domain: spi phys

text:
Laura Monge-Bartolome

B E Shi

Billy Lai

Guilhem Boissier

Laure Cerutti

Jeabaptiste Rodriguez

May Kei

Lau

Eric Tournié
email: eric.tournie@umontpellier.fr

GaSb-based laser diodes grown on MOCVD GaAs-on-Si templates

We report GaSb-based laser diodes (LDs) grown on on-axis (001) Si substrates and emitting at 2.3 µm. Two series of LDs were studied and compared. For the first series, a GaAs-based buffer layer was first grown by metal organic chemical vapor deposition (MOCVD) before growing the laser heterostructure by molecular-beam epitaxy (MBE). For the second series, a MOCVD GaSb buffer layer was added between the MOCVD GaAs buffer layer and the MBE laser heterostructure. Both series of LDs exhibited threshold currents in the 50-100 mA range and several mW output power at room temperature. They demonstrated continuous wave operation (CW) up to 70°C (set-up limited) without thermal rollover. Broad area LDs exhibited record threshold-current densities in the 250-350 A.cm -2 range for the second series of LDs, in spite of cracks that appeared during device processing. These results show that the design and fabrication steps of the buffer-layer stacks are critical issues in the epitaxial integration of GaSb-based optoelectronic devices on Si substrates and offer room for much performance improvement.

Introduction

There is an increasing interest for the integration of III-V semiconductor compounds on on-axis (001) silicon substrates. It is motivated by the excellent optical characteristics of III-V materials and the mature, low-cost and mass production capabilities of the silicon industry. Silicon photonics has indeed made great progress specially regarding the integration of passive devices, [START_REF] Thomson | Roadmap on silicon photonics[END_REF] e.g. (de)multiplexer [START_REF] Wang | Low crosstalk Bragg grating/Mach-Zehnder interferometer optical add-drop multiplexer in silicon photonics[END_REF] and splitter [START_REF] Wu | Ultra-broadband high-performance polarizing beam splitter on silicon[END_REF]. However, due to the indirect band gap of silicon, an efficient laser source is still missing, and integration of III-V material is required. Although impressive results were achieved with bonding techniques [START_REF] Hattasan | Heterogeneous GaSb/SOI mid-infrared photonic integrated circuits for spectroscopic applications[END_REF][START_REF] Jhang | InAs/GaAs quantum dot lasers on silicon-on-insulator substrates by metal-stripe wafer bonding[END_REF][START_REF] Atabaki | Integrating photonics with silicon nanoelectronics for the next generation of systems on a chip[END_REF][START_REF] Spott | Interband cascade laser on silicon[END_REF], the direct epitaxy of the III-V structures on silicon is the most promising approach for large scale integration [START_REF] Bowers | A comparison of four approaches to photonic integration[END_REF][START_REF] Liu | Photonic integration with epitaxial III-V on silicon[END_REF]. Nevertheless, the direct growth of III-V materials on silicon is very challenging. The large lattice mismatch and the polarity mismatch existing between Si and the III-Vs lead to the generation of a large density of defects that degrades the material quality and consequently the devices performance [START_REF] Kroemer | Polar-on-nonpolar epitaxy[END_REF][START_REF] Kawanami | Heteroepitaxial technologies of III-V on Si[END_REF][START_REF] Liang | Recent progress in lasers on silicon[END_REF]. Great efforts have been dedicated to address this issue [START_REF] Li | Epitaxial growth of highly mismatched III-V materials on (001) silicon for electronics and optoelectronics[END_REF][START_REF] Megalini | Strain-Compensated InGaAsP Superlattices for Defect Reduction of InP Grown on Exact-Oriented (001) Patterned Si Substrates by Metal Organic Chemical Vapor Deposition[END_REF] and lasers directly grown on silicon have been demonstrated. Most progress have been carried out on laser emitting at telecom wavelengths [START_REF] Castellano | Room-temperature continuous-wave operation in the telecom wavelength range of GaSb-based lasers monolithically grown on Si[END_REF][START_REF] Xue | 155 Mm Electrically Pumped Continuous Wave Lasing of Quantum Dash Lasers Grown on Silicon[END_REF][START_REF] Zhu | 1.5 µ m quantum-dot diode lasers directly grown on CMOS-standard (001) silicon[END_REF][START_REF] Kwoen | All MBE grown InAs/GaAs quantum dot lasers on on-axis Si (001)[END_REF][START_REF] Kwoen | High-temperature continuous-wave operation of directly grown InAs/GaAs quantum dot lasers on on-axis Si (001)[END_REF] driven by the increasing demand for data-and tele-communication, with the best performance reported to the date, achieved by GaAs quantum dot lasers (QDLs) grown on on-axis Si, thanks to a relative insensitivity to threading dislocations (TDs).

Another highly-demanded application which would benefit from photonic integrated circuits (PICs) is chemical sensing [START_REF]Global industry analysts, Inc[END_REF]. Currently, optical sensors are rather bulky and expensive, and they rely on discrete devices. PICs would lead to compact and cost-effective sensors. Regarding optical sensing, the target emission wavelength is within the mid-infrared range, where many molecules exhibit fingerprint absorption lines [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF]. III-Sb-based lasers have proven to be the unique technology able to cover the whole IR spectral range [START_REF] Baranov | Semiconductor Lasers: Fundamentals and Applications[END_REF][START_REF] Tournié | Mid-Infrared Optoelectronics[END_REF]. Laser-on-Si demonstrations include GaSb LDs [START_REF] Reboul | Continuous-wave operation above room temperature of GaSb-based laser diodes grown on Si[END_REF] and InAs/AlSb quantum cascade lasers (QCLs) [START_REF] Nguyen-Van | Quantum cascade lasers grown on silicon[END_REF] on 6°miscut silicon, which are hardly compatible with the industry standards. Recently we have demonstrated GaSb LDs emitting at 2.3 µm on on-axis silicon substrates either entirely grown by MBE [START_REF] Calvo | Mid-infrared laser diodes epitaxially grown on on-axis (001) silicon[END_REF] or grown atop a GaSb-on-Si MOCVD template [START_REF] Bartolomé | Etched-cavity GaSb laser diodes on a MOVPE template grown on a 300-mm Silicon wafer[END_REF]. This wavelength range is of interest for sensing important gases such as, e.g., methane and ammonia [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF].

On the other hand, GaAs-based buffer layers grown on Si by MOCVD and incorporating defect-filtering layers (DFLs) to reduce the density of TDs have recently emerged as suitable templates for the integration of GaAs-based or InP-based lasers [START_REF] Wan | Low Threshold Quantum Dot Lasers Directly Grown on Unpatterned Quasi-Nominal (001) Si[END_REF]. In this work we investigate the possibility to incorporate such buffer layers in GaSb-based devices.

Epitaxial growth

The epitaxial growth was carried out in two steps, first the MOCVD growth of the template and then the MBE growth of the laser structure. Two series of LDs were grown. Both had the same GaAs-based buffer structure grown by MOCVD that is depicted in Fig. 1(a). The wafer was then taken out of the reactor and cut in several pieces. One piece was reloaded into the MOCVD reactor to grow an additional 1-µm-thick GaSb buffer layer whereas another piece was kept as-grown. Both wafers were then shipped to another laboratory for laser growth by MBE. Nominally identical GaSb-based laser structures comprising a 1-µm-thick GaSb buffer layer [Fig. 1(b)] were then grown by MBE on both templates, as schematically depicted in Fig. 1(c) and 1(d). Detailed descriptions of the epitaxial growth steps are given below.

MOCVD growth

Figure 1(a) depicts the growth structure of the GaAs-on-planar Si (GoPS) template. The ∼3-µm-thick GaAs thin film was grown on a blanket 4-inch nominal (001) Si substrate with an unintentional miscut angle of less than 1°. Prior to growth, the Si substrate was subjected to a dilute HF treatment to remove the native oxide. Immediately after, the Si wafer was loaded into the AIX-200/4 MOCVD system. After annealing at 800°C for 15 min under H 2 ambient, the temperature was lowered down to 400°C for the growth of a 10-nm-thick GaAs nucleation layer. Subsequently, a 1.4 µm thick GaAs layer was grown at step-increased temperatures from 550°C to 600°C. No antiphase boundaries (APBs) were observed due to their self-annihilations during the high temperature GaAs growth [START_REF] Wan | Low Threshold Quantum Dot Lasers Directly Grown on Unpatterned Quasi-Nominal (001) Si[END_REF]. Five periods of thermal cycle annealing (TCA) between 750°C and 350°C were introduced within the 1.4 µm GaAs layer to propel and annihilate some of the TDs. In addition, two stacks of five-period In 0.154 Ga 0.846 As/GaAs strained layer superlattices (SLSs) were embedded to further filter the threading dislocations. A 900 nm thick Si-doped GaAs layer was grown on top. The threading dislocation density (TDD) of the GoPS template was quantized at 1.4×10 8 cm -2 by both cross-sectional transmission electron microscopy (TEM) and electron channeling contrast imaging (ECCI) methods.

The as-grown GoPS template was cleaved for the following GaSb growth by both MOCVD and MBE systems. Regarding the GaSb growth by MOCVD, the 1-µm-thick GaSb buffer was grown at 535°C. The reactor pressure was 100 mbar and a V/III ratio as low as 1.9 was utilized to optimize the GaSb surface morphology. An interfacial misfit dislocation array was formed at the GaSb/GaAs hetero-interface [START_REF] Li | Epitaxial growth of GaSb on V-grooved Si (001) substrates with an ultrathin GaAs stress relaxing layer[END_REF]. To further smooth the GaSb surface as well as to reduce the dislocation density, two periods of 10 nm InAs/10 nm GaSb SLSs were inserted and grown at 500°C. As a result of the smooth GaAs growth front (roughness as low as 1.3 nm) and the optimized growth condition for the GaSb thin film, the final surface roughness of the GaSb grown on GoPS template is 1.6 nm based on a 10×10 µm 2 AFM measurement.

MBE growth

The samples were first cleaned with organic solvents and oxygen plasma in order to remove any possible contaminant before being loaded into the MBE reactor. Depending on the buffer layer, the samples were treated differently. Sample V3075, with a MOCVD GaSb buffer layer, was deoxidized at 550°C under an Sb flux. Sample V3079, with a GaAs buffer layer, was deoxidized at 600°C under As flux, before a thin GaAs layer was grown to smooth out the surface. Beside substrate preparation, the laser growth-sequence was the same for both samples and is nominally identical to that reported in Ref. [START_REF] Bartolomé | Etched-cavity GaSb laser diodes on a MOVPE template grown on a 300-mm Silicon wafer[END_REF]. First, a 1 µm thick n-type GaSb buffer layer was grown at 500°C. The substrate temperature was then decreased down to 450°C for the growth of a n-doped, 500-nm-thick InAsSb layer, which acts as the bottom contact of the laser structure and a marker in LD processing. Another 1 µm thick n-GaSb layer was grown to avoid any overlap of the optical mode with the InAsSb layer. The active region, designed to emit at 2.3 µm, comprised two Ga 0.67 In 0.33 As 0.12 Sb 0.88 QWs confined by Al 0.25 Ga 0.75 As 0.02 Sb 0.98 barrier layers and was inserted at the center of a 800-nm-thick Al 0.25 Ga 0.75 As 0.02 Sb 0.98 waveguide, itself cladded by 1.3 µm thick Al 0.9 Ga 0.1 As 0.07 Sb 0.93 layers. The bottom cladding was n-doped while the top one was p-doped. Finally, a 350 nm thick p-doped GaSb layer was grown for the top contact. All layers from the LD stack were lattice-matched to GaSb besides the QWs, which exhibited a 1.5% lattice-mismatch. X-ray diffraction confirmed full relaxation of the laser structure with respect to the Si substrate whereas the QWs were strained with respect to GaSb.

Laser diode fabrication process

The process was based on standard UV photolithography and inductively coupled plasma etching. The LDs ridges were 100 and 10 µm wide. The material used for electrical isolation and sidewall protection was a 350 nm thick layer of Si 3 N 4 deposited by plasma-enhanced chemical vapor deposition. Reactive ion etching was used to open windows in the insulation layers before deposition of the electrical contacts. Both of them were taken on the top of the samples: p-contact on top of the ridges and n-contacts on the InAsSb layers. For both n-and p-contacts, Ti/Au (20/400 nm) layers were deposited by sputtering. Finally, the sample substrates were mechanically thinned down and laser bars were cleaved to different cavity lengths. No facet treatment was applied. The LDs bars were soldered epi-side-up with In on Cu heat-sinks and characterized on a probe station.

The LDs fabrication process was carried out in parallel for both samples. However, we observed the formation of cracks on sample V3075, which has a thicker buffer layer, whereas no crack was observed on sample V3079. Cracks typically arise during thermal cycles because of the different thermal-expansion coefficients of the III-V and Si materials. The V3075 is 1-µm-thicker than the sample V3079, which results in epitaxial thickness for samples V3075 and V3079 of 10.5µm and 9.5 µm, respectively. Our observation thus gives a good estimation of the thickness limit to avoid crack formation. Still, the cracks in V3075 were running parallel to the LDs ridges. Selecting LDs where the cracks were outside the ridges allowed to reliably assess the LDs performance.

Laser diode properties

Threshold current densities

Broad area LDs with 100 µm wide ridges were measured at RT under pulsed excitation (10 kHz repetition rate and 1 µs long pulse). The light output was collected by a cooled InSb photodetector. This configuration allows to precisely know the current injection-area and the device temperature, thus giving an accurate access to the threshold current density of the laser structures.

LDs of different cavity lengths, ranging from 1 to 3 mm were tested. Each cavity length has been measured individually after cleavage for better accuracy. Light output vs current density curves are shown in Fig. 2 for both series of LDs. The threshold current density is in the 250-350 A.cm -2 range for sample V3075 (with MOCVD GaSb buffer), Fig. 2(a), whereas it is in the 400-450 A.cm -2 range for sample V3079 (without a MOCVD GaSb buffer), Fig. 2(b). These results reveal a reduction of the threshold current density as large as 40% with the thickest buffer layer. Several parameters can explain this behavior. A thicker buffer layer will result in lower defect densities and thus in better laser performance [START_REF] Hantschmann | Theoretical Study on the Effects of Dislocations in Monolithic III-V Lasers on Silicon[END_REF]. Further, the InAs/GaSb SLSs inserted within the MOCVD GaSb buffer layer acted as a defect filtering layer and promoted the formation of a smooth surface, as revealed by AFM. A reduction of the TDs density could also arise from the larger thermal budget applied to the buffer stack during the oxide removal steps. Indeed, even though the oxide removal step for the sample without MOCVD GaSb layer (V3079) was performed at high temperature (600 °C), it took place before the transition to GaSb growth which created new TDs due to the ∼8% lattice-mismatch between GaSb and GaAs. The benefit of the thermal annealing occurring during the GaAs oxide removal step could therefore be mitigated by the subsequent relaxation of the GaSb layer. In contrast, when the MBE growth started on the GaSb layer grown by MOCVD (V3075), two oxide-removal steps were carried out. First, the GaAs buffer layer was annealed at 650°C in the MOCVD reactor prior to the MOCVD growth of the GaSb buffer layer. Then, the whole MOCVD stack was annealed in the MBE reactor for GaSb oxide removal. Thus, the TDs created to relax the strain at the GaSb/GaAs interface also experienced annealing, which increased their probability of interaction and annihilation. This is consistent with previous studies that demonstrated the effectiveness of thermal annealing to reduce the defect density in GaAs layers grown on Si [START_REF] Lee | Defect reduction by thermal annealing of GaAs layers grown by molecular beam epitaxy on Si substrates[END_REF][START_REF] Jung | Low threading dislocation density GaAs growth on on-axis GaP/Si (001)[END_REF] or GaSb layers grown on GaAs substrates [START_REF] Hao | Rapid Thermal Annealing on GaSb Thin Films Grown by Molecular Beam Epitaxy on GaAs Substrates[END_REF]. Our work show that a detailed study including a transmission electron microscopy analysis is needed to precisely assess the impact of every growth parameter on the defect structure of such samples. It is however beyond the scope of this paper.

Previous GaSb-based LDs grown by MBE on MOCVD GaSb-on-Si templates exhibited threshold current densities in the 650-700 A.cm -2 range. The GaSb MOCVD buffer layer did not include dislocation filters and was 500 nm thick, resulting in a total buffer layer thickness of 1.5 µm [START_REF] Bartolomé | Etched-cavity GaSb laser diodes on a MOVPE template grown on a 300-mm Silicon wafer[END_REF]. In contrast, all-MBE LDs grown on on-axis Si substrates exhibited threshold current densities in the 400-500 A.cm -2 with a 1-µm-thick buffer layer [START_REF] Calvo | Mid-infrared laser diodes epitaxially grown on on-axis (001) silicon[END_REF]. These values are similar to that obtained with V3079 with a 4-µm-buffer layer. Finally, it is noticeable that for sample V3075 the buffer-layer stack included SLSs, was 5 µm and experienced an additional annealing cycle, which lead to record threshold current densities. Altogether these results demonstrate that there is a large room for improvement in terms of threshold current densities of GaSb LDs grown on Si by a careful adjustment of the buffer layer thickness and/or compositions, and of the annealing sequence, and that a combined MOCVD / MBE growth scheme might be an appealing solution.

Ridge laser diodes

Next, narrow ridge LDs were measured at RT under CW. The light output was collected using a calibrated power-meter. Figure 3 shows the power-current-voltage (P-I-V) curves measured from 10 µm wide ridges and various cavity lengths for both V3075 and V3079 samples. The turn-on voltage is around 1 V for both samples, close the expected value for the designed QWs structure. The serial resistance varies from 4 to 6 Ω for sample V3079, comparable to values found for for GaSb based laser [START_REF] Baranov | Semiconductor Lasers: Fundamentals and Applications[END_REF]. In contrast, for sample V3075, the resistance is slightly higher and ranges from 5 to 11 Ω. This might be related to bubbles detected on the bottom contact for this sample, which means the adhesion between the metal and the semiconductor was not ideal. However, the threshold current is lower for this sample, 50 mA for a 0.92 mm cavity length and up to 130 mA for a 2.88 mm long one. For the LDs without the MOCVD grown GaSb buffer layer (V3079), it varies from 100 to 200 mA. The output power per uncoated facet reaches several mW for both samples.

The external quantum efficiency above threshold η d was extracted from the L-I curves. We studied the evolution of the inverse of η d with the cavity length, shown in the insets of Fig. 3, by fitting the experimental data with Eq. ( 1) [START_REF] Coldren | Diode Lasers and Photonic Integrated Circuits[END_REF],

1 η d = 1 η i + α i η i ln(R -1 ) L (1)
η i being the internal quantum efficiency, α i the internal losses, R the reflectivity of the facets and L the cavity length. We assumed R to be 0.3 for cleaved facets. From this analysis, we extracted the values for η i from the intercept of the curves. We obtained very similar values for both samples (33 and 36%). However, α i is notably different, being 3.7 cm -1 for sample V3075, close to the typical values found for such material system, [START_REF] Salhi | Very-low-threshold 2.4-µm GaInAsSb-AlGaAsSb laser diodes operating at room temperature in the continuous-wave regime[END_REF] and α i = 6.7 cm -1 for sample V3079. These higher performances of sample V3075 outline again the impact of the buffer layer sequence. Spectra under CW regime at RT were the measured using a grating spectrometer coupled to a cooled InSb photodetector. Figure 4 presents the obtained spectra for 10 µm wide ridges LDs taken under an injection current 50% higher than the threshold current. The emission wavelength is around 2.3 µm for both samples, as expected from the laser design, different cavity lengths and drive currents result in slightly different wavelengths.

Finally, we have performed L-I-V measurements at various temperatures, from 20°C up to 70°C, limited by our experimental set-up. The measurement was performed in CW regime with narrow ridge diodes. In Fig. 5(a) we show the results obtained for sample V3075, with a MOCVD GaSb buffer layer. The threshold current increases from 70 mA at 20°C up to 145 mA at 70°C. For sample V3079 [Fig. 5(b)] it increases from 170mA at 20°C up to 220mA at 70°C. It is worth mentioning that no appreciable thermal rollover for any of the samples could be observed, and the output power per facet reaches several mW over the whole temperature range.

The usual characteristic-temperatures can be extracted from the evolution with temperature of the threshold current (T 0 ) and external quantum efficiency (T 1 ), which are represented in a semilogarithmic plot in the insets of Fig. 5. The samples show different characteristic temperatures: T 0 = 75 K and T 1 = 116 K for sample V3075, T 0 = 102 K and T 1 = 134 K for sample V3079. In contrast to the other properties, sample V3079 performs better and shows a better thermal stability. This could be due to the higher series resistance of V3075 leading to stronger Joule heating. To clarify this point, we repeated the temperature-dependent measurements in pulsed regime (not shown). As expected, the T 0 temperatures increased for both samples: T 0 = 97 K for V3075 and T 0 = 114 K for V3079. It is noticeable however that the T 0 -difference between CW and pulsed regime is larger for V3075 than for V3079, which confirms that at least part of the poorer thermal behavior of V3075 arose from the higher series resistance that induced Joule heating. Other reasons could be a higher thermal resistance due to cracks in the sample and/or to the thicker buffer layer.

Conclusion

We have demonstrated GaSb-based LDs grown by MBE on MOCVD GaAs-on-Si template. Two series of samples were studied, for the first one, GaAs-based buffer layer was grown by MOCVD prior to the growth of the GaSb-based laser heterostructure by MBE. For the second series, a 1-µm thick GaSb buffer layer with InAs/GaSb SLSs was grown by MOCVD on top of the GaAs based buffer before the growth of the laser by MBE, which implies an additional annealing step during oxide removal. Both samples exhibited low threshold current density and CW operation at high temperature. However, the second series of LDs, with the additional GaSb buffer layer grown by MOCVD, exhibited better performance despite the appearance of cracks during processing which sets an upper thickness limit for practical applications. Narrow ridge LDs showed threshold current as low as 50 mA in CW regime with light output power of several mW and CW operation up to 70°C (set-up limited) without thermal rollover. Threshold current densities were in the range 250-350 A/cm 2 .

These results reveal that the performances of GaSb LDs grown on Si can largely be improved by a careful adjustment of the buffer layer thickness and/or compositions, and of the annealing sequence, and call for detailed investigations of these parameters. Disclosures. The authors declare no conflicts of interest.

Fig. 1 .

 1 Fig. 1. Sketch of the layer structure of a) the MOVPE GaAs template, b) the MBE laser structure, c) sample V3075 with GaSb buffer layer grown by MOCVD. d) sample V3079 without GaSb buffer layer grown by MOCVD.

Fig. 2 .

 2 Fig. 2. Light output vs current density curves under pulsed regime at RT. a) LDs with MOVPE GaSb buffer layer. b) LDs without MOVPE GaSb buffer layer.

Fig. 3 .

 3 Fig. 3. P-I-V curves under CW regime at RT a) LDs with MOVPE GaSb buffer layer. b) LDs without MOVPE GaSb buffer layer. The insets show the evolution of the inverse of the external quantum efficiency as function of the cavity length.

Fig. 4 .

 4 Fig. 4. Emission spectra under CW at RT a) LDs with MOVPE GaSb buffer layer. b) LDs without MOVPE GaSb buffer layer.

Fig. 5 .

 5 Fig. 5. L-I-V curves in CW at various temperatures. a) LDs with MOVPE GaSb buffer layer. b) LDs without MOVPE GaSb buffer layer. The insets show the evolution of the current threshold and the external quantum efficiency as function of the temperature.

Funding.

  Investments for the Future (ANR-11-EQPX-0016); H2020 Program of the European Union (REDFINCH, GA 780240).


C R Fitch

G W Read

I P Marko

D A Duffy

L Cerutti

J-B Rodriguez

Eric Tournié

S J Sweeney
email: s.sweeney@surrey.ac.uk

Thermal performance of

HAL is

The realization of optoelectronic integrated circuits (OEICs) requires an efficient, siliconcompatible electrically pumped laser operating above room temperature (RT). The indirect nature of silicon makes it unsuitable as an active region. While heterogeneous integration may currently be the most advanced approach in terms of device performance [START_REF] Cornet | Integrated Lasers on Silicon[END_REF] , the longer term goal is direct epitaxial growth of III-V lasers on silicon [START_REF] Cornet | Integrated Lasers on Silicon[END_REF] . However, the lattice constant and thermal expansion coefficient mismatch and the polar/ non-polar interface between silicon and traditional III-V laser materials causes large defect densities, leading to inefficient and unreliable lasers. Progress has been made in overcoming these challenges through the use of GaAs based 1.3 μm quantum dot lasers on silicon [START_REF] Liao | [END_REF]3 and Ga(NAsP)/GaP/Si quantum well (QW) lasers at 800-900 nm 4 . However, an alternative material system and approach is required for long-haul telecoms applications operating around 1.5 μm.

Sb-containing alloys are of interest for growth on silicon since dislocations tend to propagate parallel to the Si/III-V-Sb interface rather than into the active layers, allowing growth of high-quality active regions. GaInSb/GaSb composite quantum well (CQW) lasers have been grown by molecular beam epitaxy on 4°-off (001) silicon substrates emitting at 1.55 µm at RT in pulsed mode 5 ; near 1.55 µm in continuous wave (c.w.) on GaSb near RT 6 ; and more recently at 1.59 µm c.w. at RT on 6° miscut silicon 7 . However, further development is needed to address high threshold current densities (Jth) and temperature sensitivity 8 .

To commercialize on-silicon devices, it is important to understand the efficiency limiting mechanisms of the equivalent active regions grown on GaSb. In this paper we report on the thermal properties of GaInSb CQW devices on GaSb substrates 6 and use a range of experimental techniques to identify the principal processes limiting device performance 16 .

The test devices (A, B, C) illustrated in figure 1, consist of three compressively strained Ga0.8In0.2Sb QWs. The Al0.35Ga0.65As0.03Sb0.97 barriers and Al0.9Ga0.1As0.07Sb0.93 cladding layers are lattice-matched to the GaSb substrate. Devices B and C are CQWs formed by the insertion of one (B) and two (C) 0.45 nm Al0.68In0.32Sb barriers within each Ga0.8In0.2Sb QW. The insertion of AlInSb monolayers into the wider wells introduces additional confinement, counteracting the reduction in bandgap caused by the additional width. Further details of the fabrication of these devices is given in reference 6 .

Pulsed electrical injection (500 ns, 10 kHz) was used to minimize current heating effects. Device characteristics were measured as a function of temperature from 40-300 K using a closed-cycle cryostat system. Figure 2(a) shows the facet output intensity (L) variation with current density (J) and temperature (T) for representative device B. Figure 2(b) shows the extracted Jth variation with temperature for all three devices.

For these lattice-matched devices, defectrelated recombination is assumed to be negligible in the QW region and at low temperatures, where Jth is low, other forms of non-radiative recombination are also assumed negligible. For an ideal QW laser at low temperatures the radiative component of threshold current density, Jrad ∝ T 9 and for our devices Jrad can be seen to dominate threshold below ~150 K. The Jrad components at RT were approximated by linear extrapolation of the low temperature Jth to 300 K shown as the shaded area in figure 2(b) and in Table I. For T > 150 K, Jth increases super-linearly, suggesting the onset of non-radiative processes such as Auger recombination or carrier leakage consistent with evidence from other laser types at this wavelength [START_REF] Jin | [END_REF] .

In a simple model Jth can be expressed as 16 :

𝐽 𝑡ℎ = 𝑒𝐿 𝑧 (𝐴𝑛 + 𝐵𝑛 2 + 𝐶𝑛 3 ) + 𝐽 𝑙𝑒𝑎𝑘 ( 1
)
Where e is the electronic charge, Lz is the active layer thickness, n is the carrier density (assuming equal electron and hole carrier densities) and A, B and C are the recombination coefficients for defect, radiative and Auger recombination respectively. The Jleak term accounts for carrier leakage from the QWs. )

Temperature (K) Device A Device B Device C 1092 Acm -2 654 Acm -2 J rad (b) 471 Acm -2
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0042667

Auger recombination and carrier leakage are strongly temperature dependent which may explain the strong increase in Jth with temperature 11 . The reduction in Jth at RT from device structures A to B to C may be attributed to the increased gain volume, which reduces the threshold carrier density, nth, by lowering the band filling and increasing the photon generation rate for a given injection current. Increased optical confinement would also contribute to the reduction in nth by increasing modal gain and the stimulated emission rate.

Approaching room temperature Jth increases exponentially and, over a limited temperature range, this increase may be described by the characteristic temperature T0 12 :

𝑇 0 = ( 𝑑𝑙𝑛(𝐽 𝑡ℎ ) 𝑑𝑇 ) -1 = ( 1 𝐽 𝑡ℎ 𝑑𝐽 𝑡ℎ 𝑑𝑇 ) -1 (2)
A higher T0 is desirable as it corresponds to greater thermal stability of Jth. Expressions for the characteristic temperature due to radiative, Auger recombination and leakage effects can be derived as 12 :

𝑇 0 (𝐼 𝑟𝑎𝑑 ) = 𝑇 1 + 2𝑥 (3) 𝑇 0 (𝐼 𝐴𝑢𝑔 ) = 𝑇 3 + ( 𝐸 𝑎 𝑘𝑇 ) + 3𝑥 (4) 𝑇 0 (𝐼 𝑙𝑒𝑎𝑘 ) = 𝑇 ( 𝐸 𝑎 𝑘𝑇 ) (5)
Where x is a "non-ideality" factor, e.g. due to optical losses, and Ea is the respective activation energy for the Auger or leakage process.

The theoretical variation of T0(T) for Jth can be written as a weighted average of the individual T0 values:

1 𝑇 0 = 1 𝑇 0(𝑟𝑎𝑑) 𝑅 + 1 𝑇 0(𝑛𝑜𝑛𝑟𝑎𝑑) (1 -𝑅) (6)
where R(T) is defined as Jrad/Jth and T0(nonrad) corresponds to either the Auger or leakage process. T0(T) was measured using a five-point average and compared with a numerical model to investigate the non-radiative contribution to Jth. )

Temperature (K) J Aug =J 0 exp(-E a(Aug) /kT) J rad T (d)
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0042667

Figure 3(a) shows the measured and modelled T0(T) for all three devices for radiative recombination and carrier leakage together with the radiative and leakage limits for device B as an example. Figure 3(b) shows that a similarly good fit may be achieved assuming radiative and Auger recombination. At low temperatures T0 tends towards the radiative limits while above a break-point temperature, TB 16 , it tends towards the leakage or Auger limits. The difference in T0(T) between the three structures is consistent with the trends in Jth and highlights the improvement in performance with increasing composite well thickness where a lower nth leads to a reduction in non-radiative recombination. Figures 3(c) and 3(d) show the example of the measured Jth for device B and the result of fitting the radiative and leakage (a) or radiative and Auger (b) components from the T0 model. A similar quality of fit is found for devices A and C. The T0 data may therefore be explained by considering either leakage or Auger recombination although it is not possible to distinguish which is dominant from this analysis alone.

Using a similar approach we investigated the temperature sensitivity of the differential quantum efficiency (slope) above threshold, ηd where:

𝜂 𝑑 ∝ 𝑑𝐿 𝑑𝐼 (7)
The characteristic temperature T1 is defined as ηd(T)=η0exp(-T/T1) where η0 is a constant 13 , so:

𝑇 1 = -( 𝑑ln (𝜂 𝑑 ) 𝑑𝑇 ) -1 = -( 1 𝜂 𝑑 𝑑𝜂 𝑑 𝑑𝑇 ) -1 (8)
Equation ( 8) was applied using a three-point average to plot the experimental values of T1.

The differential quantum efficiency ηd may be expressed as:

𝜂 𝑑 = 𝜂 𝑖 𝛼 𝑚 𝛼 𝑖 + 𝛼 𝑚 ( 9
)
Here ηi is the internal quantum efficiency, αi is the internal loss and αm the mirror loss expressed as:

𝛼 𝑚 = 1 𝐿 𝑐𝑎𝑣 𝑙𝑛 1 𝑅 𝑓 ( 10
)
where Lcav is the cavity length and Rf the ascleaved facet reflectivity. Assuming the change in αm with temperature is negligible we deduce that:

𝑇 1 = 1 1 (𝛼 𝑖 + 𝛼 𝑚 ) 𝑑𝛼 𝑖 𝑑𝑇 - 1 𝜂 𝑖 𝑑𝜂 𝑖 𝑑𝑇 (11)
Terms on the left-hand side of the denominator relate to cavity losses and on the right-hand side to injection losses (e.g. carrier leakage). This decomposition allows investigation of the relative contributions to T1. We used a least squares numerical fit model to vary dαi/dT and dηi/dT to fit to the measured ηd(T) using equation (11).

Figure 4(a) shows the relative change in slope efficiency ηd for all three device structures. From this fit it is clear that dηi/dT dominates with dαi/dT having negligible effect. This confirms that the temperature sensitivity of T1 is due to injection rather than optical losses and supports the T0 analysis which identified carrier leakage as a possible contributory factor. It also indicates that Inter Valence Band Absorption This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0042667

(IVBA) and Free Carrier Absorption (FCA) are not significant because they are associated with the αi rather than the ηi contribution to ηd. Auger recombination is not expected to influence the T1 analysis since n is (ideally) pinned above threshold. An important outcome of the T1 analysis is that the efficiency data can only be explained by the presence of carrier leakage.

Both carrier leakage and Auger recombination are sensitive to band structure. Hydrostatic pressure can be used to reversibly change the band structure of a semiconductor, hence it was used to assess the dependence of the device performance on the band structure. Pressures up to 400 MPa were applied using a Unipress helium compressor system, details of which may be found in 11 .

The measured variation of Jth with pressure is shown in figure 5(a). A numerical model was created to describe how Auger recombination and carrier leakage vary with pressure to investigate their quality of fit to the experimental data.

In an ideal QW laser, where optical losses are negligible, Jrad scales with bandgap according to Jrad∝ Eg [START_REF] Liao | [END_REF] .

The pressure dependence of the leakage and Auger components take the form:

𝐽 𝑛𝑜𝑛𝑟𝑎𝑑 = 𝐽 0 𝑒𝑥𝑝 [-( 𝑑𝐸 𝑎 𝑑𝑃 ) 𝑃 𝑘 𝑏 𝑇 ] (12)
Where J0 = 1 for normalized data and dEa/dP is the net change in the respective activation energy with pressure.

For leakage, dEa/dP corresponds to the net change in band alignment between the quasi-Fermi level in the conduction band, taken to be equal to the QW electron ground state (e1), and the energy of the states into which the carriers escape. We assume that e1 changes as dElase/dP and the valence band alignment is approximately pressure independent [START_REF] Mönch | Electronic Properties of Semiconductor Interfaces[END_REF] . dElase/dP was measured to be ~11 meVkbar -1 for all three devices.

CHSH Auger recombination (where the energy of a Conduction band electron recombining with a hole in the Heavy hole band is given to a third hole in the Heavy hole band which is excited into the Spin split-off band) is sensitive to the difference between the band gap (Eg) and the spin-orbit (SO) split-off-energy (ΔSO). For our devices where Eg>ΔSO, the CHSH activation energy is given by: 𝐸 𝑎 (𝐶𝐻𝑆𝐻) = 𝑚 𝑠𝑜 2𝑚 ℎ + 𝑚 𝑐 -𝑚 𝑠𝑜 (𝐸 𝑔 -∆ 𝑆0 ) (13) where mc and mh are the electron and heavy hole band, in-plane, effective masses and mso is the SO split-off band effective mass. The CHCC Auger activation energy is:

𝐸 𝑎 (𝐶𝐻𝐶𝐶) = 𝑚 𝑐 𝑚 𝑐 + 𝑚 ℎ 𝐸 𝑔 (14)
CHCC refers to electron-hole recombination between the Conduction and Heavy hole bands accompanied by excitation of a Conduction band electron further into the Conduction band.

In ( 13) and ( 14) Eg changes according to dElase/dP. From k.p theory, mc and mso increase approximately proportionally to band gap, and hence pressure, while mh is relatively independent of pressure [START_REF] Krier | Mid-Infrared Semiconductor Optoelectronics[END_REF] . QW effective masses were calculated from a linear interpolation of the binary components from Vurgaftman et al 16 .

This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0042667

Other Auger processes have been ignored since they have previously been shown to be relatively weak [START_REF] Jin | [END_REF]17 . Due to the closeness of the e1 and ΔSO energies, CHSH is expected to dominate the Auger current at wavelengths < 2 μm 18 .

An increasing Jth with pressure is generally a strong indicator of carrier leakage from the QW to the indirect X or L valleys. In contrast, Jth decreases with pressure for CHSH/CHCC Auger processes, or for leakage from the QW to the barrier Γb band edge (when the barrier Γb band edge pressure coefficient is smaller than the QW, as here).

The QW e1 to barrier Γb, Xb and Lb minima energy offsets were calculated at RT and ambient pressure for the three structures by combining the binary energy gaps, bowing parameters and valence band offsets from Vurgaftman et al 16 , accounting for strain in the QW.

For the three structures, the range of values are: e1-Γb = 218-223 meV; e1-Xb = 275-280 meV; and e1-Lb = 299-304 meV (e1-cladding separations were all >439 meV), figure 5(b). While these energy offsets should be sufficient to confine the majority of carriers, the Fermi-Dirac distribution of carriers extends into these energies where there is a high density of states, hence increasing the recombination rate. It was also found that the energy offsets and configuration of the barrier minima are very sensitive to the bowing parameters which vary considerably in the literature 16,[START_REF] Adachi | Properties of Semiconductor Alloys: Group-IV, III-V and II-VI Semiconductors[END_REF] .

As evident from figure 5(a), the increase in Jth with pressure is stronger than that expected for leakage to the Lb-valley states. However, it is consistent with leakage to the Xb-valley dominating the increase in Jth. A good fit to the experimental results was achieved for all devices using a combination of radiative recombination, leakage to the barrier Xb minima (forming up to 43% of Jth), and a contribution of CHSH/CHCC Auger recombination or leakage to the barrier Γb or Lb minima. Shockley-Read-Hall (SRH) is likely to be a strong factor in the subsequent recombination of carriers in the barrier material.

The results of this study demonstrate the potential of GaSb-based QW lasers for silicon photonics applications in the telecoms wavelength range and opportunities for ongoing improvement.

We showed that the strong temperature sensitivity of Jth could be explained by either leakage or Auger recombination. However, the temperature sensitivity of ηd was found to be dominated by carrier injection, confirming that leakage must be present. Furthermore, from pressure-dependent measurements, carrier leakage from the QW active region to the barrier Xb valley states was found to be a key limiting factor in the performance of these devices. This could be reduced by increasing the activation energy of the leakage paths by a small increase in the lattice matched barrier Al and As fractions and without compromising optical confinement provided by the cladding. Further improvement in reducing Jth and thermal sensitivity might also be achieved by increasing the number of QWs although the relatively small improvements associated with increased gain volume of device C over B compared with B over A suggests diminishing scope for improvement. Optimization would also benefit from a detailed investigation of bowing parameters and band alignments in this system.

FIG. 2 .

 2 FIG. 2. (a) Temperature dependent LI (device B); (b) threshold current densities and radiative components (all devices).

FIG. 3 .

 3 FIG. 3. Experimental and modelled characteristic temperature and threshold current density (a) T0 (radiative and leakage) (b) T0 (radiative and Auger) (c) Jth (radiative and leakage) (d) Jth (radiative and Auger).

FIG. 4 .

 4 FIG. 4. Experimental and modelled slope efficiency (a) and characteristic temperature T1 (b).

FIG. 5 .

 5 FIG. 5. (a) Threshold current density variation with pressure -Experimental measurements (solid symbols) and theoretical dependence of the individual current paths and best fit with pressure (device B) (b) schematic band alignment.

TABLE I .

 I Threshold current densities and radiative components at 300 K.

		Device A	Device B	Device C
	Jth (Acm -2 )	1092	654	471
	Jrad (Acm -2 )	170±6	147±10	189±5
	Jrad/Jth (%)	15±1	23±2	40±1

S. Liebich, M. Zimprich, P. Ludewig, A. Beyer, K. Volz, W. Stolz, B. Kunert, N. Hossain, S.R. Jin, and S.J. Sweeney, Proc. 22nd IEEE Int. Semicond. Laser Conf. 143 (2010).

L. Cerutti, J.B. Rodriguez, and E. Tournie, IEEE Photonics Technol. Lett. 22, 553 (2010).

L. Cerutti, A. Castellano, J.B. Rodriguez, M. This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0042667

Acknowledgments This work has been partly supported by EPSRC (UK) under grant EP/N021037/1, a SEPnet PhD scholarship for D. A. Duffy, the French ANR (Project OPTOSi, No. ANR-12-BS03-002) and by the French "Investment for the Future" program (EquipEx EXTRA, No. ANR-11-EQPX-0016).

Data Availability The data associated with this work are available by request at https://doi.org/10.5281/zenodo.4353309.


Younes Boussadi

Névine Rochat

Jean-Paul Barnes

Ben Bakir

Philippe Ferrandis

Bruno Masenelli

Christophe Licitra

Investigation of sidewall damage induced by reactive ion etching on AlGaInP MESA for micro-LED application

Keywords: µLED, micro-Photoluminescence, TRPL, Cathodoluminescence, TOF-SIMS, InGaP, AlGaInP

Previous reports have studied the impact of sidewall defects on AlGaInP micro light emitting diode (µLED) only by Current-Voltage-Luminescence (I-V-L) measurements. In this work, we propose an alternative approach to investigate these defects directly after MESA formation, by coupling optical characterization techniques together with Time-of-flight secondary ion mass spectrometry (TOF-SIMS) on AlGaInP square shaped pixels of different sizes formed by BCl3-based Reactive Ion Etching (RIE). It is found that for a 6×6 µm² pixel, the light emission homogeneity is largely impacted by the sidewall defects. From emission efficiency map deduced by temperature-dependent cathodoluminescence measurements, we estimate that 86% of the 6×6 µm² pixel exhibit a lower efficiency than the center. The carriers lifetime extracted from time-resolved photoluminescence (TRPL) measurements on larger pixel begins to decrease gradually at 3 µm from the sidewall due to non-radiative recombinations. On the other hand, the TOF-SIMS analysis shows that residues of boron and chlorine remain on the surface and sidewalls of the pixel after BCl3 etching. These results show the importance to characterize the µLEDs at the MESA step and the necessity to optimize the etching process and the passivation.

INTRODUCTION

Micro light emitting diodes (µLEDs) are the most promising light sources for future high luminance display application.

Compared to liquid crystal displays or organic light emitting diodes, µLEDs show outstanding performances in term of brightness and power consumption [START_REF] Ding | Micro-LEDs, a Manufacturability Perspective[END_REF], which fueled several studies demonstrating efficient III-nitride µLED devices in blue and green emission. Despite the effort, III-nitride materials are still inefficient in red wavelength [START_REF] Mitchell | Perspective: Toward efficient GaN-based red light emitting diodes using europium doping[END_REF] whereas AlGaInPbased macro LED internal quantum efficiency exceeds 90% [START_REF] Horng | Development and Fabrication of AlGaInP-Based Flip-Chip Micro-LEDs[END_REF], [START_REF] Royo | Experimental determination of the internal quantum efficiency of AlGaInP microcavity light-emitting diodes[END_REF]. However, the miniaturization of these AlGaInP-based LEDs, with a pitch below 10 µm, is less advanced than its III-Nitride counterpart.

In general, plasma or wet etchings are used for MESA formation in µLEDs process, and the etching is known to increase surface recombinations by introducing electronic defects at the sidewalls. These defects act as non-radiative recombination centers and respond to the Shockley-Read-Hall (SRH) theory [START_REF] Olivier | Shockley-Read-Hall and Auger non-radiative recombination in GaN based LEDs: A size effect study[END_REF]- [START_REF] Hwang | Sustained high external quantum efficiency in ultrasmall blue III-nitride micro-LEDs[END_REF]. At low scale, surface properties become critical and the impact of these defects increases and leads to the diminution of the µLED external quantum efficiency (EQE) with size shrinkage [START_REF] Ding | Micro-LEDs, a Manufacturability Perspective[END_REF], [START_REF] Wong | Size-independent peak efficiency of III-nitride micro-light-emitting-diodes using chemical treatment and sidewall passivation[END_REF]. AlGaInP µLEDs suffer from a higher surface recombination velocity than III-nitride µLEDs which leads to a severe drop of the EQE with miniaturization [START_REF] Wong | Improved performance of AlGaInP red micro-light-emitting diodes with sidewall treatments[END_REF]- [START_REF] Boussadi | Characterization of micro-pixelated InGaP/AlGaInP quantum well structures[END_REF].

Several studies have been conducted in this direction, such as Oh et al. [START_REF] Oh | Light output performance of red AlGaInP-based light emitting diodes with different chip geometries and structures[END_REF] where the efficiency of red AlGaInP-based µLEDs was investigated as a function of chip size with I-V-L measurements. The authors concluded that in AlGaInP µLEDs, major losses come from SRH recombinations at sidewall defects. Wong et al. [START_REF] Wong | Improved performance of AlGaInP red micro-light-emitting diodes with sidewall treatments[END_REF] proposed sidewall passivation by atomic layer deposition of Al2O3 which improved the light output power for a 20x20 µm² device by 150 %. This improvement was attributed to the reduction of non-radiative recombination sites and the enhancement in light extraction efficiency but the EQE drop with miniaturization was still present.

Nevertheless, there is a lack of studies about the real impacted zone after MESA formation and the previous reports concerning sidewall defects in µLEDs are limited only to I-V-L characterization [START_REF] Royo | Experimental determination of the internal quantum efficiency of AlGaInP microcavity light-emitting diodes[END_REF], [START_REF] Wong | Improved performance of AlGaInP red micro-light-emitting diodes with sidewall treatments[END_REF], [START_REF] Oh | Light output performance of red AlGaInP-based light emitting diodes with different chip geometries and structures[END_REF]. These measurements take also others parameters into account such as electric contact quality and current spreading which are also size dependent [START_REF] Kou | Impact of the surface recombination on InGaN/GaN-based blue micro-light emitting diodes[END_REF]. In this work, we present an alternative approach to evaluate the impacted zone just after the MESA formation. By coupling micro-photoluminescence (µ-PL), time-resolved photoluminescence (TRPL), cathodoluminescence (CL) and TOF-SIMS characterizations on AlGaInP MESA of various sizes formed by reactive ion etching (RIE) using BCl3/Ar, we show conclusive evidence of non-radiative transitions from sidewall defects and their impact at low dimension.

EXPERIMENTAL DETAILS

InGaP/AlGaInP red LED epitaxies grown on lattice matched GaAs substrates are used to carry out our study. The LED epitaxial structure consists of an active region with five multiple quantum wells (MQW) formed by 𝐼𝑛𝐺𝑎𝑃 wells and separated by 𝐴𝑙 𝑥 1 𝐺𝑎 1-𝑥 1 𝐼𝑛 0.48 𝑃 barriers. The active region is sandwiched between three undoped layers of 𝐴𝑙 𝑥 1 𝐺𝑎 1-𝑥 1 𝐼𝑛 0.48 𝑃, 𝐴𝑙 𝑥 2 𝐺𝑎 1-𝑥 2 𝐼𝑛 0.48 𝑃 (x2 > x1) and GaAs, respectively (Figure 1). The epitaxy is then reported on Sisubstrate and processed by RIE BCl3/Ar plasma etching to form square-shaped pixels (MESA) with various dimensions (56×56 µm², 36×36 µm², 16×16 µm² and 6×6 µm²). The dispersed signals which form the spectrum are then detected with a CCD camera. The mapping data were acquired by moving the sample using an XY stage with a step of 1 µm. The sample was loaded in a He-flow cryostat and measurements were performed between 4,5 K and 296 K. Time resolved photoluminescence was used to measure the lifetime of the quantum wells structures, using a 376 nm pulsed laser diode, operating at a frequency of 5 MHz, with a pulse duration of 50 ps. The luminescence signal was collected via a single-photon avalanche diode.

Cathodoluminescence mappings were performed from room temperature to 4,5 K using an Attolight CL microscope. The Si substrate facilitates charge evacuation during CL measurements. The sample was excited by an electron beam with 10 keV acceleration voltage and a beam current between 5 and 10 nA. The luminescence was collected through an integrated light microscope (NA: 0.7) embedded within the electron objective to enhance optical emission collection. By scanning the sample, the optical spectra of each pixel of the SEM image are recorded on a CCD camera through a dispersive spectrometer (focal length: 320 mm, grating: 150 grooves/mm).

Chemical composition depth profiles of our sample were determined by TOF-SIMS measurements. The apparatus is equipped with a liquid Bismuth metal ion gun and a Cesium sputter source. Measurements were performed in dual beam configuration, alternating analysis cycles with sputtering cycles (noninterlaced mode) with Cs ions incident sputtering at 45° and the Bismuth gun as the primary probe for analysis, also with an incidence of 45°. The depth resolution was between 2 and 5 nm.

RESULTS AND DISCUSSION

In order to evaluate the impact of the miniaturization on the optical properties of MQW, µ-PL integrated intensity mappings were performed for several temperatures on a 6×6 µm 2 LED pixel (Figure 2). In the 296 K mapping, the maximum intensity is located in the middle of the pixel and decreases while approaching the edges. When the temperature is lowered, the emitted intensity becomes higher, as expected from the suppression of non-radiative recombinations in the bulk and the surface [START_REF] Lu | Study on Optical Properties and Internal Quantum Efficiency Measurement of GaN-based Green LEDs[END_REF], [START_REF] Liu | Temperature dependence of photoluminescence intensity from AlGaInP/GaInP multi-quantum well laser structures[END_REF]. This increased emission of light at the edges of the MESA gives the impression that the MESA size is increasing while lowering temperature (in figure 2, the emission can be compared with the white dashed square which represents the emitted light at 296 K). From 60 K and below, the emission becomes also more intense at the corners. We believe that it is due to an enhanced light extraction due to geometric effects. The light generated and trapped in the structure due to the high refractive index contrast can escape more easily at the corners than the centre of the pixel due to the angle formed by the shape of the corners [START_REF] Sun | Shape designing for light extraction enhancement bulk-GaN light-emitting diodes[END_REF].

µ-PL spectra from the center and the corner of the pixel are compared in Figure 3. At room temperature, only one peak related to the radiative transition from the MQW is observed at 636 nm for the two locations. While decreasing the temperature, the spectra in the two locations exhibit a similar behavior. The peak position shifts towards high energies (short wavelengths) due to the band gap shrinkage with temperature [START_REF] Kim | Optical investigation of GaInP-AlGaInP quantum-well layers for high-power red laser diodes[END_REF]. 3 where a third point from the edge is also represented. The integrated intensity from 300 K to 100 K is higher at the center compared to the other positions, due to non-radiative recombinations from sidewall defects. From 100 K to 4,5 K, we note that the PL emission becomes more intense at the edges, especially at the corner, probably enhanced by an improved light extraction. For this temperature range, small fluctuations in the PL intensity occur, particularly below 40 K where a significant drop takes place. These variations have been observed in previous works [START_REF] Morrison | Photoluminescence investigation of the carrier confining properties of multiquantum barriers[END_REF], [START_REF] Daly | Behavior of In 0.48 Ga 0.52[END_REF] and happen when the PL excitation is non-resonant [START_REF] Morrison | Photoluminescence investigation of the carrier confining properties of multiquantum barriers[END_REF]. They are explained by the trapping of carriers in other layers (barriers and cladding) which then thermally escape to recombine at the lower state of the quantum wells [START_REF] Morrison | Photoluminescence investigation of the carrier confining properties of multiquantum barriers[END_REF].

IPL(T) and I0 are the PL integrated intensities at the sample temperature T and 40 K, respectively. C1, C2 are fitting constants and kb is the Boltzmann constant. We did the fitting without including the drop of intensity after 40 K in order to obtain the best-fit parameters.

In the literature, E1 represents non-radiative loss mechanism under 60 K and its nature is still unclear. Some groups describe it as the thermalization of carriers from band-edge fluctuations due to alloy variation or well width fluctuation followed by non-radiative recombination [START_REF] Liu | Temperature dependence of photoluminescence intensity from AlGaInP/GaInP multi-quantum well laser structures[END_REF], [START_REF] Morrison | Photoluminescence investigation of the carrier confining properties of multiquantum barriers[END_REF] while others attribute it to non-radiative recombination channel in the wells [START_REF] Daly | Behavior of In 0.48 Ga 0.52[END_REF], [START_REF] Fang | Investigation of temperature-dependent photoluminescence in multi-quantum wells[END_REF].

The activation energy at high temperature (> 60K) E2 is related to the confinement of the electron-hole pair in the quantum wells. In the case of AlGaInP quantum wells, Michler et al. [START_REF] Michler | Influence of barrier height on carrier lifetime in Ga 1 -y In y P/( Al x Ga 1 -x ) 1 -y In y P single quantum wells[END_REF] followed by others studies [START_REF] Liu | Temperature dependence of photoluminescence intensity from AlGaInP/GaInP multi-quantum well laser structures[END_REF], [START_REF] Kim | Optical investigation of GaInP-AlGaInP quantum-well layers for high-power red laser diodes[END_REF], [START_REF] Liu | Temperature and injection current dependent electroluminescence study of GaInP/AlGaInP quantum well laser diode grown using tertiarybutylarsine and tertiarybutylphosphine[END_REF] consider E2 as equal to one-half of the total confinement energy. For Daly and Glynn [START_REF] Daly | Behavior of In 0.48 Ga 0.52[END_REF] and Fang et al. [START_REF] Fang | Investigation of temperature-dependent photoluminescence in multi-quantum wells[END_REF] this energy is equal to the total confinement. However, for both interpretations, the major non-radiative mechanism is explained by the thermal emission of carriers from the wells followed by non-radiative recombination in the barriers. In our case, at the center, E2 with 309 meV is in the same order of magnitude than the confinement energy in our quantum wells structure, suggesting that the major losses at the center are dominated by thermal emission [START_REF] Daly | Behavior of In 0.48 Ga 0.52[END_REF]. At the edge and the corner, E2 is much lower than the confinement energy, 76 meV and 67 meV, similar to the work done by Kim et al. [START_REF] Kim | Optical investigation of GaInP-AlGaInP quantum-well layers for high-power red laser diodes[END_REF]. In this case, the major loss mechanism is attributed to recombination centers in the Al-containing layer (barriers or interface) associated with Al-O complexes [START_REF] Kim | Optical investigation of GaInP-AlGaInP quantum-well layers for high-power red laser diodes[END_REF], [START_REF] Morrison | Photoluminescence investigation of the carrier confining properties of multiquantum barriers[END_REF]. By analogy, we can conclude that a thermal emission of carriers out of the wells is excluded at the edges and it is very likely that sidewall defects are responsible for non-radiative recombinations instead of native defects at the well/barrier interface. However, it is not possible to clearly identify the recombination centers acting at the sidewalls due to the variety of defects introduced after the etching (native oxide, dislocations, vacancies and others defects [START_REF] Wong | Investigation of reactive ion etching induced damage in GaAs-AlGaAs quantum well structures[END_REF]). TRPL measurements were conducted as well in order to confirm the non-radiative recombination process at the sidewalls.

Acquisitions were carried out from the center to the sidewall of a 16×16 µm² pixel which represents the adequate size for our TRPL acquisitions resolution. Figure 5 reports the results. In Figure 5 a) we observed that the decay time decreases when we approach the sidewall. The PL transient curves were best fit with a single exponential decay function [START_REF] Dekker | Annealing of the deep recombination center in GaInP/AlGaInP quantum wells grown by solidsource molecular beam epitaxy[END_REF] (inset in figure 5b).

𝐼 𝑃𝐿 = 𝐴𝑒 -𝜏 𝑡 ( 2
)
where A is the amplitude and τ the PL lifetime. The extracted lifetime at the center is similar to those reported in previous papers [START_REF] Dekker | Annealing of the deep recombination center in GaInP/AlGaInP quantum wells grown by solidsource molecular beam epitaxy[END_REF], [START_REF] Onishi | Doping level and type of GaInP saturable absorbing layers for realizing pulsating 650-nm-band AlGaInP laser diodes[END_REF]. Lifetime begins to decrease at 5 µm from the center until the sidewall. It is clear that this decrease comes from the non-radiative defects, which increase the recombination velocity. [START_REF] Yu | Influence of GaInP ordering on the performance of GaInP solar cells[END_REF], [START_REF] Gagliano | Efficient Green Emission from Wurtzite Al x In 1-x P Nanowires[END_REF] As µ-PL mapping has a low resolution at the scale of a few micrometers, we carried out cathodoluminescence measurements to gain around two orders of magnitude in resolution. Figures 6 and7 represent the CL mapping of 6×6 µm², 36×36 µm² and 56×56 µm² pixels. CL measurements exhibit the same behavior as µ-PL mapping. The intensity distribution becomes more homogenous across the MESA while lowering temperature. In the 6×6 µm 2 , the effect of non-radiative recombinations is more visible at edges and high temperature. It results that the LED efficiency at low dimension will be heavily impacted without proper etching process and passivation. The same behavior is observed for 36×36 µm 2 and 56×56 µm 2 pixels but the role of nonradiative recombinations from sidewall defects seems reduced at higher dimension scale (Figure 7). Due to a high surface recombination velocity [START_REF] Boroditsky | Surface recombination measurements on III-V candidate materials for nanostructure lightemitting diodes[END_REF] combined with a large carrier diffusion length [START_REF] Oh | Light output performance of red AlGaInP-based light emitting diodes with different chip geometries and structures[END_REF] in AlGaInP, the carrier generated in the low dimension pixels can diffuse more easily to sidewall defects where they are lost, which explain why the impact is less important for the larger pixels. We conducted the CL characterization on another 6×6 µm² pixel in order to check the repeatability (Figure 8). Since the CL intensity I(T) is maximum at 30 K, we calculated a map representing the emission efficiency using the ratio[14] I(296 K)/I(30 K). This calculation was carried out after an alignment of the images realized at 296 K and 30 K (Figure 8c). Luminescence intensity profiles are then extracted along a band, which crosses the pixel by its middle (vertical red band in Figure 8a) for the three maps shown in Figure 8. The intensities were normalized by the value at the center of the pixel (Figure 9). By comparing the profiles at 296 K and 30 K, we deduced that the edges of the pixel are optically inactive at room temperature over a large distance. This behavior is confirmed by the mapping of the ratio I(296 K)/I(30 K), where the efficiency is maximum at the center and decreases by approaching the edges. From Figure 8c, an emission efficiency profile was extracted along a line passing through the center of the pixel (Figure 9b). Thus, we estimated that approximatively 3.4 µm (represented by the red area in Figure 9b) out of 6 µm have an efficiency lower than 80% of the maximum value at the center. This represents 86 % of the total area of the MESA. For this calculation, the real size of the pixel (5.61 µm) was used instead of the designed size (6 µm). As expected, the oxidation occurred at the surface and the sidewalls of the MESA where are dangling bounds caused by the breaking of crystal periodicity. An oxidation could be a source of non-radiative recombinations [START_REF] Xiang | Oxygen-related deep level defects in solid-source MBE grown GaInP[END_REF] especially in Ⅲ-Ⅴ semiconductors [29][30]. Indeed, the native surface oxides are known to generate interfacial defects due to their poor stability which leads to a Fermi level surface pinning by introducing surface energy levels in the band gap [START_REF] Zhou | Brief Review of Surface Passivation on III-V Semiconductor[END_REF]. This would be one of the causes of the luminescence quenching at pixel edges revealed by CL/PL mappings.

The signal intensity of Chlorine and Boron also arises from the surface and the edges of the sample (Figure 12). Their presence comes certainly from the BCl3 source used during the etching process. Boron and Chlorine can also participate in the carrier loss at the sidewalls of the µLED by introducing energy levels in the bandgap. On one hand, Boron can act as electron compensator in InGaP with a deep mid-gap level at Ec-0.9 eV [START_REF] Henkel | Boron Implantation into G a A s / G a 0.5 I n 0.5 P Heterostructures[END_REF]. On the other hand, Chlorine acts as an electron compensator in the InP system [START_REF] Landesman | Evidence of chlorine ion penetration in InP/InAsP quantum well structures during dry etching processes and effects of induced-defects on the electronic and structural behaviour[END_REF] but there is a lack of studies about the impact of Chlorine and Boron in the InGaP/AlGaInP system [START_REF] Tukiainen | Unintentional boron contamination of MBE-grown GaInP/AlGaInP quantum wells[END_REF]. Further investigations are required to unravel their effect on LED efficiency.

Figure 12 TOF-SIMS maps of Chlorine and Boron

These results highlight the necessity to optimize the process of MESA formation and passivation, in order to suppress the EQE drop by reducing the etching-related defects. In our case, the passivation involves the removal of the native oxide layer and the formation of a thin protective layer to prevent further atmospheric oxidation by using for example sulfur treatment with ammonium sulfide (NH4)Sx [START_REF] Geum | Strategy toward the fabrication of ultrahigh-resolution micro-LED displays by bondinginterface-engineered vertical stacking and surface passivation[END_REF], [START_REF] Jeng | Effective Suppression of Surface Recombination of AlGaInP Light-Emitting Diodes by Sulfur Passivation[END_REF]. Other techniques could be used such as plasma treatment [START_REF] Polydorou | Surface passivation effect by fluorine plasma treatment on ZnO for efficiency and lifetime improvement of inverted polymer solar cells[END_REF],

nitridation [START_REF] Losurdo | N2-H2 remote plasma nitridation for GaAs surface passivation[END_REF] or passivation with film deposition [START_REF] Dingemans | Comparison between aluminum oxide surface passivation films deposited with thermal ALD, plasma ALD and PECVD[END_REF] such as ALD Al2O3 deposition [START_REF] Wong | Improved performance of AlGaInP red micro-light-emitting diodes with sidewall treatments[END_REF], [START_REF] Ferrandis | Electrical properties of metal/Al 2 O 3 /In 0.53 Ga 0.47 As capacitors grown on InP[END_REF]. Finally, these results demonstrate the possibility to conduct studies about etching impact or passivation treatment only at the MESA step which is cost effective and easier compared to I-V-L measurement that require fully processed wafers.

CONCLUSION

In summary, the emission homogeneity of AlGaInP µLED epitaxy was characterized as a function of the pixel size. From µ-PL mapping of a 6×6 µm² pixel, we observe that the maximum luminance is situated within the center of the pixel and decreases while approaching the edges. The activation energies determined from Arrhenius plots of the PL integrated intensity demonstrated that losses by thermal emission processes and non-radiative recombinations at sidewall defects occur at the center and the edges of the pixel, respectively. The CL mappings agree with the observation from µ-PL measurements and confirm that the edges are optically inactive. We have shown that the impact of etching-related sidewall defects is not confined at the first nanometers but induces carrier losses in 86 % of the 6x6 µm² pixel area. Finally, the TOF-SIMS analysis has shown that no anomaly or alloy fluctuation appear in the different layers of our sample but revealed the presence of native oxide, Chlorine and Boron which can both introduce defect levels. These results show the importance of conducting characterization at the MESA step by optimizing the etching process and the passivation.

T (K)

Figure 1 .

 1 Figure 1. Schematic of the LED structure with InGaP/AlGaInP multiple quantum wells µ-PL measurement and mapping were performed with a LabRAM photoluminescence setup from HORIBA. A 514 nm Argon laser line was focused at normal incidence by a 100× microscope objective (NA: 0.6), with an average excitation power of 5.5 mW measured at the sample and a spot size of 1 µm. PL signals from the sample were collected with the same objective (excitation objective) and dispersed through a spectrometer with a focal of 800 mm by a 100 gr/mm grating.

Figure 2 .

 2 Figure 2. µ-PL integrated intensity mappings on a 6×6 µm 2 pixel. A white dashed square with the dimension of the pixel emission at 296 K is added on each map to compare the light emission area.

Figure 3 .

 3 Figure 3. µ-PL spectra a) at the center and b) at the corner of the 6 µm pixel Figure 4 a) reports the evolution of the integrated PL peak intensity of Figure 3 where a third point from the edge is also

Figure 4 .

 4 Figure 4. a) Integrated intensity as a function of temperature b) Temperature dependence of the integrated PL intensity and solid line representing fits of experimental data with PL thermal quenching equation[17].The Arrhenius behavior shown in the Figure4. b) can be fitted using equation (1)[START_REF] Kim | Optical investigation of GaInP-AlGaInP quantum-well layers for high-power red laser diodes[END_REF], that describes two non-radiative processes E1 and E2 for low and high temperature, respectively.𝐼 𝑃𝐿 (𝑇) =

Figure 5 .

 5 Figure 5. a) Time-resolved photoluminescence decay curves as a function of position. The inset represents the corresponding µPL spectra with a peak intensity at 639.6 nm. b) Lifetime versus position. Red solid line in the inset represents the time decay fit using equation (2) [24].

Figure 6 .

 6 Figure 6. Integrated CL intensity mappings at different temperatures on a 6×6 µm 2 pixel. A white dashed square with the same dimension of the pixel at 296 K is added for each map to compare their light emission area.

Figure 7 .

 7 Figure 7. Integrated CL intensity mappings at different temperatures for 36×36 µm² and 56×56 µm² pixels

Figure 8 .

 8 Figure 8. (a) and (b), integrated CL intensity mappings at 296 K and 30 K, respectively. (c) emission efficiency mapping calculated from the ratio I(296 K)/I(30 K)

Figure 9 .

 9 Figure 9. a) Normalized intensity profiles at 296 K and 30 K and b) Emission efficiency profile extracted from Figure 8c Finally, TOF-SIMS measurements were done to probe the alloy homogeneity of the epitaxial layers.Figure 10 a) represents the depth profiles of constituent elements of a 6×6 µm² pixel. The presence of other unwanted elements such as native oxide, chlorine and boron are shown in Figure 10 b).

Figure 10 .

 10 Figure 10. a) TOF-SIMS profiles of constituent elements of a 6×6 µm 2 pixel b) TOF-SIMS profiles of oxides and contaminants (Boron contamination represented by Boron Phosphide profile)

Figure 11

 11 Figure 11 TOF-SIMS maps of native oxide ( 71 GaO2) for different depths positions

Acknowledgments

This work was performed on the NanoCharacterisation PlatForm (PFNC) of CEA-Grenoble, and was supported by the "Recherches Technologiques de Base"Program of the French Ministry of Research.


A Lazzari

M Bournel

Said

N Yahyaoui
email: naima.yahyaoui@yahoo.fr

N Sfina

J-L Lazzari

A Bournel

M Said

Performance evaluation of high-detectivity p-i-n infrared photodetector based on compressively-strained Ge 0.964 Sn 0.036 /Ge multiple quantum wells by quantum modelling

Keywords: infrared photodetectors, detectivity, band structure engineering

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

In recent years, there has been increasing effort toward the development and realisation of group IV semiconductor optoelectronic devices, recently encouraged by their possible heterogeneous integration with CMOS technology on silicon on insulator (SOI) and germanium on insulator (GeOI) substrates. The progress made on key photonics components, including laser sources, optical modulators and photodetectors, has been demonstrated in detail [START_REF] Reed | Silicon Photonics: The State of the Art[END_REF]. Due to its relatively high absorption coefficient at 1.3-1.55 μm, Ge is regarded as the best candidate material for detection in this spectral range. However, the optical response of thin vertical Ge-based high frequency photodetectors at the telecommunication wavelength of 1.55 μm is limited [START_REF] Lee | [END_REF]. An increase of the responsivity for these wavelengths can be achieved by intermixing Sn to Ge [3]. Thus, Ge 1-x Sn x alloy is an interesting alternative since its bandgap, which is smaller than that of Ge, may further improve the optical response at 1.55 μm and will push the spectral range to longer infrared wavelengths [4][5][6]. On the other hand, GeSn alloy has poor thermal stability [7,8], which prevents its application in optoelectronic devices. In addition, the large lattice mismatch with Ge (∼15%) and the extremely low (x < 1%) solid solubility of Sn in Ge makes it very difficult to grow high-quality defect-free GeSn [9]. Notwithstanding, GeSn alloys with a few per cent Sn content can only be grown under non-equilibrium conditions. Despite these difficulties, some effort has been made toward the epitaxial growth of GeSn alloys [7,8,10] and the fabrication of GeSn based devices [4]. Recently, there have been reports on GeSn p-i-n photodetectors with small Sn content for full telecommunication spectral range applications [11]. These results show that adding Sn in a p-i-n Ge photodiode matrix also increases the responsivity of the detector in the telecom wavelength range and extends the cut-off wavelength beyond 1.7 μm [12][13][14]. Su et al published the first GeSn p-i-n photodetector grown by solid-source molecular beam epitaxy with 3% Sn composition and 820 nm thick layers [14]. At 1640 nm, they measured strong reverse voltage dependence with a small optical responsivity of 50 mA W -1 under zero bias operation. Strangely, the Sn incorporation shifts the detector cut-off responsivity towards the infrared spectral range by 60 nm only. The detection wavelength of GeSn p-i-n photodetectors fabricated on Ge substrate with Sn contents up to 3.6% in the active layer has recently reached 1.95 μm [15]. Photodiodes built on lattice relaxed Ge 1-x Sn x layers [15,16] may exhibit large densities of defects, such as dislocations acting as recombination traps, resulting in an excessive dark current. Strained Ge 1-x Sn x /Ge multiple quantum wells (MQWs) may be used as an absorbing layer to adjust the absorption threshold and to reduce the dark current. However, owing to the serial resistance induced by the number of quantum barriers, a limited number of cells or coupled quantum wells in the superlattice regime should be used. In order to design such a device, we first determine the electronic properties of strained Ge 1-x Sn x on (001)-oriented Ge, such as bandgap energy and band discontinuities. Then, we propose a p-i-n infrared photodetector with an intrinsic absorbing layer formed by straincompensated Ge/Ge 0.964 Sn 0.036 /Ge multi-quantum wells. This heterostructure is modeled with a system of Schrödinger and kinetic equations self-consistently solved with the Poisson equation. The current components due to these processes contributing to the total dark current are described. The room temperature performance is finally presented and discussed in terms of responsivity and detectivity.

Material parameters

The band offsets between binary α-Sn containing alloys and Ge are not known experimentally [17]. In order to calculate the conduction and valence-band discontinuities between a Ge 1-x Sn x strained layer and (001)-oriented relaxed Ge substrate, we have adopted the calculation procedure of Van de Walle et al that we outlined in [18] using the parameters taken from [START_REF] Madelung | Physics of Group IV Elements and III-V Compounds 1st edn[END_REF][START_REF] Brudevoll | [END_REF][START_REF] Menéndez | [END_REF] and the parameters listed in table 1. The following (1)-( 4) approximated analytical laws of the conduction and valence-band discontinuities between strain split L and Γ valleys were extracted versus Sn composition: ( )

E x x x ( ) ( 1.543 2.054 ) (1)
C Δ ≅ - + Γ E x x x ( ) ( 0.249 0.853 ) (2)
L C Δ ≅ - + E x x x ( ) (1.424 0.169 ) (3) v hh , Δ ≅ - E x x x ( ) (1.121 0.159 ) (4)
E x E x E cx x Ge Sn (1 ) (1 ) (5)

= -+ -

The resulting plots of the energy gaps for compressively strained and relaxed alloys including experimental data values are summarized in figure 1. It is found that pseudomorphic Ge 1-x Sn x /Ge (001) alloys may have a direct bandgap at Sn fractions higher than 10.5% at room temperature. Regarding Table 1. Summary of the lattice constants (in angstrom), elastic stiffness constants (in 10 11 dyn cm -2 ), conduction and valence band deformation potentials, spin-orbit splitting and bulk bandgaps (in eV) of Ge and α-Sn. All symbols are used in their conventional meanings (see [START_REF] Madelung | Physics of Group IV Elements and III-V Compounds 1st edn[END_REF][START_REF] Brudevoll | [END_REF][START_REF] Menéndez | [END_REF]).

a c 11 c 12 a c (Γ) a c (L) E v,av b Δ 0 E g (Γ) E g (L)
Ge 5.6579 12.85 4.83 -8.24 -1.54 0 -2.9 0.30 0.798 0.664 α-Sn 6.4892 6.9

2.93 -6 -2.14 0.69 -2.7 0.80 -0.413 0.092 the unstrained Ge 1-x Sn x alloys, indirect-to-direct crossing occurs at a Sn fraction of 5.3% at room temperature. The latter values are consistent with the experimental crossovers found in [22] at about 17 and 6.3% respectively for temperatures around 10 K. Additional experimental evidence of the indirect -direct bandgap transition for pseudomorphic Ge 1-x Sn x /Ge (001) would be of fundamental and practical importance.

Studied structure and modeling

The structure under investigation consists of 10 periods of intrinsic Ge 0.964 Sn 0.036 /Ge QW cell. Both compressively strained Ge 0.964 Sn 0.036 and relaxed Ge barriers are 10 nm thick. The device is sketched in figure 2. The material parameters used are taken from [23][START_REF] Millman | Dispositifs à Semiconducteurs[END_REF][START_REF] Huang | [END_REF] and summarized in table 2. The compressive lattice mismatch between Ge 0.964 Sn 0.036 and Ge is 0.52% while the average mismatch of the 200 nm-thick stacks is 0.26%. Thus the chosen thicknesses are reasonable values regarding the critical thickness of Ge 0.964 Sn 0.036 layers and strain accumulation within the stack. However, thicker MQWs for better absorption would imply strain compensation through the use of Si 0.13 Ge 0.87 barriers under tensile strain. The active region is embedded between 70 nm-thick n and p-doped Ge contact layers doped at N A = N D = 1 × 10 18 cm -3 . For the sake of simplicity, we assume that there are no intrinsic impurities or defects in the host lattice. The theoretical model and numerical methods used in this paper are based on the self-consistent solving of the onedimensional Schrödinger equation in the effective mass approximation [26][START_REF] Sze | Physics of Semiconductor Devices[END_REF][START_REF] Sfina | [END_REF][29] and Poisson equations for electrons and holes. Numerically, the problem was treated using the finite differential method. The electron and hole densities n(z) and p(z) in the contact regions are calculated according to the Boltzmann statistic. Figure 3 shows the conduction-and valence-band profiles for this ten-period Ge 0.964 Sn 0.036 /Ge MQW at zero bias. The ground level is drawn for electron, light-hole and heavy-hole with the associated wave function. Electrons fill all available states in the active part of the device according to the Fermi-Dirac f E

( ) distribution. The Fermi level is linearly varying from E E p F( ) F = at the p contact to E E qV n F( ) F bias = -
at the n contact, where V bias is the applied bias. The formula after Tsu and Esaki generalized for the case of several conduction valleys and anisotropy of effective mass is then used for calculation of the tunneling current. For parabolic dispersion relations with integration over the transverse mass component only, the current density from extended and localized states is written as [30]:

( ) ( ) ( ) J V qm k T tr E V Ln E E k T E E qV k T E ( ) * 2 , 1 exp / 1 exp / d ( 10
) z f z f z z B 2 3 0 bias B bias B ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ∫ π = ℏ × × + - + - - ∞
where the transmission coefficient tr(E Z ) is deduced from the transfer matrix formalism within the step approximation as for the potential [31]; T is the absolute temperature and k B and ħ are the Boltzmann and reduced Planck constants, respectively. For an analysis of the thermally activated carrier transport, the current density can be described using the rates g g ,

i i i i 1 1 → + + → of
i i i i n i i i i n i i i n i i i n i i p i i i i p i i i p i i i p 1 1 1 1 1 1 1 1 1 1 1 1 = ∂ ∂ + ∂ ∂ = - - + + - + + - -→ - → + → - + + → -→ - → + → - + + → Figure 1.
Energy gaps of pseudomorphic and relaxed Ge 1-x Sn x alloys. The dashed red and black lines display the indirect pseudomorphic E L ε and relaxed E L R bandgaps, respectively; solid blue and black lines are the direct pseudomorphic E Γ ε and relaxed E R Γ bandgaps, respectively. Symbols correspond to available experimental data [22] and E R Γ and E L R are obtained by the empirical pseudo-potential method (EPM). where n i (p i ) is the electron (hole) concentration in the ith mesh point. This rate, defined within the thermally activated transport theory, includes the image-force effect in the following way [33]:

( ) ( ) g q k T E q hz k T exp exp 16 / ( 12
) i i n p i n p i i i C V i i i i 1 , 0 , 1 B , 3 1 0 B ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎛ ⎝ ⎜ ⎜ ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎞ ⎠ ⎟ ⎟ ω ϕ ϕ Δ ϕ ϕ πε ε = - × - - - → + + +
where hz i is the step of the mesh, ϕ i is the electrostatic potential in the ith mesh (obtained by solving the Poisson equation), ε i is the dielectric constant in the ith mesh, and 0 ω is the frequency of the local carrier oscillations along the multiple quantum well. The system of kinetic equations has been solved for the stationary case.

In the absence of the optical excitation G G 0,

ni pi = = it is worth comparing the generalized formula of the dark current density described by equations ( 10)-( 12) with the classical expression given by continuity equations [START_REF] Sze | Physics of Semiconductor Devices[END_REF] to account for additional current contributions: is the average time for the radiative and non radiative recombination process for electrons (or holes) in the ith point mesh, e.g.

J n t p t G G n n p n p p p n p n J J J n z n z p z p z D n z D p z ( 13
) i i ni pi i n i i i p i i i ni i i ni i i i i pi i i pi i i i i n i i i p i i 0 , R,NR 0 0 0 , R,NR 0 0 Tunnel Band to Band Tunnel Electrons Tunnel Holes 2 2 2 2 ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ τ τ μ ξ μ ξ μ ξ μ ξ = ∂ ∂ + ∂ ∂ = + - - + - - + + + + + ∂ ∂ + ∂ ∂ - ∂ ∂ - ∂ ∂ + ∂ ∂ + ∂ ∂
.

1 1 1 n p i n p i n p i , R,NR , R , NR = + τ τ τ
In the present work, we do not consider the contributions on the generation-recombination current of the Shockley-Read-Hall recombination of carriers on traps, e.g. n p i , NR τ → ∞ for first term of equation ( 13), neither the three carrier Auger mechanisms, nor the band-to-band tunneling mechanism that are valid assumptions for low concentrations of photo-carriers and low reverse voltages of a p-i-n photodiode. The two sets of equations ( 10)-( 12) or (13) thus account for same current contributions.

In the particular case of a GeSn absorbing layer (not MQWs), e.g. E 0 i C V , Δ = and no image-force effect, if one considers a first-order finite development on the electrostatic potential difference within a mesh, the transfer rate given in equation ( 12) reduces to: g [START_REF] Reed | Silicon Photonics: The State of the Art[END_REF].

i i n p i n p q k T 1 , 0 , ( ) i i 1 B ω ≅ + ϕ ϕ → + -+
Using the same linear development for all derivative terms of the conduction and diffusion currents given in second part of equation ( 13), by comparing with those extracted from equation ( 13), one can find [34]:

( ) ( ) ( ) D T hz k T q T hz k T q q m hz ( ) ( ) 1 . ( 14
) i n p i n p i i n p i i n p e h i 0 , , 2 B , 2 B , , 2 ⎛
⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ω μ τ ≅ = = ⊥
In the absence of tunnel barriers, this remarkable formula links the frequency of local carrier oscillations along the structure and their averaged times i n p , τ of scattering with impurities, lattice phonons and alloy disorder. It is valid only if the step of the mesh hz i is of the order of magnitude 2). The fundamental electron, light-hole and heavy-hole levels are drawn with their relative wave function at Γ and L valleys. Note the envelopes of electron and hole wave functions, meaning Ge 0.964 Sn 0.036 quantum wells are coupled with a 10 nm thick Ge spacer.

of the QW width. For a 10 nm thick Ge QW, taking a room temperature mobility of 3900 cm 2 V -1 s -1 and 1900 cm 2 V -1 s -1 for electrons and holes, one can find fs (10 15 ) ,

n p 0 , 1 ω ≅ - -respectively.

Results and discussion

Figure 4 compares the dark current-voltage (I-V) characteristics calculated at room temperature for bulk Ge 0.964 Sn 0.036 and Ge 0.964 Sn 0.036 /Ge MQW active regions. A good agreement of the calculated and experimental dark currents [15] is obtained for a 200 μm thick bulk Ge 0.964 Sn 0.036 active region, a mesa diode diameter of 150 μm, and a 9 μs [START_REF] Millman | Dispositifs à Semiconducteurs[END_REF] generation -recombination time of carriers. Such an experimental device has a typical dark-current of 1.2 10 -6 A at -1 V. The use of MQWs as the active region increases the serial resistance [22] and thus decreases the dark current around 3.1 10 -7 A for the same -1 V reverse voltage.

In order to understand the evolution of the dark current with the bias voltage, it is necessary to determine the respective influence of each component originating from the different considered mechanisms that include the conduction, diffusion, recombination and thermally activated tunnel currents. The calculation of each current component has been carried out at room temperature using the approach described in the previous section. Results are illustrated in figure 5. It is shown that the thermal diffusion and the well describe the forward bias characteristic while the behavior of the total dark current under reverse polarization thoroughly agree with the sum of the tunneling and recombination current contributions. The diffusion component remains the main mechanism for low (<0.5 V) direct bias voltages.

Next we have investigated the influence of α-Sn concentration on the I-V dark characteristics. The results of our simulations of the dark current-voltage characteristics at room temperature for a pure bulk Ge p-i-n photodiode and two devices based on ten-period strained Ge 1-x Sn x /Ge MQWs with different α-Sn compositions, are illustrated in figure 6.

The dark current density not only indicates the material quality but also determines the optical receiver sensitivity. A direct comparison with the experimental results pointed out by recent investigations [15] proves that our proposed structure allows improvement of the performance of the photodiode. The optical responsivity is obtained using the following expression:

( ) ( ) ( R q hc V V V L ( ) ( , ) ( , ) 1 exp ( , ) (15)
i i i λ η λ Ω Γα λ Γα λ α α Γα λ = + × - - +
where η i is the internal quantum efficiency, Γ is the confinement factor of the optical mode within the multiple quantum wells, V ( , ) α λ is the absorption coefficient at wavelength λ and bias V, L is the waveguide length, and Ω is the coupling efficiency, including mode size mismatch and reflection [35]. i α accounts for all the propagation losses that do not generate photocurrent. We used η i = 1, 0.38, Γ = 0.25, Ω = 120 i α = cm -1 and V ( , ) α λ was theoretically calculated according to the formula outlined in our previous work [23].

The room temperature responsivity for three reverse bias voltages (0 V, -1 V and -3 V) are given in figure 7(a). This responsivity versus wavelength (0.9-2.3 μm) shows two peaks. These peaks corresponding to the hh 1 -cΓ 1 transition energy and the strained direct bandgap of Ge 0.964 Sn 0.036 /Ge QWs are observed around 1550 nm and 1781 nm, respectively. Similarly, we can see that the responsivity decreases when the reverse bias voltage increases. Under a reverse bias voltage of -3 V, the responsivities of 0.62 A W -1 at 1550 nm and 0.71 A W -1 at 1781 nm are obtained at room temperature.

Afterwards, we investigated the effect of the concentration of α-Sn on the optical responsivity for the Ge/Ge 1-x Sn x / Ge p-i-n photodetector at zero bias. Figure 7(b) shows that an increase of the optical responsivity for higher wavelengths can be observed with increasing α-Sn content at 0 V. We found that the Ge 0.98 Sn 0.02 /Ge MQW photodetector is achieved with a responsivity of 240 mA W -1 at the telecommunication wavelength of 1.55 μm. The response of the photodetector with Sn 2% is significantly higher than that reported in [START_REF] Masini | Advances in Optical Technologies[END_REF]. In addition, a rise of 3.6% of the α-Sn amount leads to an increase greater than an order of magnitude on the responsivity. Indeed, the optical responsivity curve of the Ge 0.964 Sn 0.036 /Ge p-i-n MQW is shifted ∼500 nm to higher wavelengths compared with pure Ge. At λ = 1.781 μm, an optical responsivity of ∼306 mA W -1 is observed for the Ge 1-x Sn x /Ge p-i-n photodetector with 3.6% α-Sn, whereas the Ge reference photodetector without α-Sn shows an optical responsivity of 0.17 A W -1 . Compared to Ge photodetector, responsivity is improved in the whole wavelength range from 0.9 μm to 2.3 μm. Gassenq et al [START_REF] Gassenq | [END_REF] found that an increase of S n content enhances the responsivity of the detector in the telecom wavelength range and extends the cut-off wavelength beyond 2.4 μm.

Besides the dark current, we can test the MQW's performance by its detectivity D* which depends on the wavelength of incident light λ. The detectivity is given by the B L Sharma simplified formula:

( ) D R q J *( ) 1 2 ( ) ( 16
) 0 1 2 λ λ = -
where λ is the operating wavelength and J 0 is the dark current density.

Using this expression in the region of zero bias voltage of the p-n junction, we have calculated room-temperature specific detectivity at a 1550 nm wavelength peak of responsivity. D* 7.9 10 10 cm Hz 1/2 W -1 and ∼ 3.8 10 10 cm Hz 1/2 W -1 have been achieved under reverse bias voltage of -0.5 V and -1 V, respectively, at 300 K. We have not investigated the temperature effect. Conley et al [38] found that the detectivity of GeSn photoconductors as expected increases with Sn increasing content when temperature decreases. But their device exhibits a poor value of detectivity of about 1 109 cm Hz 1/2 W -1 at 1.55 μm, as compared to the results of Zhang et al [15]. GeSn/Ge p-i-n photodetectors operating in the infrared region (1.3-1.55 μm) are finding extensive applications in long haul and high bit rate optical communication systems and local area networks [39][40][41].

In addition to optical communication, these devices are also useful for sensing applications as they have superior electro-optical characteristics, namely low dark current, high quantum efficiency, greater sensitivity and high speed of response.

Conclusion

In summary, we have theoretically studied the group-IV semiconductor in which the GeSn relaxed alloys have a direct bandgap for 5.3% α-Sn. Our investigation predicts, at room temperature, a direct bandgap for strained Ge 1-x Sn x /Ge (001) structures at a α-Sn fraction higher than 10.5%. We have theoretically simulated the characteristics of GeSn/Ge p-i-n photodetector with Sn contents up to 3.6%. The electrical and optical properties are compared with a similar Ge p-i-n reference photodetector without Sn. An increase of Sn content shifts the optical responsivity curve to higher wavelengths compared with pure Ge. The simulation of the responsivity (0.9-2.3 μm) shows that the detectors have a photo-response up to 2.1 μm, covering the entire telecommunication range. In particular, considering the absorption of the strained direct bandgap of the Ge 0.964 Sn 0.036 /Ge quantum wells, good responsivities of 0.62 A W -1 at 1550 nm and 0.71 A W -1 at 1781 nm were obtained at a reverse bias voltage of -3 V. Consequently, Ge 1-x Sn x /Ge heterostructures are a promising candidate material not only for all telecommunication bands in optoelectronics but also for near infrared applications.

  in eV. Ge 1-x Sn x /Ge heterointerfaces have type I alignments at Γ-Γ, L-L and Γ-L respective critical points, meaning both electrons, heavy and light holes are confined into Ge x Sn x alloys. The relaxed bandgaps of Γ and L valleys in the conduction band (CB) relative to the top of the valence band (VB) are given by:

Figure 2 .

 2 Figure 2. Schematic diagram of a p-i-n photodetector. The crosssectional view shows the structure of strained GeSn/Ge multiple quantum wells grown on germanium substrate.

Figure 3 .

 3 Figure 3. Conduction-and valence-band profiles for ten-period Ge 0.964 Sn 0.036 /Ge MQWs (the values for band offset and bandgap of Ge 0.964 Sn 0.036 /Ge are summarized in table2). The fundamental electron, light-hole and heavy-hole levels are drawn with their relative wave function at Γ and L valleys. Note the envelopes of electron and hole wave functions, meaning Ge 0.964 Sn 0.036 quantum wells are coupled with a 10 nm thick Ge spacer.

Figure 5 .

 5 Figure 5. Total dark current at 300 K as a function of bias voltage from -5 V to 1 V is shown with four distinct regimes and different dominant mechanisms, the conduction current density, diffusion current density, recombination current density and tunneling current density.

Figure 6 .

 6 Figure 6. I-V characteristics of the devices with different Sn concentrations (device radius 150 μm).

  where n o and p o are the electron and hole free carrier concentrations at thermodynamic equilibrium, G ni and G pi are the electron and hole optical generation rates, i

		μ	n p ,	is the
	electron (or hole) mobility, D T ( ) i n p , = is the electron (or hole) diffusion coefficient, i T ( ) k T q i n p , B μ = n p k T q B , τ	( is the ) q m i n p e h , τ ⊥ ,
	averaged scattering times for electrons or holes,	i ξ	z = ∂ ∂ i ϕ	i
	is the applied electric field, and n p i , R,NR τ

Table 2 .

 2 Parameters at 300 K used for the simulation of the p-i-n Ge 0.964 Sn 0.036 /Ge MQW based photodetectors. Electron effective mass Ge 0.964 Sn 0.036 /Ge m * Heavy hole effective mass Ge 0.964 Sn 0.036 /Ge m * Figure4. current-voltage characteristics of a GeSn p-i-n photodetector with a Sn content of 3.6% for devices with different active region Ge 0.964 Sn 0.036 and MQW Ge/Ge 0.964 Sn 0.036 /Ge. The symbols are the experimental data taken from[15].

	Parameters					Values
	Electron effective mass Ge 0.964 Sn 0.036 /Ge m * e , Γ	0.032 m 0 [23]
					L e ,	0.078 m 0 [23]
					hh	0.199 m 0 [23]
	Light hole effective mass Ge 0.964 Sn 0.036 /Ge m * lh,	0.061 m 0 [23]
	Bandgap Ge 0.964 Sn 0.036 /Ge E g Γ-	hh	0.694 eV (present work)
	Bandgap Ge 0.964 Sn 0.036 /Ge E g Γ-	lh	0.705 eV (present work)
	Bandgap Ge 0.964 Sn 0.036 /Ge E g L hh -	0.600 eV (present work)
	Bandgap Ge 0.964 Sn 0.036 /Ge E g L lh -	0.611 eV (present work)
	Conduction band-offset Ge 0.964 Sn 0.036 /Ge E C Δ Γ	-0.053 eV (present work)
	Conduction band-offset Ge 0.964 Sn 0.036 /Ge E L C Δ	-0.008 eV (present work)
	Valence band-offset Ge 0.964 Sn 0.036 /Ge E hh V Δ	0.051 eV (present work)
	Valence band-offset Ge 0.964 Sn 0.036 /Ge E lh V Δ	0.040 eV (present work)
	Electron carrier recombination lifetime ni τ	9 μs [24]
	Electron carrier recombination lifetime pi τ	9 μs [24]
	Electron carrier mobility	ni μ	T ( )		m ( ) i e , ≈ ⊥ -1/2 3/2 T	[25]
	Hole carrier mobility	pi μ	T ( )			m ≈ ⊥ -( ) i h , 1/2 3/2 T	[25]
	Acceptor concentration, N A Donor concentration, N D			10 18 cm -3 10 18 cm -3

Present address: Faculty of Science and Art KKU Mahail Assir, King Kaled University, Saudi Arabia.