Dimitris P. Lymberopoulos

Fluid simulations of glow discharges : effect of metastable atoms in argon

A one‐dimensional fluid simulation of a 13.56 MHz argon glow discharge including metastable species was performed as an example of a coupled glow‐discharge/neutral‐transport‐reaction system. Due to the slow response time of metastables (∼10 ms) direct time integration of the coupled system requires ∼105 rf cycles to converge. This translates to prohibitively long computation time. An ‘‘acceleration’’ scheme was employed using the Newton–Raphson method to speed up convergence, thereby reducing the computation time by orders of magnitude. For a pressure of 1 Torr, metastables were found to play a major role in the discharge despite the fact that their mole fraction was less than 10−5. In particular, metastable (two‐step) ionization was the main mechanism for electron production to sustain the discharge. Bulk electric field and electron energy were lower, and a smaller fraction of power was dissipated in the bulk plasma when compared to the case without metastables. These results suggest that neutral transport and reaction must be considered in a self‐consistent manner in glow discharge simulations, even in noble gas discharges.

Two-Dimensional Self-Consistent Radio Frequency Plasma Simulations Relevant to the Gaseous Electronics Conference RF Reference Cell

Over the past few years multidimensional self-consistent plasma simulations including complex chemistry have been developed which are promising tools for furthering our understanding of reactive gas plasmas and for reactor design and optimization. These simulations must be benchmarked against experimental data obtained in well-characterized systems such as the Gaseous Electronics Conference (GEC) reference cell. Two-dimensional simulations relevant to the GEC Cell are reviewed in this paper with emphasis on fluid simulations. Important features observed experimentally, such as off-axis maxima in the charge density and hot spots of metastable species density near the electrode edges in capacitively-coupled GEC cells, have been captured by these simulations.

MODELING AND SIMULATION OF GLOW DISCHARGE PLASMA REACTORS

Large scale numerical simulations of the spatiotemporal plasma flow in low‐pressure (0.1–1 Torr) radio‐frequency capacitively coupled reactors were performed using a global plasma reactor model. Two‐dimensional argon glow discharge simulations coupled with neutral (metastable) transport and reaction provided insight on the discharge structure and radial plasma uniformity. A one‐dimensional simulation of a strongly electronegative (Cl2) discharge was also performed using the global model. Global model results suggested a ‘‘boundary layer’’ approach in which the reactor is separated into two regions: bulk plasma and sheath. The two‐region model was applied successfully to the Cl2 discharge.

Inductively Coupled Pulsed Plasmas in the Presence of Synchronous Pulsed Substrate Bias for Robust, Reliable, and Fine Conductor Etching

Inductively coupled pulsed plasmas in the presence of synchronous pulsed substrate bias are characterized in a commercial plasma etching reactor for conductor etching. The synchronous pulsed plasma characteristics are evaluated through the following: 1) Ar-based Langmuir probe diagnostics; 2) Ar/Cl2 plasma modeling utilizing the hybrid plasma equipment model and the Monte Carlo feature model for the investigation of feature profile evolutions; 3) basic etching characteristics such as average etch rate and uniformity; 4) sub-50-nm Dynamic Random Access Memory (DRAM) basic etching performance and profile control; and 5) charge damage evaluation. It is demonstrated that one can control the etching uniformity and profile in advanced gate etching, and reduce the leakage current by varying the synchronous pulsed plasma parameters. Moreover, it is shown that synchronous pulsing has the promise of significantly reducing the electron shading effects compared with source pulsing mode and continuous-wave mode. The synchronous pulsed plasma paves the way to a wider window of operating conditions, which allows new plasma etching processes to address the large number of challenges emerging in the 45-nm and below technologies.

Two-dimensional simulation of polysilicon etching with chlorine in a high density plasma reactor

A two-dimensional fluid simulation of polysilicon etching with chlorine in an inductively-coupled high density plasma source is presented. A modular approach was used to couple in a self-consistent manner the disparate time scales of plasma and neutral species transport. This way, complex plasma chemical reactions (involving electrons, ions and neutrals) as well as surface chemistry can be included in the simulation, The power deposited into the plasma was calculated by an electromagnetics module which solves Maxwells equations. The power deposition was used in the electron energy module to find the electron temperature and the rate coefficients of electron-impact reactions. These were in turn used as source terms in separate neutral and charged species transport modules. By iterating among the modules, a self-consistent solution was obtained. Quantities of interest, such as power deposition, species density and flux, and etch rate and uniformity were thus calculated, As power deposition was increased, the electron density increased linearly, the plasma became less electronegative, the degree of gas dissociation increased, and the plasma potential remained constant. The radial uniformity of the Cl atom flux was better than that of the ion flux. The reactivity of the wafer as compared to that of the surrounding electrode surface significantly affected the etch uniformity, despite the low pressure of 10 mtorr. >

Rapid two-dimensional self-consistent simulation of inductively coupled plasma and comparison with experimental data

A methodology has been developed to achieve rapid two‐dimensional self‐consistent simulation of plasma transport and reaction in an inductively coupled source of arbitrary geometry and with arbitrary plasma and surface chemistries. In this modular finite element fluid simulation the reactor was divided into bulk plasma and sheath. The bulk plasma was assumed quasineutral and the electrons were assumed to be in Boltzmann equilibrium. Separate modules computed the power deposition into the plasma, electron temperature, charged species densities, and neutral species densities. Simulation results agreed favorably with available experimental data, taken in a chlorine plasma in a Gaseous Electronics Conference reference cell, without using any adjustable parameters. Rapid convergence makes the simulation tool especially attractive for technology computer‐aided design (TCAD) applications.

A two-region model of a radiofrequency low-pressure, high-density plasma

A two-region model of a low-pressure, high-density RF excited discharge was developed. A well-mixed bulk plasma model was coupled to a collisionless sheath to predict the species density, the time-dependent electron-velocity distribution function and the ion bombardment flux and energy. The model was applied to a chlorine discharge sustained in a transformer-coupled plasma reactor. The discharge was found to be moderately electronegative; the negative ion to electron density ratio increased with increasing pressure, decreasing power and/or increasing wall recombination probability gamma of the Cl atoms, Under these conditions the dominant ion was Cl2+. On the other hand, low pressure, high power and/or small gamma resulted in a large degree of gas dissociation; the dominant ion was then Cl+. The ion flux to the walls increased linearly with power and decreased with pressure. The model predictions were in reasonable quantitative agreement with experimental measurements. The model is most useful for sorting out the complex chemistry of plasmas and for rapid evaluation of expected reactor performance.

Fluid simulations of radio frequency glow discharges: Two-dimensional argon discharge including metastables

Two‐dimensional self‐consistent fluid simulations of a 13.56 MHz argon glow discharge including metastable species were performed as examples of a coupled glow‐discharge/neutral‐transport‐and‐reaction system. The electron density was found to peak in the radial direction. The metastable density profiles showed ‘‘hot spots’’ in both axial and radial directions.

Fluid simulation of a pulsed-power inductively coupled argon plasma

A one-dimensional fluid model was developed and used to investigate the spatiotemporal dynamics of a pulsed-power inductively coupled argon plasma at 10 mTorr. Particular attention was devoted to extraction and acceleration of positive ions by a radio frequency (rf) bias applied in the afterglow stage of the discharge. For bias frequencies in the range ω/2π=100 kHz–10 MHz the rf sheath is resistive in nature. Significant oscillations of the ion flux at the driven electrode observed at ωτ≈1 are related to the finite ion transit time τ through the sheath. The latter depends on the sheath thickness which is a complicated function of time in the pulsed plasma. For a constant time-average power, the time-average ion energy flux bombarding the wafer has a minimum with respect to the pulse period. This has implications for the wafer thermal budget.

Ion density and temperature distributions in an inductively coupled high-plasma density reactor

In a low-pressure plasma, the ion temperature T/sub i/ is comparable to the gas temperature T/sub g/ in regions of weak electric fields, but T/sub i/ can be more than an order of magnitude higher than T/sub g/ near the plasma sheath.