Tunneling in Systems of Coupled Dopant-Atoms in Silicon Nano-devices
© Moraru et al. 2015
Received: 17 August 2015
Accepted: 15 September 2015
Published: 24 September 2015
Following the rapid development of the electronics industry and technology, it is expected that future electronic devices will operate based on functional units at the level of electrically active molecules or even atoms. One pathway to observe and characterize such fundamental operation is to focus on identifying isolated or coupled dopants in nanoscale silicon transistors, the building blocks of present electronics. Here, we review some of the recent progress in the research along this direction, with a focus on devices fabricated with simple and CMOS-compatible-processing technology. We present results from a scanning probe method (Kelvin probe force microscopy) which show direct observation of dopant-induced potential modulations. We also discuss tunneling transport behavior based on the analysis of low-temperature I-V characteristics for devices representative for different regimes of doping concentration, i.e., different inter-dopant coupling strengths. This overview outlines the present status of the field, opening also directions toward practical implementation of dopant-atom devices.
Within the past few decades, silicon metal-oxide-semiconductor field-effect transistors (MOSFETs) have undergone a tremendous miniaturization process [1, 2] which brings us within the era of nanoelectronics implemented in practical electronic and photonic devices. Commercially available transistors have now minimum features on the order of only a few tens of nanometers, a feat possible thanks to the great progress of nanotechnology but also to our increasing understanding of device operation at these extreme scales. Not only silicon [3, 4], but also two-dimensional materials [5–8], continue to exhibit interesting and novel functionalities when designed as MOSFETs. It is expected that further control in nanoscale will be achieved in the near future based on the steady improvement of knowledge and technology. However, it is also expected that the conventional operation mechanism of transistors—mainly based on drift-diffusion current flow—will be replaced by more fundamental physics [9, 10], such as quantum tunneling, which becomes a dominant phenomenon in nanoscale and ultimately at molecular and atomic scales as well. As transistors working based on conventional operation approach the end of their history, it becomes clear that alternatives must be developed and investigated for future generations of electronics. As a bridge between regular silicon-based nanoelectronics and future electronics at real molecular and atomic scale, a number of groups focus on the development of dopant-atom silicon nano-transistors and related devices [11–16]. Several state-of-the-art techniques have also been used to demonstrate proof-of-concept devices, either by using single-ion implantation (SII) technique  or using a scanning tunneling microscope (STM) tip atomic manipulation of Si surfaces . These results offer important insights into the fundamental levels of controllability at atomic scale, but they remain significantly complex and incompatible with CMOS processing technology.
In this Nano Review, we briefly outline the key aspects that must be addressed in order to clarify and improve the tunneling operation of dopant-atom devices. We will mainly focus on techniques that allow fabrication of dopant-atom devices with relative ease. For our devices, we use a thermal-diffusion doping technique that allows only a statistical control of the average number of dopants in the transistor channel. We also introduce selective-doping techniques that could allow, after further optimization, additional control of design parameters of silicon nano-transistors in different regimes of inter-dopant interaction strength .
We first show how individual or coupled dopants modulate the potential landscape in the channel of silicon nano-devices. For that purpose, we describe results obtained using a specially designed Kelvin probe force microscopy (KPFM) technique . We then show how dopant atoms or clusters of strongly-coupled dopants control the quantum-tunneling conductance in nanoscale transistors doped in different regimes of doping concentration. In that sense, we analyze low-temperature electrical characteristics that exhibit signatures of single-electron tunneling (SET) mediated by dopant-induced quantum dots (QDs) . Depending on the internal structure of the QD, i.e., number and interaction strength among dopants forming the QD, the current peaks exhibit distinct properties, illustrating electron transport via either atomic- or molecular-like structures.
Observation of Dopant-Induced Quantum Dots
The devices that we investigate are silicon-on-insulator field-effect transistors (SOI-FETs) with the channel usually doped with phosphorus (P) donors by thermal-diffusion doping. In silicon nano-transistors doped by such conventional doping technique, number and position of dopants in the channel cannot be precisely controlled. In order to understand the impact of dopants and of their distribution on the electrical properties of nano-transistors, it is essential to observe directly the modulation of the electronic potential induced by the dopants. For this purpose, we use a KPFM technique, specially designed to meet the requirements for measurements of dopants in devices under regular operation.
These requirements are all taken into consideration when designing our devices and the KPFM measurement system, allowing thus the observation of dopants present in the device channel with the free carriers removed. Depending on the doping concentration and channel design, it is possible to observe either isolated, individual P-donors (as schematically shown in Fig. 1b) or clusters of P-donors (as schematically shown in Fig. 1c).
Individual, Isolated Dopants in Low-Concentration Regime
In several of our previous publications, we reported the measurements of potential landscapes for devices with the channel doped with P-donors at an intermediate doping concentration level (N D ≈ 1 × 1018 cm−3) [20, 22–24]. For this concentration regime, average distance between neighboring P-donors is ~10 nm (> > 2 × r B ≈ 5 nm, with r B being the Bohr radius for P in Si). Thus, if P-donors are distributed according to a Poisson distribution, it is likely to find them reasonably isolated from each other, each locally modulating the potential of the channel. On the other hand, the potential modulation induced by such isolated P-donors is relatively low (only a few tens of meV).
We have also shown that, by increasing the temperature, free-electron screening becomes more dominant than the capture of electrons into different P-donors . This explains, based on more direct observations, why dopant-atom devices in which shallow P-donors are the active units in transport cannot work based on tunneling mechanism at elevated temperatures. An alternative approach to achieve elevated-temperature tunneling operation based on individual P-donors will be discussed in a subsequent section.
Coupled Dopants in High-Concentration Regime
In order to implement more complex functionalities, as well as to design more robust dopant-induced QDs, the QDs can be formed not by individual P-donors but by a number of P-donors placed closely to each other (within 2 × r B). In order to promote this regime, it is first of all required to increase the doping concentration (N D), ideally to values above the metal-insulator transition (MIT) concentration (for our design, typical concentration used is N D ≈ 1 × 1019 cm−3) .
Under such conditions, due to the strong interaction between neighboring P-donors, “clusters” of a larger number of donors will contribute to the formation of the QDs. It is, however, also required to isolate the highly doped QDs from source and drain leads in order to ensure the possibility of depleting the (quasi-metallic) channel. For that purpose, we use a selective-doping technique , in which a SiO2 doping mask is patterned by an electron beam lithography technique to preserve two fine non-doped regions acting as barriers on the sides of a highly doped slit. This way, the channel is doped only locally and, at the same time, self-aligned with source and drain leads, all regions having a doping concentration (N D) on the order of 1 × 1019 cm−3.
Single-Electron Tunneling via Dopant-Induced QDs
Typically, a small source-drain bias (V DS = 5 mV) is applied. The I D-V G characteristics exhibit, under such conditions, current peaks or current modulations, especially near the onset of the conduction. Such current peaks can be ascribed to Coulomb blockade transport through QDs existing in the device channel. The origin of the QDs is, at its turn, related to the P-donors purposely doped into the channel. Depending on the doping concentration regime and device design, different behaviors can be observed, allowing observation of single-electron tunneling via individual P-donors (as schematically illustrated in Fig. 4b) or multiple-donor clusters (as shown in Fig. 4c).
Tunneling Transport via Single Dopant-Atoms
In the lower-concentration regime (N D ≈ 1 × 1018 cm−3), it is expected that individual P-donors work as distinct QDs. As explained earlier, this assumption is most reasonable because, for this doping concentration regime, the average distance between neighboring P-donors is significantly larger that 2 × r B. Under such conditions, clusters of several donors are statistically unlikely to be formed. For long channels, the only way to realize tunneling conduction between source and drain would be by tunneling via an array of capacitively coupled P-donors. This condition can be useful for the design of a number of applications, such as dopant-based single-electron turnstiles [27, 28] or single-electron pumps [29, 30], but the behavior of such systems is quite complex. However, if the channel is short enough, it may be possible to identify a single P-donor as the dominant QD which completely controls tunneling transport between source and drain. Such a situation is schematically shown for a nanowire-channel SOI-FET in Fig. 4b. However, as long as the P-donors responsible for such transport are expected to be regular, shallow donors, tunneling transport is also expected to vanish at intermediate temperatures due to the significant contribution from thermally-activated carriers .
In order to enhance the tunneling-operation temperature, it is necessary to increase, first of all, the tunnel barriers. One way to do that is to take advantage of the dielectric confinement effect. It has been reported in a number of papers that dielectric confinement effect (when donors are embedded in nanostructures closely surrounded by an insulator) leads to a significant increase of the P-donors’ ionization energy [32–34]. In other words, the P-donors’ ground state becomes significantly deeper below the conduction band edge. Thus, for V G values corresponding to tunneling via the P-donor’s ground state, thermally activated conduction should be, in principle, suppressed even up to higher temperatures.
Alternatively, it may be expected that several P-donors closely located to each other (forming cluster-like configurations) can also lead to a QD with enhanced ionization energy. This cannot be the situation for the present devices, doped with a moderate doping concentration (N D ≈ 1 × 1018 cm−3) since the probability of formation of such multiple-donor clusters is reduced. This case will be discussed in the next section that deals with devices that have highly-doped channels.
Transport Via Clusters of Several Dopants
Although single dopants represent a fundamental level of control for electron transport in silicon nanodevices, for many practical applications it can be more useful to introduce a number of strongly-coupled P-donors to form the transport-QD. It was reported that, for silicon transistors with highly-doped channels, some disordered QDs can be formed due to the non-uniform distribution of dopants [37–39]. In our work, we dope our nanoscale-channels with higher doping concentration (N D ≈ 5 × 1018 − 1 × 1019 cm−3) in combination with the use of a selective-doping technique to allow more efficient depletion of the heavily-doped channels. We applied this method to fabricate narrow-channel SOI-FETs with selective doping done through a window (slit) having a final width of ~50 nm opened in a SiO2 doping mask layer . For these devices, it is critical to control as much as possible the thermal budget after doping, in order to minimize lateral diffusion of dopants within the nominally non-doped barriers. A schematic illustration of the channel of such a device is shown in Fig. 4c.
It is important to note that such molecular-like systems, with a rich energy spectrum and tunability of their properties, can also work as fundamental units for dopant-based devices, but they are significantly different than the case of individual, atomic P-donors. With further optimization of the selective-doping technique and additional understanding of inter-dopant coupling physics [25, 26] at the fundamental level and in extremely scaled-down structures, it can be expected that these systems can offer another pathway toward achieving high-temperature tunneling operation of dopant-based devices.
Pathways Toward High-Temperature Tunneling Operation of Dopant-Atom Transistors
Based on the discussion presented above, both for low-concentration and high-concentration regimes, we can identify several important factors that may play dominant roles in realizing tunneling operation of dopant-atom transistors at more elevated temperatures. This remains as a target for supporting the feasibility of such fundamental devices for practical applications. In fact, the physics involved in higher-temperature operation of dopant-based devices is practically the same involved in the operation of SETs made with lithographically-defined QDs. Therefore, it is reasonable to treat the efforts to achieve high-temperature operation in parallel for both dopant-atom devices and SETs.
We provided an overview of several recent results obtained for dopant-atom transistors in which dopants are introduced by thermal-diffusion doping in nanoscale-channels of SOI-FETs. We presented direct observations of dopant-induced potential landscapes measured using a KPFM technique, which show how individual P-donors or “clusters” of closely-placed P-donors modulate the channel potential. Electrical characteristics measured at low temperature reveal that transport occurs in these devices by single-electron tunneling mechanism. The nature of the QD is basically controlled by doping concentration and channel design. Generally, in low-concentration regime, single-electron tunneling via single P-donors is the usual transport mechanism. In the high-concentration regime, tunneling transport occurs through QDs formed by “clusters” of several P-donors located close to each other, inducing a molecular-like energy spectrum. Access to these different regimes of inter-dopant interaction is a first step toward designing and implementing practical applications that utilize systems of one or multiple dopant-atoms. This approach can provide insights into functionalities arising from atomic and, respectively, molecular systems built into the conventional Si-based electronics platform.
We tank E. Hamid, M. Anwar, R. Nowak, Y. Kuzuya, T. Tsutaya, Y. Takasu, and H. N. Tan for their support during experiments. This work was partly supported by the Grants-in-Aid for scientific research (KAKENHI 23226009, 25630144, and 26820127) from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan, and by the Cooperative Research Project of Research Institute of Electronics, Shizuoka University.
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