Self-heating effect in 1.3-μm p-doped InAs/GaAs quantum dot vertical
cavity surface emitting lasers
D. W. Xu *a), C. Z. Tong a), S. F. Yoon a), L. J. Zhao b), Y. Ding a), and W. J. Fan a)
a)
School of Electrical and Electronic Engineering, Nanyang Technological University,
Singapore 639798, Republic of Singapore;
b)
Key Laboratory of Semiconductor Materials Science, Institute of Semiconductors, Chinese
Academy of Sciences, P. O. Box 912, Beijing 100083, China.
Email: n060085@ntu.edu.sg
(Received 29 Nov 2009)
The self-heating effect in the 1.3-μm p-doped InAs/GaAs quantum dot (QD) vertical
cavity surface emitting lasers (VCSELs) has been investigated using a self-consistent
theoretical model. Good agreement is obtained between theoretical analysis and
experimental results under pulsed operation. The results show that in p-doped QD
VCSELs, the output power is significantly influenced by self-heating. About 60% of
output power is limited by self-heating in a device with oxide aperture of 5×6 μm2.
This value reduces to 55% and 48%, respectively, as the oxide aperture increases to
7×8 μm2 and 15×15 μm2. The temperature increase in the active region and injection
efficiency of the QDs are calculated and discussed based on the different oxide
aperture areas and duty cycle. © 2006 American Institute of Physics.
PACS numbers: 78.67.Hc
I. INTRODUCTION
Development of long wavelength vertical cavity surface emitting laser (VCSEL) emitting
1
at 1200nm – 1300nm is attracting great interest in laser diode research.1-9 In the case of
GaAs-based VCSELs with InAs quantum dot (QD) active region, several special merits exist
such as higher material gain and differential gain, improved dynamic properties and high
thermal stability.10,11 Therefore InAs/GaAs QD VCSELs are considered potential candidates
for advanced photonic networks in the 1300nm wavelength region.12-18 To achieve optical as
well as electronic confinement and single mode operation, an oxide-confined structure is
incorporated in the QD VCSELs. However, to date the performance of QD VCSELs still fall
short of expectation, as carrier confinement suffers significant degradation due to high
self-heating19 which limits the QD injection efficiency and further deteriorates the output
power performance.7
The self-heating effect in QD VCSELs is mainly due to the small oxide aperture area20,21
and poor hole confinement in the QD region.7 Reasons include the enhanced power density in
small device volume, high Joule heating in distributed Bragg reflector (DBR) stacks, and
electrical and thermal impedance formed by the oxide layer. Furthermore, the thin wetting
layer (WL) and closely-spaced energy levels result in significant degradation of the hole
confinement.7 Hence carriers injected in the QD VCSELs acquire energy from thermalization
and escape easily from the finite energy barrier. Based on these reasons, it is highly desirable
to characterize the self-heating effect in QD VCSELs in order to optimize the device structure
and provide further physical insight into the thermal management issues in such devices.
We have previously reported a self-consistent model based on rate equations and thermal
conduction equation to analyze the influence of self-heating on carrier occupation, quantum
efficiency, and output power in QD lasers.6,7,9 It was found that poor hole confinement is one
2
of the key factors that limit the output power in QD VCSELs. To improve the hole
confinement, p-type modulation doping 22 - 25 (p-doping) was used in our fabricated
devices.16-18 While p-doping results in high temperature stability of the threshold current in
both single-mode18 and multi-mode16 QD VCSELs, it was demonstrated that the QD
emission worsens following increase in temperature resulting in degradation of the output
power16,18 and modulation characteristics.17 In other words, self-heating strongly influences
the output power performance of p-doped QD VCSELs, and therefore, further analysis and
experimentations are needed to understand this problem. To characterize the influence of
self-heating on the output power of QD VCSELs, in this paper we present experiments on
pulsed operation of 1.3-μm p-doped InAs/GaAs QD VCSELs. The measurements of output
power are compared with theoretical simulation and the self-heating and injection efficiency
of the QD region under pulsed operation are characterized.
II. THEORETICAL MODEL
The self-consistent model of the QD VCSEL is based on rate equations and thermal
conduction equation. The rate equations describe the carrier dynamics from the GaAs barrier
to the QD levels, where three levels are assumed. As shown in the appendix, five equations
(Eqs.A1-A5) are used to describe the energy states in the barrier (Eq.A1), WL or cap layer
(CL) (Eq.A2), second excited state of the QDs (Eq.A3), first excited state of the QDs (Eq.A4)
and the ground state (Eq.A5), respectively. Phonon- and Auger-assisted relaxations are taken
into account in the model. Furthermore, the model7 also considers all possible relaxation
paths, assuming the same relaxation time, as long as the initial and final relaxation states are
3
the same. It further assumes that the electrons are injected into the QDs from the wetting
layer (WL) and escape from the cap layer (CL), and holes are injected from the CL into the
QDs and escape from the WL. The multilayer QDs are assumed to be distributed
symmetrically within the inner cavity of the QD VCSEL. From the rate equations, we obtain
the carrier occupation of the QD levels and injection efficiency (see Eq.A11 in Appendix).
The detailed description of the QD rate equations are found in Refs. 6 and 7.
The self-heating effect is described by the thermal conduction equation. The heat source
considered in the QD VCSELs includes Joule heating in the DBRs and heat generated within
the active region due to non-radiative recombination and absorption of spontaneous
emission.7 The generated heat density is used to calculate the temperature response within the
active region from the three-dimensional dynamic thermal conduction26 equation:
1 T (r , t ) 1  T (r , t )
1

[r
]  Q( J , r , t ) ,
ka t
r r
r
a
(1)
It is assumed that the temperatures of bottom metal contact and heatsink is same as the one of
ambient (T0); and the boundary conditions:
T (r , t )
T (r , t )

0
r r 0
r r rs
(2)
where r and t denote the radius of oxide aperture (0≤r≤rs) and pulsed portion of a period with
a certain duty cycle, respectively. ka and λa are the thermal diffusion coefficient and effective
thermal conductivity in the layers of the active region, respectively. The temperature
dependence of λa27 is
5
 T 4
a (T )  a (T0 )   0 
T 
(3)
J is the current density, Q(J, r, T) is the heat density, and T(r, t) is the temperature response at
4
the active region in the pulsed portion of a period. T(r, t) can be calculated from Eq. (1) by
using the Green function.26
Following each pulse, the heat generated will be dissipated until the next pulse starts.
Hence, a corresponding reduction in temperature occurs within the active region. According
to the definition of thermal conductivity and heat conduction28, the total heat dissipated from
the active region (Qdis) can be obtained from the equation below:
Qdis    2 r ci
rs
i 1
0
T (r , t )
tdis dr ,
xi
(4)
where λci is the thermal conductivity of the ith layer between the active region and bottom of
the device, xi is the thickness of the ith layer between the active region and bottom of the
device, and tdis is the time distance between two adjacent pulses (= (1 – duty_cycle) × period).
The corresponding reduction in temperature (Tdis) during tdis can be obtained from the
equation29 below:
Tdis 
Qdis
,
mc
(5)
where m and c is the mass and specific heat density of the active region, respectively. The
difference between T(r, t) and Tdis is the temperature response in the active region (ΔT) due to
the self-heating effect. The calculated ΔT is inserted into the rate equation model to
re-calculate ηQD by rate equations list in Appendix. The rate equations are for carrier
concentration in the GaAs barrier, occupation probabilities of each energy state, and photon
density, which are dependent on self-heating.7 Therefore, the calculated ηQD is also
temperature-dependent. Since the generated heat density in the active region7, 26 is dependent
on ηQD, the new ΔT obtained is compared against the original value. This self-consistent
iterative process ends when the solutions to the rate equations and thermal conduction
5
equation converge. The detailed self-consistent theoretical simulation process is found in Ref.
7. The theoretical results are compared with experimental device data to characterize the
influence of self-heating in p-doped QD VCSELs.
III. EXPERIMENTAL PROCEDURE
The layer structure of the 1.3-μm emission p-doped InAs/GaAs QD VCSEL is the same
as that reported in our previous works.16–18 The schematic cross-section diagram and its
scanning electron microscopy (SEM) image are shown in Figs. 1(a) and 1(b), respectively.
The QD-VCSEL structure is grown on n+-GaAs (100) substrate by molecular-beam epitaxy
(MBE). The QD active region is sandwiched within the 24 pairs of p-doped and 33.5 pairs of
n-doped Al0.9Ga0.1As/GaAs DBR mirrors. The p-type and n-type dopant is carbon and silicon,
respectively. 17 layers of p-doped InAs/GaAs QDs are located within the 3 intercavity
region of the QD-VCSEL. As shown in Fig. 1(c), there are five 3-layer QD groups and two
separate QD sheet layers, and each group is located around the antinode position of a
standing wave. The QDs are grown directly on GaAs and capped by a 6-nm-thick
In0.15Ga0.85As layer. Each 5-nm-thick p-doped GaAs layer is grown between two undoped
GaAs layers, whose thickness is 5nm and 12nm, respectively. A 12-nm-thick AlAs layer
embedded in the p-DBR adjacent to the active region is used to form the oxide aperture by
selective wet oxidation. SiNx is deposited as a dielectric layer, and Ti/Au and Ni/Ge/Au metal
are used as p- and n-contact electrodes, respectively. The laser is mounted on a copper heat
sink for light output power vs. injection current (L-I) measurement under pulsed operation.
The top-view of the fabricated device is shown in Fig. 1(d).
6
IV. RESULTS AND DISCUSSION
The 1.3-μm emission p-doped InAs/GaAs QD VCSELs are fabricated with oxide-aperture
area of 5×6 μm2, 7×8 μm2 and 15×15 μm2, respectively. L-I measurements were carried out
under pulsed operation at frequency (f) of 500Hz at different duty cycles, which are 1%, 2%,
5%, 10%, and continuous-wave (CW, 100%). All measurements were performed at room
temperature (RT). Figure 2 shows the measured L-I curves at different duty cycles for devices
with oxide aperture areas of (a) 5×6 μm2, (b) 7×8 μm2 and (c) 15×15 μm2. For the device with
oxide-aperture size of 5×6 μm2 (Fig. 2(a)), the saturated output power is 0.364mW at 7.5mA
under 100% duty cycle (CW operation). If the injected carriers are reduced by lowering the
duty cycle, the saturated output power can be increased up to 0.571mW, which corresponds to
duty cycle of 1% where self-heating is almost eliminated. This shows that with oxide aperture
of 5×6 μm2, the CW output power of the 1.3-μm p-doped InAs/GaAs QD-VCSEL can be
improved by nearly 60% if the self-heating effect can be eliminated completely. The output
power improvement is about 55% and 48% for the devices with oxide aperture area of 7×8
μm2 (Fig. 2(b)) and 15×15 μm2 (Fig. 2(c)), respectively. From Fig. 2, the threshold current did
not show significant dependence on the duty cycle, which is 1.3, 1.5 and 3.5mA
corresponding to these three aperture sizes, respectively. This could be due to the use of
p-doped QDs as the active layer material.18 The minor abnormality in some L-I-V curves’
shape might be due to uncertain conditions during measurement.
The output power performance of the QD-VCSELs with different oxide apertures as
shown in Fig. 2 were simulated using the self-consistent theoretical model. The calculated
maximum output powers Ps are shown in Fig. 3(a) as solid lines, and the experimental results
7
are represented as symbols. Figure 3(a) shows the good agreement between the experimental
results and theoretical simulation. The maximum output power does not vary linearly with
duty cycle. To show the improvement in output power under pulsed operation, the power
improvement ratio (Ps-Ps_cw)/Ps_cw is shown in Fig. 3(b), where Ps_cw is the maximum power
under CW operation. Higher power improvement ratio is achieved for duty cycle less than
10%, indicating that the self-heating effect is reduced when the pulse time is below 0.2ms.
Larger aperture sizes result in lower power improvement, indicating low self-heating effect in
devices with large apertures. This is consistent with the thermal resistance in the VCSEL,
which is calculated30 based on our device configuration and shown in the inset of Fig. 3(b) as
function of the oxide aperture size.
The calculated temperature increase (ΔT) in the active region of the p-doped InAs/GaAs
QD-VCSEL is shown in Fig. 4. It is observed that for devices with the same oxide aperture
size, the variation in ΔT is more evident for duty cycles from 1% to 10%. For devices with
oxide aperture area of 5×6 μm2, the difference in ΔT between 10% and 100% duty cycle is
around 4.67K at injection current of 6mA. Between 1% and 10% duty cycle, the difference in
ΔT increases to 5.45K. The same trend was also observed in devices with oxide aperture
areas of 7×8 μm2 and 15×15 μm2, indicating that self-heating effect is more significant at duty
cycles below 10%. In this region, the dissipated and generated heat densities are comparable,
and any change in the duty cycle will result in significant change in the self-heating effect.
This is consistent with the observation in Fig. 3(b), which shows that the influence of
self-heating on output power is more significant in this region.
Figure 4 shows that self-heating is also dependent on the oxide aperture area. The
8
variation in ΔT at the same current injection and duty cycle differs according to the oxide
aperture area. For oxide aperture area of 5×6 μm2, ΔT is 19.50K at 6mA and 10% duty cycle.
It reduces to 13.21K and 6.42K for oxide aperture areas of 7×8 μm2 and 15×15 μm2,
respectively, at the same injection current and duty cycle. The decrease in ΔT in devices with
large oxide aperture area at the same current injection level is mainly due to the reduction in
current density (J). Smaller J leads to lower heat generation in both the DBR and QD
regions.7, 26 Furthermore, according to Ref. 30 and inset of Fig. 3(b), an effective reduction in
thermal resistance (Rth) can be obtained when the oxide aperture area is enlarged. In this case,
the self-heating effect is less serious, thus resulting in smaller ΔT. The results of different
oxide aperture sizes and duty cycles also show that the variation in ΔT at power saturation
from 30K to 35K is less obvious. For example, for devices with oxide aperture area of 5×6
μm2 at 1% duty cycle, the power saturation occurs at around 10mA and ΔT is 34.12K.
The calculated QD injection efficiencies (ηQD) at different duty cycles and oxide aperture
areas are shown in Fig. 5. It is observed that for devices with the same oxide aperture area
and current injection, there is an obvious difference in ηQD at duty cycles less than 10%. For
example, for devices with oxide aperture area of 5×6 μm2 at 6mA injection current, the
average ηQD variation rate (=
QD
  duty _ cycle 
) is about 2.33×10-4 between 10% and 100%
duty cycle. Between 1% and 10% duty cycle, the average ηQD variation rate increases to 1.77
×10-3. Since ηQD is closely related to the self-heating effect, the high variation rate of ηQD
indicates significant self heating at less than 10% duty cycle for the same oxide-aperture size.
According to the analysis from Fig. 3 and Fig. 4, when heat dissipation is comparable to heat
generation, the change in thermal energy is significant even with slight change in duty cycle,
9
indicating larger variation in carrier thermalization and recombination. As a result, for
devices with the same oxide aperture area, the variation in ηQD is more evident between 1%
and 10% duty cycle under a particular current injection level.
It can be seen that ηQD is also influenced by the oxide aperture area. For example, ηQD is
0.746 for devices with oxide aperture area of 5×6 μm2 at 6mA injection current and 10% duty
cycle. ηQD increases to 0.767 and 0.825 for oxide aperture areas of 7×8 μm2 and 15×15 μm2,
respectively, at the same injection current and duty cycle. Similar to the analysis from Fig. 4,
for devices with larger oxide aperture area at the same duty cycle, the increase in ηQD is
mainly attributed to the reduction in current density (J). Since heat generation is reduced7, 26
at smaller J, the influence of self heating on carrier confinement is less significant.
Furthermore, according to Ref. 30 and inset of Fig. 3(b), an effective reduction in the thermal
resistance (Rth) can be obtained when the oxide aperture area is larger, thus improving the
carrier confinement and thermalization. Therefore at the same duty cycle, higher ηQD can be
obtained in devices with larger oxide aperture areas.
V. CONCLUSION
In conclusion, we have investigated the influence of self-heating on output power
performance of 1.3-μm InAs/GaAs QD VCSELs under pulsed operation. At room
temperature and frequency of 500Hz, the self-heating effect is reduced significantly and
higher output power can be achieved when the current injection time is less than 0.2ms. For
devices with oxide-aperture area of 5×6 μm2, the CW operation power can be improved by
nearly 60% if the self-heating effect can be eliminated completely The influence of
10
self-heating on output power is less serious in devices with larger oxide-aperture area. A
similar trend is also observed in the analysis of temperature response at the active region and
QD injection efficiency.
ACKNOWLEDGEMENT
The authors acknowledge the financial support from the A*STAR Singapore-Poland
Bilateral Program, SERC Grant No. 0621200015.
APPENDIX
The set of rate equations in our model includes six equations, which are for carrier
concentration in the GaAs barrier (NB), occupation probabilities of a wetting layer (WL)
quantum state (fw), the QD second excited state (f2) , first excited state (f1) , and ground state
(f0), and photon density (S), respectively. The six equations are shown below from (A1) to
(A6).
dN B
J
1 ng w f w
1
1


(1  f B )  (  ) N B ,
dt
qb t ewb b
t bw t rB
(A1)
2
2 p 
 f
df w (1  f w ) N B b f w


   i Esiw f i (1  f w )  Rwi f w (1  f i )  w ,
dt
ng w t bw t ewb i 0  g w
 t rw
(A2)
1
p
 f
g
df 2
 w Rw2 f w (1  f 2 )  Es2 w f 2 (1  f w )    i Esi 2 f i (1  f 2 )  R2i f 2 (1  f i )  2 , (A3)
dt 2 p2 
i 0  p2
 tr 2
p

g
df1
 w Rw1 f w (1  f1 )  Es1w f1 (1  f w )   2 R21 f 2 (1  f1 )  Es12 f1 (1  f 2 )
dt 2 p1 
 p1

p
 f
  0 Es01 f 0 (1  f1 )  R10 f1 (1  f 0 )  1 ,
 p1
 t r1
(A4)
2
p
  g

df 0
   i Ri 0 f i (1  f 0 )  Es0i f 0 (1  f i )   w Rw0 f w (1  f 0 )  Es0 w f 0 (1  f w )
dt i 1  p0
  2 p0 

11

 g g max ( f 0e  f 0 h  1) S
f0
1
,

t r 0 2 p0 nS a 
1  S
dS  g g max ( f 0 e  f 0 h  1) S S

 .
dt
1  S
tp
(A5)
(A6)
where in Eq. (A1), t, J, q, b, and n are time, the injected current density, electronic charge,
total thickness of GaAs barrier in the active region, and number of QD layers, respectively. fB
is carrier occupation probability in the barrier. tewb is the carrier escape time from WL or cap
layer (CL) to the GaAs barrier. tbw is the carrier transport time from doped DBR layer to the
nearest WL (CL). trB is the carrier lifetime in the barrier; and gw is a parameter that describes
the carrier concentration in the WL or CL.
In Eq. (A2), Nd is the effective modulation doping concentration, which is equal to the
product of the nominal doping concentration and QD cover rate, tbd is the hole transport time
from the doped layer to the WL (CL), ρ is the QD surface density, pi (i = 0, 1, 2) is the
degeneracy of the QD levels, where p0 = 1, p1 = 2, p2 = 4, Rwi is the relaxation rate from the
WL (CL) to the QD levels, Esiw is the corresponding escape rate, and trw is the carrier lifetime
in the WL (CL). Here i = 0, 1 and 2 represent the ground state, first and second excited state
of the QDs, respectively.
In Eq. (A3) – (A6), Rij (i, j = 0, 1, 2) is the relaxation rate between two QD levels, Esji is
the corresponding escape rate, and tri (i = 0, 1, 2) is the carrier life time in different QD levels.
S is the photon number in the optical cavity, and Sa, υg, gmax and gth are the area of the active
region, group velocity, maximum modal gain and threshold modal gain, respectively. (f0e + f0h
-1) is degree of population inversion, the calculation process is shown in Ref. 7. In Eq. (A5) (A6), Va is the volume of all QDs and Г is the optical confinement factor. ε = εmГ/Va, where
12
εm is the nonlinear gain coefficient which can be expressed as:31
2
Pcv
q
1
m  2
tp
nr m0 0 m0 E L Fho
(A7)
h
, h is Planck constant, nr is refractive index of active material, m0 is rest mass of
2
electron, ε0 is absolute permittivity in vacuum, EL is lasing energy. Fho is the full-wave
where 
half-magnitude (FWHM) of the homogeneous broadening of the QDs, t p 
1
is the
 g g th
2
photon lifetime. Pcv is the transition matrix, and Pcv is ~2m0EL for InAs QDs.32
By solving the rate equations (A1)–(A6), we obtain the carrier surface density in the
barrier nB, WL (CL) carrier surface density nw, and QD levels ni (i =0, 1, 2) at steady state,
which represent the radiative recombination carrier density. nB, nw and ni (i =0, 1, 2) can be
expressed as:
nB 
t
1
bw
1
J ng f
(  w w)
1
t ewb
 t rB q
nw  ng w f w
(A8)
(A9)
ni  2npi f i
(A10)
The QD injection efficiency of QD VCSEL can be approximated as:
2
 QD 
n
i 0
i
2
n B  n w   ni
(A11)
i 0
The output power of the QD VCSEL can be obtained using the relationship between power
and photon number:31
Pout  E L m g S
(A12)
where EL, αm and υg are the lasing energy, mirror loss and group velocity, respectively. S can
be obtained from equations (A6), (A7), and the formula on QD material gain:31, 32
13
S  2.35 2 nSa 
Fho
[( f 0 e  f 0 h  1)  fth ]
Fin
(A13)
where Sa is the active region area and ρ is the QD surface density. Fho and Fin are the
full-width at half maximum (FWHM) of homogeneous and inhomogeneous broadening of the
QDs, respectively, and (f0e+f0h-1) is the degree of population inversion. fth is the threshold
population inversion of the QD VCSEL, which is the ratio of threshold modal gain gth and
maximum modal gain gmax. 7
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16
LIST OF FIGURE CAPTION
FIG. 1. (a) Schematic cross-section diagram; (b) scanning electron microscopy (SEM) image;
(c) the distribution of QD layers in the cavity; (d) fabricated device of 1.3-µm InAs/GaAs QD
VCSEL.
FIG. 2. L-I characteristics of QD VCSELs at different pulsed duty cycles for oxide aperture
area: (a) 5×6 μm2, (b) 7×8 μm2, and (c) 15×15 μm2.
FIG. 3. (a) Maximum output power at different duty cycles and oxide-apertures; (b)
Improvement on maximum output power by controlling the pulsed duty cycles and
oxide-aperture sizes. Inset shows the thermal resistance as function of oxide-aperture size.
FIG. 4. Plots of temperature increase due to self-heating effect in the active region of 1.3-µm
p-doped InAs/GaAs QD VCSELs at different duty cycles and oxide apertures.
FIG. 5. QD injection efficiency of 1.3-µm p-doped InAs/GaAs QD VCSELs at different duty
cycles and oxide apertures.
17
(c)1.0
QD Layers
(d)
Emission
0.8
2
E
0.6
P-contact
0.4
0.2
0.0
-2000
0
2000
Optical thickness
FIG. 1. (a) Schematic cross-section diagram; (b) scanning electron microscopy (SEM) image;
(c) the distribution of QD layers in the cavity; (d) fabricated device of 1.3-µm InAs/GaAs QD
VCSEL.
18
0.6
(a)
Output Power (mW)
0.5
1%
0.4
10%
0.3
5%
2%
100%
0.2
5x6 m2, RT
f = 500 Hz
0.1
0.0
0
2
4
6
8
10
12
I (mA)
Output Power (mW)
1.0
1%
(b)
2%
0.8
100%
0.6
5%
10%
0.4
7x8 m2, RT
f = 500 Hz
0.2
0.0
0
2
6
8
10
12
I (mA)
1.8
(c)
1.6
Output Power (mW)
4
1%
2%
1.4
5%
1.2
10%
1.0
100%
0.8
0.6
0.4
15x15m2, RT
f = 500 Hz
0.2
0.0
0
5
10
15
20
25
30
I (mA)
FIG. 2. L-I characteristics of QD VCSELs at different pulsed duty cycles for oxide aperture
area: (a) 5×6 μm2, (b) 7×8 μm2, and (c) 15×15 μm2.
19
RT, f = 500 Hz.
2
5x6m
2
7x8m
2
15x15m
1.4
1.2
15x15m
1.0
2
7x8m
2
0.8
0.6
0.4
(a)
5x6m
1
2
10
100
Duty Cycle (%)
RT, f = 500 Hz
5x6 m
2
7x8 m
2
15x15 m
2
50
40
30
Thermal Resistance (K/W)
Maximum Output Power Ps (mW)
1.6
60
(Ps-Ps-cw)/Ps-cw (%)
Symbols shows measurement results;
solid lines are simulation results.
1.8
3
7x10
3
6x10
3
5x10
3
4x10
3
3x10
3
2x10
3
1x10
0
5
10
15
20
Radius of Oxide Aperture (m)
20
10
(b)
0
10
20
30
40
50
60
70
80
90 100
Duty Cycle (%)
FIG. 3. (a) Maximum output power at different duty cycles and oxide-apertures; (b)
Improvement on maximum output power by controlling the pulsed duty cycles and
oxide-aperture sizes. Inset shows the thermal resistance as function of oxide-aperture size.
20
7 x 8 m
2
5 x 6 m
2
40
RT
35 f = 500 Hz
30
T (K)
25
20
15 x 15 m
2
15
10
Solid Lines: 100% Duty Cycle
Solid Symbols: 10% Duty Cycle
Hollow Symbols: 1% Duty Cycle
5
0
0
5
10
15
20
25
I (mA)
FIG. 4. Plots of temperature increase due to self-heating effect in the active region of 1.3-µm
p-doped InAs/GaAs QD VCSELs at different duty cycles and oxide apertures.
21
Injection Efficiency (QD)
1.00
RT
Solid Lines: 100% Duty Cycle
f = 500 Hz Solid Symbols: 10% Duty Cycle
Hollow Symbols: 1% Duty Cycle
0.95
0.90
0.85
15x15m2
0.80
0.75
0.70
0.65
5 x 6 m
2
0.60
0
5
10
7 x 8 m
2
15
20
25
I (mA)
FIG. 5. QD injection efficiency of 1.3-µm p-doped InAs/GaAs QD VCSELs at different duty
cycles and oxide apertures.
22