APPLIED PHYSICS LETTERS 93, 143503 共2008兲
Common-emitter and common-base small-signal operation
of the transistor laser
B. Faraji,a兲 W. Shi, D. L. Pulfrey, and L. Chrostowski
Department of Electrical and Computer Engineering, University of British Columbia,
Vancouver, British Columbia V6T 1Z4, Canada
共Received 1 August 2008; accepted 16 September 2008; published online 9 October 2008兲
We derive analytic expressions for the transistor laser in the common-emitter and common-base
configuration and compare the performance of the transistor in these two modes of operation. We
show that the common-base operation results in a wide-band, small-signal modulation response.
This effect is due to reduced carrier lifetime in the base. The bandwidth equalization and the
suppression of the relaxation oscillation frequency are shown. A bandwidth of 48 GHz is predicted
for a vertical cavity laser biased at 10Ith. © 2008 American Institute of Physics.
关DOI: 10.1063/1.2998267兴
In the transistor laser 共TL兲, a quantum well 共QW兲 is
embedded in the base of a heterojunction bipolar junction
transistor 共HBT兲 and acts as an optical collector. The stimulated recombination changes the characteristics of the transistor and the laser, e.g., compression in the I-V characteristics of the transistor,1 decrease in the current gain of the
transistor 共␤stim ⬍ ␤spon兲, and modified carrier dynamics. One
interesting feature of the TL is the potential for an enhanced
small-signal modulation bandwidth due to the reduced carrier lifetime in the base region. The reduced carrier lifetime
is due to the reverse biased base-collector junction, which
introduces a gradient in the carrier concentration 共as shown
in Fig. 1兲. The physical parameter associated with this slope
is the base transit time 共␶t兲, which is the average time an
electron spends in transit across the base. In Ref. 2 the authors present a model based on the charge control method
and laser rate equations, which predicts a large intrinsic
modulation bandwidth in the common-emitter configuration.
However the model does not differentiate between the bulk
carriers and the QW carriers in the rate equation and does not
include the effects of the capture and escape lifetimes in the
QW,3,4 and significantly overestimates the bandwidth, i.e., a
3 dB bandwidth of 70 GHz for an edge emitting TL. By
using the concept of virtual states,5 a useful amalgamation of
the laser rate equations and the diffusion equation can be
obtained.6 This formulation is needed to correctly predict the
modulation bandwidth observed in experimental devices in
the CE configuration.7 In this work, analytical expressions
for the small-signal modulation of a TL in the common-base
共CB兲 and common-emitter 共CE兲 configurations are developed and their performances are compared. We demonstrate
that the TL modulated in the CB configuration can have a
bandwidth equalization, which significantly increases the 3
dB modulation bandwidth and its response has suppressed
relaxation oscillations.
We consider a npn HBT. The transistor is operating in its
normal, active mode, i.e., the base-emitter junction is forward biased and base-collector junction is reversed biased.
Figure 1 shows the conduction energy band of the base and
the dc excess minority carrier distribution ␦N共x兲. The carriers
injected from the emitter diffuse across the base and reach
a兲
Electronic mail: behnamf@ece.ubc.ca.
0003-6951/2008/93共14兲/143503/3/$23.00
the QW. These unbounded carriers may undergo quantum
capture to the bound states in the QW with a lifetime of ␶cap,
or diffuse across to the collector where they are swept out by
the reverse-biased base-collector junction. The carriers may
escape the QW with a lifetime ␶esc. The unbounded carriers
at x = 0 are located at the virtual bound states. These states
are localized at the QW but occupy energies higher than the
conduction energy edge of the barrier material and aid in the
conversion of carriers from the three-dimensional states
above the well to the two-dimensional 共2D兲 states within the
QW 共NQW兲 and vice versa.5
Considering that diffusion is the dominant mechanism
for transport across the base, we solve the small-signal diffusion equation
j ␻␦n = D
⳵ 2␦ n ␦ n
− ,
⳵ x2 ␶B
共1兲
subject to the boundary conditions
je = eD
d␦n
dx
x = − WB/2,
共2兲
jc = eD
d␦n
dx
x = WB/2,
共3兲
␦n共0−兲 = ␦n共0+兲 = n0 ,
共4兲
FIG. 1. 共Color online兲 Schematic of carrier diffusion and quantum capture
in the QW and the conduction band energy diagram of the base region. The
emitter is at the left side of the base 共x ⬍ −WB / 2兲 and the collector is at the
right side 共x ⬎ WB / 2兲.
93, 143503-1
© 2008 American Institute of Physics
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
␦n
Appl. Phys. Lett. 93, 143503 共2008兲
Faraji et al.
冉 冊
WB
= 0,
2
j0 = eD
␦n共0−兲
dx
共5兲
Parameter
− eD
␦n共0+兲
dx
共6兲
,
and the current relation of the transistor 共je = jc + jb兲. Solutions for je and jb are obtained.
冉
W
2 B
eD
WB cosh 2Ld
sinh
+
j e = n0
Ld
2Ld sinh WB
2Ld
jb = 2n0
冊
+ j0 cosh
eD
WB
WB
sinh
+ j0 cosh
.
Ld
2Ld
2Ld
WB
,
2Ld
共7兲
共8兲
In Eqs. 共1兲–共8兲: ␦n共x兲 is the small-signal excess carrier distribution inside the base, ␻ is the angular modulation frequency, ␶B is the carrier recombination lifetime, D is the
diffusion coefficient in the base, je is the emitter current, jc is
the collector current, WB is the base width, n0 is the virtual
states carrier concentration, and j0 is the current to the virtual
state due to diffusion. Ld is the modified frequencydependent diffusion length: L2d = 共D␶B兲 / 共1 + j␻␶B兲. At high
frequencies the diffusion can be a limiting factor as the diffusion length decreases with frequency.
The rate equations describing the QW current, virtual
states, QW bound states, and photon concentrations are
jqw n0 nqw
=
−
,
ed ␶cap ␶esc
j ␻n0 =
共9兲
j0 jqw n0
−
− ,
ed ed ␶S
j␻nqw =
TABLE I. Model parameter values used in the simulations.
冉 冊 冉
冉 冊
共10兲
冊
1
1
jqw
−
s−
+ AS0 nqw ,
ed
⌫␶ P
␶S
共11兲
⑀S0
s.
␶P
共12兲
j␻s = 共⌫AS0兲nqw −
In Eqs. 共10兲–共12兲, d is the QW width, ␶S is the spontaneous
emission lifetime, jqw is the current from the virtual states to
the 2D bound states within the QW, s is the photon density, A
is the differential gain of the active layer with respect to the
bounded carrier density 共A ⬅ vgdG / dNQW兲, ⌫ is the optical
confinement factor, S0 is the DC photon density, ⑀ is the gain
compression factor, and ␶ P is the photon lifetime.
The numerical values used in the model are summarized
in Table I. The values are chosen for a typical vertical cavity
surface emitting laser.
Figure 2 shows the 3 dB bandwidth 共BW兲 variation in
the CE and CB configurations as a function of the bias current 共IB兲. At low bias currents both configurations show
almost the same BW. As IB increases the BW of the CB
configuration increases rapidly while the BW of the CE
configuration saturates, as in the case of a regular separate
confinement heterostructure laser.8 The BW enhancement is
due to the different types of carriers used in the modulation
of the CE and CB, i.e., holes in the CE case and electrons in
the CB case. This difference can be understood from transistor charge control analysis9 where the small-signal base
current is related to stored charge in the base region through
␶S
␶B
␶cap
␶esc
␶P
d
WB
D
⌫
A
⑀
Area
Transistor laser
Unit
Source
200
200
1
10
4
10
100
26
0.05
1 ⫻ 10−5
1.5⫻ 10−17
16␲
ps
ps
ps
ps
ps
nm
nm
cm2 / s
¯
cm3 s−1
cm3
␮m2
Ref. 10
Ref. 2
Ref. 8
Ref. 8
Ref. 10
Ref. 10
Ref. 2
Refs. 2 and 9
Ref. 10
Ref. 10
Ref. 10
Ref. 10
the carrier recombination lifetime 共␶B兲, while the smallsignal emitter current is dependent on the transit time
共␶t = WB2 / 2D兲, which is in the range of 10−12 s. Two mechanisms, carrier transit through the base and stimulated emission, work in parallel to reduce the carrier effective lifetime
in the base region, thereby enhancing the small-signal BW in
the CB case.
Figure 3 shows the typical small-signal modulation response of the CB and CE configurations as the bias current is
increased. There are three main differences between CE and
CB modulation responses. First is the slope of the curves at
frequencies above the resonance: the CE configuration has a
−60 dB/ decade slope while the CB configuration shows a
slope of −40 dB/ decade at frequencies ⬍100 GHz. This
difference is due to the shift in the carrier dynamics-induced
parasitic pole of the CB configuration transfer function to
higher frequencies. The second difference is the dc gain
value: the CE configuration has a higher dc gain than the CB
configuration. Finally in the CE configuration curves, as the
bias current increases, the damping increases and the peak
corresponding to the relaxation oscillation frequency diminishes; at high bias currents, overdamping due to the gain
compression is the limiting factor which saturates the BW. In
the CB configuration, the peak corresponding to the relax50
40
Bandwidth (GHz)
143503-2
Common−Base
10Ith
30
20
1.1Ith
Common−Emitter
10
0
0
2
4
6
8
IB (mA)
10
12
14
16
FIG. 2. 共Color online兲 BW variation in the CB and CE configuration in the
transistor laser. The bias current for both configurations is varied from IB
= 1.1IB,th to IB = 10IB,th. A BW of 48 GHz is obtained for the CB configuration at IB = 10IB,th, while the maximum BW of the CE configuration is 17
GHz.
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
143503-3
Appl. Phys. Lett. 93, 143503 共2008兲
Faraji et al.
−15
−20
15
IB=3 mA
Common−Emitter
−30
−35
I =15 mA
B
16.4dB
−60 dB/dec
Transistor Gain (β, dB)
Transfer Function (dB)
−25
16dB
I =3 mA
B
−40
IB=15 mA
−45
Common−Base
−50
−55
−60
−65
1
−40 dB/dec
∆ IB=3 mA
10
5
14GHz
0
10
Frequency (GHz)
100
FIG. 3. 共Color online兲 Transfer function for the small-signal modulation of
the transistor laser considering both the CE and CB configurations. The bias
current for both configurations is varied from IB = 2IB,th to IB = 10IB,th.
ation oscillation is critically damped and the curves are flat;
most importantly there is no gain compression effect in the
CB configuration small-signal response.
Figure 4 shows the small-signal current transfer function
of j0 / jb 共the virtual states current to the base current兲, jqw / jb
共the QW current to the base current兲, j0 / je 共the virtual states
current to the emitter current兲, and jqw / je 共the QW current to
the emitter current兲 as a function of frequency. The very
interesting feature of the CB configuration is the presence of
the second resonance, which broadens the response. We believe that this resonance originates from the interplay between the base carriers and QW carriers. The dc value of the
current ratio in the CB configuration is smaller than in the
CE configuration due to the transistor gain available when
the base is modulated. A gain-bandwidth product is observed, where a higher bandwidth is obtained with the
tradeoff of a lower RF gain.
71GHz
−5
1
10
Frequency (GHz)
100
FIG. 5. 共Color online兲 Current gain of the transistor laser 20 log共␤兲. A DC
gain of 14.6dB 共=5.3兲 and f T of 71 GHz are observed. The device is biased
at IB = 10IB,th.
Figure 5 shows the small-signal transistor current gain
共␤ = ic / ib兲. This gain-frequency plot of the transistor shows a
decreasing gain at high frequencies with a f T equal to 71
GHz. The dc gain is approximately equal to the difference of
the base and emitter modulation transfer function.
In conclusion, the small-signal modulation bandwidth of
the CB configuration of the transistor laser can be much
larger than both the CE transistor laser and conventional laser diodes reported thus far. However, the dc gain of the CB
configuration is smaller than the CE configuration with the
difference being the transistor gain. Adding a wide-band amplifier stage at the emitter 共the cascode configuration兲 could
compensate the gain drop of the CB configuration. By engineering the device and epitaxy parameters, the BW of the CB
configuration may be enhanced further.
0
1
Current Ratio (dB)
−5
Common−Emitter
−10
−15
−20
1
Common−Base
10
Frequency (GHz)
100
FIG. 4. 共Color online兲 Transfer function of the current ratios for the CE
configuration 共dashed curve兲 and CB configuration 共solid lines兲. For each
configuration two plots are shown: one for virtual state currents 共blue
curves兲 and the other for QW current 共red curves兲. At high frequencies
because of the carrier dynamics 共carrier diffusion, capture, and escape兲 all
transfer functions roll over. The device is biased at IB = 10IB,th for both
configurations.
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