Single electron transistor based on Quantum Dots
by Wang Ye and Iwan (nice discussion)
Quantum dots are a special class of semiconductor materials, ranging from 2-10nm (10-50 atoms) in diameter. Basically, they are crystals composed of periodic groups of II-VI, III-V, or IV- IV materials, such as ZnO,GaAs and Ge-Si quantum dots. Due to the small size, quantum dots have unique properties different from bulk, such as the electron energy level will be discrete while the bulk’s is continuous. Until now, many devices based on quantum dots has been invented, such as quantum dot memory, quantum dot microcavity light-emitting diodes, quantum dot semiconductor laser, etc. In this section, Single Electronic Transistor (SET) based on quantum dot will be introduced.
As is well known, until now, any electronic devices like MOSFET & BJT, the current is formed by many electrons or holes move together. However, what will happen when the current is transported by just one single electron or hole (in this section, on single electron for example). This interesting topic can be realized by Single Electronic Transistor (SET). First, we have to introduce the coulomb blockade effect, which is the change of one elementary charge in a very small system each time and can be measured in the electrical and transport properties.
Coulomb blockade effect 
Fig. 12 (a) sketch of a quantum system to observe Coublumb blockade effects; (b) energy band distribution when an external voltage is applied through the dot.
In order to let one electron pass once, we can image such a quantum dot structure connected to the electrodes by tunnel junctions, as shown in Figure 12a. As many papers mentioned, the place between two junctions is an island, an island for electron. The junctions must be very thin, so that the electrons can go cross the barriers by tunnel effect, which is an identical quantum mechanism effect. Figure12b is the energies band distribution of the quantum dots, the discrete energy level is due to the small size of the quantum dots which is more like an atom or 3D quantum well which energy levels are discrete.
Suppose that there are N electrons in the dot, and we want to add only one electron into the island, for example. `We have to provide the potential energy eV to the electron by increase the voltage. If the charge in the dot is Q and its capacitance C, the potential energy is . Therefore, an energy of
need to be provided to the electron, at least if Q=0. This means that for the electron to enter the dot, the voltage, at least , have to be raised. Because the electron can move in or out the island, the electron can’t tunnel if . We can image that there must be a series stair cases in N-V curve as shown in Fig. 2, where N is the number of electron. If we keep adding more electrons one by one, we will observe discontinuities in the current through the quantum dot when the voltage increases:
, n=0, 1,2,…… (29)
Fig. 13 Charge of a quantum dot capacitor as a function of voltage, in normalized coordinates.
From the above equations, the energy necessary to change will be increase with the decrease the capacitance C. It will be easier to observe the Coulomb blockade effect if the change in electric energy much larger than the thermal energy kBT at the working temperature, where kB is Boltzmann’s constant. Therefore, the capacitance
So, if we want to observe the Coulomb blockade effect in Room temperature (300K), the capacitance must be lower than 6.2*10-18F. According to , where =8.85*10-14F/cm, is dielectric constant (16.2 for Ge), S is the area of the island facing to the junction, d is the distance of the capacitance. Supposed that =10, d=1nm, s= , then we can get r=4.7nm. So, the diameter of the island should be less than 10nm. Though this capacitance is too small to get, it can be realized using quantum dot.
Another condition to observe Coulomb blockade effect is that the number of electrons in the dot should not fluctuate in equilibrium. Let us assume that the time taken for an electron to be transferred in or out of the island is of the order of RTC, where RT is the equivalent resistance of the tunnel barrier and C the capacitance of the dot. Fluctuations in the number of electrons in the dot induce changes in potential energy of the order of . Therefore, according to uncertainty principle,
so, we can get
Single electron transistor
From the discussion above, we can see that for a basic device based on the single electron, there are two conditions have to be met. First, the change in electric energy when an electron enters or leaves the quantum dot, has to be larger than kBT, in another words is that the capacitance must be very small, this can be realized in quantum dot. Secondly, in order to avoid fluctuations in the number of electrons in the quantum dot, the resistance RT of the tunnel junction must be larger than the quantum resistance RQ=h/e2（25.8K ）, this can be realized by adjusting the thickness and the dielectric material, of course, the thickness can not be too thick to tunnel for electron.
The basic sketch map of the SET is shown in Figure 14(a). It basically consists of a quantum dot connected to the source and drain electrode through the tunnel junctions. The gate electrode coupled to the quantum dot by an insulating material, in order to avoid the electron tunnel through the barrier without bias voltage. As shown in the Figure 14(b), which is the equivalent circuit as the SET, the insulator layer formed as a capacitor, and the quantum dot is referred as a Coulomb island and is connected to the drain and source by two tunnel barriers. The number of electrons in quantum dot can be controlled by the external gate voltage, VG.
The current-voltage characteristics of the SET can be determined by applying a continuously sweeping voltage, VG to the gate electrode. Then, a charge CGVG is induced in the opposite plate of the gate capacitor, which is compensated by the tunneling of a single electron that enters the quantum dot. Due to the discrete charges that tunnel through the barriers, the current between the source and drain, IDS, will oscillate as increase the gate voltage, as shown in Figure 14(c).
(a) (b) (c)
Fig. 14 (a) Sketch map of SET,
(b) equivalent circuit, (c) current as a function of the gate voltage.
Many groups reported that their SETs can be operated in the low temperature, many of them were fabricated using conventional electron-beam lithography, so the capacitance of the island were very large. As mentioned above, the island size must be smaller than 10nm, the SET can be worked at room temperature, therefore the island must be the quantum dot. Because the quantum dot is very small, it cannot be moved to the proper place by the tool or fabricate by electron-beam lithography, it only can be grown or formed first and make the circuit around it.
Now, more and more groups used implanted oxygen technology to prepare the quantum dot for SET. Li et. al reported that they reported they successful used such a technology to fabricate the SET operated in the room temperature. The basic fabricate method as follows: first, they made a top Si/Si0.95Ge0.05/Si, 2/8/10nm respectively, multiplayer on silicon-on-insulator (SOI) substrate was patterned using electron-beam lithography and dry etching to from naorrow wire structure with the width of 20-50nm and the length of 50-120nm as shown in Fig. 4(a). Then, they oxidized the Si/Si0.95Ge0.05/Si completely, thus the Ge atoms will assemble together to form quantum dots. After thermal oxidation, a gate electrode and the circuit were fabricated.
(a) (b) (c)
Fig. 15 (a) Schematics of a Ge SET fabricated on a SiGe/SOI wafer. Ge QDs are formed by selective oxidation of Si0.95Ge0.05/SOI structure.
(b) top view TEM micrograph of a thermally oxidation Si0.95Ge0.05/SOI structure at 900℃ for 20min.
(c) Drain current as a function of gate voltage with a drain voltage of 50mV at RT.
From Figure 15, we can see that the average diameter of Ge quantum dots is less than 10nm, but the number of quantum dot in the island between the source and drain is more than 1, it is because the number of quantum dot is very difficult to control. I-V curve for the SET operated at RT is shown in Figure 15(c), as we can see that it is different from the ideal curve in Figure 14(c) due to the temperature. However, we can observe the oscillation due to the electron transfer into and out of the quantum dot.
As we can see above, this transistor can not used for signal amplification. But, we control the electron go through the junction one by one. And, the SET must be made in a small size. It would use less power, since the consumption is proportional to the number of electrons in the input current flow to the device. However, there are also some disadvantages for the SETs, the temperature effects was still a big problem for application. In such an advanced device, we are seeing two quantum charge: the quantization of charge, which allows you to have only a discrete number of electrons, as well as the quantization of the energy states assumed by those electrons
references : dari beberapa paper terbaru