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Ballistic Devices
Vikram Jagannathan
Graduate Student, University of Rochester, Rochester, NY-14620, USA – [email protected]
Abstract - With a brief introduction to ballistic phenomenon,
the theory, fabrication, working and plausible applications of
some ballistic devices are presented.
Index – Heterostructure semiconductor, 2DEG, Electron Mobility,
Mesoscopic Structure, Ballistic Transport, Ballistic Devices
I. INTRODUCTION TO BALLISTIC PHENOMENON
The ideal basis for future electronics would be a scalable
solid-state transistor with much higher speed than III-V FETs
and lower energy dissipation than current CMOS transistors. In
addition, it should utilize common materials and operate at
room temperature. One of the most important physical
parameters to describe the quality of a piece of semiconductor
material is the electron scattering length. Also referred to as the
mean-free path, it stands for the average distance between the
randomly distributed scatterers in the material, such as lattice
defects, impurities, and phonons. The electron mean-free path
is typically a few nanometers in silicon and about 100–200 nm
in high-quality compound semiconductors such as GaAs [1]. It
is known that the electrical resistance of a semiconductor
device is closely associated with the scattering length.
Conventional semiconductor devices are much larger than the
electron scattering length. As a result, electrons have to
encounter a large number of random scattering events called
Coulomb scattering, as shown in Fig. 1, to travel from one
device lead to another.
II. TWO DIMENSIONAL ELECTRON GAS
A two Dimensional Electron Gas (2DEG) is a gas of
electrons free to move in two dimensions, but tightly confined
in the third. In a heterostructure semiconductor made of
GaAs/AlGaAs, the conduction bands of GaAs and AlGaAs are
offset from each other and this allows electron to collect in the
GaAs but not in the AlGaAs. Thus they distort the conduction
band into the shape shown in Fig. 3, where there is a triangular
"well" at the interface, and this goes slightly below the Fermi
energy so that electrons can collect there. This well is so
narrow that all the electrons there behave as quantummechanical waves, forming quantized energy levels for motion
in that direction. The only degrees of freedom for the electrons
are in the plane of the interface. Thus in the heterojunction, the
2DEG is spatially separated from the ionised donors by an
undoped spacer layer [3, 4]. This greatly reduces impurity
scattering and so increases the mean free paths of the electrons
in the 2DEG layer thereby increasing the electron mobility.
Fig. 3. Band diagram of 2DEG in hetrostructure semiconductor
III. BALLISTIC DEVICES
Scattering length
Fig. 1. Electron transport in macroscopic devices
Advanced semiconductor technologies have allowed the
fabrication of mesoscopic devices that are smaller than the
electron scattering length. In such devices, electrons may travel
from one electric lead to another without encountering any
scattering event from the randomly distributed scatterers.
Instead, the electrons are scattered only at the device
boundaries, that is, moving like billiard balls as in Fig. 2. Such
electron transport is referred to as ballistic transport which
could operate in terahertz regime [2].
~ Microns or less
Fig. 2. Electron transport in mesoscopic devices
The ballistic transport can be used to construct ballistic
devices and circuitry operating at room temperatures that are
very different from conventional circuitry. It has been expected
that devices based on ballistic electron transport have superb
performance. Since electrons are free from random scattering
events, ballistic electron devices may have a very high intrinsic
working speed and a quick response. Further, the strongly
temperature dependent phonon scatterings, which in some
cases lead to serious degradation in device performance in a
traditional electron transport device, do not exist in a ballistic
device by its nature. Therefore, ballistic devices in general are
less temperature dependent [1]. Many of the new concepts are
based on the fact that the only scatterings that the ballistic
electrons experience are those from the designed device
boundaries. By simply tailoring the boundary of a ballistic
device, the electron transport can be, to a large extent, modified
and controlled. The parameters for this design are based on
simulations using a Newtonian billiard-ball model [2].
IV. BALLISTIC RECTIFIER
The best introduction to the room temperature ballistic
devices is to review experiments on a related device called the
"ballistic rectifier" developed by Song et al. in [1], as shown in
Fig. 4. The ballistic rectifier can be understood, by a simple
concept; that the electrons in the 2DEG behave as if they were
classical Newtonian charged particles. They respond to
electromagnetic fields; but they otherwise travel in straight
paths until they encounter obstacles, from which they are
reflected. The asymmetric triangular structure, seen in Fig. 4a,
deflects the electrons downward and this causes the
rectification.
Fig. 6. Schematic of the mesoscopic ballistic quantum point contact detector
In the QPC detector, as in Fig. 6, the propagating particles
are electrons which move ballistically through a short onedimensional constriction formed between the two electrodes of
the QPC. The output of the QPC detector is the electric current
I driven by the voltage difference V between the electrodes.
The current depends on the electron transmission probability,
and as a result, contains information about the state of the
system. In view of quantum computation, ballistic QPCs may
be used as readout devices for the state of a qubit.
VI. BALLISTIC Y-BRANCH SWITCH
Fig. 4. Image of the a) Ballistic rectifier and b) Bridge rectifier
In the experiment, an AC or RF source is connected across
the left and right contacts. The experimental result, as shown in
Fig 5 is that a DC voltage is developed across the top and the
bottom contacts; in other words, rectification is performed.
A device of special interest is an electron Y-Branch Switch
(YBS) [6]. The semiconductor version of YBS has a narrow
electron waveguide patterned into a “Y” configuration with one
source and two drain terminals. A lateral electric field
perpendicular to the direction of electric current in the source
channel steers the injected electron wave into either of the two
output drain arms. Fig. 7 shows an atomic force micrograph of
a YBS device.
Fig. 7. Atomic force micrograph of a YBS with neck width of 76nm
Fig. 5. The output voltage between the lower and upper leads VLU as a function
of the input current through the source and drain leads ISD
V. MESOSCOPIC BALLISTIC DETECTORS
Current interest in solid-state quantum information
processing motivates development of mesoscopic solid-state
structures that can serve both as simple quantum systems and
as detectors. Majority of the mesoscopic detectors use, as their
operating principle, the ability of a measured system to control
the transport of some particles between the two reservoirs
(sometimes source and drain). The information about the state
of the system is then contained in the magnitude of the particle
current between the reservoirs which serves as the detector
output. In the most direct form, this principle is implemented in
the Quantum Point Contact (QPC) detector [5].
As an advantage over the switching devices harnessing the
field effect, the electrons need not be stopped and reflected by
a barrier. As a consequence extremely fast switching times and
low power consumption has been predicted [6]. For terahertz
operations, the semiconductor system in which the YBS is
fabricated must have the electron mean free path longer,
relative to the junction length of the YBS drain-source region.
The 2DEG channel in heterostructure semiconductors increases
the mean free path of the electrons, making YBS to operate in
the ballistic regime.
The YBS can be directly used as ballistic logic gates.
Simulations have shown that YBS can be cascaded, i.e. the
output of one YBS can act as the input to the controlling gates
of a subsequent YBS [7]. In the same paper it was also shown
that fan-out is possible.
VII Conventional Ballistic Transistors
A. Heterojunction Bipolar Transistor
The Heterojunction Bipolar Transistor (HBT) is an
improvement of the Bipolar Junction Transistor (BJT) that can
handle signals of very high frequencies up to several hundred
GHz. The principal difference between the BJT and HBT is the
use of differing semiconductor materials for the emitter and
base regions, creating a heterojunction. The effect is to limit
the injection of holes into the base region, since the potential
barrier in the valence band is so large. Unlike BJT technology,
this allows high doping to be used in the base, forming 2DEG
layer, creating higher electron mobility while maintaining gain.
HBT from InP/InGaAs was demonstrated to run at a speed of
710 gigahertz [8]. Among other HBT applications are
optoelectronic integrated circuits and mixed signal circuits such
as analog-to-digital and digital-to-analog converters.
B. High Electron Mobility Transistor
A High Electron Mobility Transistor (HEMT) is a field
effect transistor with the 2DEG in a heterojunction as the
channel instead of an n-doped region [9]. This gives the
channel very low resistance or high electron mobility. A
commonly used combination is GaAs and AlGaAs with a thin
layer of InGaAs as shown in Fig. 8.
Fig. 9. Sketch of the ballistic deflection transistor
This ballistic deflection magnifies the effect of the gated
nonlinear conduction and is responsible for the gain of the
BDT. A small deviation at the gate results in a large deflection
at the output. This constitutes the amplification action of the
BDT.
IX. CONCLUSION
This paper reviews a novel and unique concept of electronic
devices capable of working at high gigahertz and terahertz
frequencies at room temperature. These devices use the
ballistic transport for operation. It also consumes very low
power and operates with very low noise levels and is thus
suitable for a multitude of applications like high speed
processors, RF identification, wireless fidelity, which will
revolutionize modern electronics.
REFERENCES
Fig. 8. Cross section of an AlGaAs HEMT
Major application areas are microwave and millimeter wave
communications, radar and radio astronomy.
VIII. BALLISTIC DEFLECTION TRANSISTOR
The proposed concept for the Ballistic Deflection Transistor
(BDT) is shown in the sketch Fig. 9 [10]. The white areas
represent 2DEG with high electrical conductivity, with
dimensions comparable to the mean free path, while the black
areas are zero conductivity. The ballistic transport in the 2DEG
layer provides the actual transistor nonlinearity. A bias voltage
applied at Vdd accelerates electrons from Vss towards the
central junction of the BDT. A small gate voltage modifies the
path of the electrons towards the right or the left as desired.
These electrons are then ballistically deflected from the central
triangular feature into one or the other output channels.
[1] A. M. Song, “Room-Temperature Ballistic Nanodevices”,
Encyclopedia of nanoscience and Nanotechnology, X, 1 (2004).
[2] S. Datta, Electronic Transport in Mesoscopic Systems (Cambridge
University Press, Cambridge, 1995).
[3] http://www.warwick.ac.uk/~phsbm/2deg.htm
[4] http://www.sp.phy.cam.ac.uk/SPWeb/research/wafer.html
[5] D. V. Averin, “Mesoscopic Quantum Measurements”, available
online at http://arxiv.org/abs/cond-mat/0603802
[6] E. Forsberg: "Reversible logic based on electron waveguide Ybranch switches", Nanotechnology 15, S298 (2004)
[7] T. Palm, L. Thylen, 0. Nilsson, and C. Svensson, “Quantum
interference devices and field-effect transistors: A switch energy
comparison”, J. Appl. Phys. 74, 687 (1993)
[8] Wikipedia contributors, Heterojunction bipolar transistor,
(Wikipedia, The Free Encyclopedia, 2006),
http://en.wikipedia.org/w/index.php?title=Heterojunction_bipolar_tran
sistor&oldid=67184480
[9] Wikipedia contributors, HEMT, (Wikipedia, The Free
Encyclopedia, 2006),
http://en.wikipedia.org/w/index.php?title=HEMT&oldid=93872590
[10] Q. Diduck, M. Margala, and M. J. Feldman, “A Terahertz
Transistor Based on Geometrical Deflection of Ballistic Current”,
IEEE Microwave Symposium Digest, 345 (2006)