T. R. Govindan

Two-dimensional quantum mechanical modeling of nanotransistors

Quantization in the inversion layer and phase coherent transport are anticipated to have significant impact on device performance in “ballistic” nanoscale transistors. While the role of some quantum effects have been analyzed qualitatively using simple one-dimensional ballistic models, two-dimensional (2D) quantum mechanical simulation is important for quantitative results. In this paper, we present a framework for 2D quantum mechanical simulation of a nanotransistor/metal oxide field effect transistor. This framework consists of the nonequilibrium Green’s function equations solved self-consistently with Poisson’s equation. Solution of this set of equations is computationally intensive. An efficient algorithm to calculate the quantum mechanical 2D electron density has been developed. The method presented is comprehensive in that treatment includes the three open boundary conditions, where the narrow channel region opens into physically broad source, drain and gate regions. Results are presented for (i) dr...

Coupling of carbon nanotubes to metallic contacts

The modeling of carbon nanotube-metal contacts is important from both basic and applied view points. For many applications, it is important to design contacts such that the transmission is dictated by intrinsic properties of the nanotube rather than by details of the contact. In this paper, we calculate the electron transmission probability from a nanotube to a free electron metal, which is side-contacted. If the metal-nanotube interface is sufficiently ordered, we find that k-vector conservation plays an important role in determining the coupling, with the physics depending on the area of contact, tube diameter, and chirality. The main results of this paper are: (1) conductance scales with contact length, a phenomena that has been observed in experiments and (2) in the case of uniform coupling between metal and nanotube, the threshold value of the metal Fermi wave vector (below which coupling is insignificant) depends on chirality. Disorder and small phase coherence length relax the need for k-vector conservation, thereby making the coupling stronger.

Simulation of the dc Plasma in Carbon Nanotube Growth

A model for the dc plasma used in carbon nanotube growth is presented, and one-dimensional simulations of an acetylene/ammonia/argon system are performed. The effect of dc bias is illustrated by examining electron temperature, electron and ion densities, and neutral densities. Introducing a tungsten filament in the dc plasma, as in hot filament chemical vapor deposition with plasma assistance, shows negligible influence on the system characteristics.

Ion Dynamics Model for Collisionless Radio Frequency Sheaths

Full scale reactor model based on fluid equations is widely used to analyze high density plasma reactors. It is well known that the submillimeter scale sheath in front of a biased electrode supporting the wafer is difficult to resolve in numerical simulations, and the common practice is to use results for electric field from some form of analytical sheath model as boundary conditions for full scale reactor simulation. There are several sheath models in the literature ranging from Child’s law to a recent unified sheath model [P. A. Miller and M. E. Riley, J. Appl. Phys. 82, 3689 (1997)]. In the present work, the cold ion fluid equations in the radio frequency sheath are solved numerically to show that the spatiotemporal variation of ion flux inside the sheath, commonly ignored in analytical models, is important in determining the electric field and ion energy at the electrode. Consequently, a semianalytical model that includes the spatiotemporal variation of ion flux is developed for use as boundary condit...

Uncertainty and sensitivity analysis of gas-phase chemistry in a CHF3 plasma

A global uncertainty and sensitivity analysis is performed for a detailed gas-phase reaction set in a CHF3 plasma. The goal of this paper is to ascertain the uncertainties in plasma reactor model results (plasma and radical densities) that originate from the uncertainties in the gas-phase chemistry database. We discuss the rates of reactions and their uncertainties. Comparisons with experimental data show that gas-phase rate uncertainties do not explain the disagreements at higher pressures (>30 mTorr). We also find that electron impact dissociation reactions of dominant neutrals are the largest sources of uncertainties. HF kinetics are also found to be critical in determining radical and feedstock gas densities. Relative ion densities are uncertain due to poor understanding of charge transfer mechanisms.

Monte Carlo sensitivity analysis of CF2 and CF radical densities in a c‐C4F8 plasma

A Monte Carlo sensitivity analysis is used to build a plasma chemistry model for octacyclofluorobutane (c‐C4F8) which is commonly used in dielectric etch. Experimental data are used both quantitatively and qualitatively to analyze the gas phase and gas surface reactions for neutral radical chemistry. The sensitivity data of the resulting model identifies a few critical gas phase and surface aided reactions that account for most of the uncertainty in the CF2 and CF radical densities. Electron impact dissociation of small radicals (CF2 and CF) and their surface recombination reactions are found to be the rate-limiting steps in the neutral radical chemistry. The relative rates for these electron impact dissociation and surface recombination reactions are also suggested. The resulting mechanism is able to explain the measurements of CF2 and CF densities available in the literature and also their hollow spatial density profiles.

Modelling of inductively coupled plasma processing reactors

A comprehensive model has been developed to study low-pressure, high-density plasma processing reactors. The model couples plasma generation and transport self-consistently to fluid flow and gas energy equations. The model and the simulation software have been used to analyse chlorine plasmas used in metal etching. The effect of the inductive coil frequency on the plasma characteristics has been examined and found to influence plasma uniformity only moderately. Model predictions for a CF4 plasma have been found to agree well with experimental results.

Semianalytical ion current model for radio-frequency driven collisionless sheaths

We propose a semianalytical ion dynamics model for a collisionless radio-frequency biased sheath. The model uses bulk plasma and electrode boundary conditions to predict the ion impact energy distribution and electrical properties of the sheath. The proposed model accounts for ion inertia and ion current modulation at bias frequencies that are of the same order of magnitude as the ion plasma frequency. A relaxation equation for ion current oscillations is derived, which is coupled with a damped potential equation in order to model ion inertia effects. We find that inclusion of ion current modulation in the sheath model shows marked improvements in the predictions of the sheath electrical properties and ion energy distribution function.

A coupled plasma and sheath model for high density reactors

We present a coupled plasma and collisionless sheath model for the simulation of high-density plasma processing reactors. Due to inefficiencies in numerical schemes and the resulting computational burden, a coupled multidimensional plasma and sheath simulation has not been possible for gas mixtures and high-density reactors of practical interest. In this work, we demonstrate that with a fully implicit algorithm and a refined computational mesh, a self-consistent simulation of a reactor including both the plasma and sheath is feasible. We discuss the details of the model equations, the importance of ion inertia, and the resulting sheath profiles for argon and chlorine plasmas. We find that at low operating pressures (10-30 mtorr), the charge separation occurs only within a 0.5-mm layer near the surface in a 300 mm inductively coupled plasma etch reactor. A unified simulation eliminates the use of offline or loosely coupled and oversimplified sheath models which generally leads to uncertainties in ion flux and sheath electrical properties.

Modeling of a helicon plasma source

A two-dimensional axisymmetric helicon plasma source with three-dimensional wave components is modeled. Plasma fluid equations are solved self-consistently with helicon wave equations. Electron inertia is taken into account to simulate the propagation of electrostatic wave components. The purpose of this paper is to describe the model in detail and present the results to verify wave propagation characteristics, power deposition mechanisms, especially bulk versus peripheral power absorption. We also study the effect of wave absorption characteristics on discharge plasma density and temperature profiles.