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Gain Measurement of Highly Stacked InGaAs Quantum Dot Laser with Hakki–Paoli Method

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2013 Jpn. J. Appl. Phys. 52 04CG13

(http://iopscience.iop.org/1347-4065/52/4S/04CG13)

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Gain Measurement of Highly Stacked InGaAs Quantum Dot Laser

with Hakki–Paoli Method

Fumihiko Tanoue1;2, Hiroharu Sugawara1, Kouichi Akahane2, and Naokatsu Yamamoto2

1Graduate School of System Design, Tokyo Metropolitan University, Hino, Tokyo 191-0065, Japan2National Institute of Information and Communications Technology (NICT), Koganei, Tokyo 184-8795, Japan

Received October 1, 2012; accepted December 6, 2012; published online April 22, 2013

A 147-�m-long cavity laser diode with 19 InGaAs quantum dot layers was fabricated by the ultrahigh-rate molecular beam epitaxial growth

technique, and its gain properties were investigated using the Hakki–Paoli method below the threshold current (Ith) of 111.5mA. At an injection

current of 100.3mA (0:9Ith), the positive net modal gain was in the range between 1005 and 1043 nm, corresponding to a photon energy of

45meV. The maximum net modal gain and maximum modal gain were 46.5 and 60.5 cm�1, respectively. A differential net modal gain of as high

as 3.8 cm�1/mA was observed at 0.77 times the threshold current. No gain saturation appeared below the threshold current, and injection currents

higher than 78.4mA (�0:7Ith) were required to obtain a net modal gain. # 2013 The Japan Society of Applied Physics

1. Introduction

Quantum dot (QD) laser diodes are attractive devices forimplementing superior performance such as low thresholdcurrent and high speed modulation owing to the enhancedof the optical gain through �-function-like density-of-statesof carriers in QDs.1–4) Further enhancement is expectedby increasing the number of QDs in an active region,particularly, the number of stacked layers of QDs becausethe areal density of QDs is restricted by the sizes andseparation of QDs to achieve localized states of carriers.

Molecular beam epitaxial (MBE) growth via the Stranski–Krastanov (SK) growth mode is a major technique tofabricate self-assembled QDs, and the gain properties of QDlasers prepared by this technique have been extensivelystudied. Up to 10 stacked InGaAs QD lasers operatingbetween 1.0 and 1.3 �m,5–11) which indicated a modal gain ashigh as 50 cm�1, where evaluated on the basis of mirror lossat the threshold current density and/or using the Hakki–Paoli method.12,13)

In previous works,14,15) the authors have successfullyfabricated self-assembled InGaAs QDs with a high arealdensity of 1010 cm�2 by ultrahigh-rate16,17) solid sourceMBE growth, and demonstrated room-temperature operationof a 19 stacked InGaAs QD laser diode as short as 99 �m18)

in the 1.0 �m photonic wave band (T-band).19,20) In thiswork, we fabricated 19 stacked QD laser diodes with a 147-�m-long cavity and investigated the bandwidth of the gainspectrum and gain curve below the threshold current usingthe Hakki–Paoli method.

2. Experimental Procedure

Using the ultrahigh-rate MBE technique we fabricated 19stacked In0:4Ga0:6As QD layers separated by 20-nm-thickGaAs spacer layers on a GaAs(001) substrate, as describedin Ref. 15 in detail. This active region was sandwichedbetween a 1500-nm-thick n-type Al0:3Ga0:7As lower clad-ding layer and a 1500-nm-thick p-type Al0:3Ga0:7As uppercladding layer. After capping with a 200-nm-thick GaAscontact layer on the upper cladding layer, a 50-�m-wideelectrode was defined by a photo-lithography technique.This wafer was cleaved into a stripe laser device with acavity of L ¼ 147 �m.

The device was subjected to a 1-�s-wide electric currentpulse at a duty cycle of 1% at room temperature. The outputpower characteristic was measured using an laser diode(LD) tester (Yuasa Electronic AT-143), and emission spectrawere recorded using an optical spectrum analyzer system(Yokogawa Electric AQ6370) with a wavelength resolutionof 0.05 nm.

Net modal gain (gnet) was calculated for injection currentsbelow threshold using the Hakki–Paoli method with thefollowing equation:

gnet ¼ 1

Lln

r1=2 � 1

r1=2 þ 1þ 1

Lln

1

R: ð1Þ

Here, the effective reflection coefficient R ¼ 0:36 and thepeak-to-valley ratio r13) were calculated from the Fabry–Perot oscillations of amplified spontaneous emission (ASE)spectra, as shown later in Fig. 2. At injection currents abovethreshold, gnet approaches mirror loss (�m), i.e., the secondterm on the right hand side of Eq. (1), which was evaluatedto be 69.5 cm�1.

0 50 100 150 2000

1

2

3

4

5R.T.

Ou

tpu

t P

ow

er (

mW

)

Injection current (mA)

Fig. 1. Output power versus injection current of the device.

Japanese Journal of Applied Physics 52 (2013) 04CG13

04CG13-1 # 2013 The Japan Society of Applied Physics

REGULAR PAPERhttp://dx.doi.org/10.7567/JJAP.52.04CG13

3. Results and Discussion

Figure 1 shows the output power characteristic. The thresh-old current (Ith) was 111.5mA as determined by linearfitting, corresponding to the threshold current density (Jth) of1.52 kA/cm2. This relatively high threshold current could beattributed to the mirror loss rather than the internal opticalloss (�i), which was evaluated to be 14.4 cm�1 in ourprevious study15) on the differential quantum efficiencies of19 stacked QD lasers fabricated from the same wafer.

Figure 2 shows ASE spectra obtained at injection currentsbetween 78.0 (0:7Ith) and 120.4mA (1:08Ith). As theinjection currents increased to 100.3mA (0:9Ith), a peak ofASE spectra blue-shifted from 1028 to 1022 nm possibly dueto band filling. The full width of half maximum (FWHM) ofthe envelope of the ASE spectrum at 78.0mA was as broadas 37 nm, corresponding to 42.9meV, which was attributedto inhomogeneous broadening from distributions of QDsizes.15)

From the ASE spectra at 120.4mA, the Fabry–Perot modespacing (�f ¼ c=2nL) of 255GHz was observed, and theeffective refractive index (n) was evaluated to be 4.0. Theeffective reflection coefficient was then calculated to beR ¼ ðn� 1Þ2=ðnþ 1Þ2 ¼ 0:36 and used in the calculation ofEq. (1).

Figure 3 shows net modal gain spectra calculatedusing Eq. (1). At 100.3mA, positive net modal gains rangedbetween 1005 and 1043 nm, corresponding to a photonenergy of 45meV.

Figure 4(a) plots maximum values of net modal gain (gnet)as a function of injection current. The maximum net modalgain reached 46.5 cm�1 at 100.3mA, and the correspondingmodal gain (gmod) was 60.9 cm�1 since gnet ¼ gmod � �i.The net modal gain saturated above 120.4mA and wasnearly identical to the mirror loss (�m).

The gain curve of the QD laser as a function of theinjection current density J is expressed by the empiricalEq. (2),21,22)

gnet ¼ Gsat 1� exp ��J � JtrJtr

� �� �; ð2Þ

where Gsat is the saturated modal gain on the ground-stateoptical transition, � is the non-ideality factor, and Jtr is thetransparency current density, i.e., a current density corre-sponding to zero net modal gain. From the fitting, thesaturated modal gain Gsat was evaluated to be 69.9 cm�1,comparable to the mirror loss (�m). The gain curve indicatedthat no gain saturation appeared below threshold current, andthat an injection current higher than 78.4mA (�0:7Ith) wasrequired to obtain a positive net modal gain.

Figure 4(b) shows the differential net modal gain(�gnet=�I) versus injection current evaluated by numericaldifferentiation of the maximum net modal gain. The

1.24 1.22 1.2 1.18

1000 1020 1040 1060

-60

-40

-20

0

20

40

60

80

100120.4mA100.3mA 89.2mA 83.6mA 78.0mA

Photon energy (eV)

Net

Mo

dal

Gai

n (

cm-1)

Wavelength (nm)

Fig. 3. Net modal gain spectra calculated by Hakki–Paoli method at

different injection currents.

0

10

20

30

40

50

60

70

60 80 100 120 140

0

2

4

(a)Δ

gn

et /

ΔI (

cm-1/ m

A)

Injection current (mA)

(b)

Max

imu

m n

et m

od

al g

ain

(cm

-1)

Fig. 4. Injection current dependences of (a) maximum net modal gain and

(b) derivative of maximum net modal gain (�gnet=�I). The dashed curve in

(a) was from the fitting by Eq. (2), and the dashed curve in (b) was its

derivative.

1000 1020 1040 1060

78.0mA

83.6mA

100.3mA

89.2mA

120.4mAIn

ten

sity

(ar

b. u

nit

s)

Wavelength (nm)

1.24 1.22 1.2 1.18Photon energy (eV)

Fig. 2. ASE spectra obtained at injection currents between 78.0 (0:7Ith)

and 120.4mA (1:08Ith).

F. Tanoue et al.Jpn. J. Appl. Phys. 52 (2013) 04CG13

04CG13-2 # 2013 The Japan Society of Applied Physics

differential net modal gain showed a maximum of 3.8cm�1/mA at 86.4mA (0:77Ith), and dropped off to 0.97cm�1/mA at 110.3mA (�0:99Ith) due to gain saturation.

4. Conclusions

The net modal gain spectra of 19 stacked In0:4Ga0:6As QDlaser diodes with a 147-�m-long cavity were measuredusing the Hakki–Paoli method. At the injection current of0.9 times the threshold current, the positive net modal gaincorresponded to a photon energy of 45meV. The maximumnet modal gain and maximum modal gain were evaluatedto be 46.5 and 60.5 cm�1, respectively. No gain saturationoccurred below the threshold current, and the differential netmodal gain was as high as 3.8 cm�1/mA at the injectioncurrent of 0.77 times the threshold current.

Acknowledgement

The authors acknowledge the technical assistance fromNICT Photonic Device Lab.

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04CG13-3 # 2013 The Japan Society of Applied Physics