- Email: [email protected]
AlGaAsSb quantum wells
Accepted Manuscript
Effect of Auger recombination on nonequilibrium charge carrier concentration in InGaAsSb /AlGaAsSb quantum wells Vinnichenko Maxim Ya , Ivan S. Makhov , Anatoliy V. Selivanov , Anastasiya M. Sorokina , Leonid E. Vorobjev , Dmitry A. Firsov , Leon Shterengas , Gregory Belenky PII: DOI: Reference:
S2405-7223(16)30157-8 10.1016/j.spjpm.2016.11.007 SPJPM 111
To appear in:
St. Petersburg Polytechnical University Journal: Physics and Mathematics
Received date: Accepted date:
14 November 2016 15 November 2016
Please cite this article as: Vinnichenko Maxim Ya , Ivan S. Makhov , Anatoliy V. Selivanov , Anastasiya M. Sorokina , Leonid E. Vorobjev , Dmitry A. Firsov , Leon Shterengas , Gregory Belenky , Effect of Auger recombination on nonequilibrium charge carrier concentration in InGaAsSb /AlGaAsSb quantum wells, St. Petersburg Polytechnical University Journal: Physics and Mathematics (2016), doi: 10.1016/j.spjpm.2016.11.007
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.
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Maxim Ya. Vinnichenko Peter the Great St. Petersburg Polytechnic University 29 Politekhnicheskaya St., St. Petersburg, 195251, Russian Federation [email protected] Ivan S. Makhov Peter the Great St. Petersburg Polytechnic University 29 Politekhnicheskaya St., St. Petersburg, 195251, Russian Federation [email protected]
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Anatoliy V. Selivanov Peter the Great St. Petersburg Polytechnic University 29 Politekhnicheskaya St., St. Petersburg, 195251, Russian Federation [email protected]
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Anastasiya M. Sorokina Peter the Great St. Petersburg Polytechnic University 29 Politekhnicheskaya St., St. Petersburg, 195251, Russian Federation [email protected]
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Leonid E. Vorobjev Peter the Great St. Petersburg Polytechnic University 29 Politekhnicheskaya St., St. Petersburg, 195251, Russian Federation [email protected]
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Dmitry A. Firsov Peter the Great St. Petersburg Polytechnic University 29 Politekhnicheskaya St., St. Petersburg, 195251, Russian Federation [email protected]
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Leon Shterengas State University of New York at Stony Brook New York 11794-2350, USA [email protected] Gregory Belenky State University of New York at Stony Brook New York 11794-2350, USA [email protected]
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Maxim Ya. Vinnichenkoa, Ivan S. Makhova, Anatoliy V. Selivanova, Anastasiya M. Sorokinaa, Leonid E. Vorobjeva, Dmitry A. Firsova, Leon Shterengasb, Gregory Belenkyb 1
Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia 2 State University of New York at Stony Brook, USA
Effect of Auger recombination on nonequilibrium charge carrier concentration in InGaAsSb /AlGaAsSb quantum wells
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Abstract We have experimentally studied the interband photoluminescence spectra of InGaAsSb/AlGaAsSb quantum wells with different well widths and calculated the dependence of the charge carrier concentration participating in radiative recombination on the pumping intensity. The results of theoretical calculations appeared to be in a good agreement with the experimental relationship between the photoluminescence intensity at spectral maxima and the pumping intensity. The resonant Auger recombination involving two holes and one electron and causing a significant decrease in the charge carrier concentration was detected in one of the samples. Recommendations for suppressing the harmful nonradiative Auger recombination were made to increase the operating efficiency of semiconductor injection lasers at wavelengths of about 3 μm.
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Keywords Auger Recombination; Quantum well; Semiconductor; Photoluminescence
Introduction
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This paper considers the processes associated with recombination of nonequilibrium charge carriers in nanostructures with InGaAsSb/AlGaAsSb
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quantum wells. There is much interest in studying these structures because it is possible to use them to fabricate sufficiently powerful semiconductor injection
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lasers with the wavelength range of 2–4 μm, operating in continuous-wave mode.
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Lasers emitting in the mid-infrared (mid-IR) region can be widely applied in the fields of spectroscopy of various substances, transmission of information via wireless communication lines, in security and fire control systems, in medical, military and other industries. We should note that the transparency of the atmosphere in this spectral range [1] expands the range of applications for such lasers significantly. However, fabricating the sources in the wavelength range near 3 μm has not been fully accomplished yet despite this problem’s importance. 2
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Using unipolar quantum cascade lasers at wavelengths of about 3 μm seems problematic because it is difficult to construct a semiconductor structure with significant band discontinuities between two semiconductor materials. The issue of creating lasers in this range can be approached from another perspective by extending the working range of InGaAsSb/AlGaAsSb injection lasers operating at wavelengths less than 2 μm to longer wavelengths. However, it is known from
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experiments that an increase in emission wavelength results in increased lasing threshold current and decreased radiated power of injection lasers [2].
One possible reason why lasing characteristics deteriorate at high injection levels in materials with a low band gap may be non-radiative Auger recombination, which can have a resonant character under certain conditions, leading to a marked
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increase in the recombination rate [3]. Studying the recombination mechanisms, in particular, Auger recombination which will be discussed below, is important for improving lasing characteristics. Such studies are also interesting from a fundamental point of view.
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The main method used in our study was analysis of the interband
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photoluminescence spectra which provide essential information about the
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concentration of charge carriers involved in radiative recombination.
Objects and methods
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We studied structures with InGaAsSb/AlGaAsSb quantum wells of varying widths: 4, 5, 7 and 9 nm. The compositions of the quantum well and barrier solid
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solutions were chosen so as stay within the miscibility gaps [4] and ensure that no mechanical stresses would occur in the relatively thick layers forming the barriers. All structures were grown by molecular-beam epitaxy using a Veeco GEN-930 reactor on GaSb substrates. Interband photoluminescence spectra were measured with a Bruker Vertex 80v vacuum Fourier transform infrared spectrometer. Nonequilibrium charge carriers in the samples were optically excited by radiation of pulsed laser (hν = 3
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1.17 eV). The duration of optical excitation pulses was Δt = 100 ns, the repetition frequency was 800 Hz, and the maximum average power was 2.4 mW. Interband photoluminescence was studied at the temperatures T = 77 and 300 K. The radiation was detected by a liquid nitrogen cooled InSb photodetector. The sample was mounted in a liquid nitrogen cooled optical cryostat with sample temperature
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control in the temperature range from 77 to 320 K.
Results and discussion
One of the goals of the study was to determine the contribution of nonradiative resonant Auger recombination to the processes of charge carrier InGaAsSb/AlGaAsSb
quantum wells. Resonant Auger
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recombination in
recombination in quantum wells can be observed, for example, when the energy difference between the first level of electrons, е1, and the first level of heavy holes, hh1, is approximately equal to the distance between the hh1 level and the so1
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energy level, which is the first level of the subband split by spin-orbit interaction
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[3]. Thus, two holes and one electron participate in this process of resonant Auger recombination, and the hh1 - so1 energy difference is approximately equal to the
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effective band gap value Eg*:
(1)
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E (hh1) E (so1) E (e1) E (hh1) E g* .
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Figs. 1a and 1b show examples of this type of resonant Auger recombination
when equality (1) is valid. On the contrary, when this equality does not hold, the so-called non-resonant Auger recombination involving two holes and one electron with different values of the quasi-momentum k can be observed (Fig. 1c). Momentum and energy of the particles involved are conserved during Auger recombination processes:
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ACCEPTED MANUSCRIPT E1 E3 E4 E2 ,
(2)
k1 k 3 k 4 k 2 ,
(3)
where k1, k2 and E1, E2 are the quasi-momenta and energies of the particles in the initial states 1 and 2; k3, k4 and E3, E4 are the quasi-momenta and energies of the particles in the final states 3 and 4 (see Fig. 1c). b)
c) E
E
e2 e1
Ec e2
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e1
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a)
e2 e1
3
h Eg+E(e1)+E(hh1) hh1
Ev so
hh lh so1
1 k||
hh1
hh1
4
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so
2
k||
so1
so1
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Fig. 1. Energy band diagram (a) and energy transition scheme in quantum wells where resonant (b) and non-resonant (c) Auger recombination involving two holes (open circles) and one electron (solid circles) can occur
As revealed in Ref. [3], the probability of resonant Auger recombination
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with conservation of the quasi-momenta of the particles exceeds significantly the probability of non-resonant processes. Four samples with different widths of InGaAsSb/AlGaAsSb quantum wells
(4, 5, 7 and 9 nm) were chosen for studying the recombination processes. The positions of the energy levels in all structures were calculated within the Kane model [5] taking into account the nonparabolicity of the dispersion law. This approach should be used because the energy of the electrons in the subbands is 5
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either of the same order of magnitude as the band gap or exceeding it. The parameters for the properties of the solid solutions for the calculation were taken from Ref. [6]. Compressive stress in the quantum well decreases the density of states in the heavy-hole subbands [7]. This is why the effective mass of heavy holes which is smaller compared to the bulk material was used in the calculations. Photoluminescence spectra were obtained at temperatures T = 77 and 300 K in
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order to experimentally determine the positions of the ground quantumconfinement levels e1 and hh1 in the nanostructures with different quantum well widths. The positions of the photoluminescence peaks are in a good agreement with the calculated values of the effective bandgap. Photoluminescence spectra for all four structures, measured at the lattice temperature T = 77 K and at a maximum
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optical pumping intensity, are shown in Fig. 2. Apparently, the peak intensity of the photoluminescence spectrum is determined by optical electron transitions between energy states near the bottom of the e1 subband and the top of the hh1 heavy-hole subband. The positions of this peak in the spectrum as a function of
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quantum well width are shown by the experimental points in Fig. 3. We should
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note that the absorption of exciting radiation is different for different structures, which may also lead to differences in photoluminescence intensity for these
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structures.
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0.6
1
JPL, a.u.
0.5
2
0.4
0.3
3
4
0.1
0.0 0.40
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0.2
0.45
0.50
0.55
0.60
Photon energy, eV
0.65
0.70
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Fig. 2. Photoluminescence spectra of structures with InGaAsSb/AlGaAsSb quantum wells of different width, in nanometers: 9 (1), 7 (2), 5 (3), 4 (4); the optical pumping intensity is maximal; lattice temperature T = 77 K
Fig. 3 also shows the theoretical dependences of the energy of the allowed transitions on the width of InGaAsSb/AlGaAsSb quantum wells at liquid nitrogen
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temperature. The dash-dot line 1 corresponds to the calculated energy of the transitions between the ground state of heavy holes and the first level of the
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subband split by spin-orbit interaction: E(e1) → E(hh1). The solid line 2 corresponds to the calculated energy of the transition between the ground states of
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electrons and heavy holes E(e1) → E(hh1). The dashed line 3 corresponds to the
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energy of the transitions between the first two electronic levels in quantum wells: E(e2) → E(e1). It can be seen that the position of the photoluminescence peaks is
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in a good agreement with the theoretically calculated positions of the transition energies E(e1) → E(hh1), which indicates that the calculations of the band structure were sufficiently accurate. Fig. 3 shows that equality (1) holds true only in 5-nm-wide quantum wells at T = 77 K, which allows to observe resonant Auger recombination involving two holes and one electron. Equality (1) is not satisfied for other structures, so, as mentioned earlier, only non-resonant Auger recombination can occur in them. Notice that resonant Auger recombination 7
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involving two electrons and one hole cannot be observed in our structures as curves 2 and 3 do not intersect.
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1
0.5
2
0.4 0.3 0.2 3
4
5
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Photon energy, eV
0.7
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7
8
3
9
10
Quantum well width, nm
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Fig. 3. Experimental (points) and calculated (lines) dependences of the allowed transition energy as a function of quantum well width (T = 77 K). The positions of the photoluminescence peaks for the E(e1) → E(hh1) transitions were found experimentally. The values of the E(hh1) → E(so1) (1), E(e1) → E(hh1) (2) and E(e2) → E(e1)(3) energy gaps were calculated
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The concentration of nonequilibrium charge carriers involved in radiative recombination can be obtained from analyzing the photoluminescence spectra at
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different levels of optical pumping. Fig. 4 shows the measured curves for the photoluminescence intensity (data points) in the spectral maximum (i.e., in the
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spectral region approximately corresponding to the effective band gap) versus the optical pumping level for all samples at temperature of 77 K. Unlike other structures, the dependence is apparently linear for the structure with the well width of 5 nm, where resonant Auger recombination is expected to occur (1). This is likely because nonradiative Auger recombination reduces charge carrier concentration in quantum wells involved in radiative recombination and contributing to interband photoluminescence. This interpretation can be confirmed 8
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by calculating the photoluminescence intensity at a specific wavelength as a function of charge carrier concentration. а)
b) n, 1011 cm-2
2
4
6
8
0
10
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JPLmax, a. u.
JPLmax, a. u.
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0.05
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0.0 0.0
1.0
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0.00 0.0
1
2
3
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0.8
1.0
Jpump, a. u.
Jpump, a. u.
c)
5
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n, 1011 cm-2 0
d)
n, 1012 cm-2 0.5
1.0
1.5
JPLmax, a. u.
0.2
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0.4
1.0
1.5
2.0
0.5 0.4 0.3 0.2 0.1
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1.0
JPUMP, a. u.
0.0 0.0
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0.8
1.0
JPUMP, a u.
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n, 1012 cm-2
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0.3
0.0 0.0
0.0 0.7
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JPLmax, a. u.
0.4
0.1
2.0
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0.0
Fig. 4. Experimental (points) and calculated (lines) dependences for peak photoluminescence intensity as a function of optical pumping intensity (points) and charge carrier concentration (lines) for structures with different quantum well widths, nm: 4 (a), 5 (b), 7 (c), 9 (d)
We calculated dependences of charge carrier concentrations on the photoluminescence intensity at a selected wavelength using the technique described in [8]. It should be noted that nonequilibrium charge carriers in our 9
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experiments were excited directly in the quantum wells, i.e., the pump photon energy (1.17 eV) was less than the barrier band gap (1.72 eV). Under this type of excitation, the distance between the quantum-confinement levels at which electrons and holes are produced in a quantum well is less than the pump photon energy value. A system of three heavy-hole levels and two electronic levels (see Fig. 5
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showing a diagram of optical transitions which can contribute to interband photoluminescence) was used for the calculation. It should be borne in mind that the e2 → hh3 transitions are the least likely to occur, and were not taken into account. In addition, according to the selection rules, only transitions between levels of the same parity (e1 → hh1 and e2 → hh2) are allowed in a quantum well
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of finite depth at k = 0. However, this forbiddance is removed with increasing k values, therefore, the contribution from the forbidden transitions should be taken
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into account.
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e2
fe
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e1
fh
hh1
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hh2
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Eh
hh3
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Fig. 5. Schematic energy diagram of interband radiative optical transitions in a quantum well with three hole and two electron levels. Arrows indicate the most probable optical transitions. Curves on the left are the distribution functions of electrons and holes.
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Let us introduce the following notations for the transition energies: e1hh1 Eg E(e1) E (hh1) Eg* , e1hh2 Eg E(e1) E(hh2) Eg* h12 , e1hh3 Eg E(e1) E (hh3) Eg* h13,
(4)
e 2hh1 Eg E(e2) E (hh1) Eg* e12 , e 2hh2 Eg E (e2) E (hh2) Eg* e12 h12 ,
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where e12 E(e1) E(e2) ,
h12 E (hh1) E (hh2) , h13 E (hh1) E (hh3) .
Charge carrier concentration is known to follow the expression
N e, h (T , E ) g e, h ( E ) f e, h ( E ) dE , 0
where the density of states ge,h for quantum wells are step functions: m * e, h 2
g e, h ( E )
,
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m*e,h are the effective masses of electrons and holes, fe,h are the distribution functions of electrons and holes: f e, h ( E )
1 E Fe, h 1 exp k T B
electrons and holes, respectively).
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(kB is the Boltzmann constant, Fe,h are the positions of the Fermi levels for The integral for determining the charge carrier concentration in quantum wells is an analytical expression allowing to find the equations that govern the
(1 e
(1 e
Fh k BT
Fe k BT
)(1 e
)(1 e
Fh h12 k BT
Fe e12 k BT
Ne
)e
)(1 e
NC
Fh h13 k BT
,
(5) Nh
) e NV
,
(6)
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position of the Fermi levels for electrons and holes:
where NC and NV are the effective densities of states of electrons and holes in a
NC
me*k BT 2
,
NV
mh* k BT 2
.
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two-dimensional subband, respectively;
Let us assume that the equality Ne = Nh is satisfied under optical excitation, and find the dependence of the position of the quasi Fermi levels of electrons and holes on the temperature and the concentration of charge carriers. The number of photons emitted per unit volume per unit time in the frequency interval from ν to ν+ dν for charge carrier transitions from the electron level i to the hole level j can be written as follows [8]: 12
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i j dqsp
2 n e 2 meh P2 ( h ) I (k 2 ) f e f h d h 2 3 i j m0 LQW c
(7) ,
where LQW is the quantum well width, n is the refractive index, meh is the reduced mass, Ii→j are the overlap integrals (calculated in Ref. [9]), P is the Kane matrix
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element of the momentum operator. This matrix element is expressed through the bulk band gap Eg and the electron mass m0 in the following way:
E g ( E g so ) m0 m0 ( * 1) 2 2 me ( E g so ) 3 .
(8)
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P2
Thus, the total number of emitted photons for all possible transitions (see
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Fig. 5) is written as follows:
Qsp dq spi j .
(9)
i, j
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Substituting expression (7) into formula (9) and taking into account the
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dependence of the distribution function on the Fermi level (which, in turn, depends on the temperature and concentration of charge carriers), we have determined the
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theoretical dependence of the peak luminescence intensity on the charge carrier concentration for each structure at a temperature of 77 K (see Fig. 4). By scaling the abscissa, we have found the values of charge carrier concentrations corresponding to a good agreement between the experimental points and the theoretical curve. It is evident from Fig. 4 that the concentration of the charge carriers involved in radiative recombination is lower in the structure with 4-nmwide quantum wells because, according to calculations of the band diagram, under 13
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optical pumping, charge carriers are excited only in the ground quantumconfinement levels. Charge carrier concentrations in structures with 7- and 9-nmwide quantum wells were not significantly different due to slight variations in the band diagrams. The curves of photoluminescence intensity versus pump level can be divided into three sections for all three of these samples. The amount of injected charge
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carriers is small in the initial section corresponding to a low level of optical pumping, therefore, the energy distribution of electrons and holes is described by nondegenerate statistics. Thus, the photoluminescence intensity in the spectral peak is directly proportional to the product of the injected electron and hole concentrations, i.e., the dependence is quadratic. Next, degeneration of electron gas
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occurs at average pump levels (the second section). In this case the holes remain nondegenerate due to greater density of states. Thus, the concentration of electrons in the energy range from which radiative transitions are observed remains constant, and the photoluminescence intensity at average pump levels depends only on the
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change in the concentration of injected holes, i.e., is a linear function of the optical
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pumping level. Both the electron and hole gases are degenerate at high pump levels (the third section).In this case radiative recombination involves charge carriers
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from the regions of the conduction and the valence bands where the electron and hole concentrations remain constant. The photoluminescence intensity at this
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wavelength then does not depend on the pump level, and tends to saturation. Fig. 4 shows that the dependence of peak photoluminescence intensity on
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pump intensity is approximately linear for the structure with 5 nm wide quantum wells. This corresponds to average concentrations of charge carriers participating in photoluminescence. Evidently, the structure with 5 nm wide quantum wells exhibited the lowest charge carrier concentration of all samples. As proved above, the injected charge carriers in this structure are involved in nonradiative resonant Auger recombination, which reduces their contribution to radiative recombination.
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Thus, resonant nonradiative Auger recombination can decrease the concentration of charge carriers involved in radiative recombination by almost an order of magnitude. This phenomenon reduces the quantum yield and the effectiveness of lasers. In order to eliminate non-radiative Auger recombination, the design of semiconductor injection lasers emitting at a wavelength of about 3 μm must involve carefully calculating the band diagram and checking whether
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the condition that the effective band gap be equal to the energy spacing between the ground state of heavy holes and the first level of the band split by spin-orbit interaction is not fulfilled. Conclusion
The dependence of photoluminescence intensity in the spectral peak on the
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optical pumping intensity for nanostructures with different InGaAsSb/AlGaAsSb quantum well widths is investigated. This dependence had a linear behavior for the structure with 5 nm wide quantum wells where resonant Auger recombination was expected to be observed. In order to analyze the obtained experimental results, we
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calculated nonequilibrium charge carrier concentrations as a function of optical
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pumping level.
Finally, we conclude that the concentration of the charge carriers involved in
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radiative recombination decreases in a structure where the conditions of
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nonradiative resonant Auger recombination are fulfilled.
The study was conducted with the financial support of the Government of St. Petersburg,
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the Ministry of Education and Science of the Russian Federation (government task), an RFBR grant no. 16-02-00863, and a grant of the President of the Russian Federation for young candidates of science MK-4616.2016.2.
REFERENCES
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[1] A.M. Prokhorov (Editor-in-chief), Encyclopaedia on Physics,Vol. 2, Moscow, Sovetskaya entsiklopediya (1990) 183. [2] L. Shterengas, G. Belenky, G. Kipshidze, T. Hosoda, Room temperature operated 3.1 μm type-I GaSb-based diode lasers with 80 mW continuous-wave output power, Applied Physics Letters. 92 (17) (2008) 171111. [3] L.V. Danilov, G.G. Zegrya, Theoretical study of Auger recombination
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processes in deep quantum wells, Semiconductors. 42 (5) (2008) 550– 556. [4] D.A. Firsov, L. Shterengas, G. Kipshidze, et al., Dynamics of photoluminescence
and
recombination
processes
in
Sb-containing
laser
nanostructures, Semiconductors. 44 (1) (2010) 50–58.
[5] E.O. Kane, Band structure of indium antimonide, Journal of Physics and
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Chemistry of Solids. 1 (4) (1957) 249–261.
[6] I. Vurgaftman, J. Meyer, L. Ram-Mohan, Band parameters for III–V compound semiconductors and their alloys, Journal of Applied Physics. 89 (11) (2001) 5815–5875.
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[7] J. Chen, D. Donetsky, L. Shterengas, et al., Effect of quantum well
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compressive strain above 1% on differential gain and threshold current density in type-I GaSb-based diode lasers, IEEE J. Quant. Electron. 44 (12) (2008) 1204 – 1210.
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[8] L.E. Vorob’ev, V.L. Zerova, K.S. Borshchev, et al., Charge-carrier
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concentration and temperature in quantum wells of laser heterostructures under spontaneous-and stimulated-emission conditions, Semiconductors. 42 (6) (2008)
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737–745.
[9] Z.N. Sokolova, V.B. Khalfin, Calculation of the probabilities of radiative
transitions and lifetimes in size-quantized structures, Semiconductors. 23 (10) (1989) 1117–1121.
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Effect of Auger recombination on nonequilibrium charge carrier concentration in InGaAsSb /AlGaAsSb quantum wells Vinnichenko Maxim Ya , Ivan S. Makhov , Anatoliy V. Selivanov , Anastasiya M. Sorokina , Leonid E. Vorobjev , Dmitry A. Firsov , Leon Shterengas , Gregory Belenky PII: DOI: Reference:
S2405-7223(16)30157-8 10.1016/j.spjpm.2016.11.007 SPJPM 111
To appear in:
St. Petersburg Polytechnical University Journal: Physics and Mathematics
Received date: Accepted date:
14 November 2016 15 November 2016
Please cite this article as: Vinnichenko Maxim Ya , Ivan S. Makhov , Anatoliy V. Selivanov , Anastasiya M. Sorokina , Leonid E. Vorobjev , Dmitry A. Firsov , Leon Shterengas , Gregory Belenky , Effect of Auger recombination on nonequilibrium charge carrier concentration in InGaAsSb /AlGaAsSb quantum wells, St. Petersburg Polytechnical University Journal: Physics and Mathematics (2016), doi: 10.1016/j.spjpm.2016.11.007
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.
ACCEPTED MANUSCRIPT
Maxim Ya. Vinnichenko Peter the Great St. Petersburg Polytechnic University 29 Politekhnicheskaya St., St. Petersburg, 195251, Russian Federation [email protected] Ivan S. Makhov Peter the Great St. Petersburg Polytechnic University 29 Politekhnicheskaya St., St. Petersburg, 195251, Russian Federation [email protected]
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Anatoliy V. Selivanov Peter the Great St. Petersburg Polytechnic University 29 Politekhnicheskaya St., St. Petersburg, 195251, Russian Federation [email protected]
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Anastasiya M. Sorokina Peter the Great St. Petersburg Polytechnic University 29 Politekhnicheskaya St., St. Petersburg, 195251, Russian Federation [email protected]
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Leonid E. Vorobjev Peter the Great St. Petersburg Polytechnic University 29 Politekhnicheskaya St., St. Petersburg, 195251, Russian Federation [email protected]
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Dmitry A. Firsov Peter the Great St. Petersburg Polytechnic University 29 Politekhnicheskaya St., St. Petersburg, 195251, Russian Federation [email protected]
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Leon Shterengas State University of New York at Stony Brook New York 11794-2350, USA [email protected] Gregory Belenky State University of New York at Stony Brook New York 11794-2350, USA [email protected]
1
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Maxim Ya. Vinnichenkoa, Ivan S. Makhova, Anatoliy V. Selivanova, Anastasiya M. Sorokinaa, Leonid E. Vorobjeva, Dmitry A. Firsova, Leon Shterengasb, Gregory Belenkyb 1
Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia 2 State University of New York at Stony Brook, USA
Effect of Auger recombination on nonequilibrium charge carrier concentration in InGaAsSb /AlGaAsSb quantum wells
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Abstract We have experimentally studied the interband photoluminescence spectra of InGaAsSb/AlGaAsSb quantum wells with different well widths and calculated the dependence of the charge carrier concentration participating in radiative recombination on the pumping intensity. The results of theoretical calculations appeared to be in a good agreement with the experimental relationship between the photoluminescence intensity at spectral maxima and the pumping intensity. The resonant Auger recombination involving two holes and one electron and causing a significant decrease in the charge carrier concentration was detected in one of the samples. Recommendations for suppressing the harmful nonradiative Auger recombination were made to increase the operating efficiency of semiconductor injection lasers at wavelengths of about 3 μm.
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Keywords Auger Recombination; Quantum well; Semiconductor; Photoluminescence
Introduction
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This paper considers the processes associated with recombination of nonequilibrium charge carriers in nanostructures with InGaAsSb/AlGaAsSb
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quantum wells. There is much interest in studying these structures because it is possible to use them to fabricate sufficiently powerful semiconductor injection
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lasers with the wavelength range of 2–4 μm, operating in continuous-wave mode.
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Lasers emitting in the mid-infrared (mid-IR) region can be widely applied in the fields of spectroscopy of various substances, transmission of information via wireless communication lines, in security and fire control systems, in medical, military and other industries. We should note that the transparency of the atmosphere in this spectral range [1] expands the range of applications for such lasers significantly. However, fabricating the sources in the wavelength range near 3 μm has not been fully accomplished yet despite this problem’s importance. 2
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Using unipolar quantum cascade lasers at wavelengths of about 3 μm seems problematic because it is difficult to construct a semiconductor structure with significant band discontinuities between two semiconductor materials. The issue of creating lasers in this range can be approached from another perspective by extending the working range of InGaAsSb/AlGaAsSb injection lasers operating at wavelengths less than 2 μm to longer wavelengths. However, it is known from
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experiments that an increase in emission wavelength results in increased lasing threshold current and decreased radiated power of injection lasers [2].
One possible reason why lasing characteristics deteriorate at high injection levels in materials with a low band gap may be non-radiative Auger recombination, which can have a resonant character under certain conditions, leading to a marked
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increase in the recombination rate [3]. Studying the recombination mechanisms, in particular, Auger recombination which will be discussed below, is important for improving lasing characteristics. Such studies are also interesting from a fundamental point of view.
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The main method used in our study was analysis of the interband
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photoluminescence spectra which provide essential information about the
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concentration of charge carriers involved in radiative recombination.
Objects and methods
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We studied structures with InGaAsSb/AlGaAsSb quantum wells of varying widths: 4, 5, 7 and 9 nm. The compositions of the quantum well and barrier solid
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solutions were chosen so as stay within the miscibility gaps [4] and ensure that no mechanical stresses would occur in the relatively thick layers forming the barriers. All structures were grown by molecular-beam epitaxy using a Veeco GEN-930 reactor on GaSb substrates. Interband photoluminescence spectra were measured with a Bruker Vertex 80v vacuum Fourier transform infrared spectrometer. Nonequilibrium charge carriers in the samples were optically excited by radiation of pulsed laser (hν = 3
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1.17 eV). The duration of optical excitation pulses was Δt = 100 ns, the repetition frequency was 800 Hz, and the maximum average power was 2.4 mW. Interband photoluminescence was studied at the temperatures T = 77 and 300 K. The radiation was detected by a liquid nitrogen cooled InSb photodetector. The sample was mounted in a liquid nitrogen cooled optical cryostat with sample temperature
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control in the temperature range from 77 to 320 K.
Results and discussion
One of the goals of the study was to determine the contribution of nonradiative resonant Auger recombination to the processes of charge carrier InGaAsSb/AlGaAsSb
quantum wells. Resonant Auger
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recombination in
recombination in quantum wells can be observed, for example, when the energy difference between the first level of electrons, е1, and the first level of heavy holes, hh1, is approximately equal to the distance between the hh1 level and the so1
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energy level, which is the first level of the subband split by spin-orbit interaction
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[3]. Thus, two holes and one electron participate in this process of resonant Auger recombination, and the hh1 - so1 energy difference is approximately equal to the
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effective band gap value Eg*:
(1)
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E (hh1) E (so1) E (e1) E (hh1) E g* .
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Figs. 1a and 1b show examples of this type of resonant Auger recombination
when equality (1) is valid. On the contrary, when this equality does not hold, the so-called non-resonant Auger recombination involving two holes and one electron with different values of the quasi-momentum k can be observed (Fig. 1c). Momentum and energy of the particles involved are conserved during Auger recombination processes:
4
ACCEPTED MANUSCRIPT E1 E3 E4 E2 ,
(2)
k1 k 3 k 4 k 2 ,
(3)
where k1, k2 and E1, E2 are the quasi-momenta and energies of the particles in the initial states 1 and 2; k3, k4 and E3, E4 are the quasi-momenta and energies of the particles in the final states 3 and 4 (see Fig. 1c). b)
c) E
E
e2 e1
Ec e2
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e1
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a)
e2 e1
3
h Eg+E(e1)+E(hh1) hh1
Ev so
hh lh so1
1 k||
hh1
hh1
4
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so
2
k||
so1
so1
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Fig. 1. Energy band diagram (a) and energy transition scheme in quantum wells where resonant (b) and non-resonant (c) Auger recombination involving two holes (open circles) and one electron (solid circles) can occur
As revealed in Ref. [3], the probability of resonant Auger recombination
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with conservation of the quasi-momenta of the particles exceeds significantly the probability of non-resonant processes. Four samples with different widths of InGaAsSb/AlGaAsSb quantum wells
(4, 5, 7 and 9 nm) were chosen for studying the recombination processes. The positions of the energy levels in all structures were calculated within the Kane model [5] taking into account the nonparabolicity of the dispersion law. This approach should be used because the energy of the electrons in the subbands is 5
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either of the same order of magnitude as the band gap or exceeding it. The parameters for the properties of the solid solutions for the calculation were taken from Ref. [6]. Compressive stress in the quantum well decreases the density of states in the heavy-hole subbands [7]. This is why the effective mass of heavy holes which is smaller compared to the bulk material was used in the calculations. Photoluminescence spectra were obtained at temperatures T = 77 and 300 K in
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order to experimentally determine the positions of the ground quantumconfinement levels e1 and hh1 in the nanostructures with different quantum well widths. The positions of the photoluminescence peaks are in a good agreement with the calculated values of the effective bandgap. Photoluminescence spectra for all four structures, measured at the lattice temperature T = 77 K and at a maximum
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optical pumping intensity, are shown in Fig. 2. Apparently, the peak intensity of the photoluminescence spectrum is determined by optical electron transitions between energy states near the bottom of the e1 subband and the top of the hh1 heavy-hole subband. The positions of this peak in the spectrum as a function of
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quantum well width are shown by the experimental points in Fig. 3. We should
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note that the absorption of exciting radiation is different for different structures, which may also lead to differences in photoluminescence intensity for these
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structures.
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0.6
1
JPL, a.u.
0.5
2
0.4
0.3
3
4
0.1
0.0 0.40
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0.2
0.45
0.50
0.55
0.60
Photon energy, eV
0.65
0.70
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Fig. 2. Photoluminescence spectra of structures with InGaAsSb/AlGaAsSb quantum wells of different width, in nanometers: 9 (1), 7 (2), 5 (3), 4 (4); the optical pumping intensity is maximal; lattice temperature T = 77 K
Fig. 3 also shows the theoretical dependences of the energy of the allowed transitions on the width of InGaAsSb/AlGaAsSb quantum wells at liquid nitrogen
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temperature. The dash-dot line 1 corresponds to the calculated energy of the transitions between the ground state of heavy holes and the first level of the
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subband split by spin-orbit interaction: E(e1) → E(hh1). The solid line 2 corresponds to the calculated energy of the transition between the ground states of
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electrons and heavy holes E(e1) → E(hh1). The dashed line 3 corresponds to the
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energy of the transitions between the first two electronic levels in quantum wells: E(e2) → E(e1). It can be seen that the position of the photoluminescence peaks is
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in a good agreement with the theoretically calculated positions of the transition energies E(e1) → E(hh1), which indicates that the calculations of the band structure were sufficiently accurate. Fig. 3 shows that equality (1) holds true only in 5-nm-wide quantum wells at T = 77 K, which allows to observe resonant Auger recombination involving two holes and one electron. Equality (1) is not satisfied for other structures, so, as mentioned earlier, only non-resonant Auger recombination can occur in them. Notice that resonant Auger recombination 7
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involving two electrons and one hole cannot be observed in our structures as curves 2 and 3 do not intersect.
0.6
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1
0.5
2
0.4 0.3 0.2 3
4
5
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Photon energy, eV
0.7
6
7
8
3
9
10
Quantum well width, nm
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Fig. 3. Experimental (points) and calculated (lines) dependences of the allowed transition energy as a function of quantum well width (T = 77 K). The positions of the photoluminescence peaks for the E(e1) → E(hh1) transitions were found experimentally. The values of the E(hh1) → E(so1) (1), E(e1) → E(hh1) (2) and E(e2) → E(e1)(3) energy gaps were calculated
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The concentration of nonequilibrium charge carriers involved in radiative recombination can be obtained from analyzing the photoluminescence spectra at
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different levels of optical pumping. Fig. 4 shows the measured curves for the photoluminescence intensity (data points) in the spectral maximum (i.e., in the
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spectral region approximately corresponding to the effective band gap) versus the optical pumping level for all samples at temperature of 77 K. Unlike other structures, the dependence is apparently linear for the structure with the well width of 5 nm, where resonant Auger recombination is expected to occur (1). This is likely because nonradiative Auger recombination reduces charge carrier concentration in quantum wells involved in radiative recombination and contributing to interband photoluminescence. This interpretation can be confirmed 8
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by calculating the photoluminescence intensity at a specific wavelength as a function of charge carrier concentration. а)
b) n, 1011 cm-2
2
4
6
8
0
10
0.3
0.10
0.2
JPLmax, a. u.
JPLmax, a. u.
0.15
0.1
0.05
0.2
0.4
0.6
0.8
0.0 0.0
1.0
0.2
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0.00 0.0
1
2
3
4
0.4
0.6
0.8
1.0
Jpump, a. u.
Jpump, a. u.
c)
5
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n, 1011 cm-2 0
d)
n, 1012 cm-2 0.5
1.0
1.5
JPLmax, a. u.
0.2
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0.4
1.0
1.5
2.0
0.5 0.4 0.3 0.2 0.1
0.6
0.8
1.0
JPUMP, a. u.
0.0 0.0
0.2
0.4
0.6
0.8
1.0
JPUMP, a u.
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0.2
n, 1012 cm-2
0.5
0.6
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0.3
0.0 0.0
0.0 0.7
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JPLmax, a. u.
0.4
0.1
2.0
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0.0
Fig. 4. Experimental (points) and calculated (lines) dependences for peak photoluminescence intensity as a function of optical pumping intensity (points) and charge carrier concentration (lines) for structures with different quantum well widths, nm: 4 (a), 5 (b), 7 (c), 9 (d)
We calculated dependences of charge carrier concentrations on the photoluminescence intensity at a selected wavelength using the technique described in [8]. It should be noted that nonequilibrium charge carriers in our 9
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experiments were excited directly in the quantum wells, i.e., the pump photon energy (1.17 eV) was less than the barrier band gap (1.72 eV). Under this type of excitation, the distance between the quantum-confinement levels at which electrons and holes are produced in a quantum well is less than the pump photon energy value. A system of three heavy-hole levels and two electronic levels (see Fig. 5
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showing a diagram of optical transitions which can contribute to interband photoluminescence) was used for the calculation. It should be borne in mind that the e2 → hh3 transitions are the least likely to occur, and were not taken into account. In addition, according to the selection rules, only transitions between levels of the same parity (e1 → hh1 and e2 → hh2) are allowed in a quantum well
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of finite depth at k = 0. However, this forbiddance is removed with increasing k values, therefore, the contribution from the forbidden transitions should be taken
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into account.
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e2
fe
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e1
fh
hh1
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hh2
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Eh
hh3
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Fig. 5. Schematic energy diagram of interband radiative optical transitions in a quantum well with three hole and two electron levels. Arrows indicate the most probable optical transitions. Curves on the left are the distribution functions of electrons and holes.
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Let us introduce the following notations for the transition energies: e1hh1 Eg E(e1) E (hh1) Eg* , e1hh2 Eg E(e1) E(hh2) Eg* h12 , e1hh3 Eg E(e1) E (hh3) Eg* h13,
(4)
e 2hh1 Eg E(e2) E (hh1) Eg* e12 , e 2hh2 Eg E (e2) E (hh2) Eg* e12 h12 ,
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where e12 E(e1) E(e2) ,
h12 E (hh1) E (hh2) , h13 E (hh1) E (hh3) .
Charge carrier concentration is known to follow the expression
N e, h (T , E ) g e, h ( E ) f e, h ( E ) dE , 0
where the density of states ge,h for quantum wells are step functions: m * e, h 2
g e, h ( E )
,
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m*e,h are the effective masses of electrons and holes, fe,h are the distribution functions of electrons and holes: f e, h ( E )
1 E Fe, h 1 exp k T B
electrons and holes, respectively).
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(kB is the Boltzmann constant, Fe,h are the positions of the Fermi levels for The integral for determining the charge carrier concentration in quantum wells is an analytical expression allowing to find the equations that govern the
(1 e
(1 e
Fh k BT
Fe k BT
)(1 e
)(1 e
Fh h12 k BT
Fe e12 k BT
Ne
)e
)(1 e
NC
Fh h13 k BT
,
(5) Nh
) e NV
,
(6)
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ED
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position of the Fermi levels for electrons and holes:
where NC and NV are the effective densities of states of electrons and holes in a
NC
me*k BT 2
,
NV
mh* k BT 2
.
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two-dimensional subband, respectively;
Let us assume that the equality Ne = Nh is satisfied under optical excitation, and find the dependence of the position of the quasi Fermi levels of electrons and holes on the temperature and the concentration of charge carriers. The number of photons emitted per unit volume per unit time in the frequency interval from ν to ν+ dν for charge carrier transitions from the electron level i to the hole level j can be written as follows [8]: 12
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i j dqsp
2 n e 2 meh P2 ( h ) I (k 2 ) f e f h d h 2 3 i j m0 LQW c
(7) ,
where LQW is the quantum well width, n is the refractive index, meh is the reduced mass, Ii→j are the overlap integrals (calculated in Ref. [9]), P is the Kane matrix
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element of the momentum operator. This matrix element is expressed through the bulk band gap Eg and the electron mass m0 in the following way:
E g ( E g so ) m0 m0 ( * 1) 2 2 me ( E g so ) 3 .
(8)
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P2
Thus, the total number of emitted photons for all possible transitions (see
ED
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Fig. 5) is written as follows:
Qsp dq spi j .
(9)
i, j
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Substituting expression (7) into formula (9) and taking into account the
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dependence of the distribution function on the Fermi level (which, in turn, depends on the temperature and concentration of charge carriers), we have determined the
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theoretical dependence of the peak luminescence intensity on the charge carrier concentration for each structure at a temperature of 77 K (see Fig. 4). By scaling the abscissa, we have found the values of charge carrier concentrations corresponding to a good agreement between the experimental points and the theoretical curve. It is evident from Fig. 4 that the concentration of the charge carriers involved in radiative recombination is lower in the structure with 4-nmwide quantum wells because, according to calculations of the band diagram, under 13
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optical pumping, charge carriers are excited only in the ground quantumconfinement levels. Charge carrier concentrations in structures with 7- and 9-nmwide quantum wells were not significantly different due to slight variations in the band diagrams. The curves of photoluminescence intensity versus pump level can be divided into three sections for all three of these samples. The amount of injected charge
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carriers is small in the initial section corresponding to a low level of optical pumping, therefore, the energy distribution of electrons and holes is described by nondegenerate statistics. Thus, the photoluminescence intensity in the spectral peak is directly proportional to the product of the injected electron and hole concentrations, i.e., the dependence is quadratic. Next, degeneration of electron gas
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occurs at average pump levels (the second section). In this case the holes remain nondegenerate due to greater density of states. Thus, the concentration of electrons in the energy range from which radiative transitions are observed remains constant, and the photoluminescence intensity at average pump levels depends only on the
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change in the concentration of injected holes, i.e., is a linear function of the optical
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pumping level. Both the electron and hole gases are degenerate at high pump levels (the third section).In this case radiative recombination involves charge carriers
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from the regions of the conduction and the valence bands where the electron and hole concentrations remain constant. The photoluminescence intensity at this
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wavelength then does not depend on the pump level, and tends to saturation. Fig. 4 shows that the dependence of peak photoluminescence intensity on
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pump intensity is approximately linear for the structure with 5 nm wide quantum wells. This corresponds to average concentrations of charge carriers participating in photoluminescence. Evidently, the structure with 5 nm wide quantum wells exhibited the lowest charge carrier concentration of all samples. As proved above, the injected charge carriers in this structure are involved in nonradiative resonant Auger recombination, which reduces their contribution to radiative recombination.
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Thus, resonant nonradiative Auger recombination can decrease the concentration of charge carriers involved in radiative recombination by almost an order of magnitude. This phenomenon reduces the quantum yield and the effectiveness of lasers. In order to eliminate non-radiative Auger recombination, the design of semiconductor injection lasers emitting at a wavelength of about 3 μm must involve carefully calculating the band diagram and checking whether
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the condition that the effective band gap be equal to the energy spacing between the ground state of heavy holes and the first level of the band split by spin-orbit interaction is not fulfilled. Conclusion
The dependence of photoluminescence intensity in the spectral peak on the
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optical pumping intensity for nanostructures with different InGaAsSb/AlGaAsSb quantum well widths is investigated. This dependence had a linear behavior for the structure with 5 nm wide quantum wells where resonant Auger recombination was expected to be observed. In order to analyze the obtained experimental results, we
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calculated nonequilibrium charge carrier concentrations as a function of optical
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pumping level.
Finally, we conclude that the concentration of the charge carriers involved in
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radiative recombination decreases in a structure where the conditions of
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nonradiative resonant Auger recombination are fulfilled.
The study was conducted with the financial support of the Government of St. Petersburg,
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the Ministry of Education and Science of the Russian Federation (government task), an RFBR grant no. 16-02-00863, and a grant of the President of the Russian Federation for young candidates of science MK-4616.2016.2.
REFERENCES
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[1] A.M. Prokhorov (Editor-in-chief), Encyclopaedia on Physics,Vol. 2, Moscow, Sovetskaya entsiklopediya (1990) 183. [2] L. Shterengas, G. Belenky, G. Kipshidze, T. Hosoda, Room temperature operated 3.1 μm type-I GaSb-based diode lasers with 80 mW continuous-wave output power, Applied Physics Letters. 92 (17) (2008) 171111. [3] L.V. Danilov, G.G. Zegrya, Theoretical study of Auger recombination
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processes in deep quantum wells, Semiconductors. 42 (5) (2008) 550– 556. [4] D.A. Firsov, L. Shterengas, G. Kipshidze, et al., Dynamics of photoluminescence
and
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processes
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laser
nanostructures, Semiconductors. 44 (1) (2010) 50–58.
[5] E.O. Kane, Band structure of indium antimonide, Journal of Physics and
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Chemistry of Solids. 1 (4) (1957) 249–261.
[6] I. Vurgaftman, J. Meyer, L. Ram-Mohan, Band parameters for III–V compound semiconductors and their alloys, Journal of Applied Physics. 89 (11) (2001) 5815–5875.
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[7] J. Chen, D. Donetsky, L. Shterengas, et al., Effect of quantum well
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compressive strain above 1% on differential gain and threshold current density in type-I GaSb-based diode lasers, IEEE J. Quant. Electron. 44 (12) (2008) 1204 – 1210.
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[8] L.E. Vorob’ev, V.L. Zerova, K.S. Borshchev, et al., Charge-carrier
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concentration and temperature in quantum wells of laser heterostructures under spontaneous-and stimulated-emission conditions, Semiconductors. 42 (6) (2008)
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737–745.
[9] Z.N. Sokolova, V.B. Khalfin, Calculation of the probabilities of radiative
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