Transport Behavior of Nanowire Devices

The paradigm shift caused by NW creates whole new concepts and perspectives on device physics and possibilities that conventional planar counterparts have yet to offer.

From a microscopic point of view, this kind of low-dimensional structure is suitable for studying quantum-mechanical effects. Many reports focused on the carrier transport properties in NW devices for which well-established theories of three- or two-dimensional materials are no longer appropriate. Energy bands are split into sub-bands and the energy levels become discrete by the tiny volume of NW [1-30].

Because of the nano-scale cross section that confines the wave functions of sub-bands, carriers in NW devices must transport through a large number of one-dimensional sub-bands. Quantum confinement, sub-band splitting, and surface and interface relaxation [1-31]-[1-33], etc. are among a plethora of effects that must be taken into

account in order to correctly interpret the NW characteristics, including unexpected increase of threshold voltage (VTH) with reduced NW width [1-34], oscillation of drain current and mobility [1-32], and reduced Stark effect [1-35]. Recently, dopant distribution has been identified as another major factor in influencing the carrier conduction behavior in ultra-short NW devices [1-36]. Simulation results have shown that NW transistors may approach ballistic transport [1-37], i.e., a carrier does not experience any collision with other carriers or elastic centers during its traverse from the source toward the drain. In the quasi-ballistic model proposed by Lundstrom [1-38][1-39] where there is no sufficient scattering events occurring inside a short channel MOSFET device, backscattering effects near the source start to become prominent, but since this effect is linked to the source side mobility, the concept of mobility is still relevant. On the other hand, if the channel length is scaled further (less than 10 nm [1-40]), no scattering events would occur and in this scenario the transport of carriers operates in the full ballistic regime. Drain current under ballistic transport has been shown to depend only on the carrier concentration near the source and the injection velocity at the peak of the barrier at the source side [1-41][1-42], which is determined solely by the thermal velocity in the case of non-degeneracy. Thus, the concept of mobility becomes meaningless, leading to a profound change of mindset on how the carrier transport properties should be examined. For typical short channel planar devices,

scattering defects associated with pocket implant near source/drain junctions result in mobility degradation as the channel length is made shorter [1-43][1-44]. Even though NW exhibits similar behavior that the “extracted” mobility tends to decrease with reduced channel length, this is essentially an artifact and can be explained by the

“ballistic mobility” model [1-45]. As a matter of fact, since NW has entered into ballistic regime, the measured mobility no longer determines the transport property and the actual transport behavior will not degrade with channel length scaling [1-46]. In other words, not only does NW device possess better immunity against SCE, it is also promising to provide ballistic transport when being downsized to ultra-short channel lengths. Another intriguing effect exclusive to NWs is that the drain current of linear regime (low VD) in strong inversion is found to decrease with decreasing temperature, which is shown to be caused by the inter-sub-band scattering induced by quantum confinement [1-32]. Yet, in saturation regime (high VD), this effect is diminished and the mobility-temperature relationship again resorts to what is dictated by phonon scattering.

In addition, differential conductance fluctuations are observed in output curves as the series resistance of the drain extension is changed by the interplay between inter-sub-band transitions and quasi-ballistic transport [1-47].

One concept called “quantum capacitance limit” introduced recently further highlights the performance advantage of 1-D NW device over bulk counterparts in

terms of the power delay product improvement that can be achieved from scaling [1-48].

To realize a well-behaved device that exhibits electrostatic integrity, two major conditions should be fulfilled. First, the maximum of surface potential in the channel that governs the injection of carriers from the source is mainly modulated by the gate voltage instead of the drain voltage. Second, the oxide capacitance ought to be much larger than the inversion layer or quantum capacitance, which is the change of channel charge with respect to the surface potential. The first condition is always met as long as the channel length is much longer than the natural scaling length [1-49], whereas the second one is dependent on the operation state of the device. In the off-state, the quantum capacitance is nearly zero because the channel charge shows little variation.

However, in the on-state, this capacitance is proportional to the density of states present in the channel [1-50], which increases with the gate voltage in a bulk device.

Accordingly, the modulation of the surface potential is less efficient in the on-state, explaining the gradual increase of the subthreshold swing with a larger gate voltage of a conventional device. The scenario is vastly different in the case of 1-D NW device for which the density of states is inversely proportional to the square root of the difference between the carrier energy and surface potential [1-50]. Consequently, it is easier for NW to reach the so-called quantum capacitance limit, where the gate dielectric capacitance readily exceeds the quantum capacitance and the gate electrode is still able

to provide ideal control of the surface potential in the on-state. In other words, the thickness of the gate dielectric in a 1-D NW transistor required to meet the criterion of quantum capacitance limit can be thicker and is much more technologically feasible than the bulk devices.

To fully capture the underlying physical mechanisms of NW requires devices with sub-10 nm channel length, which are still difficult to fabricate if not impossible [1-15], thus most works only use theoretical formalism to predict the transport behavior of NW devices. Some commonly utilized ones are Boltzmann transport equation [1-51], non-equilibrium Green’s function (NEGF) [1-52][1-53], and quantum diffusion method [1-54]. Each of these approaches is suitable only for some specific conditions depending on the temperature and channel length considered. Additional approximations are needed as well to simplify the complexity of NW band structures and reduce the computational time. Hence, it still takes further advance in process technology and development of more precise theoretical modeling to gain a comprehensive insight into the potential of NW transistors.