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Theory of highly-strained InAs quantum well lasers
grown on InP for optical communications at 2 µm
Zoe C. M. Davidson1∗, Judy M. Rorison1∗, and Christopher A. Broderick2,3
1Department of Electrical and Electronic Engineering, University of Bristol, Bristol BS8 1UB, U.K.
2Tyndall National Institute, University College Cork, Lee Maltings, Dyke Parade, Cork T12 R5CP, Ireland
3Department of Physics, University College Cork, Cork T12 YN60, Ireland
∗Email: zoe.davidson@bristol.ac.uk
Abstract: We present a theoretical analysis of highly-strained InAs quantum well lasers
grown on InP for use in next-generation hollow-core fibre optical communications close
to 2 µm, and validate our calculations against recent experimental data. © 2022 The
Author(s)
1. Introduction
The exponential growth of the internet and the continued proliferation of internet-enabled devices is pushing ex-
isting optical communications networks towards their fundamental physical limitations, threatening an impending
“capacity crunch”. This creates a strong mandate to access spectral regions beyond the 1.55 µm band employed in
existing long-haul telecoms networks based on single-mode silica optical fibre, with the aims of reducing loss, re-
ducing latency, and supporting high-bandwidth data transmission [1]. By fulfilling these criteria, photonic crystal
hollow-core fibres (HCFs) have emerged as a promising candidate transmission medium for next-generation opti-
cal communication networks. Minimum losses in HCFs are expected to occur for wavelengths close to 2 µm [2],
creating strong incentive to develop efficient semiconductor lasers operating in this wavelength range.
While GaSb-based heterostructures have traditionally been relied upon to achieve emission close to 2 µm,
extending the spectral range accessible using InP substrates is an attractive proposition. Firstly, as the incumbent
technological platform at 1.55 µm, InP offers high-quality and low-cost fabrication on large-diameter wafers in
established foundries. Secondly, extending the wavelength range accessible to InP delivers the potential to exploit
advances in InP-based photonic integration, allowing to develop photonic integrated circuits not only for optical
communications, but also for sensing applications at the interface of the near- and mid-infrared spectral ranges.
Experimental investigations of highly-strained InP-based quantum well (QW) lasers have demonstrated im-
pressive performance, including sub-100 A cm−2threshold current density and characteristic temperature T0com-
parable to GaSb-based devices [3]. It is well established from previous investigations of 1.3 and 1.55 µm QW
lasers that compressive strain is beneficial to laser performance [4], suggesting that highly-strained InP-based QW
lasers constitute an attractive approach to 2 µm emission. We present a theoretical analysis of InAs/In0.53Ga0.47 As
QWs lasers grown on InP for optical communications close to 2 µm, verify the accuracy of our calculations via
comparison to recent experimental data, and quantify the threshold properties as a function of QW thickness.
2. Theoretical model
We focus our analysis on separate confinement heterostructure (SCH) laser structures consisting of compressively
strained InAs QWs surrounded by unstrained In0.53Ga0.47 As barriers, with optical confinement provided by un-
strained InP cladding layers. We calculate the electronic properties of these InAs/In0.53Ga0.47 As QWs using an
8-band k·pHamiltonian in conjunction with a reciprocal space plane wave expansion method. The single-particle
eigenstates obtained from our QW k·pcalculations are then used to explicitly compute inter-band optical ma-
trix elements, which are in turn employed to compute spontaneous emission (SE) and optical gain spectra in the
quasi-equilibrium approximation. Assuming exemplar internal losses of 4 cm−1and a cavity length of 1 mm, we
estimate the threshold gain gth, which allows to extract the threshold carrier density nth and differential gain at
threshold dg
dn. Repeating this analysis as a function of QW thickness twe identify the wavelength range across
which InAs/In0.53Ga0.47 As QWs provide optical gain, and quantify trends in the threshold characteristics.
3. Results
The results of our calculations are partially summarised in Fig. 1. Figure 1(a) shows the calculated band off-
sets, and the electron and hole ground state probability densities, for a 5 nm thick InAs QW having unstrained
In0.53Ga0.47 As barriers. We find type-I band offsets, but note that the large compressive strain |εxx|=3.13% in
the InAs layer produces a conduction band (CB) offset ∆ECB ≈0.15 eV that is ≈0.1 eV lower than previously
predicted [5]. The associated low electron ionisation energy, ≲3kBTat room temperature, suggests the potential
importance of losses via thermal leakage of electrons from the active region during operation. This necessitates
engineering of the CB offset in these QWs to enhance electron confinement and suppress current leakage.
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
-6 -4 -2 0 2 4 6
CB
HH
LH
SO
∆ECB =153 meV
∆EHH =175 meV
|Fe1(z)|2
|Fh1(z)|2
(a)
t=5 nm
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
-6 -4 -2 0 2 4 6
CB
HH
LH
SO
∆ECB =153 meV
∆EHH =175 meV
|Fe1(z)|2
|Fh1(z)|2
(a)
t=5 nm
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
-6 -4 -2 0 2 4 6
CB
HH
LH
SO
∆ECB =153 meV
∆EHH =175 meV
|Fe1(z)|2
|Fh1(z)|2
(a)
t=5 nm
0.0
0.2
0.4
0.6
0.8
1.0
1.9 2.0 2.1 2.2 2.3 2.4 2.5
(b)
t=5 nm
0.0
0.2
0.4
0.6
0.8
1.0
1.9 2.0 2.1 2.2 2.3 2.4 2.5
(b)
t=5 nm
0.0
0.2
0.4
0.6
0.8
1.0
1.9 2.0 2.1 2.2 2.3 2.4 2.5
(b)
t=5 nm
2.0
2.1
2.2
2.3
2.4
2.5
3 4 5 6
T=293 K
1.0
1.2
1.4
1.6
1.8
2.0
3 4 5 6
8
10
12
14
16
18
20
T=293 K
◦
◦
(c)
Energy, E(eV)
Position, z(nm)
InAs/In0.53Ga0.47As band offsets
Energy, E(eV)
Position, z(nm)
InAs/In0.53Ga0.47As band offsets
Energy, E(eV)
Position, z(nm)
InAs/In0.53Ga0.47As band offsets
Calc. SE/meas. PL (arb. units)
Wavelength, λ(µm)
Theory vs. experiment
4 K
100 K
150 K
200 K
250 K
293 K
Calc. SE/meas. PL (arb. units)
Wavelength, λ(µm)
Theory vs. experiment
Theory
Experiment
Calc. SE/meas. PL (arb. units)
Wavelength, λ(µm)
Theory vs. experiment
λpeak (µm)
t(nm)
nth (×1012 cm−2)
dg
dn (×10−16 cm2)
QW thickness, t(nm)
Threshold characteristics
Fig. 1. (a) Band offsets and ground state probability densities for a 5 nm InAs/In0.53Ga0.47As QW grown on InP.
(b) Measured photoluminescence (open circles) and calculated spontaneous emission (solid lines) spectra for the
QW of (a). Experimental data are from Ref. [5]. Inset: peak gain wavelength at threshold vs. QW thickness t. (c)
Calculated threshold sheet carrier density nth (blue) and differential gain at threshold dg
dn(red) vs. t.
Figure 1(b) compares our calculated temperature-dependent SE spectra to the measured photoluminescence
spectra of Ref. [5]. We find good agreement with experiment by assuming a hyperbolic secant lineshape of width
4 meV in our calculations. Using this lineshape, we compute the material (optical) gain spectrum at a given injected
carrier density by transforming the SE spectrum. The resulting calculated peak gain vs. carrier density allows to
extract the threshold (sheet) carrier density nth and differential gain at threshold dg
dn, which are shown in Fig. 1(c)
using closed blue and open red circles, respectively. Optimum laser performance is obtained by simultaneously
(i) minimising nth, which minimises losses associated with non-radiative defect-related and Auger recombination
(the associated current densities being respectively ∝nth and ∝n3
th), and (ii) maximising dg
dn, which maximises
the modulation bandwidth and mitigates chirp [4]. Our single-QW calculations – without optimised CB offset
– suggest impressive characteristics, with calculated nth and dg
dnvalues close to those calculated previously for
optimised multi-QW InP-based pseudomorphic and GaAs-based metamorphic 1.3 and 1.55 µm QW lasers.
Non-radiative recombination will play a critical role in determining the performance of these QW lasers. The
low critical thickness, tc≈5 nm for pseudomorphic InAs/InP, can potentially promote defective growth. Addi-
tionally, losses associated with hot-hole-producing Auger recombination dominate the threshold current density at
and above room temperature in InP-based 1.3 and 1.55 µm QW lasers, limiting the characteristic temperature T0
to ≲100 K [4]. Auger recombination rates are strongly wavelength dependent, with hot-electron-producing pro-
cesses becoming increasingly important with increasing wavelength in InP-based materials. Additional analysis is
therefore required to identify and quantify routes towards mitigating Auger recombination in 2 µm QW lasers.
4. Conclusions
Highly-strained InAs QWs grown on InP substrates constitute an attractive approach to develop high-performance
diode lasers in the 2 µm spectral range, where photonic crystal HCF losses are minimised. Our calculations,
which are in good agreement with recent experimental data, indicate that InAs/InP QW lasers offer a combination
of low threshold carrier density and high differential gain. This suggests significant promise to exploit the mature
InP technological platform to develop low-cost, efficient QW lasers as light sources for next-generation telecoms.
This work was supported by the University of Bristol (UOB; Doctoral Studentship to Z.C.M.D.), by the National Univer-
sity of Ireland (NUI; Post-Doctoral Fellowship in the Sciences to C.A.B.), and by Science Foundation Ireland (SFI; project
no. 15/IA/3082).
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