Optics and Photonics Journal, 2013, 3, 248-251
doi:10.4236/opj.2013.32B058 Published Online June 2013 (http://www.scirp.org/journal/opj)
Base Width Variations and its Effects on Frequency
Response of Double Hetero-structure Long Wavelength
Transistor Laser
Mohammad Reza Farjadian, Hassan Kaatuzian, Iman Taghavi
Photonics Research Laboratory (PRL), Electrical Engineering Department, Amirkabir University of Technology, Tehran, Iran
Received 2013
ABSTRACT
In this paper we investigate the effects of base width variation on performance of long wavelength transistor laser. In
our structure with increasing the base width, the cut off frequency increases until 367 nm with 24.5 GHz and then
abruptly fall. In 100 nm base width, we have 17.5 GHz cut off frequency, and overall ac performances become opti-
mized, although, other parameters like optical losses and threshold current density are not optimized.
Keywords: Transistor Laser; Quantum Well; Long Wavelength; Optical Confinement Factor
1. Introduction
Transistor lasers (TL) have been recently received con-
siderable attentions due to their promising applications in
photonic and optoelectronic circuits [1]. Incorporated
within the base region of the TL is one (or more) quan-
tum wells QW, which plays an important role in device
behavior. Using carrier confinement within the QW re-
gion, stimulated emission in room temperature with
lower threshold current density can be achieved. Re-
cently, multiple QW-TLs have been shown for their su-
perior optical and electrical performances. Among other
key structural factors affecting on the device perform-
ance is the position of the active region [2]. Since the
first successful demonstration of the laser emission (1μm
wavelength) at room temperature in 2006 [3] using
strained InGaAs QW in GaAs base layer, several ex-
perimental and theoretical studies have been appeared in
literature, albeit for the same emission wavelength, i.e.
near IR. In order to take the full advantage of TLs for
directly-modulated high-speed systems, however, we
need laser emission with wavelengths around 1.3μm for
minimum dispersion or 1.55μm for minimum attenuation
[4], called Long Wavelength Transistor Laser (LWTL).
Despite their similarities in behavior and structure, the
TLs differ from the conventional diode lasers (DL), par-
ticularly in terms of highly-doped base region. Figure 1
schematically displays the structure of our LWTL.
We have assumed N-InP/p–In0.53(Al0.4Ga0.6)As0.43/N-InP
double Hetero-structure TL in which the base and emit-
ter/collector regions are treated as the waveguide and the
cladding layers, respectively. An undoped, compressively
strained In0.58Ga0.42As QW of 8 nm is placed in the mid-
dle of the base region.
In the following section, we first explain our calcula-
tion approach has been described. The simulation results
for optical confinement factor, optical losses and fre-
quency response are shown and discussed in section
three. We also use experimental data to compare our re-
sults with other works [5]. Finally, we conclude in sec-
tion 4.
Figure 1. Structure of Transistor Laser in our model.

M. R. FARJADIAN ET AL. 249
2. Model
2.1. Description
Under forward bias condition, the minority electrons are
injected from emitter to the base region where they dif-
fuse toward the collector junction. Carriers capture by
QW into the QW results in a discontinuity in the slope of
carrier density profile. Assuming direct gap material for
the QW, the captured electrons can be radiatively recom-
bined with holes to produce stimulated emission if elec-
tron density reaches the threshold value [6].
2.2. Parameter
Illustrate in Figure 2 is the charge control model for
LWTL in which we assumed the base width (WB) is the
main variable in this work. The width of QW is Wqw and
its distance from emitter junction is Xqw. In addition, we
located the QW in the middle of the base region to ensure
symmetric beam profile for the TL. NB and Nqw are the
base doping concentration and the bounded carrier den-
sity in QW, respectively.
Bulk charge life time, τrb0, is the recombination life
time of carriers in the base region except QW. It related
to the bimolecular radiative recombination coefficient,
Brad [7]:
0
1
rb rad B
BN
  (1)
Electron capture time in QW, τcap, includes the transit
time of electrons from emitter junction to the edge of
QW and their capture by the QW. Assumed uniformed
diffusion constant throughout the base region [8], the
first term in τcap can be calculated as:
2
2
qw
cap
X
D
  (2)
Figure 2. Charge control model for LWTL.
where D is the diffusion constant. The second term is a
small time (<1 ps) which is necessary for electrons to be
captured to the virtual states of the QW.
Effective recombination lifetime in QW, τqw
eff is rela-
tive to stimulated emission life time (τst) and spontaneous
emission life time (τqw) [6]:
111
eff qw st
qw

 
 (3)
3. Results
As previously described, we focused on the base width
variations and its effects the TL behavior including the
optical confinement factor and optical loss. Other struc-
tural parameters have been extracted from experimental
data [5].
3.1. Optical Confinement Factor
Optical Confinement Factor (OCF) has significant im-
pact on the DC and AC characteristics of LWTLs. One
can distinguish between two separate waveguides, one of
them related to QW and the other related to the rest of
the base region.
Using a modified approach similar to the method de-
scribed by [9], we calculated the OCF values for afore-
mentioned regions of QW and base region. The results
are illustrated in Figure 3 as a function of the base width.
It is evident that large waveguide results in higher values
for the OCF.
3.2. Optical Losses
The optical losses of the base region can be individually
04080120 160 200 240280 320 360 400
10
-1
10
0
10
1
10
2
W
B
(nm )
Optical Confinment Factor ,

( % )
Waveguide
Quantum Well
Figure 3. Optical Confinement Factor variations due to
base width variations.

M. R. FARJADIAN ET AL.
250
calculated for intrinsic loss due to inter valence band
absorption and mirror loss. Mirror loss can be simply
calculated by:
12
11
ln
2
mLRR





B
(4)
where R1, R2 are the facet reflectivity and L is cavity
length. Using experimental sample parameters, we have
assumed R1= R2 = 0.3 and cavity length of 800μm.
On the other hand, the intrinsic loss in active region
related to optical confinement factor in QW (ΓQW) and
waveguide (ΓWG) which reads:

P
iWGQW
kN    (5)
where NB is the base doping concentration, kP is the inter
valence band absorption (IVBA) coefficient. We as-
sumed kP = 4×10-17 cm-2 and NB = 1×1019 cm-3 as the
base doping concentration while OCF for QW and
waveguide is varied with the base width.
The total optical losses can be, therefore, calculated as
the sum of intrinsic and mirror losses:
Tmi

  (6)
As can be seen in Figure 4, an increase in the base
width can cause more optical loss in the base region.
3.3. Frequency Response
We used the procedure that was described in [6] to simu-
late the frequency response of the device in conjunction
with the approach described in [7] for calculation of pa-
rameters. The results are illustrated in Figure 5.
0255075100 125 150 175 200
101
102
103
104
105
W
B
(nm )
Intrinsic Optical Loss,

(m
-1
)
N
B
= 5 * 10
18
cm
3
N
B
= 1 * 10
19
cm
3
N
B
= 1. 5 * 10
19
cm
3
Figure 4. Intrinsic optical loss variation due to base width
variation.
Frequency response of LWTL has significant effects
on performance and application of LWTL. In Figure 5
we see that in base width lower than 100 nm, the maxi-
mum of absolute amplitude of frequency response be-
comes lower, and also has lower cut off frequency.
In upper 100 nm base width, the frequency response
become sharp but cut off frequency become larger.
According to the Figure 6 we see a discontinuity on
the cut off frequency around 367 nm base widths in this
structure. With increase of base width above 100 nm, the
frequency response becomes worse. Also the type of
system can be changed. In base width above 367 nm, we
have band pass filter and under that amount, we have low
pass filter. In design of LWTL we have trade-off be-
tween several performances and applications of LWTL,
but this is reasonable using 100 nm for base width.
015 20 30 4050
-50
-40
-30
-20
-10
0
10
20
Frequenc y (GHz)
M odulat ion Res pons e (dB )
Figure 5. Frequency response of LWTL with different base
width.
0100 200 300 400 500 600 700
0
5
10
15
20
25
Frequenc y (GHZ )
W
B
( nm )
N
B
= 1 * 10
19
cm
3
N
B
= 1. 25 * 10
19
cm
3
N
B
= 1. 5 * 10
19
cm
3
Figure 6. Cut frequency of LWTL with different base width.

M. R. FARJADIAN ET AL.
251
According to the Figure 6 we see a discontinuity on
the cut off frequency around 367 nm base widths in this
structure. Also, with change base doping concentration
(NB) this base width changed but discontinuity on cut off
frequency exist. With increase of base width above 100
nm, the frequency response becomes worse. Also the
type of system can be changed. In base width above 367
nm, we have band pass filter and under that amount, we
have low pass filter. In design of LWTL we have trade-
off between several performances and applications of
LWTL, but this is reasonable using 100 nm for base
width.
4. Conclusions
In transistor laser, like conventional transistor used in
electrical circuits, base width has significant effect on
AC and DC performance of device. Change in base
width causes to change several parameter of transistor,
like frequency response, transient response, and DC
characteristic of device. For the verification of our model,
we use an experimental structure with emission wave-
length of 1.55μm. We changed base width and observed
its effects on optical confinement factor and optical loss
and frequency response. With increase of base width,
OCF become better but optical loss increases, so we
cannot increase base width so much. In frequency re-
sponse, with increase base width we have discontinuity
in cut off frequency around 367 nm and electron transient
time and bulk recombination become dominant. In near
367 nm base width we have 24.5 GHz cut off frequency
which is the maximum value it can reach. But the fre-
quency response has not suitable form because of sharp
response. Also the type of filter in this system become
change and in base width above 367 nm we have band
pass filter with sharp response. In design and also by
trade off with this result and figures, 100 nm base widths
have optimum performance, but with different applica-
tions it can be changed. In this base width we have 17.5
GHz cut off frequency.
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