Transcript Single Electron Devices

Single Electron Devices
Transistors
Single-electron Transistors
 Transistors
– What are transistors?
– How do they work?
A transistor is a device that functions only in one direction, in which it
draws current from its load resistor. The transistor is a solid state
semiconductor device which can be used for amplification,
switching, voltage stabilization, signal modulation and many other
functions. It acts as a variable valve which, based on its input
current (BJT) or input voltage (FET), allows a precise amount of
current to flow through it from the circuit's voltage supply.
Fig 1. NPN Transistor using two diodes and connecting both anodes together
 One cathode is tied to common (the emitter); the other cathode (the
collector) goes to a load resistor tied to the positive supply. For
understanding, the transistor is configured to have the diode signal
start up unimpeded until it reaches ~ 0.6 volts peak. At this point the
base voltage will stop increasing. No matter how much the voltage
applied from the generator increases (within reason), the "base"
voltage appears to not increase. However, the current into that junction
(two anodes) increases linearly: I = [E - 0.6]/R.
Fig 2. Graph of how the base voltage acts with increasing input voltage.
As the voltage increases from 0 to 0.5 volts there is no current. However, at 0.6
a small current starts to show which is drawn by the base. The voltage at the base
stops increasing and remains at 0.6 volts, and the current starts to increase along
with the collector current. The collector current will slow down at some point until it
stops increasing. This is where saturation occurs. If this transistor was being used
as a switch or as part of a logic element, then it would be considered to be switched
on.
 Single-electron Transistor
- what problem does it help solve?
- what is its operation?
 Problem of Making More Powerful Chips
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Intel co-founder Gordon Moore that the number of transistors on a chip will
approximately double every 18 to 24 months. This observation refers to what
is known as Moore’s Law.
This law has given chip designers greater incentives to incorporate new
features on silicon.
The chief problem facing designers comes down to size. Moore's Law works
largely through shrinking transistors, the circuits that carry electrical signals. By
shrinking transistors, designers can squeeze more transistors into a chip.
However, more transistors means more electricity and heat compressed into
an even smaller space. Furthermore, smaller chips increase performance but
also compound the problem of complexity.
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To solve this problem, the singleelectron tunneling transistor - a device
that exploits the quantum effect of
tunneling to control and measure the
movement of single electrons was
devised. Experiments have shown that
charge does not flow continuously in
these devices but in a quantized way.
Fig 3. A single-electron transistor
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The single-electron tunneling (SET) transistor consists of a gate electrode that
electrostaticaly influences electrons traveling between the source and drain
electrodes. The electrons in the SET transistor need to cross two tunnel
junctions that form an isolated conducting electrode called the island. Electrons
passing through the island charge and discharge it, and the relative energies of
systems containing 0 or 1 extra electrons depends on the gate voltage. At a
low sourcedrain voltage, a current will only flow through the SET transistor if
these two charge configurations have the same energy
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The SET transistor comes in two versions that have been nicknamed metallic
and semiconducting.
 SET Transistor Function
The key point is that charge passes through the island in quantized units. For
an electron to hop onto the island, its energy must equal the Coulomb energy
e2/2C. When both the gate and bias voltages are zero, electrons do not have
enough energy to enter the island and current does not flow. As the bias
voltage between the source and drain is increased, an electron can pass
through the island when the energy in the system reaches the Coulomb
energy. This effect is known as the Coulomb blockade, and the critical voltage
needed to transfer an electron onto the island, equal to e/C, is called the
Coulomb gap voltage.
 What is this “island”?
Fig 4
(a) When a capacitor is
charged through a resistor, the
charge on the capacitor is
proportional to the applied
voltage and shows no sign of
quantization. (b) When a
tunnel junction replaces the
resistor, a conducting island is
formed between the junction
and the capacitor plate. In this
case the average charge on
the island increases in steps
as the voltage is increased (c).
The steps are sharper for more
resistive barriers and at lower
temperatures.
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Left: Equivalent circuit of an
SET
Center: Energy states of an
SET. Top Coulomb blockade
regime, bottom transfer regime
by application of VG=e/2CG
Right: I-(Va )-characteristic for
two different gate voltages.
Solid line VG= e/2CG, dashed
line VG =0
Here n1 and n2 are the number of
electrons passed through the tunnel
barriers 1 and 2, respectively, so
that n = n1 - n2, while the total
island capacitance, C∑, is now a
sum of CG, C1, C2, and whatever
stray capacitance the island may
have.
 The most important property of the single-electron transistor is
that the threshold voltage, as well as the source-drain current in
its vicinity, is a periodic function of the gate voltage, with the
period given by
∆Qe = e, ∆U= e/C0 = const.
The effect of the gate voltage is equivalent to the injection of charge
Qe = C0U into the island and thus changes the balance of the charges
at tunnel barrier capacitances C1 and C2, which determines the
Coulomb blockade threshold Vt. In the orthodox theory, the
dependence Vt (U) is piece-linear and periodic.
The expression for the electrostatic energy W of the system:
W = (ne - Qe)2/2CS - eV[n1C2 + n2C1]/CS + const
The external charge Qe is again defined by Qe = C0U and is just a convenient
way to present the effect of the gate voltage U.
The Coulomb blockade threshold
voltage Vt as a function of Qe at T -> 0.
At a certain threshold voltage Vt
the Coulomb blockade is
overcome, and at much higher
voltages the dc I-V curve gradually
approaches one of the offset linear
asymptotes:
I -> (V +sin(V)´e/2C∑)/(R1+R2). On
its way, the I-V curve exhibits
quasi-periodic oscillations of its
slope, closely related in nature to
the Coulomb staircase in the
single-electron box, and expressed
especially strongly in the case of a
strong difference between R1 and
R2.
Source-drain dc I-V curves of a symmetric
transistor for several values of the Qe, i.e.
of the gate voltage
Applications of SETs
 Quantum computers
– 1000x faster
 Microwave Detection
– Photon Aided Tunneling
 High Sensitivity Electrometer
– Radio-Frequency SET
Tunneling Probability
 Fabrication of the
Ti/TiOx SET
 Barrier Height 285meV
 Er = 24
 18nm wide junction
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Choose doping of 10^18 and 10^23
W=[2Er*Eo*Vbi/eNd]^1/2
W(n=10^18)= 2.75e-6 cm^-3
W(n=10^23)= 8.69e-9 cm^-3
 To find E field divide Barrier height by Width
 E(n=10^18)= 1.03e5 V/cm
 E(n=10^23)= 32.8e6 V/cm
 Substituting E into Tunneling Prob Equation
 T= exp{ (4* (2m*)^1/2*phi^3/2 )/ (3eEhbar)}
 T(n=10^18) = exp{-3187}=0
 T(n=10^23) = exp{-10.021}=.0000444
Conclusion:
At higher dopings, the tunneling probability
starts to get better and electrons can move
across the junction.
Main Problems with SETs
 Operation at Room Temp
– Capacitor Size
 Fabrication
– Chemical Fabrication
 Couloumb Islands
 Tunneling junctions
 Gate between substrate and Coulomb islands
 Charge Offset
– 1 electron at a time
Single Electron Devices
 Group Members
– Jonathan Sindel
– Latchman,Kamivadin
– Wayne Lyon