The most important and difficult part of QCL epitaxy is fabrication of active region superlattice. The active region superlattice is built of two ternary compounds. The wells are made of InxGa1-xAs while barrier layers consist of InyAl1-yAs layers. In the present case these are In0.53Ga0.47As and In0.52Al0.48As layers lattice matched to InP substrate. It is however not recommended to calibrate the growth of thin layers using bulk layers parameters. In MBE technology the composition and growth rate of thin layers in QCL active region can differ by as much as 2% from those of bulk layers because of burst effect of effusion cells. The calibration based on the growth of single superlattice is not sufficient because in this case X-ray diffraction measurements allow for direct determination of only two parameters; the superlattice zero order peak position (SL0) and period thickness. To fit simulated 2θ/ω curve to experiment in dynamical diffraction theory a three different variables should be taken into account: InxGa1-xAs and InyAl1-yAs composition as well as superlattice period. The solution of above described problem is double test superlattice structure, described in the following section.
4.1. Double Superlattice Test Structures
The double superlattice test structure is a method used for precise determination of the structural parameters of periodic heterostructure [
16]. This approach was applied by us to calibrate the In
xGa
1-xAs/In
yAl
1-yAs superlattice active region of quantum cascade laser devices. In the present work the double superlattice test structures were grown according to scheme shown in
Figure 3.
The double SLs were grown on the 500 nm thick Iny’Al1-y’As buffer layer. As the first the 4 nm period superlattice (SL1) was grown, the second one was SL2 with 6 nm period. A thinner superlattice SL1 consisted of 60 periods and the thicker one SL2 of 40. On the top of the double superlattice test structure the 500 nm Inx’Ga1-x’As layer was grown. The nominal layers thicknesses in InxGa1-xAs/InyAl1-yAs SL1 were the same and equal to 2 nm. The same thickness of 2 nm was also InyAl1-yAs layer in SL2, while planned InxGa1-xAs layer in SL2 was two times thicker than the one in SL1. It was realized by different deposition times of the InxGa1-xAs layer in SL1 and SL2.
The thicknesses of InxGa1-xAs and InyAl1-yAs layers of investigated double SLs were chosen as follows: in SL1 thicknesses correspond to typical for the injector region whereas in SL2 they are typical to quantum wells of active region. The nominal indium stoichiometric coefficient for Inx(x’)Ga1-x(x’)As layers (superlattice and the overlayer) was x(x’) = 0.533 and for Iny(y’)Al1-y(y’)As it was y(y’) = 0.522 (superlattice and the buffer). The buffer and the overlayer were incorporated into test structures to resemble the situation in QCL.
The method of determination of superlattice layers thicknesses and compositions is presented below. The basis of this analysis was the assumption that the growth rates of In
xGa
1-xAs (
VInGaAs) and In
yAl
1-yAs (
VInAlAs) layers are the same in the two superlattices SL1 and SL2 and that the growth rate is linearly dependent on deposition time, which is true for very thin layers with similar thicknesses. It was examined by us in different experiment. The
VInGaAs and
VInAlAs are directly related to layers thicknesses according to:
where
d1,2 InGaAs, InAlAs are the thicknesses of In
xGa
1-xAs and In
yAl
1-yAs layers in SL1 and SL2;
t1,2 InGaAs and
t1,2 InAlAs are the growth times of layers. The only known were values of growth times:
t1 InAlAs =
t2 InAlAs = 14 s;
t1 InGaAs = 13 s;
t2 InGaAs = 26 s. The thicknesses of In
xGa
1-xAs and In
yAl
1-yAs layers of SL1 and SL2 can also be expressed by formulas:
where
n1,2 InGaAs and
n1,2 InAlAs are the number of In
xGa
1-xAs and In
yAl
1-yAs monolayers in each supelarlattice (for In
yAl
1-yAs this number is the same);
aInGaAs and
aInAlAs are the perpendicular lattice constants of In
xGa
1-xAs and In
yAl
1-yAs superlattice layers. The perpendicular lattice constants
aInGaAs and
aInAlAs can be calculated using formula from [
17]:
where
a0 InGaAs, InAlAs are bulk lattice constants of In
xGa
1-xAs and In
yAl
1-yAs layers calculated using the Vegard’s law;
aInP lattice constant of InP substrate; C
11 InGaAs, InAlAs and C
12 InGaAs, InAlAs are the elastic stiffness constants of ternary compounds. The knowledge of real values of stoichiometric coefficients
x and
y is required to calculate
aInGaAs and
aInAlAs from eq. (7). For this purpose, the self-consistent analysis of HRXRD diffraction curves of double test superlattice structures was performed. The investigation was made as follows.
First, the period thickness of SL1 and SL2 (
DSL1 and
DSL2) and values of perpendicular lattice mismatch (Δa/a)
⊥ SL1 SL2 were directly obtained from the measured 2θ/ω curve. Because the
DSL1 and
DSL2 are solved as follows:
and after substituting eqs. (5), (6) to (8) and (9) it resulted:
Further, subtracting (11) from (10) and including that
d2 InGaAs = 2
d1 InGaAs the thickness of In
xGa
1-xAs layer in SL1 was obtained experimentally from:
then thickness of In
yAl
1-yAs layer was calculated from:
The information about the thickness of InxGa1-xAs and InyAl1-yAs layers in SL1 allowed to calculate the growth rates of layers in SL1 and SL2 from (3) and (4). At this stage the InxGa1-xAs and InyAl1-yAs thickness of SL1 and SL2 layers and VInGaAs and VInAlAs were experimentally found. The single InxGa1-xAs and InyAl1-yAs superlattice thicknesses layers were used to calculate the average perpendicular lattice constant of superlattice 1 and 2 which allowed to obtain the (Δa/a)⊥ SL1 and (Δa/a)⊥ SL2. Then the calculated values of perpendicular lattice mismatch of SL1 and SL2 were compared with the experimental one. The lattice constant of single InxGa1-xAs and InyAl1-yAs superlattice layers and average lattice constants of SL1 and SL2 were found by changing the values of x and y until the calculated and experimental values of (Δa/a)⊥ SL1 and (Δa/a)⊥ SL2 were equal to each other. The method of this analysis was named self-consistent because determination of: thicknesses and stoichiometric coefficients of single layers in SL1 and SL2, lattice constant of layers and average lattice constant of superlattices and finally the perpendicular lattice mismatch of SL1 and SL2 takes place for these superlattices simultaneously. After this procedure, using the obtained structural parameters, the simulation of 2θ/ω diffraction curve was done and compared with experimental one. Independently, apart from the procedure, the stoichiometric coefficients of top Inx’Ga1-x’As layer and Iny’Al1-y’As buffer were determined directly from the simulation and comparison with the measured curve.
The discussed procedure was applied to find calibration parameters for four: #1, #2, #3 and #4 double test superlattices;
Figure 4. In this figure the superlattice satellite peaks of SL
1 and SL
2 are marked.
The comparison of measured curves for SL #4 and simulated one is shown in
Figure 5a,b. The simulation very well reproduces the angular positions and intensities of each individual peaks.
The structural parameters of heterostructures obtained from the analysis of HRXRD curves are presented in
Table 3. Furthermore during the self-consistent procedure the growth rates of superlattice In
xGa
1-xAs and In
yAl
1-yAs layer thicknesses were also calculated. These values are not showed in
Table 3 but can be easily calculated from eqs. (3) and (4).
4.2. Practical Realization of Epitaxial Technology
The practical application of the method of optimizing the growth process of QCL lasers with the use of double superlattice test structures is presented in this chapter. The starting point was the calibration of the compositions and growth rates of the Inx’Ga1-x’As and Iny’Al1-y’As bulk layers. It was realized by growing test layers with a thickness of 500 nm for both of these materials. Then, the X-ray diffraction characterization was performed and the growth parameters were corrected by appropriate change of beam fluxes. The procedure was repeated until lattice matched compositions for Inx’Ga1-x’As and Iny’Al1-y’As layers were obtained.
Based on these values, a test double superlattice heterostructure was made. Due to the burst effect when the shutters of the effusion cells are opened, thin layers and bulk layers in the MBE technology are characterized by a different growth rates and compositions for the same process parameters. Typical for the QCL laser, a thin layer with a thickness of 2 nm grows approximately 13 s, while the growth of bulk layer with a thickness of 500 nm takes about 40 min. In the latter case, long-term stabilization takes place and the effect of material vapor explosion (Burst effect) is negligible. In the case of thin layers, the total growth of the layer takes place during this effect, and thus we obtain different growth rates and layer compositions. This difference is small, but noticeable and with such a complicated device as a quantum cascade laser, it is significant for its operation. Therefore, different flux and temperature settings of the effusion cells should be used for thick waveguide layers and for thin layers of the active area superlattice. In our case, this was accomplished by calibrating the growth parameters for the thick layers and introducing a temperature offset during the growth of the thin layers of the test superlattices. As a rule, these values are not large and amount to -1 °C for the Ga source and -2 °C for the Al source. At source temperatures reaching several hundred degrees, these differences are small and allow for a quick change in the growth rate between thin and thick layers.
Using a standard temperature ramp of 10 °C/min, it takes 6 s for Ga and 12 s for Al, respectively, which is comparable to the growth of a single layer in the superlattice of the laser active region. This tuning is done without the use of growth interruptions. After the end of the buffer growth, and at the beginning of the superlattice growth, the temperature of Ga changes during the growth of the first thin layer of In
yAl
1-yAs, similarly during the growth of the next In
xGa
1-xAs layer, the temperature of Al changes. Calibration of the composition for thin layers, starting from the compositions adjusted for thick layers, relays on finding the values of the cell temperature offsets for Ga and Al giving the compositions lattice matched to the InP substrate for thin layers of the test superlattice. The whole thing usually takes a few iterations (test processes). The entire cycle is graphically depicted in
Figure 6a for In
xGa
1-xAs layers and
Figure 6b for In
yAl
1-yAs layers.
For the test structure #1, the growth conditions obtained during the calibration of compositions for bulk layers with a thickness of 500 nm were used, which were characterized by a very good lattice match to the InP substrate. For superlattice layers, however, these conditions led to different compositions with a difference of about 1% in composition for InxGa1-xAs and about 2% difference in composition for InyAl1-yAs. It can be seen that after 3 to 4 iterations it was possible to obtain matched compositions of both layers for the double superlattice test structure. During this procedure, the growth rate of the thin layers also changes.
Based on the test structures of the double superlattice, knowing the growth time of both InxGa1-xAs and InyAl1-yAs layers, we are able to calculate the growth rate of individual materials. During the growth of the full device structure, these growth rate values are used to calculate the growth time of the laser active area. The layer thicknesses in the test superlattice are selected so as to correspond to the typical thicknesses of the well and barriers of the injector and the active area. Such a calibration procedure allows for precise and unambiguous determination of the deposition parameters for thin layers.
Then, a series of complete laser structures were fabricated. When making a series of laser structures, the effusion cells were calibrated to obtain the same flux values with only minor temperature corrections. At the end of the series of heterostructures, the double superlattice test structure was performed again to unambiguously check whether the conditions of the epitaxial process had not changed. This is necessary because the measurement of cascade laser structures using X-ray diffraction methods, due to the very high degree of complexity of the layer system, allows direct measurement of only the total period of the superlattice of the active area and the position of the zero peak informing about the average lattice constant of layers forming the active area.
Determination of the composition and thickness of individual layers forming the superlattice of the active area is carried out by simulation of the diffraction curve, taking into account the intensities of satellite peaks of higher orders. This gives a certain degree of freedom and makes it possible to determine several combinations of thicknesses and compositions giving an almost identical appearance of the simulated diffraction curve. However, this dispersion is small and reaches about 0.1% in the composition of the layers and about 0.1 nm of the thickness of individual layers forming the active region. Nevertheless, it cannot be said in this case that it is a measurement result, but only an approximate simulation result. Therefore, the execution of the double superlattice test structure at the end of a series of instrument processes is so important, as it allows for unambiguous determination of the thickness and composition of thin layers. It is a check confirming the credibility of the obtained results.
Thanks to such a procedure, we obtain the possibility of continuous control of growth parameters, in particular maintaining stable compositions and thicknesses of In
xGa
1-xAs and In
yAl
1-yAs thin layers forming a superlattice. This is especially important for such complex heterostructures as the active region superlattice, where only direct measurement of the position of the zero peak and the period of the active region is possible. In this case, the simulation of individual compositions and layers thicknesses is also based on the results obtained on the test structures of the double superlattice made before and after a series of device heterostructures, so that the performed HRXRD simulations reflect the real parameters of the heterostructure as best as possible.
Figure 7a presents the relative deviations of the actual period thickness from the planned value for six consecutively grown heterostructures of QCL lasers. The corresponding position of the SL0 peak for these structures is shown in
Figure 7b.
Between the QCL#3 and QCL#4 processes, a test superlattice was made to better control the parameters of the deposited layers. The obtained result confirmed the good agreement of the obtained parameters and allowed for the continuation of the deposition of the next three device structures. Then, the double superlattice test structure was performed again to check the stability. It showed that the deposition parameters of the heterostructure changed slightly. Therefore, another series of double superlattice test heterostructures were grown in order to calibrate the compositions of individual layers in accordance with the planned values. Such a procedure allows for the continuous maintenance of high accuracy of compositions and growth rates for thin layers in the superlattice, which results in high homogeneity and repeatability of the manufactured device heterostructures.
In addition to the measurements of directly measurable parameters, diffraction profiles were also simulated for the entire series of six full quantum structures of cascade lasers. These simulations were supported by additional results obtained from double superlattice test structures performed before, during and after a series of device heterostructures. This was related to the need to obtain the best fit of the simulated curve to the experiment. The simulations performed for full laser structures show slight fluctuations in the composition of thin layers in relation to the plan. The compositions of the In
xGa
1-xAs and In
yAl
1-yAs layers forming the active region superlattice for individual QCL laser heterostructures are shown in
Figure 8a,b, respectively. The dotted lines show the compositions matched to the InP substrate.
The obtained compositions of thin wells and barrier layers in the active region of the QCL laser show a very good fit to the planned values and high stability for the entire series of heterostructures. The In content in the InxGa1-xAs layers was x = 0.532% (-0.1% to +0.5%), and for the InyAl1-yAs layers y = 0.522% (-0.4% to +0.2%). The period thickness was d = 68 nm (-0.5% to +0.3%), while the position of the zero peak (nominally 300 ppm) ranged from -130 ppm to 660 ppm. The obtained parameters prove a very good match of compositions and thicknesses, as well as high control of the parameters of the growth process for the whole series of device processes. Obtaining composition and thickness dispersion below ±0.5% for structures as complex as QCL lasers is an extremely difficult and demanding technological issue. The average SL0 peak position below ±500 ppm from nominal position indicates very good lattice matching of the deposited layers with respect to the InP substrate. These values are the best verification of the described method of conducting and optimizing the epitaxial process, allowing for high degree of control and repeatability both from run to run and between growth campaigns.
4.3. Growth of Device Structures
The full device structure consisted of active periods embedded into waveguide. The layer sequence of one period of the structure, in nanometers, was:
4.1 (IB), 3.1,
0.8, 4.6,
0.8, 5.4,
0.7, 5.5,
0.8, 4.6,
2.1 (EB), 4.0,
1.0, 3.5,
1.6, 3.6,
2.2, 3.2, 1.7, 3.2,
2.5, 3.3,
2.6, 3.1 nm. The active period was repeated 60 times in grown laser structures. The waveguide from the bottom side was formed by a low doped InP (2×10
17cm
−3) substrate and from the top by 2.5 μm thick AlInAs layer covered by heavily doped InGaAs plasmonic and contact layer. Such construction of the waveguide was dictated by the need to optimize its thermal properties. The different thicknesses of InGaAs layers enclosing laser core were used to symmetrize transverse field distribution in the waveguide The details of the layer structure of grown devices are listed in the
Table 4.
Table 4.
Layer structure of In0.533Ga0.467As/In0.522Al0.478As/InP laser.
Table 4.
Layer structure of In0.533Ga0.467As/In0.522Al0.478As/InP laser.
200 nm |
InGaAs:Si |
n=2×1019cm−3
|
Contact layer |
500 nm |
InGaAs:Si |
n=8×1018cm−3
|
Plasmonic Layer |
2,5 µm |
InAlAs:Si |
n=5×1016cm−3
|
Upper Waveguide |
200 nm |
InGaAs:Si |
n=4×1016cm3
|
4.08 μm |
60 x InGaAs/InAlAs |
Active Region (AR) |
500 nm |
InGaAs:Si |
n=4×1016cm−3
|
Lower Waveguide |
500 µm - Substrate |
InP |
n=2×1017cm−3
|
In order to minimize number of oval defects two gallium cells was used. The growth was performed also with two In sources used simultaneously and one aluminum source. The heterostructures were lattice matched to InP substrate. The growth rate of In0.533Ga0.467As was 0.182 nm/s and that of In0.523Al0.478As was 0.195 nm/s, which corresponds roughly to 0.65 µm/h and 0.70 µm/h, respectively.
For growth of In
0.533Ga
0.467As two indium and two gallium effusion cells were used simultaneously. This was made to minimalize the amount of oval defects in the heterostructures [
18]. For growth of In
0.523Al
0.478As two indium and one aluminum cells were used. The growth temperature was set to T = 520 °C for all of the layers except QCL’s bulk In
0.523Al
0.478As waveguide layer which was grown at T = 480 °C [
19]. The V/III ratio was approximately equal to 39 for all the layers except In
0.523Al
0.478As bulk cladding layers for which it was 45. The arsenic flux was then 1.6x10
−5 Torr and 1.9×10
−5 Torr, respectively. During the growth the substrate was rotated with velocity of 10 min
−1 for all layers except the active region for which it was 60 min
−1.
The QCL structure exemplary diffraction curve is presented in
Figure 9a. As can be seen a numerous narrow and intense satellite peaks are observed. This indicates that the period thickness and stoichiometric coefficients
x and
y of In
xGa
(1-x)As and In
yAl
(1-y)As AR layers were not changed during the growth process. The most intense: SL0 superlattice, InP substrate and In
0.5375GaAs and In
0.5189AlAs layers peaks are observed in the angular range of 63-63.5 degrees and detailed view is showed in
Figure 9b. The angular position of individual peaks in relation to the InP peak allowed to determine the perpendicular lattice mismatch of: Active Region – 400 ppm, In
0.5375GaAs – 920 ppm and In
0.5189AlAs –300 ppm. Furthermore the reciprocal lattice space maps of symmetrical 004 and asymmetrical -2-24 reflections around InP were measured (
Figure 9c,d). It is seen from these that reciprocal lattice points are narrow and diffuse scattering around these points is very low indicating low defect density. The heterostructure is also not relaxed.
The grown structures were processed into mesa Fabry–Perot lasers using standard processing technology [
21]. For the isolation layer, Si
3N
4 was used. Low resistivity electrical contacts were alloyed at 370 °C for 60 s. The Ti/Pt/Au alloy was used to the epi-side, and AuGe/Ni/Au for the low doped substrate side. The lasers were cleaved into bars with the length of 4 mm and mounted epi-side up on Au-plated AlN submount. The stripe width was W= 20 μm. The devices with uncoated facets were measured. The temperature of the laser was controlled by Peltier element.
Figure 10 shows emission spectra of the lasers in the temperature range from 10 °C to 40 °C. The inset in the figure shows light-current and voltage-current (LIV) characteristics for the same temperatures. The lasers were pulse driven by 200 ns pulses with 5 kHz repetition. The laser power drop above 5 A is caused by heating of the device because we use InAlAs waveguide, which has rather poor thermal conductivity (0.05 Wcm
−1K
−1) as compared to thermal conductivity of InP (0.68 Wcm
−1K
−1). This particular construction of waveguide has been imposed by lack of P-cell in our system.
The emission spectra were measured by Fourier spectrometer and cooled MCT detector. The peak of room temperature (20 °C) emission shows a perfect fit to theoretically predicted wavelength of 13.64 μm and proves precise control of epitaxial process.