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\begin{document}

\title{Room-temperature high-speed mid-infrared quantum cascade laser with
\selectlanguage{greek}π-\selectlanguage{english}shape metal contact\selectlanguage{english}}



\author[1]{Xu Gao}%
\author[2]{Ke Yang}%
\author[2]{Yi-xuan Zhu}%
\author[2]{Junqi Liu}%
\author[2]{Shenqiang Zhai}%
\author[2]{Shuman Liu}%
\author[2]{Ning Zhuo}%
\author[2]{Jinchuan Zhang}%
\author[2]{Lijun Wang}%
\author[2]{Fengqi Liu}%
\author[1]{Xiao-hua Wang}%
\author[1]{Zhi-peng Wei}%
\affil[1]{Changchun University of Science and Technology Jilin}%
\affil[2]{Institute of Semiconductors Chinese Academy of Sciences}%


\vspace{-1em}



  
  \date{June 17, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
We demonstrate a high-speed 8.5 \selectlanguage{greek}μ\selectlanguage{english}m quantum cascade laser with room
temperature continuous wave operation. The maximum output power of 141
mW is obtained at 20 . The parasitic capacitance of the device is
decreased from 36.6 pF to 7.1 pF by monolithic integrating a \selectlanguage{greek}π-\selectlanguage{english}shape
metal contact electrode. This results in an increase in the -3 dB RF
modulation bandwidth from 870 MHz to 4.5 GHz compared with the
conventional electrode configuration.%
\end{abstract}%



\sloppy


Room-temperature high-speed mid-infrared quantum cascade laser with
\selectlanguage{greek}π-\selectlanguage{english}shape metal contact

\textbf{Xu Gao\textsuperscript{1,2,3}, Ke Yang\textsuperscript{2,3},
Yi-xuan Zhu\textsuperscript{2,3}, Jun-qi Liu\textsuperscript{2,3,},
Shen-qiang Zhai\textsuperscript{2}, Shu-man Liu\textsuperscript{2,3},
Ning Zhuo\textsuperscript{2}, Jin-chuan Zhang\textsuperscript{2,3},
Li-jun Wang\textsuperscript{2,3}, Feng-qi Liu\textsuperscript{2,3,4},
Xiao-hua Wang\textsuperscript{1,} and Zhi-peng
Wei\textsuperscript{1,}}

\emph{\textsuperscript{1}State Key Laboratory of High Power
Semiconductor Lasers, School of Physics, Changchun University of Science
and Technology, Changchun 130022, China}

\emph{\textsuperscript{2}Key Laboratory of Semiconductor Materials
Science, Institute of Semiconductors, Chinese Academy of Sciences,
Beijing 100083, China}

\emph{\textsuperscript{3}College of Materials Science and
Opto-Electronic Technology, University of Chinese Academy of Sciences,
Beijing 101408, China}

Email: jqliu@semi.ac.cn; biewang2001@126.com; and zpweicust@126.com

We demonstrate a high-speed 8.5 \selectlanguage{greek}\emph{μ}\selectlanguage{english}m quantum cascade laser with
room temperature continuous wave operation. The maximum output power of
141 mW is obtained at 20 . The parasitic capacitance of the device is
decreased from 36.6 pF to 7.1 pF by monolithic integrating a \selectlanguage{greek}π-\selectlanguage{english}shape
metal contact electrode. This results in an increase in the -3 dB RF
modulation bandwidth from 870 MHz to 4.5 GHz compared with the
conventional electrode configuration.

\emph{Introduction:} High-speed quantum cascade lasers (QCLs) are
essential for a plethora of applications in free-space optical
communication (FSOC) {[}1{]}, high-sensitivity spectroscopy {[}2{]},
mode-locking {[}3{]}, etc. Due to the particularity of the transition
between subbands, the theoretical modulation bandwidth of QCLs can reach
the order of 100 GHz {[}4{]}. However, higher electrical parasitics
limit the modulation performance of QCLs, various approaches have been
proposed to reduce electrical parasitics. Using thicker chalcogenide
glass (Ge\textsubscript{0.25}Se\textsubscript{0.75}) as insulating
material to achieve 7 GHz modulation response at 20 K. Single-mode
buried grating QCL using thickened SiO\textsubscript{2} as insulating
layer achieves a flat frequency response of 3 GHz at room temperature
{[}5{]}. A frequency response of 15 GHz at 77 K is achieved through the
integration of microstrip lines with dielectric laser waveguide {[}6{]}.
A single-mode distributed feedback (DFB) QCL integrated with a
three-terminal microwave coplanar waveguide structure displayed 3-dB
bandwidth of up to 6.6 GHz {[}7{]}. High-frequency modulation of 3-dB
bandwidth at 5.6 GHz achieved by buried heterostructure ultrashort
resonator {[}8{]}. The RC constant is reduced by inserting a matching
printed circuit, and the 3-dB bandwidth is increased from about 0.9 to
2.2 GHz {[}9{]}. Although high-speed QCLs have been studied a lot, most
of these devices can only operate below room temperature.

In this letter, we propose a room temperature high-speed QCL emitting at
8.5 \selectlanguage{greek}\emph{μ} \selectlanguage{english}m with the maximum continuous wave (CW) output power of 141
mW at 20 . After optimization of the monolithically integrated \selectlanguage{greek}π-\selectlanguage{english}shape
metal contact electrode, a parasitic capacitance is reduced to a very
low value of 7.1 pF resulting in a high -3 dB RF-modulation bandwidth of
4.5 GHz.

\emph{Design and fabrication:} The QCL structure was grown on an n-doped
InP substrate by metal-organic chemical vapor deposition (MOCVD) with an
active-region (AR) structure similar to Ref. {[}10{]}. The layer
thicknesses in nanometers, starting from the first injection barrier,
are as follows:\textbf{4.0} /1.3/\textbf{1.0} /5.2/\textbf{0.9}
/5.1/\textbf{1.0} /4.7/\textbf{1.6} /3.6/\textbf{2.2} /2.9/\textbf{1.8}
/2.7/\textbf{1.9} /\emph{2.6/\textbf{2.0}/2.4/\textbf{2.5}/}
2.5/\textbf{3.1} /2.3, where InAlAs barriers are in bold, InGaAs wells
in roman, and underlined numbers correspond to the doped layers (Si, 2 \selectlanguage{ngerman}×
10\textsuperscript{17}cm\textsuperscript{-3}). The epitaxial layer
sequence starting from the InP substrate is as follows: 0.5 \selectlanguage{greek}\emph{μ} \selectlanguage{english}m
InP buffer layer (Si, 1 \selectlanguage{ngerman}× 10\textsuperscript{17}
cm\selectlanguage{english}\textsuperscript{-3}), 3 \selectlanguage{greek}\emph{μ} \selectlanguage{english}m lowdoped InP cladding layer (Si, 4
\selectlanguage{ngerman}× 10\textsuperscript{16} cm\selectlanguage{english}\textsuperscript{-3}), 300 nm InGaAs
confinement layer (Si, 5 x
10\textsuperscript{16}cm\selectlanguage{english}\textsuperscript{-3}), 35 periods InGaAs/InAlAs
active structure, 300 nm InGaAs confinement layer (Si, 5 x
10\textsuperscript{16}cm\selectlanguage{english}\textsuperscript{-3}), 3.3 \selectlanguage{greek}\emph{μ} \selectlanguage{english}m low-doped
InP cladding layer (Si, 4 \selectlanguage{ngerman}× 10\textsuperscript{16}
cm\selectlanguage{english}\textsuperscript{-3}), 0.4 \selectlanguage{greek}\emph{μ} \selectlanguage{english}m graded-doped InP layer (Si, 1 \selectlanguage{ngerman}×
10\textsuperscript{17}cm\selectlanguage{english}\textsuperscript{-3} -- 1 x
10\textsuperscript{18}cm\selectlanguage{english}\textsuperscript{-3}), and 0.3 \selectlanguage{greek}\emph{μ} \selectlanguage{english}m InP
contact layer (Si, 5 \selectlanguage{ngerman}× 10\textsuperscript{18} cm\selectlanguage{english}\textsuperscript{-3}).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\emph{a}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\emph{b}

\textbf{Fig. 1} \emph{Device structure diagram.}

\emph{a} Structure diagram of conventional QCL

\emph{b} Structural diagram of QCL with \selectlanguage{greek}π-\selectlanguage{english}shape electrode. Inset: The
size of \selectlanguage{greek}π-\selectlanguage{english}shape electrode.

The conventional double-channal~planar~buried~heterostructure (BH)
device structure is shown in Figure 1a, which is processed into a BH
configuration with a ridge width of 10 \selectlanguage{greek}\emph{μ} \selectlanguage{english}m. The fabrication
process is the same as that described in Ref. {[}10{]}. For packaging,
the chips were soldered epi-up on AlN submounts to improve heat removal
efficiency. Then the submounts with chips were mounted on the copper
heat sinks with indium solder followed by wire bonding. The parasitic
capacitance of the entire device can be roughly composed of three
parts:\selectlanguage{greek}\emph{C\textsubscript{total} = C\textsubscript{bypass} +
C\textsubscript{InP:Fe} + C\textsubscript{AR} =
ε\textsubscript{0}ε\textsubscript{s}S/d}\selectlanguage{english} , as shown in the illustration,
where \selectlanguage{greek}\emph{ε\textsubscript{s}}\selectlanguage{english} is sheet-permittivity of InP:Fe and
AR,\emph{S} is pumped area, \emph{d} is thickness of the layer. To
reduce bypass capacitance, we skillfully removed the redundant Ti/Au
contact around the current injection
window~through~standard~photolithography~and~etching as shown in Figure
1b, only leaving the current injection window portion and enough pad
area for bonding wires. The size of the pad is as shown in the
illustration, which just meets the size of the gold wire. This makes the
metal contact electrode look like \selectlanguage{greek}π-\selectlanguage{english}shape. The whole top electrode area
is reduced from 6.8 \selectlanguage{ngerman}× 10\textsuperscript{5} \selectlanguage{greek}\emph{μ}
\selectlanguage{english}m\textsuperscript{2}to 2.37 \selectlanguage{ngerman}× 10\textsuperscript{5} \selectlanguage{greek}\emph{μ}
\selectlanguage{english}m\textsuperscript{2}\emph{.} The processed wafer was cleaved into 2 mm
bars, and a high-reflectivity coating consisting of
Al\textsubscript{2}O\textsubscript{3}/Ti/Au/Ti/Al\textsubscript{2}O\textsubscript{3}(200/10/100/10/120
nm) was applied on the back facet with the front facet left uncoated.

\emph{Experiments and discussion:} For characteration, the laser was
mounted on a holder containing a thermistor combined with a
thermoelectric cooler (TEC) to monitor and adjust the sub-mount
temperature. The emitted optical power was measured with the calibrated
thermopile detector placed in front of the laser facet without any
correction. The spectra of devices were tested by a Fourier transform
infrared spectrometer with a resolution of 0.25 cm\textsuperscript{-1}.

Figure 2a shows the CW power-current-voltage (P-I-V) characteristics of
a QCL with \selectlanguage{greek}π-\selectlanguage{english}shape metal contact electrode at different heat sink
temperature and a conventional QCL at 20 \selectlanguage{ngerman}°C. The QCL with \selectlanguage{greek}π-\selectlanguage{english}shape metal
contact electrode CW output power ranging from 181 mW at 10 \selectlanguage{ngerman}°C to 60 mW
at 40 °C.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\emph{a}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\emph{b}

\textbf{Fig. 2} \selectlanguage{greek}\emph{Electrical and optical characteristics of a
conventional QCL and a QCL with π-shape electrode during CW operation.}\selectlanguage{english}

\emph{a} P-I-V characteristics for various heat sink temperatures

\emph{b} CW spectra for various pumping currents at 20 \selectlanguage{ngerman}°C.

At 20 °C, the device exhibited a threshold current of 400 mA and a
maximum CW output power of 141 mW. The traditional QCL have a maximum
output power of 148 mW. According to the I-V characteristic curve of the
device, it can be calculated that the differential resistance above the
threshold current is about 5 \selectlanguage{greek}Ω. \selectlanguage{english}Figure 2b we present the CW lasing
spectra of the QCLs at 20 \selectlanguage{ngerman}°C and the injection current is 440 mA. The
device exhibits multimode lasing with a center wavelength around
8.5\selectlanguage{greek}\emph{µ} \selectlanguage{english}m.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\textbf{Fig. 3} \selectlanguage{greek}\emph{Normalized electrical rectification data of a QCL
with π-shape electrode at different bias-currents between 0.9
I\textsubscript{th} and 1.6 I\textsubscript{th}. Inset: The experimental
setup for a microwave rectification measurement.}\selectlanguage{english}

To characterize the high frequency modulation performance of the
devices, we applied a microwave rectification technology {[}11{]}. The
inset of Figure 3 shows a diagram of the experimental setup. In this
measurement, a microwave signal and a direct current (DC) bias are
injected into the laser through a bias-T. The laser is DC biased at
different currents, while the RF power is kept at 10 dBm. An1.024 kHz
amplitude modulation is added to the RF generator by an additional
arbitrary function generator while sweeping from 100 MHz to 15 GHz in
steps of 100 MHz. Figure 3 shows the normalized electrical rectification
curves for a QCL with \selectlanguage{greek}π-\selectlanguage{english}shape metal contact electrode measured at
widespread driving currents ranging from 0.9 I\textsubscript{th} (360
mA) to 1.6 I\textsubscript{th} (640 mA). Further increase in modulation
bandwidth with the increasing DC current is observed. It is also in good
agreement with literature {[}6-8{]}, where similar results were obtained
above lasing threshold.

Figure 4 shows the comparison results of the normalized electrical
rectification data and corresponding fitting results at 1.6
I\textsubscript{th} of a conventional QCL and a \selectlanguage{greek}π-\selectlanguage{english}shape QCL. As can be
seen, the -3 dB bandwidth of the conventional QCL is 870 MHz and the
\selectlanguage{greek}π-\selectlanguage{english}shape electrode QCL is 4.5 GHz. By fitting the measured value with the
theoretical curve (dashed line) of the rectification model, the
corresponding capacitance value can be extracted. It can be obtained
that the parasitic capacitance of the conventional structure QCL is 36.6
pF, while the parasitic capacitance of the \selectlanguage{greek}π-\selectlanguage{english}shape electrode QCL is 7.1
pF. The test results show that after integrating a \selectlanguage{greek}π-\selectlanguage{english}shape electrode,
the parasitic capacitance of the device is reduced effectively,
resulting in an increase of the -3 dB modulation bandwidth from 870 MHz
to 4.5 GHz.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

\textbf{Fig. 4} \selectlanguage{greek}\emph{The comparison results of the normalized
electrical rectification data of a conventional QCL and a π-shape
electrode QCL.}\selectlanguage{english}

\emph{Conclusion:} We have demonstrated a CW high-speed QCL with
emitting wavelength of 8.5\selectlanguage{greek}\emph{μ} \selectlanguage{english}m and output optical power about 141
mW at 20 . By monolithic integratin\emph{g} a \selectlanguage{greek}π-\selectlanguage{english}shape metal contact
electrode, the parasitic capacitance of the device is effectively
reduced from 36.6 pF to 7.1 pF and the -3 dB modulation bandwidth is
increased from 870 MHz to 4.5 GHz compared with the conventional
electrode configuration. The device shows a high application potential
in FSOC, active mode locking, etc.

\emph{Acknowledgments:} This work was supported in part by the National
Natural Science Foundation of China under Grant Nos. 61835011, 61991430,
and the Key Program of the Chinese Academy of Sciences under Grant Nos.
XDB43000000.

? 2022 The Authors. \emph{Electronics Letters} published by John Wiley
\& Sons Ltd on behalf of The Institution of Engineering and Technology

This is an open access article under the terms of the Creative Commons
Attribution License, which permits use, distribution and reproduction in
any medium, provided the original work is properly cited.

References

1. Pang, X., Ozolins, O., Zhang, L., Schatz, R., Udalcovs, A., Yu, X.,
Jacobsen, G., Popov, S., Chen, J., and Lourdudoss, S., 'Free-Space
Communications Enabled by Quantum Cascade Lasers', Phys. Status Solidi
A, 2021, 218, (3), p. 2000407.

2. Villares, G., Hugi, A., Blaser, S., and Faist, J., 'Dual-Comb
Spectroscopy Based on Quantum-Cascade-Laser Frequency Combs', Nature
Communications, 2014, 5, (1), p. 5192.

3. Hillbrand, J., Andrews, A.M., Detz, H., Strasser, G., and Schwarz,
B., 'Coherent Injection Locking of Quantum Cascade Laser Frequency
Combs', Nature Photonics, 2019, 13, (2), pp. 101-104.

4. Haldar, M.K., 'A Simplified Analysis of Direct Intensity Modulation
of Quantum Cascade Lasers', IEEE Journal of Quantum Electronics, 2005,
41, (11), pp. 1349-1355.

5. Zhou, Y.H., Zhai, S.Q., Liu, J., Liu, F., Zhang, J., Zhuo, N., Wang,
L., and Wang, Z., 'High-Speed Quantum Cascade Laser at Room
Temperature', Electronics Letters, 2016, 52, (7), pp. 548-549.

6. Calvar, A., Amanti, M.I., St-Jean, M.R., Barbieri, S., Bismuto, A.,
Gini, E., Beck, M., Faist, J., and Sirtori, C., 'High Frequency
Modulation of Mid-Infrared Quantum Cascade Lasers Embedded into
Microstrip Line', Applied Physics Letters 2013, 102, (18), p. 181114.

7. Hinkov, B., Hugi, A., Beck, M., and Faist, J., 'Rf-Modulation of
Mid-Infrared Distributed Feedback Quantum Cascade Lasers', Optics
Express, 2016, 24, (4), pp. 3294-3312.

8. Zhou, Y.H., Liu, J.Q., Zhai, S.Q., Zhuo, N., Zhang, J.C., Liu, S.M.,
Wang, L.J., Liu, F.Q., and Wang, Z.G., 'High-Speed Operation of
Single-Mode Tunable Quantum Cascade Laser Based on Ultra-Short Resonant
Cavity', AIP Advances, 2021, 11, (1), p. 015325.

9. Yang, K., Liu, J., Zhai, S., Zhang, J., Zhuo, N., Wang, L., Liu, S.,
and Liu, F., 'Room-Temperature Quantum Cascade Laser Packaged Module at
~8 \selectlanguage{greek}μ\selectlanguage{english}m Designed for High-Frequency Response', Electronics Letters, 2021,
57, (17), pp. 665-667.

10. Fei, T., Zhai, S.Q., Zhang, J.C., Zhuo, N., Liu, J.Q., Wang, L.J.,
Liu, S.M., Jia, Z.W., Li, K., Sun, Y.Q., Guo, K., Liu, F.Q., Wang, Z.G.,
'High power \selectlanguage{greek}λ\selectlanguage{english}\textasciitilde{} 8.5 \selectlanguage{greek}μ\selectlanguage{english}m quantum cascade laser grown by
MOCVD operating continuous-wave up to 408 K', Journal of Semiconductors,
2021, 42(11): 112301.

11. Liu, H.C., Jianmeng, L., Buchanan, M., and Wasilewski, Z.R.,
'High-Frequency Quantum-Well Infrared Photodetectors Measured by
Microwave-Rectification Technique', IEEE Journal of Quantum Electronics,
1996, 32, (6), pp. 1024-1028.

\selectlanguage{english}
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