Single-Electron Devices
Qiaoyan Yu, Student Member, IEEE
Abstract—The operation principle of single-electron devices
(SEDs) is reviewed. Single-electron box, transistor, and trap are
presented. Current SED applications are introduced, particularly
silicon single-electron memory and logic. SED implementation
challenges and future research are proposed.
speaking, the digital single-electron devices operating at room
temperature require Ea few electron-volts and minimum
feature size ~ 1 nm, so that thermally-induced random
tunneling events can be avoided.
-eε
-e
Index Terms—single-electron device; single-electron box;
single-electron transistor; silicon single-electron memory; silicon
single-electron logic.
-e
F
F
I. INTRODUCTION
Fig. 1 The basic concept of single-electron control: a conducting control island
INGLE electron devices (SEDs) are based on the
controllable single electron transfer between small
conducting “islands”. In 1909, Millikan first illustrated the
manipulation of single electrons; however the single-electron
device cannot be implemented in solid state circuit until late
1980s, due to limited fabrication techniques. SEDs have
already been applied in several important scientific
experiments [6-8] and are feasible in unique scientific
instrumentation and metrology. In addition, some exciting
ideas may revolute logic and memory design in silicon-based
circuit design area [9, 10]. Furthermore, it has been shown the
promising future that replacing silicon transistors with
single-electron transistors (SETs) [6, 8, 11-14].
B. Orthodox theory
Reference [3] formulated the orthodox theory of
single-electron tunneling, which plays an important guiding
role in the history of single-electronics. A single electron
randomly tunnels through a particular tunnel barrier with a
certain rate Γ, which depends on the electrostatic energy
reduction of the system as a result of this tunneling event, as
shown in Fig. 2. This is because the rate is proportional to the
number of occupied quantum states in the electron source.
S
II. OPERATION PRINCIPLE
A. Basic Physics
Assume a small metal sphere (also called island, shown in
Fig.1) which is been electroneutral initially, i.e. zero net charge.
In this state, no electrical field occurs beyond the border of the
island. When an external force F brings a single electron (-e)
from outside close to the island, an electrical field ε is generated
by the nonzero net charge. The electrical field is oppositely
proportional to the square of the island size, so it may become
very strong for nanoscale structures [1], [2].
Charging energy Ec is a more accurate measurement on this
charge effect than electrical field. As the island size is
comparable with the de Broglie wavelength of the electron
island, the energy scale is described by electron addition energy
Ea, the sum of charging energy Ec and quantum kinetic energy
of the added electron Ek. To reduce the thermal fluctuation
impacts on Ek, Ec should be the dominant of Ea. Generally
Manuscript received December 12, 2006.
Q. Yu is with University of Rochester, Rochester, NY 14627 USA
(corresponding author to provide phone: (585)275-1769; fax: (585)273-2073;
e-mail: qiaoyan@ece.rochestere.edu).
(a)
(b)
Fig.2 (a) Energy diagram of a tunnel junction (b) Single-electron tunneling rate
Γ vs. the electrostatic energy loss ∆W[1]. R is the resistance of the tunnel
barrier, e is electron charge, and kB is Boltzmann constant, T is temperature.
III. TYPICAL SINGLE-ELECTRON DEVICES
A. Box
Single-electron box is the conceptually simplest device. As
shown in Fig. 3 (a), it is composed of a small island, which is
separated from a large source electrode by tunnel barrier. Gate
electrode is another electrode, which is used to apply an
external electrical field on the small island. As the
electrochemical potential of the island is changed by the
external electrical filed E, electron tunneling effects occur
through the tunnel barrier. The free energy (Gibbs) energy of
the system is illustrated in (1). The island charge Q is a step
function of the applied voltage U, as defined in (2) and (3).
Here, C0 and C∑ are the island-gate capacitance and total
capacitance, respectively. Qe is the external charge. The
increasing gate voltage U leads to more electrons on the island.
W = Q 2 / 2CΣ + (C0 / CΣ )QU + const
Q = ne − Q e
Q e = UC0
(2)
q
island
V1
Source
+q1
-q1
+q2
C1
Vb
gate
V2
Drain
-q2
C2
Cg
Vg
(1)
Fig. 4 Schematic of single-electron transistor circuit
(3)
However, two major drawbacks prevent single-electron box
from being an electronic circuit component [6]. (1) This
structure cannot store information, because the charges stored
in the island are a function of applied voltage U; (2) it is hard to
measure its charge state, due to no dc current carried in the box.
Tunnel
Barrier
Small island
-
+
+
+
+
Q=-ne
E
Source
Electrode
Tunnel junctions
- C
- 0
-
Qe-ne
+ Gate Electrode
+
+
U
+
-Qe
(a)
(b) [5]
Fig.3 Single-electron box (a) schematic (b) island charge Q (=-ne)as a function
of gate voltage. Blue: at vanishing small temperature transition between states
differing in the island charge by a single electron are sharp. Red: at elevated
temperatures the steps are thermally broadened.
B. Transistor
1) Coulomb blockade
The schematic of the single electron transistor with biased
voltages is shown in Fig. 4. First assume the gate voltage Vg is
zero. If the biased voltage Vb is less than the threshold voltage
VC (=e/CΣ), no electron can tunnel through the two tunnel
junctions, because there is not sufficient energy to charge the
island. This behavior is so called Coulomb blockade. When Vb
is greater than VC, current will flow through the circuit as
shown in Fig. 5 (a). The charge q contained in the whole island
is as follows:
q = – q1+ q2 + q0 = -ne +q0
(4)
Here, q0 is the background charge, which is non-integer and
resulted from impurity, and e is the electron charge.
(a)
(b)
Fig.5 I-V curve of SET (a) zero Vg (b) changed Vg
2) Coulomb oscillation
Now assume Vg is not zero. The charges in the whole island
are modified by the gate voltage Vg as follows:
(5)
q = -ne + q0 + Cg (Vg – V2)
The regions where current flowing through increase at the cost
of the remaining Coulomb blockade region, therefore,
increasing the bias voltage will increase the line-width of the
oscillations.
Besides, thermal broadening at higher temperature or a
discrete energy spectrum also considerably changes the form of
oscillations.
3) MOSFET and SET comparison
Compared with usual metal-oxide-semiconductor field-effect
transistor (MOSFET), SET replaces inversion channel with
two tunnel barriers embedded in a small conducting island. The
most important characteristics of the single-electron transistor
is that both threshold voltage and source-drain current is a
periodic function of the gate voltage. The periodic dependence
is resulted from the effect of Vg is equivalent to the injection of
charge into the island, and hence changes the balance of the
charges at tunnel barrier capacitance, which determines the
coulomb blockade threshold voltage.
C. Trap
Single-electron trap has more than two tunnel junctions in the
island, which is separated by tunnel barriers [7, 8]. This device
operates like an internal memory, and can store two or more
bits of information by changing Vg applied on the device’s
island, as shown in Fig.6. First, the gate electrode is provided
with a sufficiently high gate U+, and the electrons are driven
into the edge island. Then, Vg is decreased to the initial level, so
the electrons are trapped in the island. By reducing voltage
further, the electrons can be removed from the trap. However,
the lifetime of a certain state is basically constrained by the
thermal activation over the energy barrier and co-tunneling.
(a)
single-electron circuits, they cannot generate currents directly.
Basically, single-electron device logics have two categories:
SET-based logic and charge state logic [9]. The current of the
former one is produced by the sequence of single-electron
tunneling. The corresponding bit is represented by the voltage,
which is generated by the accumulation of plural electrons.
Si-based researches on SET-based logic circuits, such as
Inverter, NAND and XOR gates, have been demonstrated. In
contrast, the bit of the charge state logic is represented by the
elementary charge. The representative devices are quantum
cellular automation (QCA) and single-electron binary decision
diagram (BDD) [11-14].
V. CHALLENGE AND CONCLUSION
(b)
Fig.6 Single-electron trap (a) schematic (b) static characteristics of the device
IV. SINGLE-ELECTRON DEVICE APPLICATIONS
A. Memory
Currently, SED memories have become the most important
SED application, for either electron storage or charge sensing.
Because of small dimensions, the SED is very promising for
high density memory design. In addition, memory usually has a
periodic and simple structure, so it is possible to implement
memory with SEDs.
However, the background charge is too random to be
employed in VLSI circuits, which is proved by the statistical
distribution of the Coulomb blockade threshold and the energy
barrier height of the island array. In addition, the background
charge also leads to the unreliability of the SET readout. The
charge trapped in the island can be easily imitated by a random
charged impurity [9].
Single-electron transistor/field electrical transistor hybrid
design (SET/FET hybrid) is a background-charge-insensitive
memory. The minimum feature of this memory is about 3 nm,
which is much larger than the requirement for single-electron
digital circuits. And the absence of storage capacitor inside the
memory makes it more attractive for high density purpose. The
main drawbacks are slow write process and insensitive to the
applied voltage. Crested tunnel barriers are proposed to
overcome those disadvantages, at the cost of fabrication
difficulty.
Experiments turn the theoretical models into reality. K. Yano
et al. [10] showed single electrons are captured in the channel
of certain stand-alone grains. Its main disadvantage is
inherently irreproducible. S. Tiwari at IBM [11] separated the
electron-capturing island and a MOSFET channel, which
overcome the granular limitation on the channel.
B. Logic
The SET is the primary device to substitute the MOSFET in
conventional logic gates. Although Coulomb blockade and
single-electron tunneling are dominant phenomena in
SEDs have shown promising applications in metrology,
terahertz radiation diction and imaging. Because of natural
small dimension, SED is a potential solution for continue
silicon scaling. In addition, low power dissipation can be
achieved in circuits composed of single-electron devices.
Metallic structures can be fabricated with vertical and lateral
islands and tunnel barrier structures at temperature up to 77K.
GaAs and silicon based SEDS have been already demonstrated.
However, fabrication is still the most difficult challenge of SED
application. Electron beam lithography and scanning probe
techniques offer the best prospects for the future. Besides, some
more esoteric techniques based on atomic particle deposition
and colloid chemistry may also provide some benefits.
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