Observation of Transformation from Quantum Shuttle to Single-Electron Tunnel in Nanopillar Transistor∗

We reports observation of giant switching currents in nanopillar transistors at 300 K. It is found that these signals represent mechanical vibration due to the interaction of charging electron and the elastic materials of silicon and silicon nitride. Specifically, when an electron is charged to penetrate the SiNx/Si/SiNx multilayer, an electrical force will be initiated to make it vibrate. In addition, such motion will couple to the electronic state in the central Si island for the optimal exchange of elastic and quantum energy. As a consequence, in some mechanical modes, these coupled vibrations will make the transistor functioning like a self-coordinated switching pump for persistent tunnel of electrical current. [DOI: 10.1380/ejssnt.2009.518]


I. INTRODUCTION
Recently, the interaction of single-electron tunnel [1][2][3][4] and mechanical vibration in various quantum-dot transistors (SETs) has become an interesting topic for the understanding of how mechanical feedback can influence their transport behavior.It is known that such transport is featured by a series of isolated peaks in current-voltage (I-V) characteristics and the spacing between neighboring peak defines the charging energy Ec of an electron.While prior to the kind of process, Coulomb blockade (CB) strictly prohibits electrical current to flow.Notably, several recent studies have pointed out that that new features will appear in the CB and quantum shuttle [5,6] can make the central box vibrate with its amplitude reaching a stable limit at a large bias.Later, it is demonstrated that such vibration will induce detectable noises [7,8].As such, in this work, we examine these effects by conducting low-voltage measurements.Indeed, we observe many giant switching noises.We analyze them with a simple model and the results show that vibration is initiated by constant energy exchange in between electronics and mechanics at nanometer scale.

II. EXPERIMENTAL DETAILS
Our transistor, schematically shown in Fig. 1, was fabricated on a p-type (100) silicon wafer [9].The central box features a silicon island separated from the top and bottom electrodes by an nitride layer as illustrated by a TEM picture in Fig. 2.This cavity has a critical length of 3 nm and is intimately coupled to an side gate.The fabrication process is as follow; first we deposited multilayer structure of SiN x (3-nm)-polysi (3-nm)-SiN x (3-nm) in low-pressure chemical vapor sequentially, then we chemical etch to create a nominal plateau of ∼ 200 × 140 × 210 nm 3 .The electrode of source ∼ 200 nm was located at the bottom thick with a sheet resistance of ∼ 30 Ω/cm 2 by doping ∼ 1 × 10 19 cm −3 P + in the mixed gas of SiH 4 and PH 3 .To prevent electrical shortage, a short time oxidation (∼ 1.5 nm) was used by rapid thermal annealing for 30 sec to seal the nanopillar.
The electrode of drain was made on the top of nitride.To do this, a layer of tetraethylorthosilicate (TEOS) ∼ 200 nm thick was grown to level the height of the plateau and then spun coated a layer of photoresist (PR).After the process of another development, the exposed TEOS in the upper-right area was cleaned off following another chemical etch to further miniaturize the nanopillars (a short oxidation was also applied).The non-removable PR was used as a hard-mask for the coming wet etch in H 2 O and HF (ratio 50 to 1) for about 1 minute.This lateral etch then created an underneath cut and also opened an active zone (see Ref. [10]).After the strip of the PR, silicon was defined at a normal angle with respect to the  source.The overlapped region thus defines the dot that has a size dimension of ∼ 20 × 20 × 15 nm 3 .To further squeeze the dot, technique of self-limiting oxidation was used to add another ∼ 3 nm oxide, totaling of ∼ 6 nm thick to yield a quantum dot of ∼ 9 × 9 × 3 nm 3 .Sputter deposition and the final etch of Al (300 nm) was carried out to provide a side gate near the dot.
Devices were then loaded into a probe station (Thermal Cascade) for I-V measurements by using a three-terminal HP 4156 C which has 1 mV and 10 fA resolutions in ambient environment.Because of the small junction size, the typical current measured is very low in the range of sub pico-amp.The high junction resistance ∼ 10 12 Ω also reflects the excellent insulation of SiN x when electrons have to pass through the double barriers.Of all measurements, the bias voltage is always kept low (less than 1 V) in order to fit the need of low power operation.

III. RESULTS AND MODEL ANALYSIS
In Fig. 3, the data clearly shows many switching currents [10] that are distributed evenly between positive and negative, thus indicating that there is strong electromechanical coupling between the central box and the transport current.Integration of the power t 0 IdV delivered during that the span is zero, in favoring Coulomb blockade [5,6].The smooth reduction of I ds also suggests that the device vibrates like an oscillator [11] and at V ds ≤ 0.1 V, the frequency is found at about 10 3 ∼ 10 4 Hz by the modeling analysis in Fig. 6.Once the bias is above 0.25 V, the frequency increases to 10 8 ∼ 10 9 Hz for the resonance tunnel of single-electron as detected in Fig. 4 [12].Physically, such process can be understood by the mechanism as illustrated in Fig. 5, where the central box is connected horizontally to a linear spring K with a damper C. When an electrical force applied on them, the whole system will vibrate.To be proved in the following, such concept is useful as it not only can provide a microscopic origin for the dynamics, but it also can precisely describe the cur- rents measured.Based on the scenario, we model the system by an ordinary second-order differential equation (1), where variable x represents displacement and f (t) represents the forcing function.In the case of impulse x(t) = X 0 e −ξωnt cos(ω d t + φ). ( Since f (t) equals QeEt = 1.5 × 10 −9 t (eVs/m), Q = (n e ) 2/3 A where n e denotes the free charge density in electrode, A = 9 × 10 2 nm 2 the tunnel area, E = V d /d = 1.7 × 10 −10 V/m the maximum electrical field, Vd the maximum bias, and d = 3 nm the central Si layer thickness.In the charging period of 0.5 second, I is determined to be 1.5 × 10 −9 (eVs/m), ∆X = 1.6 Åfor a m = 1.56 × 10 −21 Kg and a ω d = 10 3 Hz.By using the electromechanical formula of I ds = ∆V n e eω d , the current induced can be calculated with e = 1.6×10 −19 C and ∆V the net volume deformed.As presented in Fig. 6, for a ω d (xi = 6 × 10 −3 ) of ∼ 10 8 Hz [11], the maximum I ds (t) found is ∼ 0.5 pA, which is in excellent agreement with the data.

IV. CONCLUSIONS
In conclusion, we have examined electron transport in nanopillar transistors at room-temperature.From the observation of giant switching currents at low bias, we find that electromechanical coupling is significantly in the silicon made quantum device.A simple model is proposed to quantitatively explain the data.The advance of analyzing such complicated behavior is important as is can help engineers and scientists to understand how elastic transistor will response themselves when they are operated at low voltages.
FIG. 2: TEM picture of the central layers.