Charging of dust particles on surfaces
Zoltán Sternovsky, Mihály Horányi, and Scott Robertson
Physics Department, University of Colorado, Boulder, Colorado 80309 – 0390
Experimental investigations have been made of the charge on dust particles resting upon a metal surface in vacuum. The surface is agitated so that the particles drop though a small hole and a Faraday cup beneath measures the charge on each particle. The surfaces are metals (Hf, Zr, V, W, Co, Ni, Pt and stainless steel) and the dust grains are both metallic conductors (Zn, V, and stainless steel) and insulators (silica and alumina) in the size range of 50 – 200 microns. The
contact charge is consistent with a model based upon the grain capacitance and the effective contact potential between the grain and surface. An electric field above the surface induces an additional charge on metallic grains consistent with Gauss's law. The induced charge on insulating grains increases with repeated contact. UV irradiation may increase or decrease the charge depending upon the relative importance of photoemission and photoconductivity.
1Dust particles are a nuisance in plasma processing of semiconductors, cause a
2rich variety of phenomena in laboratory plasmas, and play an important role in planetary
3and space physics. The motion of dust particles in space can be strongly affected by their charge if there are electric or magnetic fields. Charge also contributes to adhesion
4through the force exerted by the image charge. Suspended particles become charged by
5,6collection of electrons and ions from the local environment, or by photoemission.
Particles resting upon surfaces can also become charged due to a difference in the electrochemical potential of the particle and of the surface. There may be additional charging induced by electric field above the surface. We describe experiments in which the charges on dust particles initially upon a surface are measured after they have fallen through a small hole in the surface. The measured charges show the effects of particle size, the difference in contact potential, and of an applied electric field. For sufficiently clean metallic particles and surfaces, the charge on the particles is predictable from simple theoretical arguments considering the properties of the materials. For oxidized metallic particles and surfaces, the induced charge is predictable but the contact charge depends upon surface properties rather than bulk properties of the material. For nonconductors, both the contact charge and induced charge can be measured but are difficult to model because the charge on nonconductors resides in patches that may vary in number and size depending upon the history of contacts. In the experiments, dust samples of zinc, stainless steel, vanadium, silica (SiO), and alumina (AlO) were 223
investigated on numerous metal discs (Hf, Zr, V, W, Co, Ni, Pt, and stainless steel).
In Sec. II below we describe the charging theory of dust particles on surfaces, including the effects of an electric field. The apparatus and experimental techniques are described in Sec. III. In Sec. IV measurements of the charge on conducting and insulating dust grains are presented for both the contact and induced charging. The effect of UV irradiation is also briefly investigated. In Sec. V is a summary and discussion.
A. Induced charging due to electric fields
A metallic dust particle resting upon a metal surface in the presence of an external electric field will become charged by induction. For a spherical dust grain of radius r and
a homogenous electric field E perpendicular to the surface, the induced charge is: 0
2；？ , (1) Q，4?：1.64Er00
7,8,9where is the permittivity of free space. The surface charge is enhanced by a factor ：0
of 1.64 over the value it would have if there were a uniform field E above a surface of 0
2area 4?;r. This enhancement is due to the concentration of the electric field at the particle's location. In the case of dust particles with high electrical resistivity the time ?
for relaxation of a nonuniform charge distribution is characterized by a time constant
9, where is the relative dielectric constant. For most metallic particles, this (，：：?：0rr
time scale is many orders of magnitude shorter than one second. Materials with resistivity
11higher than 10 Ωm charge more slowly. For example, the time constant for alumina
1213with resistivity ρ ~ 10 - 10 Ωm and relative permittivity is of the order of ：，9，10r
several minutes. The time to charge by induction will also depend upon the resistivity at the points of contact with the surface.
B. Charging by the contact potential difference
The contact charging of metals by metals is well understood on the basis of thermodynamic equilibrium and the band theory of solids. The charge transfer brings the electrochemical potential (Fermi energy) to the same level throughout the two metals. The metal with the larger work function charges negatively. A contact potential difference is built up between the metals equal to the difference in work functions ；
，19；？divided by the elementary charge where C. Typical V，；，；ee，1.602，10cBA00
metal work functions (see Table I) are 4 to 5 eV and thus differences are 0 to 1 eV. During the process of separation of the dust particle from the surface, the capacitance between them decreases and thus the potential difference increases if the charge remains fixed. For sufficiently short distances, the increasing potential difference drives a tunneling current in the direction to maintain a constant . The tunneling current Vc
decreases with increasing distance and is effectively stopped at a critical distance that z0
10is of the order of nanometers. The final charge on the separated particle is then
determined by and the capacitance calculated at the critical distance. The capacitance Vc
of a sphere with radius r separated from a plane at a distance z is: 0
1 , (2) ；？；？Cz，4?：r~，lnzr0002
11where is Eulers constant. In case of rough surfaces, the contact capacitance ~，0.577
of the sphere/plane system is of the order of the classical capacitance between a smooth sphere and a smooth plane whose separation is equal to the average asperity heights 10,11. Thus, the expected contact charge on metals after separation is in ；？Q，VCzhC0
case of smooth surfaces and in case of rough surfaces with . ；？Q，VChh((zC0
There is evidence that some of the metallic grains used in our experiment have an
12oxide coating. Harper describes a model for the contact potential of oxidized metal surfaces. This model assumes the presence of an adsorbed layer of oxygen atoms on the outside of the oxide layer. Since oxygen atoms have acceptor levels below the metal Fermi energy, electrons tunnel from within the dust particle through the oxide layer and occupy some of the acceptor levels. These transferred electrons bring the oxygen acceptor level into a thermodynamic equilibrium with the metal. Consequently, the oxidized metal behaves like a metal with a work function equal to the depth of the oxygen acceptor level. This is typically about 5.5 eV and is not strongly dependent on the nature of the metal.
C. Metal-insulator contacts
The charging in metal – insulator contacts is generally greater than in metal –
metal contacts because of the absence of the tunneling current as a limiting process. The observed surface charge densities for different insulators after contact with a metal
210，5，3surface are in the C/m range. The charge is immobile and localized to ?~10，10
the area of the contact. The electric field intensity above a charged spot on a grain
57；？ is in the range of 10 – 10 V/m, that approaches the dielectric strength E，?：：？10r
12of common insulators.
In most insulators, the electrons lie in a full energy band that is well below the Fermi energy of a metal. The empty conduction band of the insulator is close to the vacuum level. However, there is no completely forbidden gap in insulators. Localized electron energy levels exist due to impurities, defects in the crystal structure, and the presence of a surface. The contact potential between a metal and an insulator depends upon energy states within the insulator band gap and the Fermi energy of the metal. Since numerous experiments (see Ref. 9, 10 and references therein) have found the amount of transferred contact charge to vary linearly with the metal work function, it is customary to assign an “effective” work function to insulators. Triboelectric series of insulators have
9 been constructed in this way.
The charge transfer mechanism in metal – insulator contacts is primarily by
electron transfer. Other processes, such as ion transfer or charged material transfer are
9,10believed not to play an important role. There isn’t a comprehensive theory for the
electron transfer. Calculations of the amount of charge transfer to an insulator have been
10based upon two models: 1) The electrons tunnel to or from localized states near the insulator surface and the amount of charge is limited by the distance the electrons can tunnel from the metal to the empty state of the insulator and vice versa. 2) The insulator and the metal come to a thermodynamic equilibrium due to the transferred charge as in a metal – metal contact. The charge transfer process is observed to occur within ~1 s in
10most cases. However, repeated contacts usually lead to enhanced charging which indicates that an equilibrium is not achieved in a single contact. It is generally assumed that the repetition of contact increases the effective contact area, which results in
10 enhanced charge transfer.
III. EXPERIMENTAL APPARATUS
The apparatus (Fig. 1) is a variation on a previously described apparatus for
13,1415measuring the charge on particles dropped through plasma or UV radiation. It
consists of a simple dust dropper and a Faraday cup beneath. The dropper is a thin metal disc mounted horizontally inside a vacuum chamber. The disc has a small central hole through which the dust may drop. The disc is agitated by an electromagnet that acts upon a small permanent magnet attached to the disc. A capacitor discharge generates a current pulse through the electromagnet. The amplitude of the agitation is determined by the initial charge on the capacitor. An electric field may be applied above the dropper disc by an additional circular electrode at a distance d = 10 mm above the dropper disc. The
application of voltage V to the upper disc results in a homogenous electric field
A small amount of dust is spread upon the disc with the intent to keep the inter-grain distances larger than the grain size so that the grains charge through contact with the dropper disc rather than through contact with one another. The capacitor voltage is set to drop dust particles less frequently than one on every pulse. This results in drops
primarily of single dust grains. The dropped dust particles are collected in the Faraday cup where the charge is measured. The Faraday cup is connected to a sensitive electrometer working as an integrator followed by two AC coupled bandpass amplifiers.
5The sensitivity of the electrometer (5.14 ， 10 electrons/Volt) is determined from
4calibration. The electrical noise of the output is about 10 elementary charges (0.02 V
amplitude). A data acquisition card in a computer is triggered by the pulse to the dust dropper and records the output from the electrometer. An impact of a charged dust particle to the Faraday cup makes a voltage pulse with a height that is proportional to the amount of its charge. Multiple impacts can be distinguished by their more complicated waveforms.
The process of falling through the hole may affect the charge on the particle. For example, a particle that rolls into the hole and falls may have a different charge from one that bounces then passes through the hole without contact. The rather large spread in the data may in part be due to different paths taken through the hole. In the case of charge induced by an electric field, a neatly drilled hole was found to result in a larger measured charge than a hole with sloping sides made by piercing the disc with a needle. This difference may be a result of the sloping sides of the hole partially shielding the particle from the electric field. Our data are for drilled holes about 1 mm in diameter.
Experiments were performed with different materials for both the dust and the dropper disc. The discs were made of Hf, Zr, V, W, Co, Ni, Pt, and stainless steel, in the form of a thin foil with thickness in the range 0.02 to 0.2 mm. The discs were cleaned in organic solvents. For experiments on contact electrification, the discs were cleaned also in diluted phosphoric acid followed by distilled water. The dust powders (zinc, stainless
steel, vanadium, silica, and alumina) were sorted by size using sieves. The size intervals in microns were 38-45, 45-53, 53-63, 63-75, 75-90, 90-106, 106-125, 125-150, 150-180, and 180-212. No cleaning procedure was applied to the dust samples. Photomicrographs of some dust samples are shown on Fig. 2. The particles are angular blocks rather than the spherical shape assumed in Eqs. (1) and (2).
The experiments were performed in a vacuum created by a 150 l/s turbomolecular
，6pump. The experiments took place in vacuum below torr. A few experiments 1，10
were performed at increased pressure to determine the effect of charge leakage through gas.
IV. EXPERIMENTAL RESULTS AND DISCUSSION
A. Induction charging of metallic grains
The charge induced by an applied electric field was measured as a function of the intensity of the electric field. These measurements were performed on zinc dust grains of 90 – 106 ?m placed on a stainless steel dropper disc. Figure 3 shows the mean value of the charge on sets of 100 grains for different values of electric field. The charge varies linearly with the electric field intensity and changes polarity with the applied electric field. A positively oriented electric field induces positive charge on the dust grains and vice versa as expected from Gauss's law. The mean value of the charge is in good agreement with Eq. (1) using half the average particle size for radius. However, the
standard deviation is large, on the order of 30 – 70 % of the mean value, and exceeds the
spread expected from the size dispersion of the zinc grains (solid lines). Typical charge distributions for five values of electric field are shown in Fig. 4 for the case of negative charge on the grains. In addition to the shift of the maximum toward larger charge with increasing electric field intensity, it can be observed that a few grains have charges several times larger than the mean value. The irregular shape of the zinc granules used in this experiment (Fig. 2) or perhaps grains stuck together can explain the large deviations from the mean value.
The linear regression to the data (not shown in Fig. 3) crosses the y-axis at
that is below the noise level of the electronics. This absence of significant Q，？5400e0
contact charge is probably due to both surfaces being oxidized and having ~ 5.5 eV effective work function.
A second experiment investigated the induced charge as a function of the dust
5particle radius with a constant electric field of V/m. The data, Fig. 5, are for E，1.5，10
sieved stainless steel dust particles placed on a stainless steel disc. The measured charge is approximately quadratic function of the grain size as expected from Eq. (1). The dashed line represents the theoretical curve with the mean particle radius
；？ where and are the lower and upper size limit determined r，d？d4ddmeanminmaxminmax
by the sieves. The larger deviation from the theoretical curve at the largest dust size is probably caused by this sample having more particles at the low end of the size range (125 ?m) than at the high end (150 ?m). The standard deviations of the measured charges
are 30 – 40 % of the mean.