Single Electron Devices. Transistors Single-electron Transistors. Transistors What are transistors? How do they work?
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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
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
- what problem does it help solve?
- what is its operation?
Fig 3. A single-electron transistor
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.
(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.
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
∆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.
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
At higher dopings, the tunneling probability starts to get better and electrons can move across the junction.