Excitonic transitions in highly efficient (GaIn)As/Ga(AsSb) type-II quantum-well structures

Semiconductor lasers are essential devices for telecommunications and optical data transfer.^1,2 In particular, the near infrared spectral region with wavelengths exceeding 1.2 μm is of particular interest for data transfer through optical fibers. Unfortunately, devices emitting in this spectral window typically suffer from significant Auger losses.^3,4 In an attempt to suppress this intrinsic loss mechanism, type-II heterostructure designs can be utilized as the active region of an infrared “W”-laser configuration.^5,6 Here, the electrons and holes are spatially separated into adjacent layers of rather large bandgap materials and recombine across the interfaces (see Fig. 1). Through proper choice of the constituent materials, the “W”-design allows for an increased flexibility in the design of devices with reduced Auger losses, high gain, and an emission wavelength of λ > 1.2 μm.⁷ 

In this paper, we present a (GaIn)As/Ga(AsSb)-based “W”-multiple quantum well heterostructure (MQWH) desired for use as active medium in a vertical-external-cavity surface emitting laser (VECSEL) for the application in the near infrared. The “W”-MQWH is investigated using photoluminescence (PL) spectroscopy and photomodulation reflectance (PR) spectroscopy. The results are analyzed using a fully microscopic theory to reveal the complex structure of electron and hole states and their type-I or type-II character upon excitation.

The samples were grown by metal organic vapor-phase epitaxy (MOVPE) on semi-insulating GaAs(001) substrates with a growth rate of approximately 0.4 nm/s. A 250 nm thick GaAs buffer layer was deposited on the substrate at 600 °C, while the “W”-MQWH was grown at 550 °C. The “W”-MQWH is made up of a Ga(As_1−ySb_y)−quantum well (QW) surrounded by two identical (Ga_1−xIn_x)As-QWs and enclosed by a barrier consisting of GaAs and Ga(As_1−zP_z) for strain compensation. This unit is repeated ten times. Here, we investigate two samples. Layer thicknesses and respective compositions presented in the following were determined very accurately using high resolution X-ray diffraction (HR-XRD).^8,9 The first sample has a Sb and In content of 17.3% Sb and 22.0% In and the respective layer thicknesses are 4.0 nm and 5.7 nm. A 10 nm GaAs layer and a 144 nm Ga(As_0.959P_0.041) layer form the barriers. The second sample contains 21.3% Sb and 21.6% In in the “W”-MQWH layers, which are of the same thickness as in the first sample. Its barriers are composed of a 10 nm GaAs layer and a 140 nm Ga(As_0.954P_0.046) layer. In the following, the samples will be identified by their Sb content. The structure and the resulting confinement potentials for electrons and holes are depicted schematically in Fig. 1.

The PL was measured using a diode pumped solid-state laser to excite the samples at 532 nm. The excitation laser was chopped; so, the PL could be amplified using lock-in technique. The detection was done by a standard setup consisting of a 0.5 m grating spectrometer and a liquid-nitrogen cooled germanium detector.

PR measurements are used to reveal the excitonic states. This is advantageous, because in modulation spectroscopy the derivatives of the transition bands are enhanced compared to conventional reflectance spectroscopy due to the largely disappearing background. Furthermore, very weak structures, such as type-II excitations, can be observed.^10,11 The PR is measured in line-scan mode at room temperature. The light from a standard tungsten-halogen lamp is dispersed by a 1 m Czerny–Turner grating monochromator. The spectral resolution of the system is set to 1.5 nm. Higher diffraction orders are suppressed by either a color glass long-pass filter or a Si-wafer. The setup features metal-coated all-reflective optics to eliminate any chromatic errors. In particular, off-axis parabolic mirrors were used for all focusing optics minimizing astigmatism. The light is focused on to the sample to a diameter of about 0.5 mm under an angle of about 30° to the sample's surface normal. All reflected light is then relayed on single-stage thermoelectrically cooled (GaIn)As photodiode operating with a small bias. The sample was modulated by a weakly focused 532 nm diode-pumped solid-state laser at a photon flux of approximately $1×108/cm2$⁠, which was mechanically chopped. Due to the above bandgap excitation, the modulation results from both, a modulation of the built-in electric field near the surface of the crystal^12,13 as well as from changes in the population of the conduction and valence bands.¹⁴ The absolute reflectance and the modulated signal were electronically separated by a passive frequency crossover and acquired simultaneously by the same lock-in amplifier. Additionally, a background including PL was recorded and subtracted from the signal. The normalized differential reflectance $ΔR/R$ is then calculated straight forwardly from the in-phase part of the differential reflectance (⁠$ΔR$⁠) and the unmodulated absolute reflectance (⁠$R=R*−PL$⁠) corrected for the background PL.

In Fig. 2, the room-temperature PL (red lines) and the PR (black lines) are depicted. Below 1.2 eV, the PR spectra are scaled by a factor of 3 for better visibility. For both, the 17.3% Sb and the 21.3% Sb sample, several signatures in the PR can be seen as indicated by the arrows. We can distinguish two energy ranges with very different oscillator strengths. As we will elucidate below, the PR spectra below about 1.2 eV (range “indirect”) are dominated by excitations across the (GaIn)As/Ga(AsSb) interface, whereas range “direct” is dominated by spatially direct transitions.

The strong features around 1.435 eV and 1.470 eV in both samples can be attributed to the GaAs barrier and substrate¹⁵ and the Ga(AsP) cladding layers, respectively.¹⁶ Furthermore, for both samples, a very strong type-II luminescence is observed in the infrared, due to the recombination of electrons in the (GaIn)As and holes in the Ga(AsSb). Remarkably, the PR measurements allow for observing the corresponding type-II excitation at 1.066 eV for the 17.3% Sb sample and at 1.010 eV for the 21.3% Sb sample. This is astonishing because the oscillator strength of the type-II transition is rather weak. It is most interesting to note that even further excited type-II states marked by the blue arrows in Fig. 2 in the “indirect” range could be identified. For the 17.3% Sb sample, one state can be observed at an approximately 1.180 eV, whereas the 21.3% Sb sample exhibits two excited states around 1.112 eV and 1.160 eV, respectively.

For both the samples, three further transitions around 1.230 eV, 1.255 eV, and 1.325 eV can be observed, as indicated by the blue arrows in Fig. 2. With the help of the theoretical analysis discussed below, these signatures can be assigned to type-I transitions in the (GaIn)As. We will discuss the oscillator strength of the transitions in the framework of the microscopic theory. In both samples, the direct excitonic transitions are located almost at the same energy, which can be explained by the fact that the In content in the (GaIn)As differs only by 0.4%. The type-II transitions exhibit different energies in both samples, because the Sb content is different by about 4%. This strongly influences the bandgap and the respective valence-band energy of the Ga(AsSb)¹⁷ and therefore eventually the type-II transitions.

To support the identification of the observed transitions, we compare the experimental findings with the results obtained from a fully microscopic model. To compute the change of the reflectivity between excited and unexcited semiconductor heterostructures, we apply the semiconductor Bloch equations (SBE).^18–20 This way, we access the complex optical susceptibility $χ(ω)$ whose imaginary part is directly proportional to the absorption and the real part yields the refractive index change. The SBE are evaluated at the second Born level to properly account for the intrinsic microscopic carrier scattering effects.^21,22 To model the sample inhomogeneities of the experimental samples, we apply an inhomogeneous broadening to our theoretical spectra by convolving them with a Gaussian distribution of the bandgap energies.²³ 

After computing the refractive index spectra, we use Fresnel's formula to calculate the reflectivity.²⁴ To obtain the PR, we then use the reflectivity derived under unexcited conditions and a second one where we take the modulation via optical excitation into account.²⁵ In addition to the PR, our calculations yield the eigenenergies and the carrier wave functions within the active region of the semiconductor heterostructure. Thus, we can identify whether a transition is of type-I or type-II character.

In all our calculations, we use 8 × 8 multiband $k·p$ theory for the band structure.^21,26 To take care of local charge separation, we solve the microscopic Schrödinger–Poisson equation.²⁷ The confinement potentials, wave functions, and band structure details are used to compute the optical and Coulomb matrix elements needed in the evaluation of the SBE. The material parameters used to evaluate the microscopic and macroscopic response of the semiconductor sample can be found in Ref. 8.

In the following, we perform a systematic comparison of the experimental PR results with calculated spectra. Figure 3 presents the PR spectra for both samples, where the calculations were performed at low excitation carrier density conditions of $1×10−9/cm2$ and a temperature of 300 K. For the unexcited sample, we use an inhomogeneous broadening of 4 meV. Due to excitation induced dephasing, the inhomogeneous broadening is increased to 12 meV for the excited sample. For illustration, we also show the calculated absorption spectra for both samples. We notice a very good overall theory–experiment agreement of the excitation peak positions. All of the main signatures in the PR have a corresponding peak in the calculated absorption. Our theory reproduces all small signals in “indirect” region between 1 eV and 1.2 eV very well, both in position and relative size. Only the signatures for energies higher than 1.2 eV (“direct” region) are slightly off with respect to the size of the experimental signal. We believe that the origin of this deviation is due to the assumption made in our theoretical evaluation that the carriers are in fully relaxed quasi equilibrium Fermi distributions, whereas in the experiment, some of the carriers are probably still in energetically higher states.

Based on the good agreement for the peak positions, we use the corresponding electron and hole wave functions to identify the nature of the observed signatures (see Fig. 4). Electrons confined in the two (GaIn)As wells can be in one of the two almost degenerate states e1 and e2. A type-II transition appears when the respective hole which recombines with an electron from state e1 or e2 is confined in the Ga(AsSb) well. Both samples with their different Sb concentrations in the quantum wells have three confined hole states h1, h2, and h3 in the Ga(AsSb) well (see Fig. 4(a)). Every possible transition between one of the first two electron states and one of the first three hole states is, therefore, a type-II transition through the interface between the (GaIn)As and Ga(AsSb).

All possible type-I transitions are energetically higher and exhibit also a higher dipole transition strength, as can be seen in Fig. 3. Figure 4(b) presents the hole wave functions participating in the transitions producing the strong features in Fig. 3. All of them have a very similar shape belonging to either e1 or e2, which explains that the respective dipole transition probability is high and result in a significant contributions to the PR spectrum. We marked all transition with a relative strength of at least 10% in Fig. 3; the height of the corresponding gray lines depicts the relative dipole transition strength.

An interesting difference between both samples is caused by the 4% difference in their Sb concentration. On one hand, all type-II transitions have higher energies for the sample containing 17.3% Sb due to a smaller valence band offset. On the other hand, the type-II transitions are weaker compared to the type-I transitions due to a stronger hole localization for the sample with an Sb content of 21.3%.

In conclusion, we were able to explain the complex structure of electron and hole states involved in the excitonic PR spectra of (GaIn)As/Ga(AsSb) “W”-shape quantum-well heterostructures. The energetically lowest three transitions observed in the PR experiments all clearly exhibit a type-II character with the holes in the Ga(AsSb) well and the electrons in the cladding (GaIn)As wells. The comparison of experimental PR measurements and microscopic model calculations reveals the first clear direct transition to be caused by the h4 and h5 hole states. The dipole transitions of the type-II signals are much smaller in comparison to the direct transitions due to the reduced wave function overlap, which explains the weaker experimental signatures. We could also show that the type-II character can be varied by changing the Sb concentration in the innermost Ga(AsSb) quantum well. It is worth mentioning that the quantum efficiency of these structures is very high despite the type-II character, which makes this quantum well system a promising material for laser application in the near infrared.

The Marburg work was a project of the Sonderforschungsbereich 1083 funded by the Deutsche Forschungsgemeinschaft (DFG). S.G., N.W.R., and J.V. gratefully acknowledge the financial support of the DFG in the framework of the GRK 1782. The work at the University of Arizona was supported by the AFOSR BRI Grant FA9550-14-1-0062.