Quantum Single Sensor | Deposition Rate & Ion Energy Analysis

Quantum Single Sensor

Weighing Up Your Options

The Quantum energy resolved gridded quartz crystal microbalance is a unique instrument to measure the ratio of ions to neutrals hitting a surface inside a plasma reactor, sometimes called the ion neutral fraction.

This cutting edge instrument also measures the deposition rate, ion energy, ion flux and bias voltage.

The ratio between neutrals and ions arriving at a surface, be it biased or grounded is now measurable by this groundbreaking system.


Features

Substrate Bias Compatible | High RF Bias Resistant |
Easily Installed | High Temperature Resistant | No Cooling Required


Applications

Ion-Neutral Depostion Rate Mapping | Process Uniformity |
Process Development | Equipment Design




Overview

The Quantum Single Sensor measures the ion neutral fraction or the flux ionization fraction arriving at a surface inside a plasma reactor. It also measures the deposition rate, ion energy, ion flux and bias voltage at any location inside a plasma reactor. The Quantum Single Sensor or gridded quartz crystal microbalance is widely used in many sectors across industry and research, such as plasma deposition, coatings, plasma sputtering, PECVD, etching and ion beam. It provides the flux ionization fraction, a measurement which is vital in most plasma applications but so far has been very hard to achieve. Ionization ratios find applications in researching new processes, confirming new recipes and models and can be used in the development of new tools and plasma processes.

The sensor consists of 19" rack mounted electronics unit, vacuum feed-through, sensor holder which sits at any position inside a plasma chamber, even on a powered electrode and a replaceable Button Probe sensor. Users connect to the electronics unit with a laptop or a PC and take measurements using the Quantum intelligent software suite. It comes with a number of holder options ranging from 100mm to 450mm which depends on the users application. In most cases users will select a 100mm sensor and physically move the sensor to different locations around the chamber. For other applications the user will select a sensor holder to match the size of their substrate or their electrode and in this case the sensor is located in the center of the holder plate.

The Quantum Single Sensor measures plasma while users adjust the input parameters to find the best ionization levels for their application. The system also takes useful measurements such as bias voltage, ion energy and ion flux. It is perfect for users researching plasma recipes, ionization, plasma processes, tool development and fundamental plasma research.

Quantum System Indicators

Plasma Parameters Measured

  • Ion Neutral Fraction (1 Location)
  • Ion Energy (1 Location)
  • Ion Flux (1 Location)
  • Bias Voltage (Average)

Measurement Functionality

Time Averaged Measurements
This provides an average over time of the ion flux fraction and the ion energy distribution arriving at the substrate position

Time Trend Measurements
This allows the user to obtain information on the variation of the ion flux fraction and the ion energy distribution as time progresses through a particular process. This feature does not require external synchronisation and the timescales involved can be in range of seconds to hours.

Features

Quantum Ion Neutral Fraction Analyser Electronics and Software

Electronics UnitThe Quantum Electronics Unit is built to the highest quality with an eye catching design and built to withstand the most demanding of laboratory environments. The 19” Rack Mounted Unit contains the most advanced architecture designed to offer the most efficient measurements and analysis as close to real time as possible.

Software Suite

The Quantum Neutral Software Suite offers the most advanced analysis of any plasma measurement instrument on the market today. Carefully crafted over the past ten years by some of the world’s leading scientists in Plasma Measurement. The analysis has been peer reviewed in multiple publications and cited in hundreds. The user interface is designed to be easy to use and clutter free reducing the need to spend time figuring out how to use the system.

Button Probe Holder

The holder is available in various sizes (100mm, 150mm, 200mm, 300mm & Custom Shapes). It sits on a grounded or biased electrode and is used to hold the replaceable Button Probe Sensors. It is available a number of materials including aluminium, anodised aluminium & stainless steel (custom materials are available).

Sensor Holder

The Quantum Neutral Sensor Holder sits at the substrate position inside a plasma reactor. It can be placed at any position and even on a biased electrode. It can withstand temperatures up to 200°C without the need for cooling. The main purpose of the sensor holder is to hold the replaceable Button ProbeTM sensors and to provide the customer with the option to match the holder size to that of their substrate. The holders are available in 100mm, 150mm, 200mm, 300mm, 450mm as standard and custom size holders are available on request.Holder Options

Replaceable Button Probe

Button ProbesDue to the harsh environments inside most plasma reactors we have designed the sensors to be replaceable. Depending on factors such as deposition rate and corrosive chemistries the sensors can have a life time of 10’s of hours to 100’s of hours inside a plasma reactor. With this in mind we have designed the sensor (Button Probe™) to be disposable. Once the measurements start to drift you can simply replace the sensor and continue your measurements with very little down time.

Installation

Time in the lab is expensive and with this in mind we have designed our systems to allow users to be up and running is a very short period of time. For the beginner we have a “quick start” mode which allows users get the data they need as soon as they pump down their reactor and for the more advanced user we allow full access to the raw data.

Further Product Information

Measuring Parameters

Ion Energy Range 2000eV - Vdc
Ion Current 2mA DC max
Ion Flux Ranges Std: 0.01 - 50 (A/m²)
IEDF Resolution ± 1eV nominal
Crystal Measurement Channels 1

Crystal Monitor

Frequency Range 3.5MHz to 6.1MHz
Frequency Resolution 1 Hz
Mass Resolution (at crystal) 12.3ng/cm²
Mass Resolution (at sensor surface) 372.73ng/cm²
Film Thickness Resolution (Copper)
Measurement Update Rate 10 measurements / sec minimum

RFEA Probe

Probe Configuration 4-grid
Button Probe Diameter 33mm
Holder Diameter 100mm (4”), 300mm (12”) as standard
Holder Thickness 5mm
Max Operating Temperature 200ºC
Max RF Bias Voltage 1kV pk-to-pk
Max DC Bias Voltage -1940V
RF Bias Frequency Range 400kHz to 80MHz
Probe Enclosure and Holder Material Aluminium, anodised aluminium, stainless steel* and ceramic (Al2O3)*
RFEA Probe Cable Length 650mm standard (custom available)

*on request

Feed-Through Assembly

Flange Type CF40 (custom available)

Control Unit Electronics

Grid Voltage Range -2kV to +2kV
Current Range 100pA to 2.4mA
Connectivity USB 2.0

Application Software

Operating System Windows 2000 / XP / Vista / Windows 7 / Windows 8

Operating Parameters

Pressure (Pascal) 0 to 40Pa*
Pressure (Torr) 0 to 300mTorr*
Density (for Ar at 3eV) 1012 to 1018m-3
Gas Reactivity Inert to highly reactive
Power Frequency 400kHz to 80MHz

*dependent on ion mean free path

The Quantum Single Sensor used in Plasma Sputtering applications

Measurement of deposition rates and ion energy distributions using the Quantum System

Abstract

Thin films of various materials are deposited on semiconductor wafers for a variety of applications in integrated circuit manufacturing. The rate of deposition is controlled by neutral and ionic species arriving at the substrate surface. In sputtering processes, the ionization fraction, defined as ratio of ion to total (total = ion + neutral) deposition rates, is mainly determined by the applied cathode power, chamber pressure and the target material (since the ionization potential is material dependent). Thin film quality and deposition rates are strongly dependent on the fraction of ionization and therefore measurement of ionized flux fraction at the substrate is becoming crucial for process development and control. A compact retarding field energy analyzer with embedded quartz crystal microbalance (QCM), known as the Quantum system1, has been developed to measure deposition rate, ionization fraction and ion energy distribution arriving at a substrate location.

QC02: Measurement of deposition rates and ion energy distributions using the Quantum System

The Quantum Single Sensor used in Dusty Plasma applications
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The Quantum Single Sensor used in Plasma Etching applications
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The Quantum Single Sensor used in HiPIMS Plasma applications
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The Quantum Single Sensor used in Ion Beam Plasma applications
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The Quantum Single Sensor used in PECVD applications
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The Quantum Single Sensor used in Space Plasma applications
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Introduction

Plasma processes are commonly used to deposit thin films on substrates for a variety of applications. The rate of deposition is controlled by the neutral and ion species bombarding the substrate surface. Magnetron sputtering and HiPIMS are two types of deposition plasma process which see widespread use in industry.

HiPIMS processes produce high plasma densities during a short lived pulse of extremely high power density to the target. During the pulse the electron density in the ionization region close to the target surface can be of the order of 1018- 1019 m-3[1, 2]. For magnetron sputtering processes the plasma density is typically much lower with plasma densities up to 1017 m-3. The corresponding ionization mean-free-path for sputtered particles is of the order of 1 cm in HiPIMS compared to 50 cm in magnetron sputtering for typical process conditions. Therefore, the fraction of the sputtered particles that are ionized can vary significantly for different processes. The target material also plays an important role in determining the ionization fraction since the ionization potential is material dependent. Thin film deposition rates are strongly dependent on the ionization fraction and therefore measurement of the ionization fraction and the ionised flux fraction to the substrate is becoming critical for process development.

Measurements of the ionization fraction in deposition processes have been reported by many researchers over the last two decades. Optical emission spectroscopy measurements made by Bohlmark et al [8] indicate the ionization fraction of sputtered Ti in a HiPIMS can be up to 90%. Measurements using a quartz crystal microbalance (QCM) in combination with a retarding field energy analyser (RFEA) show that the ionized flux fraction at the substrate was as low as 4.5% in another HiPIMS process [9].

The Quantum deposition rate monitor was developed specifically to measure the ionised flux fraction and the neutral flux fraction at the substrate location under processing conditions. This system is suitable for most type of deposition processes including magnetron sputtering, HiPIMS, PCVD etc. This system consists of the Semion RFEA with an integrated QCM, with some similarities to the design proposed by Green et al. [14]. The QCM element provides a direct measurement of the deposition rate at the substrate while the RFEA grids can be configured to turn on and off the ion flux to the quartz crystal. In this way the deposition rate can be determined when both neutrals and ions are present and when only neutrals are present. From these two measurements the ionized flux fraction is easily determined.

2. Quartz Crystal Microbalance

The use of a piezoelectric quartz crystal resonator to measure mass was first investigated by Sauerbrey in 1959 [ ]. It was found that the change in resonant frequency of the crystal was proportional to the mass of a uniformly deposited layer on the crystal surface. He showed that for small masses of material the shift in resonant frequency is independent of the material properties. Because of this simple relationship, quartz crystal resonators are used extensively to measure thin film deposition rates in plasma processes. The original theory proposed by Sauerbrey has been extended over time to allow measurement of ever greater mass loads deposited on the crystal.

The resonant frequency of the standard A-T cut quartz crystal exhibits a strong temperature dependency and must be kept at a constant temperature to provide reliable results. New quartz crystal materials have been developed to provide a flat frequency response up to several hundred degrees Celsius. This avoids the need for water cooling at the moderated temperatures experienced in many plasma processes. Technical challenges surrounding the accurate measurement of the resonant frequency shift have also been addressed. Technologically advanced quartz crystal microbalance devices are now available from many suppliers.

2.1. Quartz Crystal Resonators

A standard QCM measures a mass per unit area by measuring the change in frequency of a quartz crystal resonator. The resonance is altered by the addition/removal of a small mass of material on/from the surface of the resonator. The crystal is comprised of a circular disk of a piezoelectric material sandwiched between two electrodes. The top view of one such crystal is shown below.

Crystal resonator
Figure 1. Crystal resonator used in the Quantum deposition rate monitor.

Quartz is one member of a family of crystals that experience the piezoelectric effect. The trademarked MQTM material from Tangidyne Corporation is another and preferred in the Quantum product due to its flatter frequency response versus temperature.

The piezoelectric effect causes a mechanical deformation in the crystal when a voltage is applied. The resultant alternating current through the quartz crystal induces oscillations in the crystal structure. With an alternating current between the electrodes of a properly cut crystal, a standing shear wave is generated. The Q factor can be as high as 106. This extremely narrow resonance band results in a highly stable oscillator. Therefore, a high level of accuracy in the determination of the resonance frequency is possible. The standard QCM exploits this ease and precision for sensing. Standard equipment allows frequency resolution down to 1 Hz. Standard crystals designed for QCM products have fundamental resonant frequencies in the 4 – 6 MHz range.

2.2. Deposition Rate Determination

Sauerbrey [7 ] was the first to realize that a quartz crystal resonator could be used to measure an extremely small mass of a substance deposited on the crystal surface. His theory is still used extensively in modern deposition rate monitoring systems.

Sauerbrey’s Equation

Sauerbrey derived the following relationship

where Δf is the change in resonant frequency of the crystal in Hz, Cfis the sensitivity factor of the crystal in Hz.ng-1.cm2 and Δm is the change in mass per unit area in gcm2. This relationship assumes that the additional material has the same electro-acoustic properties as that of the underlying crystal. In this case the sensitivity factor is given by

where f0 is the unloaded resonant frequency of the crystal in Hz, is the density of the crystal material in g.cm-3 and crystal in g.cm-1.s-2. μx is the shear modulus of the Since the deposited material is assumed to have the same properties as that of the crystal, a number of criteria must be satisfied for the Sauerbrey equation to apply:

  • The deposited mass must form a rigid layer
  • The deposited mass must be distributed evenly on the crystal surface
  • The frequency change Δf0 / f0 ≤ 0.02 [ ]

Z-Match Equation

If Δf0 / f0 ≤ 0.02 then the so-called Z-match equation, derived by Lu and Lewis, should be applied. These authors analyzed the loaded crystal by modeling a resonator split into two components i.e. the main crystal and the deposited film. This analysis led to the following equation:

where Nx is the frequency constant for the crystal in Hz.cm, Rz is the Z-factor of the material deposited such that

is the density of the deposited material, μ is the shear modulus of the deposited material and f is the resonant frequency of the loaded crystal. The parameter Rz introduces the ratio of acoustic impedance of the crystal to that of the deposited film. It can be shown that if the ratio of acoustic impedances is one i.e. the crystal and deposited material are the same, then the Z-match equation reduces to the Sauerbrey equation.

Film thickness

The growth rate of the deposited film is often the parameter of most interest to researchers. The thickness Tk f of the deposited film can be calculated from equation (3):

The Z-match equation has been shown to be in good agreement with experiments for frequency changes up to 40% [ ]. Certain types of films, such as organic polymers, have viscoelastic properties that are not accounted for in these simple models and significant departures from equations 3 and 4 are to be expected. Recent advances have led to the extension of these models to incorporate liquids and viscoelastic materials. However, the equations presented above cover the majority of applications for which the Semion deposition rate monitor is applicable.

RFEA with Integrated QCM

The idea of using an RFEA with integrated QCM to measure the ionised flux fraction has been around for a number of decades. Rossnagel and Hopwood [ ] used one such device to measure metal ionisation fractions in ICP plasmas. The use of mesh components with large orifices limited its use to very low density to avoid plasma forming inside the device.

Green et al improved on the original design considerably by incorporating mesh components with much smaller apertures. This design was also capable of being DC biased at the substrate potential.

Semion Deposition Rate Monitor

A schematic of the Quantum deposition rate monitor is shown in figure 2.

Figure 3.1-1: Schematic of the Quantum deposition rate monitor.

Unlike other devices, the crystal is embedded in the RFEA. Other research devices have been developed by simply building a grid stack around the off- the-shelf deposition rate monitor, including the large metal water cooled support structure. This approach eliminates the possibility of miniaturizing the device and reduces the operating pressure range that can be achieved.

The Quantum deposition rate monitor incorporates only the crystal which is approximately 250µm thick. When combined with the stack of grids, insulators and mechanical housing the overall thickness of the device is 5 mm. The total depth, from orifice to crystal, is approximately 1 mm which allows the sensor to be operated to at least 50 mTorr in Argon without ion collisions inside. Other designs reported on in the literature [ ] have depths which are at least 10 times that of the Quantum deposition rate monitor.

A major advantage of the Semion product over other devices is that the sensor can be placed on dc, pDC or rf biased substrates without the need for any modification of the substrate holder. This allows the user to measure ionised flux fractions directly at the substrate location under real processing conditions.

Theory of operation

The entrance orifice is 5 mm in diameter and allows a sample of ions, neutrals and electrons into the analyser for detection. A first grid G0 is placed over the entrance orifice to reduce the open diameter exposed to the plasma, to a size equivalent to the grid aperture size. In this device the grid aperture size is a 25 µm x 25 µm square. For proper operation the aperture size should be less than the Debye length to prevent plasma forming inside the analyser. The aperture size used is less than the Debye length, near the substrate, for most applications encountered.

A second grid G1, insulated from G0 (all grids are insulated from each other to allow independent biasing), is biased with a negative potential relative to G0 to repel any electrons that may enter the sensor.

A third grid G2 is biased with a positive potential sweep to generate a gradually increasing retarding field to discriminate incoming ions based on their kinetic energy [ ] - when the sensor is being operated in RFEA mode. When the sensor is being operated in deposition rate monitor mode then G2 can be biased with a positive potential to repel all incoming ions or it can be biased such that all incoming ions pass through unperturbed. The deposition rate at the crystal can thus be determined with and without the ion fraction.

A fourth grid G3 is biased negative 10 volts with respect to the fifth grid G4, when the device is operated in RFEA mode. G4 collects the ion current passing G3 to generate the current –voltage characteristic from which the ion energy distribution is calculated. G3 suppresses secondary electron emission from G4. When operated in deposition rate mode, G3 and G4 are biased to the same potential as G2

The crystal terminates the stack of components. It is held at the same DC potential as G4 so that ions travelling from G4 to the crystal do not experience an additional electric field which might prevent them from being detected. The crystal is also excited with a radio frequency bias to cause it to resonate at its natural frequency. The shift in resonant frequency due to deposition on the crystal surface is monitored and enables the deposition rate to be calculated.

Calibration

The deposition rate measured by the crystal at the bottom of the gridded structure will deviate from the deposition rate at the sensor surface. The ions arrive at normal incidence to the sensor surface because they are accelerated in the sheath electric field adjacent to the surface. Therefore, the ions entering the sensor orifice travel straight through to the crystal surface. The neutral species, on the other hand, arrive at the sensor surface with an isotropic distribution. The neutrals entering the orifice do so with a spread of trajectories – some will be lost to the side walls and some will make it to the crystal for detection. This ‘shadowing’ effect has been addressed for specific discharge geometry by Green et al [ ]. The deposition rate seen by the crystal at bottom of the grid stack can be determined from the following relationship

where Rsurf is the deposition rate at the sensor surface (that seen by the substrate), Rcrystal is the deposition rate at the crystal, G accounts for the reduction in neutral flux reaching the crystal due to the shadowing effect and Tg is the transmission factor of each grid where n is the number of grids used. The 3 grids used by Green et al had 52.7% transmission each giving Tgn = 14.6%. The aspect ratio of their device (depth/width) was approximately 15/18 as shown in the schematic below [ ]. It was shown that this ratio can be used, with reasonable accuracy, to estimate the percentage of neutrals reaching the crystal as a result of side wall shadowing. Therefore, the aspect ratio of 15/18 gives G =16.6% and Rcrystal = 2.4%× Rsurf which compared favourably with their experimentally determined value of 1.6%.

Green et al also give a plot of theoretically calculated values for G as a function of sensor aspect ratio (see figure 5 in reference [ ]). This will be used as a guide for estimating G for the Semion QC deposition rate monitor.
The Quantum deposition rate monitor utilizes 5 grids, each with 50% transmission giving a value for Tn of approximately 3%. This is significantly less than that of Green et al due to incorporation of 2 additional grids to ensure correct operation of the RFEA element of the device. However, the shadowing effect is much less due to the small internal depth of the sensor. The aspect ratio is approximately 1/5 from which the total flux reaching the crystal is estimated to be about 70%. Therefore, Rcrystal = 2.1% × Rsurf, which is crystal surf very similar to that of the device designed by Green et al.Given the fact that the neutral flux is reduced by approximately 98% and the ion flux, due to the directional nature, is reduced by 97% an accurate experimental calibration is required since small errors in the estimation of Tn and G can cause the calculated deposition rates to deviate significantly from reality. To provide the best possible calibration of the device a second quartz crystal is incorporated into the sensor design, close the gridded element. The reference crystal is located at the surface of the sensor housing and so there is no neutral flux loss due to the aspect ratio shadowing effect. There are no grids used either, which eliminates the transmission effect described above. At the beginning of each experimental run a calibration can be performed in which the deposition rates of both crystals are compared to find a scaling factor for the crystal at the bottom of the grid stack.

Figure 3: Schematic of the Quantum deposition rate monitor showing the gridded element and the reference crystal side by side.

References

[1] J.T. Gudmundsson, P. Sigurjonsson, P. Larsson, D. Lundin, and U. Helmersson, J. Appl. Phys. 105, 123302 (2009).
[2] J. Bohlmark, J.T. Gudmundsson, J. Alami, M. Lattemann, and U. Helmersson, IEEE Trans. Plasma Sci. 33, 346 (2005).
[3] J.T.Gudmundsson, Vacuum 84, 1360 (2010).
[4] V. Kouznetsov, K. Macák, J.M. Schneider, U. Helmersson, and I. Petrov, Surf. Coat. Technol. 122, 290 (1999).
[5] J. Vlcek, P. Kudlacek, K. Burcalova, and J. Musil, Europhys. Lett. 77, 45002 (2007).
[6] J. Bohlmark, J. Alami, C. Christou, A.P. Ehiasarian, and U. Helmersson, J. Vac. Sci. Technol. A 23, 18 (2005).
[7] K. Macák, V. Kouznetsov, J. Schneider, U. Helmersson, and I. Petrov, J. Vac. Sci. Technol. A 18, 1533 (2000).
[8] J. Bohlmark, J. Alami, C. Christou, A.P. Ehiasarian, and U. Helmersson, J. Vac. Sci. Technol. A 23, 18 (2005).
[9] B. M. DeKoven, P. R. Ward, R. E. Weiss, D. J. Christie, R. A. Scholl, W. D. Sproul, F. Tomasel, and A. Anders, Society of Vacuum Coaters 46th Annual Technical Conference Proceedings, p. 158, San Francisco, CA, USA, May 3-8 (2003).
[10] J.A. Hopwood in J.A. Hopwood (ed.): Thin Films: Ionized Physical Vapor Deposition (Academic Press, San Diego, 2000).
[11] M. Samuelsson, D. Lundin, J. Jensen, M. A. Raadu, J. T. Gudmundsson, and U. Helmersson, Surf. Coat. Technol. 15, 591 (2010).
[12] S. Konstantinidis, J.P. Dauchot, M. Ganciu, M. Hecq, J. Appl. Phys. 99, 013307 (2006).
[13] A.P. Ehiasarian,W.-D. Münz, L. Hultman, U. Helmersson, I. Petrov, Surf. Coat. Technol. 163–164, 267 (2003).
[14] K. M. Green, D. B. Hayden, D. R. Juliano and D. N. Ruzic, Rev. Sci. Instruments 68, 4555 (1997).
[15] D. Gahan, B. Dolinaj and M. B. Hopkins, Rev. Sci. Instrum., 79, 3, 2008.
[16] D. Gahan, B. Dolinaj and M. B. Hopkins, Plasma Sources Sci. Technol., 17, 3, 2008.
[17] C. Hayden, D. Gahan and M. B. Hopkins, Plasma Sources Sci. Technol., 18, 2, 2009.
[18] K. Denieffe, C. M. O. Mahony, P. D. Maguire, D. Gahan and M. B. Hopkins, J. Phys. D: Appl. Phys., 44, 7, 2011.
[] F. Tomasel, and A. Anders, Society of Vacuum Coaters 46th Annual Technical Conference Proceedings, p. 158, San Francisco, CA, USA, May 3-8 (2003).
[] G. Sauerbrey, Z. Physik 155: 206. 2 (1959)

Measurement of deposition rate and ion energy distribution in a pulsed dc magnetron sputtering system using a retarding field analyzer with embedded quartz crystal microbalance

Sharma S1, Gahan D2, Scullin P2, Doyle J2, Lennon J2, Vijayaraghavan RK1, Daniels S1, Hopkins MB2

1. Impedans Ltd, Chase House, City Junction Business Park, Northern Cross, Dublin 17, Ireland
2. National Centre for Plasma Science and Technology, Dublin City University, Dublin 9, Ireland

Published 04 April 2016

Abstract

A compact retarding field analyzer with embedded quartz crystal microbalance has been developed to measure deposition rate, ionized flux fraction, and ion energy distribution arriving at the substrate location. The sensor can be placed on grounded, electrically floating, or radio frequency (rf) biased electrodes. A calibration method is presented to compensate for temperature effects in the quartz crystal. The metal deposition rate, metal ionization fraction, and energy distribution of the ions arriving at the substrate location are investigated in an asymmetric bipolar pulsed dc magnetron sputtering reactor under grounded, floating, and rf biased conditions. The diagnostic presented in this research work does not suffer from complications caused by water cooling arrangements to maintain constant temperature and is an attractive technique for characterizing a thin film deposition system.

View online at aip.scitation.org/doi/abs/10.1063/1.4946788


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