Frequency Rf Bias Research Articles

Second-harmonic currents in rf-biased, inductively coupled discharges

Capacitively-coupled plasmas generate strong current or voltage signals at harmonics of their driving frequencies. Inductively coupled plasma (icp) systems generally do not, unless they are equipped with capacitively-coupled rf bias, which generates strong signals at harmonics of its driving frequency. Recently, however, at an asymmetric, rf-biased electrode, a current component was detected at the second harmonic of the inductive source frequency, not the rf-bias frequency. The origin of this current is here investigated (in argon discharges at 1.3 Pa) by comparison with measurements made at a symmetric electrode and predictions made by two numerical models. The first simulates the sheath at the rf-biased electrode; the second models the plasma. Because capacitive coupling from the inductive source was minimized by a Faraday shield, the nonlinearity of the sheath contributes negligible second-harmonic current. Modulation of the photon flux in the plasma, however, produces a second-harmonic current photoemitted from the rf-biased electrode. The external circuitry and nonlinear inductive coupling produce a second-harmonic sheath voltage, which in turn generates second-harmonic current both directly and through a transit-time effect. The second model simulates how electrons emitted from the electrode—and then reflected at the quartz dielectric window of the inductive source—are deflected by the electric and magnetic fields in the plasma. It also gives predictions for the transit-time effect. Magnetic deflections and the transit-time effect usually dominate the electric deflection. Together these three mechanisms produce a second-harmonic current that has a Fourier amplitude approximately half the current that is elastically reflected at the icp window. These results suggest it may be possible to use the second-harmonic current to determine the elastic reflection coefficient at the window.

Effects of RF bias frequency and power on the plasma parameters and ash rate in a remote plasma source

The effects of the RF bias frequency (2–27.12 MHz) and power (0–50 W) on plasma parameters, i.e., effective electron temperatures, electron densities, and electron energy probability functions (EEPFs), were investigated in a remote plasma source. A small cylindrical Langmuir probe based on the Druyvesteyn method was used for the measurements. When the bias power was changed from 0 W to 10 W for each bias frequency, the electron density decreased and the effective electron temperature increased at a given antenna power. As the 2 MHz bias power increased to 50 W, the electron density increased remarkably, whereas the effective electron temperature decreased. Simultaneously, the EEPF evolved from a Druyvesteyn-like distribution to a nearly Maxwellian distribution. In contrast to 2 MHz, when increasing the bias power of 12.5 MHz or 27.12 MHz, there was no distinct change in the effective electron temperature by the bias power and the electron density increased slightly or barely changed. Moreover, the EEPFs retained a Druyvesteyn-like distribution during the bias power increase. These results reveal that the plasma parameters are more controllable at lower bias frequencies, and the analysis is presented in relation to the electron heating mechanism. Therewithal, the ash rate for a 2 MHz bias power was observed to be the highest among the three frequencies when the discharge was operated with pure oxygen.

“Virtual IED sensor” at an rf-biased electrode in low-pressure plasma

Energy distribution and the flux of the ions coming on a surface are considered as the key-parameters in anisotropic plasma etching. Since direct ion energy distribution (IED) measurements at the treated surface during plasma processing are often hardly possible, there is an opportunity for virtual ones. This work is devoted to the possibility of such indirect IED and ion flux measurements at an rf-biased electrode in low-pressure rf plasma by using a “virtual IED sensor” which represents “in-situ” IED calculations on the absolute scale in accordance with a plasma sheath model containing a set of measurable external parameters. The “virtual IED sensor” should also involve some external calibration procedure. Applicability and accuracy of the “virtual IED sensor” are validated for a dual-frequency reactive ion etching (RIE) inductively coupled plasma (ICP) reactor with a capacitively coupled rf-biased electrode. The validation is carried out for heavy (Ar) and light (H2) gases under different discharge conditions (different ICP powers, rf-bias frequencies, and voltages). An EQP mass-spectrometer and an rf-compensated Langmuir probe (LP) are used to characterize plasma, while an rf-compensated retarded field energy analyzer (RFEA) is applied to measure IED and ion flux at the rf-biased electrode. Besides, the pulsed selfbias method is used as an external calibration procedure for ion flux estimating at the rf-biased electrode. It is shown that pulsed selfbias method allows calibrating the IED absolute scale quite accurately. It is also shown that the “virtual IED sensor” based on the simplest collisionless sheath model allows reproducing well enough the experimental IEDs at the pressures when the sheath thickness s is less than the ion mean free path λi (s < λi). At higher pressure (when s > λi), the difference between calculated and experimental IEDs due to ion collisions in the sheath is observed in the low energy range. The effect of electron impact ionization in the sheath on the origin and intensity of low-energy peaks in IED is discussed compared to ion charge-exchange collisions. Obviously, the extrapolation of the “virtual IED sensor” approach to higher pressures requires developing some other sheath models, taking into account both ion and electron collisions and probably including even a model of the whole plasma volume instead of plasma sheath one.

Influence of pulsed bias frequency on the etching of magnetic tunneling junction materials

The effect of different bias frequencies during the etching of magnetic tunneling junction materials in an inductively coupled plasma with rf pulse biasing (50% duty percentage) on etch characteristics was investigated. The decrease of rf bias frequency from 13.56 MHz to 400 kHz while keeping the same average dc bias voltage at −300 V increased not only the etch rates of MTJ related materials but also the etch selectivities. We observe improved etch characteristics of CoFeB and CoPt, and also improved etch profiles of CoPt, CoFeB and MTJ (CoPt/MgO/CoFeB) masked with nanoscale W(100 nm)/Ti(20 nm)/Ru(5 nm) at lower bias frequencies. The observed improvements are attributed to the higher sputter yields due to the wider ion energy distribution (with increase high energy component) for the metal carbonyl related compounds formed during the etching of MTJ materials with CO/NH3 etchant gas.

Model for Effects of RF Bias Frequency and Waveform on Si Damaged-Layer Formation during Plasma Etching

We investigated damaged-layer formation on the Si substrate surface induced by high-energy ion bombardment during plasma processing, by focusing on ion energy distribution function (IEDF). We introduced a modified range theory for the projection of incident ions and applied the model to damaged-layer formation under various plasma conditions – various rf bias frequencies and waveforms, furthermore their single- or dual-frequency bias configurations. Damaged-layer thickness and residual defect site density after the wet-etch process following the plasma treatment were simulated. The IEDF having more high-energy ions induces the formation of thicker damaged layer than in the case of a monochromatic ion energy when the average ion energies are the same. However, we found that, owing to the stochastic effect on the ion-projected range, the effects of bias frequency and the waveform were suppressed, i.e., the thickness of the damaged layer and the density of residual defect sites are weakly dependent on IEDFs under the same average incident ion energy. The present findings obtained by the model prediction are significant and useful for designing bias configurations for future plasma processes.

Model for Effects of RF Bias Frequency and Waveform on Si Damaged-Layer Formation during Plasma Etching

Model for Effects of RF Bias Frequency and Waveform on Si Damaged-Layer Formation during Plasma Etching

Bias frequency dependence of pn junction charging damage induced by plasma processing

Plasma-induced charging damage to pn junction in metal-oxide-semiconductor field-effect transistors (MOSFETs) was studied by using an inductively coupled plasma (ICP) reactor with Ar gas. The junction leakage current ( I leak) was measured for various source/drain to well in MOSFETs and simple diode structures. Two different rf bias frequencies, 13.56 MHz and 400 kHz, were utilized to investigate the effect of frequency on an increase in I leak. The I leak of n +/p and p +/n junctions was found to increase by a plasma treatment. In particular, more severe damage was observed for n +/p junction in both n-channel MOSFETs and the diodes. These observed results imply that plasma plays a role primarily as a positive current source. With regard to the rf bias frequency effects, samples exposed to the 400-kHz plasma were found to suffer from larger I leak than those to the 13.56 MHz. From capacitance–voltage ( C– V) measurement of junction capacitance changes, we also clarified that the observed increase in I leak was attributed to the defect density at pn junction created by the plasma charging damage.

Effect of bias in patterning diamond by a dual electron cyclotron resonance–radio-frequency oxygen plasma

Arrays of microhole patterns are fabricated on the surfaces of diamond films through a physical mask in a dual microwave electron cyclotron resonance/radio-frequency oxygen plasma. It is found that nanotips with high aspect ratio form in the microholes, and then through-holes are fabricated with a further increase of etching time. Optical emission spectroscopy was employed to calculate oxygen atom density and evaluate the variation of the plasma excitation temperature. The plasma excitation temperature and the O atom density present significant dependences on the voltage of rf bias V b at a high frequency of 13.56 MHz, suggesting that the application of the rf bias not only strengthens ion bombardment on the material surface, but also induces the variations of the bulk plasmas including the increase of O atom density. Whereas, both the plasma excitation temperature and the O atom density remain nearly unchanged with V b under the bias frequency of 400 kHz. The etching process depends on the rf-bias frequency and voltages, which are correlated with the measured plasma characteristics.

Ion energy distributions at a capacitively and directly coupled electrode immersed in a plasma generated by a remote source

Ion energy distributions are investigated in an inductively coupled radio-frequency discharge at low pressures. A Langmuir probe is used to characterize the discharge and a retarding field energy analyzer measures the ion flux and energy distributions impacting a remote rf driven electrode. Comparisons are made between capacitive and direct coupling of the rf bias potential. The effects of ICP power, rf bias voltage (0–75 V amplitude), bias frequency (0.5–20 MHz) and discharge pressure (0.2–1.2 Pa) are presented. Results are shown for Ar, O2 and Ar–He discharges. A double layer was observed during source characterization measurements in an O2 discharge; however, the focus of this paper is on the behavior of ions through capacitively and directly coupled plasma sheaths.

Retarding field analyzer for ion energy distribution measurements at a radio-frequency biased electrode

A retarding field energy analyzer designed to measure ion energy distributions impacting a radio-frequency biased electrode in a plasma discharge is examined. The analyzer is compact so that the need for differential pumping is avoided. The analyzer is designed to sit on the electrode surface, in place of the substrate, and the signal cables are fed out through the reactor side port. This prevents the need for modifications to the rf electrode--as is normally the case for analyzers built into such electrodes. The capabilities of the analyzer are demonstrated through experiments with various electrode bias conditions in an inductively coupled plasma reactor. The electrode is initially grounded and the measured distributions are validated with the Langmuir probe measurements of the plasma potential. Ion energy distributions are then given for various rf bias voltage levels, discharge pressures, rf bias frequencies--500 kHz to 30 MHz, and rf bias waveforms--sinusoidal, square, and dual frequency.

Effect of rf Pumping Frequency and rf Input Power on the Flux to Voltage Transfer Function of rf-SQUIDs

We present the results on the correlation between the flux to voltage transfer function, Vspp, of the rf-SQUID and the rf-bias frequency as well as rf-bias power. Measurements were performed for different SQUID gradiometer samples chosen from the same batch or different batches. In order to have full control on the electronics parameters, an experimental rf-SQUID circuit was designed and implemented with an operation frequency of 600 MHz to 900 MHz. According to our findings, it has been observed that at any particular rf-bias power, Vspp vs. rf-bias frequency shows Sinc-like behavior. We observed that the main lobe maxima exist close to the resonance frequency of the LC tank circuit and by changing only the power, amplitude of the main lobe and side lobes can be controlled. The Vspp vs. rf-bias power analysis shows that maximum of Vspp, strongly depends on the bias frequency. This can be correlated with the S11 parameter of LC tank circuit. We also observed that the devices from the same batch show main lobe maxima at different frequencies and/or power. Our SQUIDs with high working frequency gave their maxima at lower rf-bias powers leading to the need of having high frequency electronics with low bias power handling capabilities. It has also been observed that the SQUIDs from the same chip show similar characteristics regarding Vssp vs. frequency and power while the SQUIDs from different batches show completely different behavior for a fixed LC tank circuit configuration.

Effects of wafer impedance on the monitoring and control of ion energy in plasma reactors

Ion kinetic energy in plasma reactors is controlled by applying radio-frequency (rf) substrate bias, but the efficiency and reproducibility of such control will be affected if the wafer being processed has a significant electrical impedance. Here, the effects of wafer impedance were studied by modeling and electrical measurements. Models of wafer impedance were proposed and tested by comparing model predictions to measured electrical wave forms. The tests were performed in an inductively coupled plasma reactor in 50% Ar, 50% CF4 gas at a pressure of 1.33Pa (10mTorr), rf bias frequencies of 0.1–10MHz, rf bias amplitudes of 20–300V, and inductive source powers of 100–500W. At high bias frequencies, the dominant contribution to the wafer impedance was the capacitance of the gap between the wafer and its chuck. At low bias frequencies, however, a resistance associated with the contact between the wafer and the chuck became significant. Electrical wave forms and ion energy distributions were most sensitive to wafer impedance at low bias frequencies and low bias amplitudes. At low bias frequencies, model predictions indicate that the wafer impedance produces an undesirable variation in surface potential, sheath voltage, and ion energy across the wafer surface. Because it neglects wafer impedance effects, a technique that analyzes electrical wave forms to determine ion currents, sheath voltages, and ion energy distributions was found to suffer significant errors at low bias frequencies and amplitudes. Nevertheless, the technique provided accurate results at moderate to high bias frequency and amplitude.

Simulation of ion transport characteristics in a collisionless rf sheath

With a self-consistent fluid model, we study the transport characteristics of the collisionless radio frequency (rf) sheath in a high density plasma and calculate the spatiotemporal ion density and the potential drop across the sheath in one rf cycle for an rf-bias frequency of 13.56 MHz. We also study the effects of the rf frequency on the voltage at the electrode, the sheath width, the ion energy distribution (IED) and the ion angular distribution (IAD) at the electrode. The simulated results indicate that the incidence angles of the ions impinging on the electrode are less than 8° when the ion velocity in the direction perpendicular to the sheath field is assumed to be a Boltzmann distribution. It is concluded that the rf frequency plays a crucial role for the energy and angular distributions of ions impinging on the electrode surface, and the IED and IAD are affected by the plasma density and the rf-bias power.

Analytical model for ion angular distribution functions at rf biased surfaces with collisionless plasma sheaths

The article presents an analytical model for evaluation of ion angular distribution functions (IADFs) at a radio frequency (rf)-biased surface in a high-density plasma reactor. The model couples a unified rf sheath model to an assumed ion velocity distribution function-based formulation for determining the IADF under any general rf-bias condition. Under direct-current (dc) bias conditions the IADF profile shape shows a strong dependence on the bias voltage and the ion temperature is relatively independent of the plasma electron temperature, ion density, and the ion mass. The model establishes the importance of rf-bias frequency in determining the IADF. For conditions where the sheath current wave form is sinusoidal, low bias frequencies result in a large-angle tail contribution to the IADF which can potentially lead to poor anisotropic plasma etching behavior. The large-angle tail is absent at higher bias frequencies. An increase in bias power leads to a general narrowing of the IADF, but the large-angle tail for the IADF at low frequencies persists despite increasing bias powers. Therefore, plasma etch anisotropy can be improved by increasing bias powers only if the bias frequency is sufficiently high. Tangential ion drift velocities introduce azimuthal angle dependence on the IADF and a shift in the peak IADF to off-normal polar angles. While the location of the peak IADF in the azimuthal direction is dictated purely by the direction of the drift velocity, the shift in peak IADF in the polar angle depends on both the drift velocity as well as the bias frequency.

Dynamic model and electrical characteristics for rf-biased electronegative plasma sheath

The dynamic model for the sheath of an RF-biased electronegative plasma is developed. The low-pressure high-density plasma conditions are assumed and considered as an electric-field-free boundary. The Bohm criterion for collisionless sheath is assumed to be valid and the presheath region is separately considered in calculating the sheath properties. The electron density n/sub e/ and the electronegativity /spl alpha/ /spl equiv/ n/sub -//n/sub e/ are taken to be determined independently of the sheath dynamics. The time-resolved wave forms of the sheath potential and thickness are obtained. The characteristics for the RF power dissipation mechanisms are also investigated. The RF bias power is assumed to be dissipated through two power loss channels - the first is due to ion acceleration in the sheath and the second is due to the electron heating at the plasma-sheath boundary. From the power loss point of view, the equivalent circuit model is developed and the sheath impedance is calculated. The electronegativity, as well as the current and RF bias frequency, is found to be an important factor in determining the electrical characteristics for the RF-biased electronegative plasma sheath.

Probability theory of the velocity distribution of ions incident on a radio-frequency biased wafer

Ion velocity distribution (IVD) at a radio frequency (rf) biased wafer is obtained analytically using probability theory. The obtained IVD is explicitly correlated to macroscopic plasma parameters such as rf bias amplitude, rf bias frequency, penetration depth of bias potential, mass of an ion, and time-averaged potential drop. This analysis is applicable for the case when the rf period of biasing is much shorter than the time that ions take in traversing the sheath.

Measuring the ion current in high-density plasmas using radio-frequency current and voltage measurements

The total current or flux of ions striking the substrate is an important parameter that must be tightly controlled during plasma processing. Several methods have recently been proposed for monitoring the ion current in situ. These methods rely on passive, noninvasive measurements of the radio frequency (rf) current and voltage signals that are generated by plasma-processing equipment. The rf measurements are then interpreted by electrical models of the plasma discharge. Here, a rigorous and comprehensive test of such methods was performed for high-density discharges in argon at 1.33 Pa (10 mTorr) in an inductively coupled plasma reactor, at inductive source powers of 60–350 W, rf bias powers up to 150 W, and rf bias frequencies of 0.1–10 MHz. Model-based methods were tested by comparison to direct, independent measurements of the ion current at the substrate electrode made using lower frequency (10 kHz) rf bias and modulated rf bias. Errors in two model-based methods are identified and explained by effects that are present in the high-density plasmas but are not included in the models. A third method, based on a new, more accurate numerical sheath model, gives values of the ion current in agreement with the independent measurements.

Sheath model for radio-frequency-biased, high-density plasmas valid for all omega/omega(i)

A model is proposed for sheaths in high-density discharges, with radio-frequency (rf) bias applied at frequencies omega comparable to omega(i), the ion plasma frequency at the edge of the sheath. The model treats ion dynamics using fluid equations, including all time-dependent terms. Model predictions for current, impedance, and power were compared to measurements performed in high-density discharges in argon at 1.33 Pa (10 mTorr) at rf bias frequencies from 0.1 to 10 MHz (omega/omega(i) from 0.006 to 1.8) and rf bias voltages from 1 to 200 V. Model predictions were in good agreement with measurements, much better than that obtained by models that neglect time-dependent ion dynamics. In particular, differences of as much as 40-50 % between power measurements and the power predicted by previous models are now explained and eliminated. The model also explains why methods of extracting plasma parameters from electrical measurements using previous sheath models may fail, and it suggests more accurate methods of extracting these parameters.

Effect of bias voltage waveform on ion energy distribution

Ion energy distribution (IED) is one of the primary factors governing the etching or deposition characteristics in plasma-aided microelectronics manufacturing processes. This article explores the influence of rf bias voltage waveform and frequency on the IED. It is demonstrated that the sheath voltage above the wafer is reasonably similar to the rf voltage on the biased substrate. Since the IED correlates well with the sheath voltage if the ion transit time through the sheath is smaller than the rf time period, the IED can be controlled by means of the rf bias voltage. The voltage waveform controls the shape of the distribution while the frequency determines its width. The sinusoidal waveform leads to a distribution that peaks at high energies and gradually decreases with decreasing energy. Square wave results in a sharp step in the IED at high energies, the width of which can be controlled by means of the blocking capacitance. The triangular waveform generates a constant IED over a considerable range of energy. It is also demonstrated that, by utilizing the correlation between the IED and applied voltage waveform, one can design voltage waveforms that produce distributions with specific features.

Effects of radio frequency bias frequency and radio frequency bias pulsing on SiO2 feature etching in inductively coupled fluorocarbon plasmas

The effect of radio frequency (rf) bias frequency on SiO2 feature etching using inductively coupled fluorocarbon plasmas is investigated. It is found that the rf bias frequency can have an important effect on SiO2 feature etch rate, microtrenching phenomena, and SiO2-to-photoresist etch selectivity. In addition, the effect of rf bias pulsing on inductively coupled fluorocarbon plasma SiO2 etching has been studied and a model that describes the data well is presented. The model assumes that fluorocarbon deposition occurs while the rf bias is off, fluorocarbon etching occurs during the first part of time that the bias is on, and substrate etching occurs once the fluorocarbon material has been removed from the substrate.