Langmuir Spatial Probe Theory

Introduction

The concept of the Langmuir probe was developed almost a century ago and is named after its inventor Irving Langmuir. The Langmuir probe was the first diagnostic tool used for studying plasmas in detail and it is still widely used today. Langmuir probes, in principle, provide a simple and relatively inexpensive diagnostic for measuring the plasma parameters. However, there are a number of issues in the design and interpretation of Langmuir probe characteristics which have led in the past to a wide disparity in measured parameters obtained under similar conditions. Part of this difficulty results from an imprecise knowledge of the RF discharge parameters, voltage, current and deposited power, but this has been partially resolved by the availability of VI probes to make accurate measurements of the discharge RF parameters.

In-situ layout of the Single Langmuir Probe in a typical plasma chamber setup

Figure 1: In-situ layout of the Single Langmuir Probe in a typical plasma chamber setup

Theory of Operation

The Langmuir is a conducting wire placed inside the plasma with a variable bias, V applied. The current I, is measured as a function of V. This is called the I(V) characteristic and it has three regions; the electron collection region, the electron retardation region and the ion collection region.

Simple Langmuir Probe Schematic

Figure 2: Simple Langmuir probe schematic

Modern Langmuir probe systems are quite complex diagnostic systems with many features to prevent the pitfalls of probe diagnostics; some of which are less than obvious to the non- expert. Even with these precautions the probe system will be limited to a range of plasma conditions where accurate results are obtainable.

Current Voltage I(V) characteristic of a single Langmuir probe

Figure 3: The Current Voltage I(V) characteristic of a single Langmuir probe

A probe system can provide the following parameters: floating potential, Vf, which is the point where ion collection current equals electron retarding current. This is the potential at which an isolated object will float when placed in the plasma. The plasma potential, Vp, is the potential of the space the plasma occupies. It is normally positive with respect to the surrounding chamber to prevent excessive loss of electrons. Below Vp the electrons are retarded by the probe potential and the electron current falls off at a rate that depends on the electron average energy. Above Vp we enter the electron collection region. It is possible to calculate the electron density, Ne from the magnitude of the current at the plasma potential. The ion density, Ni is determined from the ion current in the ion collection region. A difficulty here is that the ion current needs to be extrapolated back to the plasma potential, Vp, to make accurate measurement of Ni.[1] This requires a theory to understand ion orbits around the probe and the effect of collisions in the sheath. The electron temperature, kTe, is determined from the rate at which the electron current falls in the electron retarding region. Here again, the best accuracy is achieved when the ion current is extrapolated and removed from the total current. Finally the electron energy distribution function (EEDF), can be obtained from the second derivative of the I(V) characteristic with zero energy at the plasma potential. The EEDF requires an accurate removal of the ion current and an accurate determination of the Plasma potential, Vp. It is possible to integrate the EEDF to get the electron density and the average electron energy and these measurement are independent and can be used as checks on the values of Ne and KTe derived directly from the I(V) characteristics.

The Langmuir probe can obtain data as a function of position with a resolution of a few mm and in time with resolution in the range of ns. The order of presentation of the parameters above can loosely be regarded as in order of difficulty, with the floating potential being the easiest to obtain and the EEDF being the most complex.

A suitable benchmark of a high quality EEDF can be obtained from the two-temperature structure in the case of the low-pressure RF discharge in Ramsauer-type gas such as argon[2] and the EEDF of a molecular gas which has a characteristic hole in gases such as nitrogen[3] due to the large in-elastic cross-section associated with vibrational excitation. These features are well characterised but difficult for a probe system to resolve and can act as a bench-mark on the quality of a probe system. A major objective of a commercial Langmuir probe system design is that it can be operated by an inexperienced operator and give reliable results.

Plasma can be formed either by a direct current (DC), a radio frequency (RF) current or microwave MW source. In the case of an RF plasma the plasma potential will tend to follow the RF bias by a amount that depends on both the amplitude of the RF but more importantly the configuration of the plasma; with a symmetrical parallel plate configuration having the highest magnitude of fluctuations of Vp and the inductive coupled plasma often having the lowest fluctuations in Vp. The removal of RF fluctuation in Vp relative to ground is normally achieved by means of the Passive Probe method first developed by Gagne and Cantin[4]. The probe is forced to float at the RF potential by ensuring that the probe-plasma impedance, Zp, is much less than the probe-ground impedance, Zs. The probe circuit is then a potential divider with the RF potential appearing across Zs and the probe floats relative to the plasma potential. When Zs > > Zp the characteristic is similar to a DC characteristic with the RF voltage fluctuations removed.

Schematic of Passive RF Compensation

Figure 4: Schematic of passive RF compensation

The Impedans Langmuir probe uses a high impedance RF filter to maximise Zs and the probe shaft is metallic with a thin ceramic layer to capacitively couple the probe to the plasma and minimise the Impedance between the probe tip and the plasma. The plasma to ground impedance is normally low at RF. This shunt capacitance of the ceramic coated probe holder dominates the plasma-probe impedance but has no effect on the direct current collected to the probe, the large area of the holder ensures that Zp is as small as possible. The probe holder diameter is minimised to prevent the probe structure from depleting the plasma. The blocking impedance is Zs > 100 kΩ over a broad range of frequencies.

Passive probe compensation works well at frequencies above 1MHz, where the plasma parameters are not modulated by the RF. At lower frequencies, < 1MHz, the plasma parameters change depending on the phase of the applied voltage waveform. Passive compensation is no longer valid below 1MHz and we need to move to time resolved measurement of the I(V) characteristic. This is achieved by using a sync signal coherent with the power source and an Advanced Boxcar Mode developed by Impedans.

Figure 5: Applied theories for electron and ion collection

The video above demonstrates the probe collecting ion and electron current, depending on the polarity of the potential sweep. At very low pressures the ion current to the probe is limited by orbital motion due to the ions angular momentum. As pressure increases collisions in the sheath reduce the effect of orbital motion. The probe calculates the number of collisions and applies the correct theory.

References:

[1] M.B. Hopkins J. Res. Natl. Inst. Stand. Technol. Vol. 100, No. 4, p. 415
[2] M. M. Turner, R. A. Doyle, and M. B. Hopkins, Measured and simulated electron energy distribution functions in a low-pressure radio frequency discharge in argon, Appl. Phy. Letts. 62(25), 3247 3249 (1993).
[3] M. M. Turner and M. B. Hopkins, Anomalous sheath heating in a low pressure RF discharge in nitrogen, Phys. Rev. Lett. 69, 3511 (1992).
[4] R. R. J. Gagne and A. Cantin, J. Appl. 43, 2639 2647 (1972).

 

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Theory of Operation: Langmuir Probe