AlGaAsSb quantum wells

Accepted Manuscript The effect of Auger recombination on the nonequilibrium carrier recombination rate in the InGaAsSb/AlGaAsSb quantum wells Maxim Vinnichenko, Ivan Makhov, Roman Balagula, Dmitry Firsov, Leonid Vorobjev, Leon Shterengas, Gregory Belenky PII:

S0749-6036(17)30980-1

DOI:

10.1016/j.spmi.2017.05.065

Reference:

YSPMI 5046

To appear in:

Superlattices and Microstructures

Received Date: 20 April 2017 Revised Date:

30 May 2017

Accepted Date: 30 May 2017

Please cite this article as: M. Vinnichenko, I. Makhov, R. Balagula, D. Firsov, L. Vorobjev, L. Shterengas, G. Belenky, The effect of Auger recombination on the nonequilibrium carrier recombination rate in the InGaAsSb/AlGaAsSb quantum wells, Superlattices and Microstructures (2017), doi: 10.1016/ j.spmi.2017.05.065. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

The effect of Auger recombination on the nonequilibrium carrier ACCEPTED MANUSCRIPT

recombination rate in the InGaAsSb/AlGaAsSb quantum wells Maxim Vinnichenkoa,*, Ivan Makhova, Roman Balagulaa, Dmitry Firsova, Leonid Vorobjeva, Leon Shterengasb and Gregory Belenkyb a

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Peter the Great St. Petersburg Polytechnic University, 29 Polytechnicheskaya str., St. Petersburg 195251, Russia b Department of Electrical and Computer Engineering, State University of New York at Stony Brook, New York, 11794 USA *[email protected]

Abstract

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Time dependencies of interband photoluminescence are studied in InGaAsSb/AlGaAsSb quantum well structures with various barrier materials and quantum well widths. The

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experimentally determined dependencies of photoluminescence intensity on the optical pumping level are compared with calculated dependencies of photoluminescence intensity on the nonequilibrium carrier concentration. Time of charge carrier trapping into quantum wells and the energy relaxation time related to the polar optical phonon emission were obtained from analysis of the photoluminescence dynamics at different optical pumping levels. The recombination rates with respect to nonradiative Shockley–Read–Hall and Auger recombination were determined. It

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is shown that, at certain parameter sets, resonant Auger recombination can exist in InGaAsSb/AlGaAsSb quantum well structures, which should results in the decrease of the

Keywords

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concentration of carriers taking part in the radiative recombination.

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quantum wells; Auger recombination; optical phonons; recombination rate

1. Introduction

Today semiconductor lasers are widely used in telecommunication, spectroscopy,

ecological monitoring, medicine, etc. The greater part of such devices is based on the nanostructures with quantum wells (QWs). The deep understanding of the factors affecting the recombination rate and lifetime of nonequilibrium charge carriers is necessary for the optimization of the semiconductor laser parameters. Characteristics of injection semiconductor lasers are determined by the ratio between the rates of radiative and non-radiative recombination of nonequilibrium carriers. The Auger recombination is one of the most important mechanisms 1

of non-radiative recombination, because it can significantly degrade the characteristics of lasers

ACCEPTED MANUSCRIPT based on the narrow-gap materials [1, 2]. In some cases, Auger recombination can become resonant, which increases the non-radiative recombination rate by 2–3 orders of magnitude [1, 2] and causes the corresponding decline of the laser parameters. Our work is devoted to the investigation of charge carrier recombination in InGaAsSb/AlGaAsSb QW nanostructures developed for mid-infrared injection lasers (wavelengths λ = 2–4 µm) emitting in the continuous wave operation mode at room temperature [3 - 5]. Lasers with λ = 2–4 µm can be used for

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different applications: ecological monitoring, chemical and biological spectral analysis, remote detection of explosives, medical diagnostics and treatment, infrared illumination in detection systems, telecommunications, and so on. Such a wide application range is possible because the absorption lines of different gases and organic compounds CO2 (2004 and 2680 nm), CO (2330

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nm), C2H2 (3030 nm), CH4 (3330 nm) are located in this spectral range.

Auger recombination in narrow-gap semiconductors was first studied using the photoluminescence (PL) dynamics in Ref. [6]. In our study we analyze the PL dynamics and

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Auger recombination using resonant optical excitation directly in QWs and determine the dependence of the Auger recombination rate on the excitation level in InGaAsSb/AlGaAsSb QW structures. Time of charge carrier trapping into quantum wells and the energy relaxation time related to the polar optical phonon emission were obtained from analysis of the

2. Samples

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photoluminescence dynamics at various optical pumping levels.

Five samples containing InGaAsSb/AlGaAsSb QWs with different width (4, 5, 6, 7, and

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9 nm) were grown by molecular beam epitaxy in a Veeco GEN930 reactor. All layers of the structures, except the QW layers, were lattice-matched with the GaSb substrate. Each structure had ten In0.53Ga0.47As0.24Sb0.76/Al0.7Ga0.3As0.056Sb0.944 quantum wells. The QWs were separated by

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barriers with a thickness of 50 nm. The solid solution composition of the QW material was chosen according to the procedure described in Refs. [7, 8] in order to keep the QW material out of the miscibility gap. The band profile of InGaAsSb/AlGaAsSb quantum well structures for our studies was determined using material parameters taken from the Ref. [9]. The energy levels were calculated using simplified Kane’s model [10] taking into account the nonparabolicity of the subbands. This model is necessary to use because electron energy in the subbands in the investigated structures is comparable with the band gap or even exceeds its value. Kane model application to the quantum well structures is briefly described in [11].

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We chose S-type basis functions to describe conduction band bottom: |Sα>, |Sβ>, where

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spin parts of the wave function α and β describe spin projection on the z-axis 1/2 and -1/2, respectively. Top of the valence band wave function basis was chosen as in [12]:

1 ( X + iY )α , 2 i 3 / 2,1 / 2 = [( X + iY )β − 2Zα ] 6 1 [( X − iY )α + 2Zβ ] 3 / 2,−1 / 2 = 6 i ( X − iY )β , 3 / 2,−3 / 2 = 2 3 / 2,3 / 2 =

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(1)

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where the first number is the total momentum, and the second one is its z-axis projection. The X, Y, Z functions transform as x, y, z under coordinate transformation. Basis of wave functions

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describing the top of spin-orbit split subband is:

[( X + iY )β + Zα ] 3 i 1 / 2,−1 / 2 = [− ( X − iY )α + Zβ ]. 3 1

(2)

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1 / 2,1 / 2 =

The Hamiltonian operator in such basis has the form described in [12]. Strain was taken into account by introducing the deformation part proportional to the strain tensor to the Hamiltonian as in [13]. We neglected the terms proportional to k2 and higher

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orders of wavevector. Electronic spectrum was determined using transfer matrix method. Boundary conditions are discussed in [14].

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The calculated dependencies of the energy gaps between first heavy hole (hh1) and first split off by spin-orbit interaction (so1) subbands, between first electron (e1) and heavy hole (hh1) subbands and between first (e1) and second (e2) electron subbands, on the QW width are shown in Fig. 1 and marked as (1), (2) and (3) respectively. Our goal was to investigate the influence of nonradiative Auger processes on the carrier

concentration and recombination rate. The condition of the resonant Auger recombination is the equality of effective band gap and the energy separation between the first heavy hole level and the spin-orbit split-off level [1, 2]:

E(e1) – E(hh1) = E(hh1) – E(so1).

(3)

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Photoluminescence peak positions for all samples are presented in Fig. 1 by solid dots.

ACCEPTED MANUSCRIPT According to the energy spectrum calculation in QWs of different width (see Fig. 1) the resonant Auger recombination condition of Eq. (3) is satisfied only in the structure with 5 nm wide QWs at the liquid nitrogen temperature (T = 77 K). In other samples, condition of Eq. (3) is not satisfied but nonresonant Auger recombination involving two holes and an electron with different values of the quasi-momentum can occur. Diagram of resonant Auger process involving

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two holes and an electron is presented in inset of Fig. 1.

1

0.5

2

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0.6

e2

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e1

3

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photon energy (eV)

0.7

hh1

0.3

so1

0.2 4

5

6

7

8

9

quantum well width (nm)

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Fig. 1. Experimental positions of the photoluminescence peaks related to the transitions e1→hh1 (circles) and calculated energy gaps (lines): E(hh1)–E(so1), E(e1)–E(hh1), E(e2)-E(e1) marked as 1, 2 and 3, respectively. T = 77 K. The inset shows the energy band diagram and transition

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be observed.

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schemes in QWs where resonant Auger recombination involving two holes and an electron can

3. Experimental setup

The recombination times in nanostructures lie in the nanosecond time range. So, these

phenomena can be investigated through the picosecond spectroscopy. We studied the photoluminescence dynamics using the up-conversion method [15, 16]. The Nd-glass laser was used as a source of exciting photons (hν = 1.17 eV). Pumping pulse duration was ∆t = 150 fs, pulse repetition rate was 100 MHz and maximal average excitation power was 30 mW. The radiation beam was focused onto the structure surface into a spot ~10 µm in diameter. The PL emission of the samples was mixed with the delayed reference radiation of the 4

pumping laser in a nonlinear periodically poled lithium niobate (PPLN) crystal, which resulted in

ACCEPTED the radiation with a frequency equal to the MANUSCRIPT sum of the PL and excitation frequencies. Then it was directed into the spectrometer filtering the radiation at the maximum of the spectrum and detected by a cooled photomultiplier (sensitivity range: 160 - 930 nm). Positions of the PL spectral maximum for each structure were different, and it also shifted with the temperature change; therefore, the system was tuned using the wavelength at the signal’s maximum for each measurement. The computer-controlled delay line allowed us to obtain a 10 ns time shift

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between PL and reference signals whilst the time resolution of the system was approximately 0.5 ps. The PL dynamics was studied at the temperatures T = 77 and 300 K.

Photoluminescence spectra were studied using the Bruker Vertex 80v vacuum Fourier transform infrared spectrometer with the liquid nitrogen cooled InSb photodetector (sensitivity

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range: 1000 - 5400 nm). During stationary PL studies, optical excitation of the samples was performed with diode pulsed laser (hν = 1.17 eV). Pulse duration of the optical excitation was ∆t = 100 ns, repetition rate was 800 Hz and maximum averaged power was 2.4 mW. The

4. Results and discussion

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stationary PL was studied at the temperatures T = 77 and 300 K.

In order to confirm the calculated energy diagram we measured the interband photoluminescence spectra of InGaAsSb/AlGaAsSb QWs at different pumping levels at

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temperatures T = 77 and 300 K. Symbols in Fig. 1 show the PL peaks positions at T = 77 K at maximum pump level (the variation of the pump level did not lead to a significant shift of the PL peak positions). Our experimental results agree well with theoretical predictions of transition

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energies e1→hh1. Transitions hh1→so1 and e2→e1 were not observed in PL spectra due to their low probability.

The intensity of photoluminescence at the peak of its spectral dependence is determined

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by optical transitions of electrons between energy states near the bottom of the electron subband e1 and the top of the hole subband hh1. The fast relaxation of excited electrons from the higher energy states occurs due to the intrasubband emission of polar optical (PO) phonons. Hence, analysis of the increase of the photoluminescence intensity JPL on the picosecond time scale (appropriate transient is shown in Fig. 2 for 5 nm wide QWs, curve 1; dependencies for other structures are quite similar) allows us to determine the time of intrasubband emission of PO phonons τPO. For all investigated samples and temperatures the PL dynamics curves are almost identical.

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From the set of rate equations for electron concentrations at energy levels in QWs we derive the equation for timeACCEPTED dependence ofMANUSCRIPT the PL intensity in case of the direct pumping in the QW: J PL (t ) = J 0 (1 − exp( −t / τ ) ) ,

(4)

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where J0 is the maximum of PL intensity, τ is the time of electron capture to the QW and subsequent relaxation to the level e1. We assumed that PL intensity at the initial stage is directly proportional to the charge carrier concentration. By approximating the JPL(t) with the dependence Eq. (4) we find τ at different pump levels. For example, for the structure with 5 nm

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wide QW the energy of electrons excited directly in the QW was about 450 meV and, assuming that the energy of the longitudinal PO phonon is 30 meV (like in GaSb [17]), one can suggest that in this structure 15 PO phonons are emitted to balance the energy excess. So the whole

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capture time τ taken from Eq. (4) could be distributed between 15 PO phonons therefore the phonon emission time τPO for one PO phonon is about 0.25 ps for structures with 4, 5, 7 and 9 nm wide QWs InGaAsSb/AlGaAsSb. This estimation is rather crude, since the electron energy relaxation can also occur through the emission of PO phonons in the GaAs, InSb, InAs sublattices with PO phonon energy 36, 25, 30 meV, respectively. Also, the last electron which

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emits the PO phonon will have the energy E: k BT < E < hv PО (where kB is the Boltzmann constant), with the energy relaxation time τE. In case the carrier concentration is high enough, this energy can relax via electron-electron scattering with the characteristic time of the same magnitude: τE ≈ τPO.

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It should be mentioned that all PL dynamics curves have a slight dip at the time delay interval between 8 and 10 ps. The initial part of PL temporal dependences where the dip is

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revealed is shown in Fig. 3. This dip is more prominent at high optical pumping intensities and at low lattice temperatures. Possibly, this dip is caused by the excitation-pulse-induced ejection of electrons from the e1 subband and holes from the hh1 subband that had been created by the preceding laser pulse and did not have enough time to recombine before the arrival of the next pulse. We should note that such dip is almost absent in the PL of 5 nm wide QWs. This can be explained by the large probability of nonradiative Auger recombination that affects the radiative recombination: PL intensity is lower and therefore we were not able to observe this dip.

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1.0

1

2

0.6

J

PL

(a. u.)

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50

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100 150 200 250 300 350 400

t (ps)

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Fig. 2. Normalized PL dynamics curves at T = 300 K in case of optical pumping directly into 5 nm wide InGaAsSb/AlGaAsSb QWs (curve 1) and into the barriers of 17 nm wide

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InGaAsSb/InAlGaAsSb QWs (curve 2). Curve 2 is taken from [7].

500

300

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J

PL

(a. u.)

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200

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100

5

10

15

20

(a. u.): 1 0,84 0,64 0,51 0,41 0,34 0,25

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t (ps)

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0

JPUMP

Fig. 3. The initial part of temporal dependencies of the PL intensity at T = 77 K in case of optical excitation directly in the 7 nm wide InGaAsSb/AlGaAsSb QWs. Upper curve corresponds to the maximum level of excitation; lower curve corresponds to the a quarter of the maximum level of excitation.

In order to confirm estimated relaxation times we used results of PL dynamics obtained in [7] for similar structure with a narrower bandgap of the barrier material which was achieved by adding indium to the solid solution of the barrier InAlGaAsSb. This structure contained four 17 nm wide quantum wells. In this structure, electron–hole pairs are excited not only in QWs but also in the barrier regions which results in the more complicated PL dynamics rise (see Fig. 2, 7

curve 2). Abovementioned Ref. [7] was devoted to analysis of the PL dynamics decay, whereas

ACCEPTED we focused on the PL dynamics rise. RiseMANUSCRIPT time for the 17 nm QWs sample is approximately a hundred picoseconds and has slow and fast components (see curve 2 in Fig. 2). Rise time of the PL in our experiments for pumping directly into QW is about a few ps (see curve 1 in Fig. 2 for 5 nm wide QWs). It should be mentioned that dependencies obtained for 4, 7, 9 nm wide QWs are similar. Upon excitation in the barriers, the PL rise time is defined not only by the electron energy dissipation in the QWs, but also by the time of charge carrier trapping into the QWs,

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mostly related with carrier diffusion. From the set of rate equations of electron concentration at energy levels in QWs and in the barrier we received the equation for the approximation of PL

  t ⋅ 1 − exp −   τ2 

 t     ⋅ exp −     τ3

 ,  

(5)

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   t  J PL (t ) =  J 1 ⋅ 1 − exp −   + J 2     τ1  

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dynamics for the case of pumping into the barrier:

where τ1 is the fast PL rise time after the excitation pulse, τ2 is the inertial PL rise time (time interval ~50 – 100 ps in Fig. 2, curve 2), and τ3 is the characteristic PL decay time (time value more than 150 ps in Fig. 3). It should be noted, that the PL decay time τ3 is not the same as the charge carrier lifetime. The lifetime can be determined taking into account the time dependence

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of the concentration of charge carriers (see below). All PL dynamics curves in case of pumping into the barrier region were approximated with the Eq. (5) resulting in the dependence of τ1, τ2, τ3 times on the pumping intensity JPUMP. All exited electrons can be separated into two groups: electrons exited directly in the region of QWs and in the barrier region. Both groups contribute to

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PL, but the processes of relaxation to the e1 level are different. The fast PL rise time τ1 is defined by the relaxation of electrons excited directly in the QW region. Obtained τ1 does not depend on

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pumping intensity. The time of polar optical phonon emission τPO = 0.28 ps was derived from the τ1. In spite of the different composition of structure layers and simplified approximation procedure, PO phonon emission time in the structures with 17 nm wide InGaAsSb/InAlGaAsSb QW (pumping into the barrier) and InGaAsSb / AlGaAsSb (pumping into QWs) were approximately equal. The inertial time τ2 is in the range of 50...100 ps and increases with increase of pumping intensity. This time is determined by the processes of diffusion and ballistic flow of carriers from the barrier to the QW, where they are then relaxated. Rise time τ2 is much longer than the time defined only by the intraband relaxation τ1. The processes of electron trapping from barrier to the QW were also analyzed in Ref. [7]. Trapping time was determined there by comparing the PL dynamics at the wavelength corresponding to the radiative recombination in barrier material in the structure with 8

InGaAsSb/InAlGaAsSb QWs and in a layer of the same material InAlGaAsSb without quantum

ACCEPTED wells. The time obtained was about 70 ps MANUSCRIPT and is in a good agreement with our estimation of τ2. We should note that in Ref. [7] trapping time was determined from PL dynamics decay in contrast to our analysis of the PL dynamics rise. Analysis of the PL dynamics decay (characterized by the time τ3) allows us to determine the nonequilibrium charge carrier lifetimes associated with different mechanisms of recombination. The recombination rate R defined as the reciprocal carrier lifetime, R = 1/τ, was

−1

dJ PL

t ≈0

dt

,

(6)

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PL  1 dn 1  dJ  R=− =− n dt J PUMP  dJ PUMP 

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determined from the following relation (as described in the Ref. [7]):

intensity: n |t ≈0 ∝ J PUMP .

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where electron concentration at the initial stage of relaxation is proportional to the pumping

Using the experimental PL dynamics (for example, see Fig. 2 and 3) we obtained the derivatives used in the Eq. (6) and so the recombination rate R dependence on pumping intensity at temperatures of 77 and 300 K (see Fig. 4 for 5 and 7 nm wide QWs at T = 77 К). All recombination rate dependencies except one look similar: recombination rate is constant for

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structures with 4, 7 and 9 nm wide QWs and belongs to the range of 0.4..0.5 ns-1. It is the recombination rate related to the non-radiative Shockley–Read–Hall (SRH) recombination because it does not depend on the excited carrier concentration. Similar value of SRH

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recombination rate was obtained in Ref. [18] for GaInSb/InAs/AlGaSb superlattice Recombination rate dependencies confirm that in 5 nm wide QWs resonant Auger recombination is observed (as we supposed earlier). Auger recombination rate is proportional to the squared

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carrier concentration RAuger(n) = C·n2 [7], were C is the Auger recombination coefficient. From Fig. 4 we obtained the Auger recombination coefficient for 5 nm wide QW: C2D = 10-15 cm4/s for 2D carrier concentration and C3D = 2.5·10-29 cm6/s. In structures without resonant Auger recombination this coefficient is two – three orders of magnitude less [7].

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R (ns )

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JPUMP (a. u.)

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Fig. 4. The dependence of the recombination rate on the pumping intensity at T = 77 K for the

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InGaAsSb/AlGaAsSb QW samples with a 5 nm (curve 1, squares) and 7 nm (curve 2, cycles)

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wide QW.

5. Conclusion

The behavior of the PL dynamics in picosecond and nanosecond time ranges is studied for InGaAsSb/InAlGaAsSb QWs with different barrier materials and QW widths. The dependencies of the photoluminescence intensity at the spectral maximum on the pumping intensity and carrier concentration were experimentally and theoretically investigated. The times

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of charge carrier capture into QWs, the energy relaxation times related to the PO phonon emission were obtained at different optical pump levels. The recombination rate with respect to nonradiative Shockley–Read–Hall recombination and nonradiative Auger recombination was determined. It is shown that, at certain parameters, resonant Auger recombination can be

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observed in InGaAsSb/AlGaAsSb QW structures, which should results in the decrease in the

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concentration of carriers taking part in the radiative recombination.

Acknowledgments

This work was supported by by U.S. Army Research Office No W911TA-16-2-0053, the Russian Foundation for Basic Research (grants 16-02-00863 and 16-32-60085), Russian Federation President grant for young scientists No МК-4616.2016.2 and the Ministry of Education and Science of the Russian Federation (state assignments, projects 3.933.2017/4.6, 3.5518.2017/7.8 and 3.6153.2017/7.8).

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[9]

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[12]

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[13]

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[8]

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[7]

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[6]

[14]

[15] [16] [17] [18]

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Resonant Auger recombination between first electron subband and first heavy hole subband and first split off by spin-orbit interaction is experimentally observed. Times of charge carrier capture into QWs and emission time of polar optical phonon in InGaAsSb/InAlGaAsSb QWs are experimentally determined. The recombination rate with respect to nonradiative Shockley–Read–Hall recombination and nonradiative Auger recombination is determined.

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