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IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 51, NO. 5, MAY 2004
Reduction of Base-Transit Time of InP–GaInAs
HBTs Due to Electron Injection From an Energy
Ramp and Base-Composition Grading
Gal Zohar, Shimon Cohen, Victor Sidorov, Arkady Gavrilov, Benny Sheinman, and Dan Ritter, Member, IEEE
Abstract—The dc current gain of InP–GaInAs heterojunction
bipolar transistors with varying base thickness and composition
was measured. Much larger composition grade values than previously reported were achieved using strain compensation. A simple
two-parameter Monte Carlo simulation was developed to interpret the results. The simulation yields an accurate plot of the base
transit time versus base thickness. Clear evidence for the reduction
of base transit time due to hot electron injection was observed in
devices with thin uniform bases. The current gain of 45-nm-thick
graded base devices saturated as the grading was increased beyond
standard values. Grading did not increase the gain of devices with
a 20-nm-thick base.
Index Terms—Base-composition grade, base-transit time, heterojunction bipolar transistor (HBT).
I. INTRODUCTION
II. BASE TRANSPORT THEORY
A. Base-Transit Time: Thermal Injection From the Emitter
Expressions for the base-transit time in thin-base bipolar
junction transistors (BJTs) with no energy ramp at the emitter
can be obtained by directly solving the Boltzmann transport
equation [6] or by the scattering theory (flux method) [7]. Both
methods yield similar results. The flux method result
(1)
is simple to use. In (1),
is the base-transit time,
the base
is the electron diffusivity. The velocity
is
width, and
given by
R
EDUCTION OF base-transit time in heterojunction
bipolar transistors (HBTs) due to injection of electrons
from an abrupt energy ramp was proposed by Kroemer long
before advanced HBTs were demonstrated [1], [2]. However,
today’s speed records of InP HBTs are obtained with either
abrupt or graded base–emitter junctions, namely with and
without injection from an energy ramp [3]–[5]. It thus appears
that the injection of energetic electrons does not substantially
improve the high-frequency performance of HBTs having base
thicknesses larger than 30 nm. Base-composition grading [1],
on the other hand, is widely used in advanced HBT structures,
and is believed to improve device performance.
In this paper, we study the benefits of electron injection from
an energy ramp and base composition grading by measuring
the dc current gain of devices with varying base width and
composition. It is found that electron injection from an energy
ramp significantly reduces base-transit time only in bases that
are less than 30 nm thick. A much more significant reduction
of the base-transit time is obtained by composition grading of
30–50-nm-thick bases. An important but unexplained observation is that contrary to the prediction of theory, the composition
grading effect saturates. No further reduction of the base-transit
time is obtained for grade values larger than 10%.
Manuscript received October 28, 2003; revised February 4, 2004. The review
of this paper was arranged by Editor J. N. Burghartz.
The authors are with the Department of Electrical Engineering, Technion,
Haifa, 32000 Israel.
Digital Object Identifier 10.1109/TED.2004.826828
(2)
is the electron effective mass, Boltzmann’s conwhere
stant, and the temperature. In Ga In As at room temcm/s.
perature
An alternative method for solving the Boltzmann transport
equation in the base layer of BJTs is a single-parameter Monte
Carlo simulation [8]. The simulation calculates the impulse response of the base by recording the transit time of each electron injected from the emitter. The momentum distribution of
the injected electrons at the base–emitter junction is a velocity
weighted Maxwellian [9]. The single parameter of the simulation is the momentum relaxation rate, which is obtained from
the electron diffusivity. A momentum relaxation event is modeled by a Gaussian momentum distribution and the rate of momentum relaxation events is determined by Poisson statistics.
We have simulated base transport in BJTs using this approach,
and compared the results to (1). For long and short bases, i.e.,
when either the first term or the second term in (1) dominates,
the simulation reproduces the results of (1). For the transition
region between long and short bases, the base-transit time obtained from the simulation is up to 12% longer than that given
by (1). As mentioned in [6] and in [7], the analytic results are
an approximation, which depends on the particular choice of the
boundary conditions. It is therefore not surprising that the results
of the Monte Carlo simulation are not identical to the analytic
expression.
The above discussion elucidates that the electron diffusivity is
the key parameter that determines the base-transit time in BJTs.
0018-9383/04$20.00 © 2004 IEEE
ZOHAR et al.: REDUCTION OF BASE-TRANSIT TIME OF InP–GaInAs HBTs DUE TO ELECTRON INJECTION
659
TABLE I
REPORTED VALUES OF ELECTRON DIFFUSION COEFFICIENT IN P-TYPE GaInAs
It was measured and calculated in heavily doped p-type GaInAs
by several authors, as summarized in Table I. The most relevant and precise experimental result is obtained from the frequency response of HBTs with a thick base [8]. In thick-based
HBTs, the base-transit time is the dominant delay time of the device, and can therefore be accurately evaluated. Moreover, the
effect of injection from the energy ramp can be safely ignored in
thick-based HBTs. We have used the electron diffusivity value
of 110 cm s throughout this paper.
B. Base-Transit Time: Hot Electron Injection From the Emitter
No analytic expression for the average base-transit time of
abrupt base–emitter junction HBTs is available in the literature.
Hence, we have used the simple Monte Carlo approach to interpret our experimental results. Ballistic injection of electrons
was modeled in the simulation by assigning a forward velocity
of
cm/s to the electrons emerging from the emitter. The energy relaxation of the injected electrons was modeled by a single
average parameter, the energy scattering rate . There are various ways to introduce an average energy relaxation rate into
the simulation. We have tested several options, and verified that
the results do not significantly depend on the particular choice
made. Below, we describe the option that was used to generate
the results presented in this paper.
Denoting the momentum scattering rate by , we assumed
that the probability that the first collision is an energy scattering event is
and a momentum scattering event
. An energy relaxation event was modeled in the
simulation by a thermalized Gaussian velocity distribution and a
uniform angle distribution in the forward direction only. A momentum relaxation event of an energetic electron was assumed
identical to that of a thermalized electron, namely, it produced a
thermalized Gaussian velocity distribution with a uniform angle
distribution. Thus, the total energy relaxation rate in our simulation was
. The momentum scattering rate was assumed
equal for thermalized and hot electrons.
The value of the electron momentum relaxation rate was
set to
s
using
and the Einstein
relation. The value of the energy relaxation rate was set to
s . This value was chosen to obtain
s , so that the energy relaxation mean free path
of the hot electrons is about 30 nm. The value of the energy
relaxation mean free path determined by electroluminescence
spectroscopy is 18 6 nm [13], while theory predicts a value
of 60 nm [12].
C. Transit Time of a Composition-Graded Base
Using the drift diffusion approach [14], one obtains that for
linear composition grading [15]
(3)
and
is the difference between
where
the bandgap at the collector and emitter edges of the base. To be
must be identical in both equations.
consistent with (1)
For short bases, the drift diffusion approach and, hence, (3),
is not valid [15]. We have therefore used our simple Monte
Carlo simulation to model graded base transport. The value
of the quasi-electric field induced by grading of the strained
As base was obtained from the expression given in
Ga In
[16] for the bandgap of this material versus the deviation
from lattice-matched layer composition
(4)
The second-order term in the above equation was neglected so
that a constant electric field was obtained for a linearly graded
base composition. Thermal electrons in the simulation were
allowed to accelerate due to the presence of the electric field.
Hot electrons injected from the energy ramp were assigned
an effective mass 3.3 times larger than the thermal effective
electron mass to take nonparabolocity into account [17].
III. ROLE OF ELECTRON INJECTION FROM AN ENERGY
RAMP—NO COMPOSITION GRADE
Hot-electron effects were studied in this paper by comparing
the base width dependence of the gain of abrupt HBTs to that
predicted by theory for thermal injection. Similar work was published before [18], [19], however, more data on thin-base HBTs
is presented here and the theoretical analysis is much more precise. A series of abrupt base–emitter junction InP–GaInAs HBT
samples were prepared, with the base layer width varying between 10–45 nm. The remaining layer structure was identical
in all samples. The samples were grown by a compact metalorganic molecular beam epitaxy system [20]. Carbon and tin
served as p-type and n-type dopants, respectively. The p-type
cm , and hole
doping level in the base was about
mobility about 45 cm Vs. The base sheet conductance versus
base width is plotted in Fig. 1. The linear dependence confirms
the nominal values of the base width. The curve intersects the
width axis at about 6 nm, probably due to Fermi-level pinning at
the exposed surface and some etching during the selective wet
etch process.
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IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 51, NO. 5, MAY 2004
Fig. 1. Extrinsic base sheet conductance versus base width.
Fig. 3. Base-transit time versus base width. Calculated results are for the
uniform composition case. Experimental results for graded base [21].
Fig. 4. Variation of gallium content relative to lattice-match value versus
position in the base and collector layers. Grading of the collector prevents
formation of an energy barrier.
Fig. 2.
Measured and calculated current gain versus base width.
The measured maximum dc current gain versus base width
is plotted in Fig. 2. The solid line is obtained from the expresusing (1) with
cm s, and with an
sion
determined to fit the 45-nm-thick
electron lifetime
base-gain value. Clearly, the gain of the very thin-base devices
is much higher than predicted by (1). A calculation of the basetransit time by the Monte Carlo simulation, which includes hot
electron injection, resolves this conflict. We conclude that injection from an energy ramp significantly affects base-transit time
in bases less than 30 nm thick.
The calculated base-transit time with and without hot electron injection is shown in Fig. 3. As mentioned above, the values
obtained by the Monte Carlo simulation for the BJT case were
larger by 10%–12% than the results obtained from (1). Hot
electron injection reduced the base-transit time mainly in very
narrow bases. Very thin bases are currently not used, but will
eventually be used in future scaled-down devices. Experimental
results obtained from high frequency measurements of abrupt
base–emitter junction HBTs with a composition-graded base
[21] are shown in the figure as well. We first note the excellent agreement between our simple theory and the measured
data. Furthermore, it can be seen that composition grading of
the base does not substantially reduce base-transit time for 25and 33-nm-thick bases. This result was confirmed by our experiments, described below.
IV. COMPOSITION GRADING OF THE BASE LAYER
A curve of the dc current gain versus composition grade in
the base is useful for detecting changes in the base-transit time
assuming that electron lifetime does not significantly vary with
base composition. This assumption is not valid for doping grade,
which was recently introduced to further accelerate the electrons
in the base [22]. Previous experiments showed that for 50-nmthick compositionally graded bases, the gain drops abruptly due
is larger than 10%
to defects introduced by the strain when
[23]. Here, we have used strain compensation to eliminate this
up to 35% with no colproblem, and were able to increase
lapse of the gain. The variation of the composition along the
base and collector layers employed to achieve stain compensation is described in Fig. 4. At the base–emitter junction the
As layer is set to
gallium content of the Ga In
(grade) above the lattice-match value, and at the base collector
(grade) below the lattice-match value. The
junction to
collector layer is graded across a distance equal to one third of
the base width to prevent the formation of an energy barrier. The
total integrated strain of the entire structure is nominally zero.
of a variety of devices are
Curves of the gain versus
shown in Fig. 5. Although the gain does not collapse, it satu. It is unlikely that the observed saturarates at
tion is caused by an exact cancellation of the effect by defect
formation.
A comparison of the experimental data to the prediction
of the drift diffusion model is shown in Fig. 6. Clearly, the
ZOHAR et al.: REDUCTION OF BASE-TRANSIT TIME OF InP–GaInAs HBTs DUE TO ELECTRON INJECTION
661
The experimental results included in Fig. 3 indicate that composition grading of the base does not significantly reduce the
base-transit time in abrupt thin-base HBTs. The results shown
in Fig. 7 support this conclusion: for 20-nm-thick bases, hardly
any change in gain can be observed with composition grading.
V. CONCLUSION
Fig. 5. Current gain versus composition grading of strain compensated HBTs
having a 45-nm-thick base for two extrinsic base sheet resistance values: 485
10 = and 390 10 = .
6
Fig. 6.
6
Measured and calculated current gain versus base grading.
Fig. 7. Current gain versus base composition gradient in abrupt base–emitter
HBT with a 20-nm-thick base.
drift diffusion expression does not agree with our data. It
predicts a fourfold decrease of the base-transit time when
is increased from 10% to 30%. The Monte Carlo simulation,
on the other hand, does predict a less pronounced increase of
the gain with composition gradient. Yet, the gain predicted
by the simulation is twice as high as the experimental data at
high composition gradients. More work is required to resolve
this important discrepancy.
The experimental results combined with the simulation presented in this paper enabled us to derive the base-transit time in
various HBT structures. It appears that as base dimension are
scaled down ballistic injection may play some role in the reduction of the base-transit time. Base composition grading, on the
other hand, is more helpful in thicker bases.
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Gal Zohar was born in Haifa, Israel, in 1972. He received the B.A. degree in physics and the B.Sc. degree in material engineering in 1999, and the M.Sc.
degree in electrical engineering in 2003, all from the
Technion, Israel Institute of Technology, Haifa.
During his graduate studies, he carried out research
on base transport in InP-based HBTs. He is currently
with the Quality and Reliability Group, Intel, Haifa,
Israel.
Shimon Cohen received the Practical Engineering
degree in electrooptics from the Technion, Israel Institute of Technology, Haifa, in 1981.
From 1981 to 1991, he worked on epitaxial crystal
growth and growth of hydrogenated amorphous silicon at the Technion, Israel Institute of Technology.
Since 1991, he works on the growth of InP-related
materials using metal–organic molecular-beam epitaxy. His main interest is in physics and the technology of epitaxial crystal growth.
Victor Sidorov received the M. Sc. degree (with
honors) in chemistry from Voronezh University,
USSR, in 1985.
Since 1995 he is a Senior Research Assistant at
Microelectronics Research Center, The Technion,
Israel Institute of Technology, Haifa, working on
III-V microwave and optoelectronic device and
circuits manufacturing. Prior to this, he held an
Engineer-Researcher position at Mizur Micromechanics Technologies working on microsensors
manufacturing and micromachinning. He is now
also with the Weizmann Institute of Science, Rehovot, Israel, working on
nanotechnology projects.
Arkady Gavrilov was born in St. Petersburg, Russia,
in 1960. He received the Diploma in optics from the
Mathematical Zveriev Physical Institute, St. Petersburg, in 1985.
He is currently with the Technion Microelectronics
Center, The Technion, Israel Institute of Technology,
Haifa, Israel, where he develops the microfabrication
technology of indium phosphide based HBTs.
Benny Sheinman was born in Israel in 1969. He received the B.Sc. and M.Sc. in electrical engineering
from The Technion, Israel Institute of Technology,
Haifa, in 1991 and 1998 respectively. He is currently
pursuing the Ph.D degree in electrical engineering at
the Technion.
His research focus is on design, growth, and modelling of InP-based HBTs and on microwave optoelectronic circuits.
Dan Ritter (M’99) received the B.Sc, M.Sc, and
Ph.D. degrees in electrical engineering from The
Technion, Israel Institute of Technology, Haifa in
1981, 1984, and 1989, respectively.
He then carried out post-doctoral research for
three years at AT&T Bell Laboratories, Murray
Hill, NJ. In 1992, he joined the Technion Electrical
Engineering Department, where he is currently an
Associate Professor. His group has been using the
metalorganic molecular beam epitaxy method to
grow the epitaxial layers. His main research interest
is physics and the modeling of indium phosphide based devices. The focus of
his current activity is heterojunction bipolar transistors.