due to a 1.7 % higher Sb content using the nominal well width or a 0.3 % higher In content when the (GaIn)As well thickness is simultaneously increased by 1 nm. However, these deviations are well within the typical uncertainties for real samples. Remarkably, for sample B, Figs. 3(b) and 3(d), we find an excellent agreement with the nominal structure parameters even without any adjustments.

On the basis of our accurate reproduction of experimental PL, we can now use the optimized structure parameters to compute the expected gain properties. For this purpose, we evaluate the semiconductor Bloch equations,^{14,15}

with the microscopic polarization *p*_{λ,ν,k}, the Coulomb renormalized energies $E$, and the Coulomb renormalized field $U$,

*E*(*t*) describes a weak probe pulse. Higher order scattering processes are summarized inside the last term of Eq. (3). We treat electron–electron and electron–phonon scattering at the level of the second Born approximation.^{19,21} From the microscopic polarization, we obtain the absorption/gain spectra of the system via $\alpha ( \omega ) \u221d\omega Im \u2211 \lambda , \nu , k d \lambda , \nu ( k ) p \lambda , \nu , k ( \omega ) / E ( \omega ) $.

Examples of the results are shown in Figs. 3(e) and 3(f) for carrier densities ranging from 0.1 to 3 × 10^{12}/cm^{2}. We obtain gain for carrier densities above 2 − 3 × 10^{12}/cm^{2} with the gain maxima reaching 500/cm for a carrier density of 3 × 10^{12}/cm^{2}. These values are in the same order of magnitude as those of typical type-I structures^{24} indicating that the designed “W”-structures should perform well in laser applications.

In conclusion, we designed and experimentally realized a type-II gain medium and theoretically analyzed the measured PL spectra. On the basis of these results, we can conclude that this material system is very promising for laser applications.

## ACKNOWLEDGMENTS

The Marburg work is a project of the Sonderforschungsbereich 1083 funded by the Deutsche Forschungsgemeinschaft (DFG). The work at Nonlinear Control Strategies Inc. is supported via STTR Phase II, Contract # FA9550-13-C-0009.