discharge plasma and ion -surface interactions
TRANSCRIPT
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Chapter 4
Discharges, Plasmas, andIon-Surface Interactions
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Discharges, Plasmas, and
Ion-Surface Interactions
Sputtering
An ionized gas or plasma
active electrodes that participate in the deposition
Low temperature processing
Eject of atoms by momentum transfer
EvaporationVacuum environment
Passive electrode
Thermally induced evaporation
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Two Sputtering Systems
Several kilovolts are applied and gas pressures usually range from a few to a hundreds
millitorr.
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Plasma
Quasi-neutral gas that exhibits a collective behavior in
the presence of applied electromagnetic fields.
Weakly ionized gases consisting of a collection of
electrons, ions, and neutral atomic and molecular species.
Types of plasmas
Stars (density n < 10
7
cm-3
)Solar winds (density n < 107cm-3)
Coronas (density n < 107cm-3)
Ionosphere (density n < 107cm-3)
Glow discharge (density n = 108~ 1014cm-3)
Arcs (density n = 108~ 1014cm-3)
High-pressure arc (density n ~ 1020cm-3)
Shock tubes (density n ~ 1020cm-3)
Fusion reactors (density n ~ 1020cm-3)
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http://fusedweb.pppl.gov/CPEP/Translations.html
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Principal Glow Discharge Mechanism by
Biased Parallelplate
1. A stray electron near the cathode carrying an initial current iois accelerated towardthe anode by the applied electric field (E).
2. After gaining sufficient energy the electron collides with a neutral gas atom (A)
converting it into a positively charged ion (A+), i.e., e-+ A2e-+ A+.
3. Two electrons are generated and are accelerated and bombard two additional
neutral gas atoms, generating more ions and electrons, and so on.
4. Meanwhile, the electric field drives ions in the opposite direction.5. Ions collide with the cathode, ejecting, among other particles,secondary electrons.
6. Secondary electrons also undergo charge multiplication. (step 2)
7. The effect snowballs until a sufficiently large avalanch current ultimately causes
the gas to breakdown.
http://webhost.ua.ac.be/plasma/pages/glow-discharge.html
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Avalanche Breakdown
AeAe 2
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Townsend Equation
)1(1 de
d
oe
eii
electrodesbetweenDistancedtcoefficienemissionelectronsecondaryTownsend
tcoefficienionizationTownsend
currentchargei
e
::
:
:
Townsend ionization coefficient represents the probability per unit length of ionization
occurring during an electron-gas atom collision.
Townsend secondary-electron emission coefficient is the number of secondary electronsemitted at the cathode per incident ion.
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Townsend Ionization Coefficient
Eq
Ei
e
1
fieldelectricApplied
potentialIonizationE
distancetraveling
chargeElectronq
tcoefficienionizationTownsend
i
:
:
:
:
:
E
Eq
Ei
e
1
For an electron of charge q traveling a distance , the probability of reaching the
ionization energyEiis .
We may associate with the intercollision distance or mean free path in a gas. Since
~P-1, we expect to be a function of the system pressure.
Ene
rgyE
Probability
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nLA
L
A
L
PRT
N
V
n A #
d
2dA
1
2
PPdN
RT
A
Mean-Free Path
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Derivation of Townsend Equation
(a) The total current I = I-(x) + I+(x), a sum of electron and ion components, is
constant, i.e., independent of x and time.
(b) At the cathodeI-(0)= Io+ eI+(0), with Ioa constant.
(c) Across the gap,d[I-(x)]/dx = I-(x), i.e.,I-(x)= I-(0)exp x.
(d) At the anode,I+(d) =0.
Cathode Anode
d
xdx
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Breakdown Voltage
)]1(1[
d
e
d
oe
eii
Townsend equation
Breakdown is assumed to occur when the denominator of the Townsend equation is equal
to zero, i.e., .1)1( d
e e
1
2
P
PN
RT
A
moleculegasaofDiameter:
EE
ii V
q
E
ee
11
BBB dVde e
EEE1)1(
BPd
APdVB
)ln(
constantsBA :,
electrodesbetweenDistanced
tcoefficienemissionelectronsecondaryTownsend
tcoefficienionizationTownsend
currentchargei
e
:
:
:
:
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http://www.seas.ucla.edu/prosurf/Publications/paper22-IEEE.pdf
Y. P. Raizer, Gas Discharge Physics.New York: Springer-Verlag, 1991.
Paschens Curve
B
P
BPdAPdVB
)ln(
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Paschens Curve
At low values ofPdthere are few electron-ion collisions and the secondary electron yield
is too low to sustain ionization in the discharge.
At high pressures there are frequent collisions, and since electrons do not acquire
sufficient energy to ionize gas atoms, the discharge is quenched.
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Types and Structures of DischargesTownsend discharge
A tiny current flows initially due to the small number of charge carriers in the system.
With charge multiplication, the current increases rapidly, but the voltage, limited by the
output impedance of the power supply, remains constant.Normal glow
When enough electrons produce sufficient ions to generate the same number of initial
electrons, the discharge becomes self-sustaining.
The gas begins to glow now and the voltage drops accompanied by a sharp rise in current.
Initially, ion bombardment of the cathode is not uniform but concentrated near the
cathode edges or at other surface irregularities.As more power is applied, the bombardment increasingly spreads over the entire surface
until a nearly uniform current density is achieved.
Abnormal discharge
A further increase in power results in both higher voltage and cathode current-density
levels.
The abnormal discharge regime has now been entered and this is the operative domain for
sputtering and other discharge processes such as plasma etching.
Arc
At still higher currents, the cathode gets hotter. Now the thermionic emission of electrons
exceeds that of secondary-electron emission and low-voltage arcs propagate.
Arc is a self-sustained discharge that supports high currents by providing its own
mechanism for electron emission from negative or positive electrodes.
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http://science-education.pppl.gov/SummerInst/SGershman/Structure_of_Glow_Discharge.pdf
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Currentvoltage (iV ) characteristics of direct current (dc) electrical discharge
http://www.spectroscopynow.com/Spy/pdfs/jwfeed/sample_0471606995.pdf
Vbis the breakdown voltage,
Vnis the normal operating voltage, and
Vdis the operating voltage of arc discharge.
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http://www.exo.net/~pauld/origins/glowdisharge.html
http://en.wikipedia.org/wiki/Electric_glow_discharge
http://en.wikipedia.org/wiki/Image:Glow-discharge-schematic.gifhttp://en.wikipedia.org/wiki/Image:Glow-discharge-schematic.gif -
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Sprite light in the atmosphere (left) and in a laboratory glow discharge tube (right). In
both cases, the light near the positive (anode) end is red and arises from the collisional
excitation of neutral nitrogen molecules by free electrons. Also in both cases, the light
near the negative (cathode) end is blue and arises from the collisional excitation of N2+
ions by free electrons.
http://www.physicstoday.org/pt/vol-54/iss-11/captions/p41cap3.html http://www.emitech.co.uk/sputter-coating-brief3.htm
Sprite and Glow Discharge Tube
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A glass tube, about 16 inches long and 1 1/2 inches in diameter, is hermetically
sealed at both ends. Two metal probes are fused into the tube at each end. Thephysicist applies a potential of a few thousand volts across both probes. With the aid
of a vacuum pump he sucks the airout of the tube, thus lowering the pressure inside
the glass tube.
http://www.newjerusalemnetwork.net/emmanuel/great_wall3.html
Regions in the DC Glow Discharge Tube
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http://www.newjerusalemnetwork.net/emmanuel/great_wall3.html
Regions in the DC Glow Discharge Tube
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AFirst of all, a narrow beam of red lightmoves across the inside of the tube, fromone electrode to the other. As the pressure continues to fall, the beam of light
becomes thicker and soon fills the whole space between the electrodes. Near the one
electrode there appears a blue glow, and at the other a dark space.
If the physicist continues to rarefy the air in the tube, the blue glow turns into a thin
red sheathof light close to the electrode [identified in the illustration to the top-left
as A].
BAfter a region of darkness, known as 'Crookes' dark space' after its discover, thereappears with a well defined edge, the palest part of the electrical discharge, a faint
blue columnof light known as the ' negative glow.
CThis blue glow fades gradually into another dark space, which is followed by aweak red-violent glowknown as the ' posit ive column' or 'plasma.
D In the final stage of the experiment, the air in the tube is rarefied until all thedischarge phenomena disappear. Then, however, the right-hand end of the glass
glows with a Green Fluorescent Light.
Pages 16-18, "Physics For The Modern Mind," Walter R. Fuchs http://www.newjerusalemnetwork.net/emmanuel/great_wall3.html
Regions in the DC Glow Discharge Tube
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Regions in the DC Glow Discharge TubeAlthough the general structure of the discharge has been known for a long time, the
microscopic details of the charge distributions, behavior, and interactions within these
regions are not totally understood.
Cathode
Aston dark
The Aston dark space is very thin and contains both low energy electrons and high
energy positive ions, each moving in opposite directions.
Cathode glow
Beyond the Aston dark the cathode glow appears as a highly luminous layer thatenvelops and clings to the cathode.
De-excitation of positive ions through neutralization is the probable mechanism of
light emission here.
Cathode dark (Crookes)
Next to cathode glow is the cathode dark space, where some electrons are energized to
the point where they begin to impact-ionize neutrals; other lower energy electronsimpact neutrals without ion production.
Because there is relatively little ionization this region is dark.
Most of the discharge voltage is dropped across the cathode dark space.
Cathode dark space is commonly referred to as the cathode sheath.
The resulting electric field serves to accelerate ions toward their eventual collision
with the cathode.
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Regions in the DC Glow Discharge Tube
Negative glowHere the visible emission is apparently due to interactions between assorted secondary
electrons and neutrals with attendant excitation and de-excitation.
During sputtering the substrate is typically placed inside the negative glow before the
Faraday dark space so that the latter as well as the positive column do not normallt
appear.
Faraday darkPositive column
Anode dark
Commonly referred to as the anode sheath.
Anode
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Yu. P. Raizer. Gas Discharge Physics. Springer, Berlin, 1991.
Light intensity
Potential V
Field E
Current
Charge density
Charge density (total)
Potentials along the Tube
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Plasma Sources Sci. Technol. 12 (2003) 295301
Regions in the Glow Discharge Tube II
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Potentials along the Tube
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)(1 NNqdxdE
Edx
dV
NN
0
0
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Fundamental of Plasma Physics
Plasma species: electron (ne), ions (ni), and neutral gas (no)
Electron has highest velocity
Electrically neutral: ne= ni
Degree of gas ionization: fi= ne/(ne+no)
fi= 10-4
for glow discharge
Particle energies and temperature:
For glow discharge:
Electron energy = 1 to 10 eV (typically 2 eV)
Effective characteristic temperature Te= E/kB= 23000 K
Neutral gas energy = 0.025 eV, (To= 293 K)
Ion energy = 0.04 eV (Ti= 500 K), acquired from electric field.
Low pressure glow discharge is a nonequilibrium cold plasma.
(if in equilibrium: Ti = To= Te= T)
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Motion in Plasma Species
qn
j4
v
Electrical current density Particle flux Charge
m
TkB
8v
Surface are charged negatively due to greater electron bombardment. ve>vi
4
vv
vv
n
M
RTnd
RT
M
RT
Mn x
xx
2)
2exp(
2 0
2
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m
TkB
8
v
gme28
101.9
KTe 23000
122231038.1 KskgmkB
scme /105.9 7v
gm Ari23
23)( 1064.6
1002.6
40
KTi
500scme /102.5
4v
Charging of Surface in a Plasma
The implication of this calculation is that an isolated surface within the plasma charges
negatively initially because of the greater electron bombardment.
Subsequently, additional electrons are repelled while positive ions are attracted.
Therefore, the surface continues to charge negatively at a decreasing rate until the
electron flux equals the ion flux and there is no net current.
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Mobility: velocity per unit electric field E/v
Mobility in an Electric Field
v
vv
mq
tmq
dt
dm coll
E
E ][
Collision frequency
Electric force Frictional drag
vv coll
t][
m
qm
q
Ev
In the steady state, 0dt
dv
)/( Ev
Typical mobilities for gaseous ions at 1 torr and 273 K range from ~ 4 102cm2/V-s
(for Xe+) to 1.1 104cm2/V-s (for H+).
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Diffusion
dx
dnDnJ
dx
dnDnJ
iiiii
eeeee
E
E
Charge Neutrality, nnnJJJ ieie ,
dx
dn
n
DD
ie
ei
)(
)(
EElectric field developed by separation of charge
An electric field develops because the difference in electron and ion diffusivities
produces a separation of charge.
Physically, more electrons than ions tend to leave the plasma, establishing an electric
field that hinders further electron loss but at the same time enhances ion motion.
)(
)(
ie
ieeia
DDD
Ambipolar diffusion coefficient
Both ions and electrons diffuse faster than intrinsic ions do.
i i C i i i
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Electron Motion in Combined Electric Field
)( Bqdt
md
FforceLorentz
vv
E
elare parallandB E
surfacetargetthetonormalev
0E
Btoangleanate v
Btoangleanate
v
qB
mr
r
mBq
sin
)sin(sin
2
v
vv
Clearly, magnetic fields prolong the electron residence time in the discharge andenhance the probability of ion collisions.
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Electron Motion in Combined Electric Field
dicularare perpenandB E
Electrons emitted normally from the cathode ideally do not even reach the anode but
are trapped near the electrode where they execute a periodic hopping motion over its
surface.
02
2
2
2
2
2
dt
zdm
dt
dxqBq
dt
ydm
dt
dyqBdt
xdm
e
e
e
E
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-5.00E+03
-4.00E+03
-3.00E+03
-2.00E+03
-1.00E+03
0.00E+00
0.00E+00 2.00E-04 4.00E-04 6.00E-04 8.00E-04 1.00E-03 1.20E-03
2
)cos1(
ce
c
m
tqEy
)sin
1(t
t
B
tx
c
c
E HzBm
qB
frequencyCyclotron
Gaussin
e
c )(
6108.2
Electron Trace
Electrons repeatedly return to the cathode at time intervals of /c.
q (Coul) E (V/m) c m
e(Kg) B (Gauss)
1.60E-19 10000 2.80E+07 9.11E-34 10
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Electron Motion in Glow Discharge Plasma
dicularare perpenandB E
Electrons repeatedly return to the cathode at time intervals of /c.
Electron motion is strictly confined to the cathode dark space where both fields are
present.However, if electrons stray into the negative glow region where E is small, they
describe a circular orbit before collisions may drive them either back into the dark
space or forward toward the anode.
Confinement in crossed fields prolongs the electron lifetime over and above that in
crossed fields, enhancing the ionizing efficiency near the cathode. A denser plasma
and larger discharge current result.
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Radial Electric Potential around an Isolated
Positive Ion
Tk
rqV
ieBenrn
)(
)(
0 Vnn ie ))(
1()(
)(
Tk
rqVnenrn
B
i
Tk
rqV
ieB
Tk
rVqnnnq
dr
rdVr
dr
d
r Bo
i
o
ei
)()()]([1 22
2
equationPoisson
)exp()(D
r
r
qrV
2qn
Tk
i
BoD
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Debye Length
Outside of a sphere of radius Dthere is effectively no interaction between the ion
and the rest of the plasma.
In the case of an inserted electrode, Dis a measure of the plasma sheath dimension.
)exp()(D
r
r
qrV
2qn
TklengthDebye
i
BoD
eVTkcmn
B
i
210
310
cmD
2101
Debye length is a measure of the size of the mobile electron cloud required to
reduce V to 0.37 (i.e., 1/e) of its initial value.
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Electron Plasma Frequency
http://farside.ph.utexas.edu/teaching/plasma/lectures/node6.html http://www.irf.se/~ionogram/ionogram/javascaling/PlasmaFreqForBeg.html
When charged particles are separated by a short distancexthe polarization,
P= qnx, where n =n+= n is the number density of the particles.
http://www.physics.ox.ac.uk/users/jelley/ESupdates05.ppt
The restoring electric field Eis given by P/oso
Electronplasma frequencywp, given by wp2= ne2/me o
o
nqkkxF
2
o
xnqqE
dt
xd
2
2
2
m
qnxP
om
nq
m
k
2
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Electron Plasma Frequency
Hznm
nqe
oe
ee
32
1098.8
Consider that an external electric field is suddenly turned on, displacing plasma
electrons over some length.
If it is just suddenly turned off, the electron displacement induces a field that pulls
the electrons back to their original position.
But the inertia of the electrons will cause them to overshoot the mark and
harmonically oscillate about the equilibrium site.
2qn
Tk
i
BoD
e
e
B
i
Bo
oe
eDe
m
Tk
qn
Tk
m
nqv
2
2
The product of Dand eis essentially equal to the electron velocity.
If the frequency is less than ethe dielectric constant is high and the plasma appears
opaque to such radiation.
On the other hand the plasma becomes transparent to radiation at frequencies greater
than ewhere the dielectric constant drops.
,109,10 8310
HzcmnFor ee a frequency much larger than that typically used in
AC (RF) plasmas.
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Plasma Criteria
1. System dimension >> Debye length D >> D Only in this way the quasineutrality of the bulk of the plasma be ensured.
2. Shielding electrons drawn into the Debye sphere >> 1 (at least) ND= 4D
3ne/3
3. Electrons should interact more strongly with each other than with the
neutral gas. Under this conditions, particle motion in the plasma will be controlled by
electromagnetic forces rather than by gas fluid dynamics.
eVTk
cmnn
B
ei
2
10 310
cm
D
2101 2qn
Tk
i
BoD
43
104~3
4
eDD
nN
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AC Effects in Plasmas
tqdt
xdm oe sin2
2
E
2e
oo
mqx E Maximum electron displacement amplitude
Assuming no collisions of electrons with neutrals,
2
2
2
)()(
2
1
e
oooo
m
qxqE
EE Ionization energy
eVE Aro 7.15)(,
)1056.132(56.13 6HzMHzf cmVo /5.11
EField Strength required to ionize gas.
Eo= 11.5 V/cm is an easily attainable field in typical plasma reactors.
No power is absorbed in the collisionless harmonic motion of electrons, however.
For electrons undergo inelastic collisions,
Electron motion is randomized and power is effectively absorbed from the RF source.Even smaller values of Eo can produce ionization if, after electron-gas collisions, the
reversal in electron velocity coincides with the changing electric-field direction.
Through such effects RF discharges are more efficient than their DC counterparts in
promoting ionization.
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Electrodeless Reactors
Inductive coupling
Capacitive coupling
However, for the deposition of films by RF sputtering, internal cathode targets are
required.
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Electrode Sheaths
Cathode Sheath Anode Sheath
Tk
VVq
n
n
B
fp
e
e )(
exp*
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Electrode Sheaths
Both anode and cathode surfaces will be at a negative floating potential (Vf) relative to
the plasma potential (Vp)
Lower electron density in the sheath means less ionization and excitation of neutrals.Less luminosity there.
Large electric fields are restricted to the sheath regions.
It is at the sheath-plasma interface that ions begin to accelerate on their way to the target
during sputtering.
The plasma is typically some ~ 15 volts positive with respect to the anode.
Tk
VVq
n
n
B
fp
e
e )(
exp*
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Electrode Sheaths
Tk
VVq
n
n
B
fp
e
e )(
exp*
The number of electrons (ne*) that can gain enough energy to surmount this barrier is
given by
Considering the electrical flux balance between electrons and ions near the cathode, itgives
i
e
e
e
m
m
n
n 3.2*
(Derivation detail not given.)
eVgem
m
q
TkVV
e
ieBfp 10~.,.)
3.2ln(
2
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Ion Motion in Sheath
Free fall, collisionless manner
Mobility limited, repeated collision
2/3
2
2
9
4V
m
q
d
Ej
s
o Free fall or space charge limited
2
38
9V
dj
s
o
EMobility limited
thicknesssheathd
thicknesssheathaacrossappliedvoltageV
s:
:
It turn out that free fall model, also known as the Child-Langmuir equation, better
describes the measured cathode-current characteristics.
This is certainly true at low pressures where few collisions are likely.
Sh h D k S Thi k
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Sheath Dark Space Thickness
The sheath dark space is sometimes visible with the unaided eye and is therefore
considerably larger than calculated Debye lengths of 100 m.This means that a large planar surface behaves differently from a point charge when both
are immersed in plasmas.
Instead of electrons shielding a point charge, bipolar diffusion of both electrons and ions
is required to shield an electrode, and this physically broadens the sheath dimensions.
D
a
eB
fp
sTk
VVqd
]
)([~
)(4
3
)(3
2
pressureslowerapressureshigher