Ion Energy Distribution Function

Ion Energy Distribution Function

Introduction:

Plasma plays a vital role in a wide range of applications, from plasma processing and surface modification to ion implantation and thin film deposition. Understanding the behaviour of ions within a plasma is essential for optimizing these processes. One crucial parameter that characterizes ion behaviour is the ion energy distribution function (IEDF). Accurate measurement of the IEDFs provides direct insights into ion energy, velocity, and flux. In this article, we will explore the concept of the IEDF, its measurement techniques, factors influencing its shape, and the importance of precise IEDF measurement. We will also highlight Impedans Ltd.’s advanced diagnostic solutions in this field. 

Introduction to Ion Energy Distribution Function

The Ion Energy Distribution Function (IEDF) is a probability distribution function that describes the energy distribution of ions within a plasma. It provides valuable information about the likelihood of finding ions at different energy levels. In other words, the IEDF represents the proportion of ions with a specific energy in the plasma population. It provides valuable information about the population of ions at different energy levels, velocities, and fluxes. This function is crucial for understanding the kinetic behavior of ions and their interactions with other plasma constituents and surfaces.

Plasma processes such as etching and thin film deposition involve the acceleration of ions to the surface of a substrate across a plasma sheath. The plasma sheath is a region of charge imbalance between a wafer/substrate placed inside the plasma and the bulk plasma. It arises because of the difference between speeds of electrons and ions hitting the surface of the substrate, charging the surface with respect to the plasma. This results in the plasma having a positive ‘plasma potential’ relative to the substrate surface, and ions will be accelerated across this potential. The IEDF is a representation of the energies with which ions will bombard these surfaces with. 

If the ions are hitting a grounded surface, then the IEDF will typically look like the below left figure, where the peak energy corresponds the plasma potential. 

If the surface is biased with a negative DC voltage it will cause the sheath to grow larger. The ions will be accelerated to hit the surface with a higher energy and the peak of this curve will shift upwards, to a value of the plasma potential + the bias voltage. However, if there is an RF bias, the sheath will be constantly growing and shrinking. The IEDF will consist of two peaks now due to the difference in transit times of ions entering the sheath at the maximum and minimum RF voltages. An example of this can be seen in the above right figure. 

The total area under the curve of IEDF represents the flux of ions reaching to the substrate. The IEDF analysis also provides information about maximum ion energy, ion energy spread and mean energy which are helpful in understanding ion-surface interactions during thin film deposition, ion implantation, and other plasma processes. 

Section 2: Measurement Techniques for Ion Energy Distribution Function

Several techniques have been developed for the accurate measurement of the IEDF. Common methods include retarding field energy analysers, time-of-flight analysers. 

Retarding field energy analysers work based on the principle of energy analysis, where they measure the energy distribution of ions by applying an electric field to retard or slow down the motion of ions before they reach the collector. They consist of a series of electrostatic grids that are placed in the path of ions. Electrostatic fields are changed and the ion current to the collector is measured to build up an IEDF measurement. These provide a real time measurement of the IEDF which can observe rapid changes in the ion energy during plasma processes. From these you can monitor the evolution of ion energies in your plasma over time, for example throughout a pulsed plasmas cycle as well.

The relatively simple design makes RFEAs considerably easy to use, and suitable for a wide range of ion energy measurements in many different plasma systems. 

Time-of-flight analysers (TOFAs) measure the time taken by ions to travel a known distance under the influence of an applied electric field. They begin by extracting ions from the plasma using an electrostatic grid or other extraction mechanisms. The extraction process typically involves applying a pulsed electric field that accelerates ions away from the plasma source. The ions are then propagated through a region of known length, usually a drift region, before reaching the collector. During this region the ions are not influenced by any electric fields. Once they reach the collector the time taken for them to travel this distance is measured very precisely. By knowing this time, and the ion mass, the time take, and distance travelled very accurately, researchers can reconstruct the energy distribution of ions (IEDF). TOFAs can be used for a wide range of energies for a high energy resolution, but are typically require data accumulation over multiple plasma discharges. This limits the real time capability of these detectors. Furthermore, the data analysis to reconstruct the IEDF is intensive and requires specialist knowledge and sophisticated data analysis techniques. 

Section 3: Factors Affecting the Ion Energy Distribution Function

Several plasma parameters have a direct influence on the shape and characteristics of the IEDF within a plasma. Gas pressure, power, electron temperature, and applied electric fields play significant roles. 

Higher gas pressure will reduce the mean free path of ions travelling and accelerated across the plasma sheath. This results in more collisions, and an increased energy spread in the IEDF as demonstrated in the below figure showing IEDF plots with increased pressures. More collision will hinder the ions reaching the surface so the flux will also reduce as suggested by low intensity peaks in the below image with increasing pressure.

Electron temperature impacts the peak energy of the IEDF, with higher temperatures shifting the distribution to higher energies. The relationship between electron temperature (Te) and the peak energy of the IEDF can be described using the Maxwell-Boltzmann distribution: 

g(E) ∝ exp(-E/Te) 

More practically, the power applied to a plasma will have a direct effect on the IEDF. If the substrate remains grounded, a higher applied power will result in more flux and a larger peak in the IEDF. This is demonstrated in the figure below left. Below right shows the effect of increasing the power applied directly to the substrate on the IEDF. Higher bias power results in IEDF shift toward higher energy and the distribution width also increases. 

Section 4: Applications of Ion Energy Distribution Function Measurement

The Ion Energy Distribution Function (IEDF) has a significant impact on various plasma processes, influencing the behavior of ions and their interactions with surfaces and other particles within the plasma. Understanding and accurately measuring the IEDF is essential for optimizing plasma processes and achieving desired outcomes.  

In plasma etching, the IEDF determines the energy and flux of ions bombarding the substrate surface. A well-characterized IEDF is crucial for controlling the etch rate, selectivity, and surface damage during the etching process. Measuring the IEDF helps ensure consistent and controlled etching, leading to improved process repeatability and uniformity. 

In plasma-enhanced thin film deposition, the IEDF influences the ion flux and energy arriving at the substrate. This, in turn, affects the film’s microstructure, adhesion, and properties. By measuring the IEDF, researchers can optimize the film growth process, resulting in films with desired properties and characteristics. 

Similarly in Ion implantation, the IEDF is critical in determining the depth profile and concentration of ions implanted into a material’s surface during ion implantation processes. Accurate measurement of the IEDF helps achieve precise ion implantation and controlled doping profiles, essential for semiconductor device fabrication and material engineering. 

The IEDF also plays a critical role in process transfer and scaling up processes in industry. Knowledge of the IEDF allows for efficient optimization of plasma parameters for different scales and equipment configurations. 

Section 5: Impedans Ltd.’s Solutions for IEDF Measurement

Mention pulsing, building up time resolved IEDFs, high voltages. 

Impedans Ltd offers advanced diagnostic systems designed for precise IEDF measurement. Their Semion retarding field energy analysers and provide high resolution, wide energy range coverage, and compatibility with various plasma sources and biasing techniques. Below are examples of IEDFs measure in an Argon plasma in 13.56 MHz RF CCP system using an Impedans Semion RFEA placed on powered (left) and grounded (right) electrode. 

Impedans provide a wide range of sensors for various applications, including the Semion pDC which has the high time resolution that can measure the evolution of ions from a pulsed discharge, even resolving the ion evolution of a HiPIMS plasma. Another advanced version of RFEA is a Quantum system that incorporates a quartz crystal on the collector to measure the deposition rate for both ions and neutral species.   

Impedans Ltd.’s diagnostic tools empower researchers and industry professionals to obtain reliable measurements of the IEDF, enabling a deeper understanding of plasma behaviour and improving process control. These solutions facilitate process optimization, plasma parameter tuning, and the development of tailored plasma-based technologies. 

Conclusion:

The ion energy distribution function is a key parameter in plasma physics, offering valuable insights into ion behaviour, energy distribution, and flux within a plasma. Accurate measurement and characterization of the IEDF are essential for optimizing plasma processes, controlling ion energy and flux, and improving thin film properties. 

Impedans Ltd, with its expertise in diagnostic solutions, provides reliable and advanced tools for precise IEDF measurement. By leveraging Impedans Ltd.’s cutting-edge technologies, researchers and industry professionals can unlock new frontiers in plasma physics and make significant advancements in their respective fields. 

References and further reading: 

1. Lieberman, M. A., & Lichtenberg, A. J. (2005). Principles of Plasma Discharges and Materials Processing. John Wiley & Sons.
2. Chen, F. F. (1984). Introduction to Plasma Physics and Controlled Fusion (Vol. 1). Springer.