Controlling the charge of dust particles in an afterglow by modulating the plasma power

A dust particle immersed in a glow-discharge plasma has long been known to have a charge that is negative, while the plasma is powered. However, in the afterglow, following the stopping of the plasma power, a large positive charge can collect on the particle, as was shown recently for particles in a cathodic sheath. While that outcome of positive charging in the afterglow may be common, an experimental discovery reported here reveals that the opposite outcome is also possible: a particle can develop a negative charge in the afterglow, if the plasma had previously been operated with a modulated power. Before stopping the plasma power off altogether, in a run with power modulated at a low duty cycle of 4.5 % , the particle’s residual charge was negative, but it was positive in a control run without modulation. This result points to a way of controlling the charge of dust particles in a decaying plasma, which can be useful for mitigating defects in semiconductor manufacturing.


Introduction
While the charging of dust particles in a plasma under steady conditions has been studied intensely since at least 1978 [1], only more recently have studies been reported for charging in the unsteady conditions of a temporal afterglow plasma, i.e. the decaying plasma after the power that sustained a laboratory plasma is stopped.This charging in the afterglow is significant in semiconductor manufacturing because contamination of surfaces such as wafers can occur immediately after the plasma power has been stopped, when particles that had been electrically suspended in the plasma fall to the wafer below.Controlling the afterglow charge as well as the afterglow electric field offers a way of mitigating defects resulting from the falling of these particles, as we suggested recently [2].
Perhaps the earliest hint of dust particles having a charge in an afterglow was a 1995 experiment by Barkan and Merlino [3].A convincing experimental study, along with a theory for charging in an afterglow, was presented in 2003 by Ivlev et al [4].Since then, experimental studies  have been more frequent, as reviewed recently by Couëdel [42].In more recent discovery in our laboratory, we found that dust particles could acquire a large positive charge, with tens of thousands of elementary charges, in an afterglow [43].
While afterglow charging is still not fully understood, there is a much better understanding of charging under steady conditions.In a laboratory plasma that is powered steadily, dust particles generally maintain a negative charge .
That charge is generally expected to be proportional to both the particle diameter and the kinetic energy of electrons.Measurements of the charge, in an argon plasma that is steadily powered by radio-frequency signals, are commonly of order −10 000 e for a ten-micron diameter [43], i.e. about −1 electronic charge per nm of diameter.Most importantly, we note that this charge is large and negative.
In an afterglow, ions and electrons do not immediately vanish, but gradually move to the plasma chamber walls, where they are absorbed [4,41].The duration of this afterglow is typically a millisecond or longer, and it tends to last longer if the gas pressure is high.During this afterglow, the charge of a dust particle can change, so that it no longer has the same value as during plasma operation [4,42,77].The value of the charge can vary in the afterglow until a final moment, when the ion and electron densities have diminished to a point where they are too small to further change the particle's charge measurably, and at that point the dust particle's charge is said to be 'frozen' [4,42,43,77] at a value called the 'residual' charge, which we denote as Q res .
In our 2021 paper [43], we reported an experimental discovery that dust particles can attain a residual charge that is not negative, but is instead positive and quite large.We measured positive charges as large as +16 000 e for a 8.69 µm diameter particle, which was located in a cathodic sheath.Along with those experimental data, we also presented a quantitative model, where a dust particle collects streaming ions in the presence of an electric field, and it attains its maximum possible charge when it becomes sufficiently positive to repel the most energetic ions that are present.
Those experimental results, along with improvements in the theoretical understanding of the afterglow conditions that determine the residual charge, have created an opportunity to develop practical methods of controlling the charge.We have proposed that these methods of controlling the charge in the afterglow can have an application in semiconductor manufacturing, by allowing a controlled lifting of particles so that they do not land on critical surfaces and thereby cause defects, after the plasma power is stopped [2].
In this paper, we report a further development that can be useful in controlling the residual charge of a dust particle.We discovered that by modulating the radio-frequency power, before stopping it to create the afterglow, it is possible to have a different outcome for the residual charge.A residual charge that is negative, instead of positive, was the outcome when the plasma was modulated before stopping its power.We performed two experimental runs in the same chamber, using the same dust-particle size, gas, and radio-frequency power.In the control run, the radio-frequency (RF) power was operated constantly, i.e. with 100% duty cycle, until it was stopped at t = 0.The other run used modulation of the RF power, with a 1 ms period and a duty cycle of only 4.5%.In other words, these two runs were performed at two extremes of duty cycle.We found that in the modulated run, the dust particle attained a negative residual charge of about −12 000 e, while in the control run it was positive, at about +8500 e.This result suggests a method of controlling the charge in the afterglow, by modulating the RF power, whether throughout the plasma operation as in our experiment, or at least in the final milliseconds before switching the power off.

Plasma operation
The experiment was performed in the same plasma chamber as in our earlier experiments [43,[77][78][79], but with an RF power circuit, sketched in figure 1, that was modified by adding an RF switch.This switch (Analog Devices, ADG901) allowed repeatedly turning the plasma power on and off, with a desired period and duty cycle.The plasma was produced by applying an RF potential between the powered lower electrode and grounded chamber.In plasma-on condition, the RF waveform was 13.56 MHz, with a 244 V peak-to-peak amplitude that was measured with a 100X probe on the lower electrode.The vacuum base pressure was 0.03 mTorr before the experiment, while during the experiment Argon gas was admitted to maintain a pressure of 13 mTorr, which is high enough that the sheath above the lower electrode was collisional.A gas inlet and a pumping port were located at the chamber's bottom.To counteract any leaks or outgassing, there was gas flow, with a rate of 0.4 SCCM that was sufficiently low to avoid any detectable wind acting on the particles.
Two runs were performed with different duty cycles: 100% in our control run, and 4.5% in our modulated run.In the latter run, the modulation period was 1 ms, with power-off and power-on intervals of 955 and 45 µs, respectively.The latter value was chosen to be slightly larger than the minimum of 40 µs that we found to be required for stable levitation of the dust particles.This stable levitation assures that after the power is turned off, the dust particles will move together with the same velocity.Having the same velocity is desirable for using equation (1) to obtain the charge in the afterglow because the crucial input to that formula is the acceleration of the particle, obtained from the time series of particle velocities as they fall.
For t < 0, i.e. during plasma operation, the lower electrode maintained a negative DC self-bias.A self-bias, which is typical for capacitively coupled RF glow-discharge plasmas, develops naturally so that electrons and positive ions collect equally, during one RF cycle, on the powered electrode.The value of the self-bias was −41 V for our modulated run, as seen in figure 2. For the control run, the self-bias was greater, at −114 V, indicating a different overall balance of electron and ion loss in the chamber, as compared to the modulated run.
At t = 0, the ion density had a value that we estimated by interpreting the waveform for the lower electrode voltage, as described in the appendix.Averaged over the entire plasma chamber volume, at t = 0 the ion density was ≈2 × 10 9 cm −3 for the control run, and ≈5 × 10 8 cm −3 for the modulated run.
For t > 0, i.e. after the plasma power was stopped, the voltage on the lower electrode no longer had an RF component, but it still had a waveform that was useful for interpretation [43].This waveform, for t > 0, varied on a time scale at least three orders of magnitude more slowly than when the RF Experimental setup.During plasma operation, radio-frequency (RF) power was applied through a coupling capacitor C coupl to the lower electrode, while the grounded chamber walls served as the other electrode.An RF switch allowed operating the RF power either with a 100% duty cycle, or with a modulation having a defined timing for power-on and power-off operation, as sketched in the timing diagram.The RF power was stopped altogether at t = 0 to begin the afterglow.The side-view camera viewed particles as they fell, with an illuminating laser not shown here.
power was on.This variation of the waveform during the afterglow had two contributions, corresponding to two mechanisms for changes in the charge that was stored on the 50 nF coupling capacitor.First there was a collection of ions or electrons on the lower electrode, which was dominant for 0 < t < 2 ms.Second, there was a slower discharging of the capacitor through a resistance of about 100 MΩ, which was the only significant mechanism for t > 2 ms, when the ion and electron densities were negligible.

Dust particles during plasma operation
The dust particles were melamine-formaldehyde microspheres.The specifications provided by the manufacture [80] were a diameter of 8.69 µm, with a dispersion of ±0.11 µm, and a mass of m d = 5.2 × 10 −13 kg, which neglects any mass loss due to vacuum exposure [81].We chose melamine formaldehyde microspheres because they are monodisperse and resist sticking together, so that their mass is better known.Their large diameter allowed imaging them individually.Our results should extrapolate to smaller particles because particle charge and charging time vary with a simple scaling with particle size [82].
Near the beginning of a run, we introduced only about 10 3 dust particles into the top of the plasma chamber.This was done by agitating a shaker, causing the particles to drop into the plasma, where they became electrically charged.Because they were so massive, and so few in number, they settled in a single horizontal layer, located above the lower electrode at a height where the downward force of gravity was balanced by an electric force, as in our previous experiments [43,[77][78][79].Due to the considerable mass of particles larger than 1 µm diameter, the electric force required for levitation is available Voltage on lower electrode, measured in (a) the control run with 100% duty cycle, and (b) the modulated run with a 4.5% duty cycle and 1 ms period.Plasma power was stopped at t = 0, which was the beginning of the afterglow.During plasma operation for t < 0, the RF waveform was centered at a DC self-bias, at the level indicated by the dashed lines in the insets, which was −114 V for the control run, and −41 V for the modulated run.The coupling capacitor C coupl that allowed the self-bias to be maintained during plasma operation also had the effect of holding the same potential during the afterglow.However, in the first 2 ms there was a small upward change ∆V, as shown in the insets with an enlarged vertical scale.We attribute ∆V mainly to the collection of ions in the afterglow, so that its value allows a determination of the total ion charge and ion density at t = 0. not in the bulk plasma but the lower electrode sheath [48].We know that the dust particle charge had a negative polarity during plasma operation, in both runs, because levitation requires an upward direction for the electric force acting on the dust particles, and there was a negative bias on the lower electrode at all times.This levitation is the result of the time-averaged electric force balancing the downward force of gravity.In the modulated run, most of the time-averaged force happens during the plasma-off time, since the duty cycle was very low.During the brief plasma-on time, the values of the electric field and charge cannot be measured separately, but it is known that the time average of their product balances gravity.Because we used only a small number of dust particles, they did not deplete electrons in the plasma to a significant extent, as can occur in experiments with larger numbers of dust particles [42].
It is an essential phenomenon that a dust particle's charge during the afterglow can be different, even to an extreme degree, from its value during plasma operation.That is so because in the afterglow, the ions and electrons have different parameters as well as different spatial arrangements.During plasma operation, the sheath above the lower electrode collapses and expands at 13.56 MHz, so that there is a brief interval in each RF cycle when electrons can collect on the dust particles.In the afterglow, on the other hand, the sheath is quite different, being essentially a DC cathodic sheath.During the earliest times in the afterglow, the electrons cool rapidly [43], so that they lack the kinetic energy required to penetrate into the DC cathodic sheath where the dust particles are located.Thereafter, collection of electrons would be suppressed, inside a steady DC cathodic sheath.

Charge measurement
To measure the residual charge Q res of the dust particles, we used our free-fall method.Here we will summarize this method, with aspects specific to the present experiment.Further details can be found in [43], where we first reported the method.The method centers on measuring the acceleration of free-falling particles in the presence of gravity and an electric force.This falling motion occurs over several tens of milliseconds, which is longer than the lifetime of electrons and ions in the afterglow, so that during our camera observations, the electric field was essentially a constant vacuum field.The value of this vacuum field, denoted E falling , can be obtained from this chamber's vacuum potential, which has a slightly nonlinear vertical profile obtained from a solution of LaPlace's equation [43], which is applicable for t > 2 ms when the electrons and ions have departed the chamber (which is of course different from the potential profile when the plasma was present, due to Debye screening).We can then use the difference of two accelerations, the observed particle acceleration a and the acceleration of gravity g, to calculate the residual charge as In this formula, the sign convention is for a, g and E falling to all have positive values in the downward direction.Since the lower electrode was cathodic, E falling was in fact downward.Thus, if measurements show that a > g, the particle's charge must be positive, while if a < g it must be negative.
To obtain the acceleration a of the particles, we analyzed images of them as they fell.For this purpose, we used a 12-bit Phantom v5.2 video camera, viewing from the side and recording at 1000 frames per second, as in [77,79].For illumination, we used a vertical sheet of laser light, so that the camera imaged a vertical cross-section of the dust layer.The camera was triggered to begin recording at t = 0. Due to their large size, individual particles could be measured easily in each A linear fit yields the acceleration a, which we use as an input to equation (1) to obtain the dust particle's residual charge Qres in the afterglow.It is obvious that the slope of the velocity time series is a > g in the control run, indicating that Qres is positive, while the charge is negative in the modulated run (b), where a < g. video frame.In our image analysis, we measured the height of about 30 particles, which fell together at nearly the same rate.We averaged the heights of those particles in each frame, yielding the time series of height shown in figure 3(a) for the control run, and figure 3(b) for the modulated run.Using a centraldifference method, we then calculated the velocity time series as the particles fell, also shown in figure 3. The velocity data points fall on a straight line, which we fit to obtain the acceleration a, as the input to equation (1).We note that the acceleration was constant during the fall of the particles, indicating that gas drag was not a significant force at our low gas pressure.
Our chief result is that in the two runs, the residual charge Q res was very different, and in fact it did not even have the same polarity.In the control run in figure 3(a), the slope of the velocity time series exceeds g, i.e. a > g, indicating a downward electric force.The direction of this force shows that, as they fell, the dust particles were attracted to the lower electrode.Since that electrode had a negative bias at all times, an attraction requires that Q res must have a positive polarity in the control run.However, Q res had a negative polarity in the modulated run, as indicated by the slope a < g in the velocity data of figure 3(b).Quantitatively, Q res was +8500 e in the control run, and −12 000 e in the modulated run, as calculated using equation (1).
To confirm our results, we performed four repetitions of the control run, and four repetitions of the modulated run as well, keeping all the conditions the same.Always using the same analysis method, we found that the values of Q res varied less than ±1%, among the four repetitions of each run.
We also performed a third run, in a test intended to help explain the negative charging that we observed in the modulated run.This third run was similar to the control run, but at a lower RF power so that the ion density during plasma operation was reduced to the same level that prevailed at the end of plasma operation in our modulated run.Data from this third run, provided in the supplementary material, indicate a positive charge of +3500 e.
We note that the particle's charge in the afterglow is unrelated to its initial value during plasma operation.For the particle size and plasma density in our experiment, at the beginning of the afterglow the charge was able to change on a time scale of microseconds [82], which is orders of magnitude faster than the development of electron and ion conditions in the afterglow.Thus having ample time to adjust in response to the new conditions of the ambient electrons and ions, the particle's charge reaches its afterglow value without depending on its earlier value during plasma operation.For this reason, in the interpretation of our results for the value of the charge in the afterglow, it is of no great consequence that the charge during plasma operation had a magnitude that was not measured, and that could have been different in the control vs modulated runs.(Those two runs had a different selfbias during plasma operation, and therefore a different electric field, which in turn would have altered the ion flow and other parameters of the ions and electrons during plasma operations, thereby causing the charge during plasma operation to differ for those two runs.

Discussion
We performed an experiment to investigate how modulating the plasma power, before extinguishing it altogether, can alter the residual charge of a dust particle in the afterglow.The effect of modulation was found to be quite large.
In the experiment, RF power was applied through a coupling capacitor to the lower electrode, where the other chamber surfaces were grounded.This power was operated with a 4.5% duty cycle and a 1 ms period in the modulated run, while in a control run the RF power was applied constantly, i.e. with a 100% duty cycle.Polymer microspheres were electrically levitated during this plasma operation.When the power was stopped at t = 0, the afterglow began.The particles fell toward the lower electrode, and measuring their acceleration allowed us to measure their residual charge Q res .
We discovered that Q res was negative in the modulated run, with a large value of −12 000 e, i.e. about −1.4 e per nm of particle diameter.On the other hand, in the control run we found that Q res was positive, with a large value of +8500 e, i.e. +1.0 e per nm of diameter.The positive charging in the control run was as we observed in our first experiment [43], which similarly used unmodulated RF power.
For the modulated run, on the other hand, our finding of a negative charge was unexpected.Moreover, we are presently unable to explain this result.The dust particle is located in a cathodic sheath, when the afterglow began, just as it was in the control run, so that one might expect that it would collect only ions during the afterglow, which would lead to positive charging.
We tested a first hypothesis for the negative charge, in the modulated run, with an unsuccessful result.This hypothesis centers on ion density, which at t = 0 was greater in the control run than in the modulated run.There is no doubt that a dust particle had a negative charge during the plasma operation, in both runs, as shown by the levitation for t < 0. As soon as the plasma power was ended at t = 0, the ions, even though dwindling in number, can nevertheless collect on the dust particles so that its charge will become less negative and perhaps eventually positive.This positive trend in the charge must end, however, when the ion density becomes very low, which is an event called freezing.In the modulated run, the ion density started at a lower value, which would presumably result in an earlier freezing of the dust particle's charge.The test of this hypothesis is a comparison of the modulated run and the third run, which had nearly the same value of ion density at t = 0.If the hypothesis were true, we would expect the same residual charge in these two runs.However, they had entirely different outcomes: Q res was negative in the modulated run, but positive in the third run, despite having the same ion density at t = 0. Thus, a low ion density, by itself, does not explain our result of negative charging, following the end of powering a modulated plasma.
We can suggest a second hypothesis, centering on a momentary reversal of the electric field.In this description, the field reversal could drive a burst of electrons downward toward the dust layer.Besides the negative charging of the dust, there are additional data supporting this hypothesis: for 55 < t < 145 µs there is a reversal in the waveform for the voltage on the lower electrode, where the electrode's becomes more negative, figure 2. Due to the coupling capacitor, that reversal of the voltage on the electrode would be consistent with a collection of negative charge on the lower electrode, which could the from the same burst of electrons that also charged the dust negatively.This second hypothesis, which we discuss further in the supplementary material, is difficult to test experimentally as doing so would require spatiotemporal diagnostics in the sheath region, but we can suggest that a particle-in-cell simulation could be useful for this purpose.
There are practical applications for our discovery, that the residual charge can be controlled by using plasma modulation.In the semiconductor manufacturing industry, capacitively coupled RF power is widely used for deposition and etching of thin films.Moreover, this RF power is often modulated [83,84].Particle contamination can be a costly problem in manufacturing, and for this purpose we have proposed [77] schemes for controlling the charge of the particle in the afterglow so that it can be lifted electrically.The finding reported in the present paper indicates an additional approach for controlling the residual charge: purposefully modulating the RF power, before stopping it to begin the afterglow.
During plasma operation for t < 0, electrons and ions are continuously generated in the plasma volume.Meanwhile, the lower electrode collects both ions and electrons, and it does so in equal numbers when averaged over time.When powered by a RF waveform, the lower electrode collects only ions during most of an RF cycle, but it does collect electrons during a brief yet intense interval, when the sheath collapses onto the electrode surface [85].
Later, in the afterglow for t > 0 when the electrode is no longer powered, plasma generation ceases.Both electrons and ions will then gradually depart the chamber by collecting on the various surfaces of the chamber.At this time, the sheath above the lower electrode will have a very different character than it had during plasma operation: it will become a cathodic DC sheath, where essentially no electrons penetrate to the lower electrode due to its negative bias.That negative bias greatly exceeds the kinetic energy of any electron, especially as the electrons cool rapidly in the first few microseconds of the afterglow, as shown in the supplementary material of [43].Electrons, thus, can only collect on the other surfaces of the chamber, which are grounded, and not on the negatively biased electrode.Ions, meanwhile, will tend to stream toward the that same electrode, attracted by its negative potential.If the lower electrode has a sufficiently large area, it will collect most of the ions that were present in the plasma chamber.
The sheath above the lower electrode will change significantly after t = 0, when the RF power is no longer applied.The first change will occur at t = 0, when electrons no longer make periodic incursions into the sheath all the way to the powered electrode as they do in an RF sheath.Within a microsecond, electrons will exit the sheath, leaving only ions.The second change will be a gradual adjustment of the sheath thickness, toward the new equilibrium value that is typical of a DC sheath, and this will occur on an ion-acoustic time scale of tens of microseconds or longer.As the instantaneous sheath edge adjusts in this process, it may overshoot the equilibrium value, due to the inertia of ions, before it steadies at the new equilibrium value.The third change will be slower, over the course of a millisecond as ion density is depleted throughout the chamber and the DC sheath thickness gradually increases.During this period of a gradually increasing sheath thickness, the DC electric field of the sheath will correspondingly diminish gradually.(We can expect that this evolution of the sheath will occur not only for t > 0, but also during the plasma-off period of the modulated run, and the diminished DC electric field profile during that period will cause the particles to be levitated at a lower height.)

A.2. Estimate of ion density in the experimental runs
The collection of ions can be measured, over the course of time, as a diminishment of the negative charge stored on the coupling capacitor C coupl .This accumulation of ion charge partially cancels some of the charge stored in the capacitor, so that in the time interval 0 < t < 2 ms the lower electrode's bias rises by an amount ∆V, as compared to the DC self bias that prevailed when the plasma power was on for t < 0. The value of C coupl was large enough that it did not significantly discharge through any resistance, during the 2 ms that ions collected on the lower electrode (the RC time to discharge the capacitor in our experimental setup was 3 s, as reported earlier [43]. This potential change ∆V during the afterglow can be seen in both figure 2(a) for the control run, and figure 2(b) for the modulated run.For the latter, we can confirm the measurement of ∆V using the data during a power-off interval of the modulated plasma operation, for example −1 ms < t < 0.04 ms in figure 2(b), since those conditions are essentially the same as during the first millisecond of the afterglow.
For the modulated run, by inspecting the waveforms in figure 2, we estimate that ∆V ≈ 5 V for the modulated run, and ∆V ≈ 19 V for the control run.We can convert this measurement into an estimate of the ion density as follows.The number of ions collected on the lower electrode was Dividing N i by the total volume of the plasma chamber yields an estimate of the volume-averaged ion density n i , at t = 0.In the control run, the value of ∆V implies the collection of N i = 6 × 10 12 ions, which indicates a volume averaged ion density n i = 1.5 × 10 9 cm −3 .For the modulated run, the values are N i = 1.5 × 10 12 and n i = 5 × 10 8 cm −3 .The lower value of ion density in the modulated run indicates that the ramp-up of ionization did not reach a steady level, during the brief 45 µs power-on interval.

A.3. Complications that limit the precision of the ion-density measurements
We describe these ion-density values as estimates, rather than precise measurements, because of two complications.
First, some ions might not be collected on the lower electrode.This measurement method requires that an electrode have a large area and a strong negative bias during the entire afterglow, so that almost all the ions in the chamber are collected on that electrode, while repelling almost all electrons.However, some ions may nevertheless be collected on the other chamber surfaces, which are grounded, so that our method might under-estimate of the number of ions in the chamber.(A related effect would be a collection of ions on the dust particles during the afterglow, but this cannot occur to a significant extent in our experiment due to the small number of dust particles that we used.)Second, the shape of the voltage waveform is not a simple monotonic trend, but includes brief reversals in the first 280 µs.We performed a test that ruled out the possibility that these reversals are an artifact of our circuit.In that test, we operated the circuit with the same RF waveform without plasma, and the reversals were absent.That test suggests that any explanation of the reversals likely involves spatio-temporal factors in the movement of electrons and ions when the sheath edge adjusts to the sudden lack of an RF potential on the powered electrode.
Taking into account these complications, we cannot claim that the ion densities that we obtain are particularly precise.Our general impression is that the values may be accurate to within a factor of two, at best.For comparison, Langmuirprobe measurements of ion density, which are local whereas our method is global, also have some systematic complications, so that ion densities measured with probes are often subject to substantial uncertainties as well.

Figure 1 .
Figure 1.Experimental setup.During plasma operation, radio-frequency (RF) power was applied through a coupling capacitor C coupl to the lower electrode, while the grounded chamber walls served as the other electrode.An RF switch allowed operating the RF power either with a 100% duty cycle, or with a modulation having a defined timing for power-on and power-off operation, as sketched in the timing diagram.The RF power was stopped altogether at t = 0 to begin the afterglow.The side-view camera viewed particles as they fell, with an illuminating laser not shown here.

Figure 2 .
Figure 2.Voltage on lower electrode, measured in (a) the control run with 100% duty cycle, and (b) the modulated run with a 4.5% duty cycle and 1 ms period.Plasma power was stopped at t = 0, which was the beginning of the afterglow.During plasma operation for t < 0, the RF waveform was centered at a DC self-bias, at the level indicated by the dashed lines in the insets, which was −114 V for the control run, and −41 V for the modulated run.The coupling capacitor C coupl that allowed the self-bias to be maintained during plasma operation also had the effect of holding the same potential during the afterglow.However, in the first 2 ms there was a small upward change ∆V, as shown in the insets with an enlarged vertical scale.We attribute ∆V mainly to the collection of ions in the afterglow, so that its value allows a determination of the total ion charge and ion density at t = 0.

Figure 3 .
Figure 3. Time-series measurements of the height and downward velocity of the dust particle layer, for (a) the control run, and (b) the modulated run.The lower electrode is located at zero height.The velocity data points fall on straight lines, indicating constant acceleration after the plasma density became negligible at t = 2 ms.A linear fit yields the acceleration a, which we use as an input to equation (1) to obtain the dust particle's residual charge Qres in the afterglow.It is obvious that the slope of the velocity time series is a > g in the control run, indicating that Qres is positive, while the charge is negative in the modulated run (b), where a < g.