polyimides - indico · 2018. 11. 14. · kohlrausch relaxation this time dependence is known since...
TRANSCRIPT
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Polyimides
ChemistryConduction
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History ...
The PMDAODA polyimide used for GEMs derives from research between 1955 and 1965 in the Film Department of E. I. du Pont de Nemours and Company.
C.E. Sroog, A.L. Endrey, S.V. Abramo, C.E. Berr, W.M. Edwards & K.L. Olivier, Aromatic Polypyromellitimides from Aromatic Polyamic Acids, Journal of Polymer Science Part A 3 (1965) 13731390. [Wiley] doi: 10.1002/pol.1965.100030410.C.E. Sroog, Reflections on “Aromatic Polypyromellitimides [...]”,Journal of Polymer Science Part A 34 (1996) 2065–2066. [accessible] doi: 10.1002/pola.1996.844
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Trademarks
PMDAODA polyimide is sold under various registered trademarks such as:
Kapton®: E. I. du Pont de Nemours and CompanyApical®: Kaneka Texas Corporation...
The GEMs used for our measurements have been built (at CERN) from Apical® grade 200NP polyimide film.
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Polyimide
Polyimide is the collective name for a group of polymers that are:
mechanically strong: tensile strength of 100230 MPa;thermally stable: keeps properties till 200240 °C;fire resistant: chars but does not burn;chemically resistant: oil, solvents, weak organic acids;electrically insulating: resistivity of 1016 cm and more.
Here we deal with one member of the family: PMDAODA.
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PMDA
One ingredient for making polyimide is 1,2,4,5benzenetetracarboxylic dianhydride, commonly known as pyromellitic dianhydride or PMDA:
[Structure diagram from NIST]
Carbonyl groupsattract electrons
Substitute O by N toallow polymerisation
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ODA
The other ingredient is 4,4’oxydianiline or ODA:
It gets its name from the two aniline groups:
Nitrogen has electrons to spare
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PMDAODA reaction
Sequence:N is attracted by the carbonyl group,the anhydride ring is broken andintermediate polyamic acid forms,if heated, the ring closes again between COOH and NH:
[From Varun Ratta, PhD thesis, Virginia Tech, 1999.]
+ heat H2O
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PMDAODA
Combined, this gives the building block of polyimide:
The name comes from the imide group:
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Crossbonding
Crossbonding occurs between the N's of one chain and the O's from a neighbour:
[From Varun Ratta, PhD thesis, Virginia Tech, 1999.]
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Protons: polyamic acid (PAA)
Note the intermediate acid, i.e. an H+ donor:
This only happensif heat is provided.
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PAA PI vs baking temperature
The quantity of remaining PAA depends on the baking temperature.
The proton density therefore also varies.
[H. Oji et al., Memoirs of the Synchrotron Radiation Center, Ritsumeikan University, Kyoto, Japan 8 (2006) 187188.]
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Chargingup current
When applying voltage across a new GEM, a current flows:
not constant (i.e. not a resistor)decay is not exponential (i.e. not a capacitor);decay is not linear (i.e. not evacuation);
but a power law.
E = 100 kV/cm100 cm2 GEM
Data: seeMythra's talk
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Kohlrausch relaxation
This time dependence is known since 1854 at least. Also known as Curievon Schweidler behaviour.
Numerous models have been proposedH. Kliem, Kohlrausch relaxations: new aspects about the everlasting story, doi: 10.1109/TDEI.2005.1511096.
One of the simplest models specifically assumes ions (e.g. protons, not electrons) as charge carriers and has thin insulating barriers between dielectric medium and electrodes.
Rudolf Hermann Arndt Kohlrausch(November 6th 1809, Göttingen March 8th 1858, Erlangen)
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Kohlrausch relaxation
Hopping model (3d, MC) including Coulomb force of neighbouring ions, mirror charges and external field.
Elec
trode
Elec
trode
PolyimideBarriers
Efield
protons
Herbert Kliem
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Discharge current
The initial charge carriers stay in the polyimide, as can be seen by switching off the HV.
The discharge current has reverse polarity and obeys a Kohlrausch law.
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Initial carrier field
Once moved to the polyimide surfaces, the initial charge carriers generate an additional electric field.
Charges at the electrodepolyimide interfaces have no effect: the electrodes are conductors.
However, the charge on the polyimidegas interfaces is a potential source of field distortions.
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Initial carrier density
The transit time gives a lower limit on the mobility of the initial charge carriers:
Combining with the initial resistivity:
one finds an upper limit for the carrier density:
which is in line with E. Sacher's estimate (1979). [doi: 10.1109/TEI.1979.298160]
=T
E t
5010−4 cm105 V /cm 104 s
= 510−12 cm2
V.s
51016cm
n = 1qe
31013/cm3
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Field due to initial charge carriers
The polyimide volume from where carriers can reach the gas interface is
Which gives as surface charge deposit per hole:
Only a noticeable effect at the upper limit.
106 ion+106 e
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Initial steadystate current
Protons, and perhaps other ions, are likely candidates for the role of initial charge carriers.
There is only a finite supply of these and once they are accumulated on the surfaces, their contribution to the conductivity of the polyimide diminishes.
After the transient, some conductivity remains – for long periods of time – pleading in favour of electrons/holes as steadystate carriers (another possibility would e.g. be heavy, slowmoving ions).
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Electron affinity
All anhydrides are by their nature electrophilic and PMDA has the highest electron affinity amongst the common dianhydrides: 1.90 eV. [Varun Ratta, PhD thesis, Virginia Tech, 1999.]
Polyimide has an electron affinity calculated to be 1.4 eV. [Sherif A. Kafafi, 10.1016/00092614(90)85647U ]
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Steadystate resistivity
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Steadystate resistivity
The steadystate resistivity in Apical® grade 200NP appears to be larger than other PMDAODA polyimide:
The resistivity is a strong function of temperature.
Thermal activation energy found to be 1.7 eV, in line with the electron affinity.[G.M. Sessler et al., Electrical conduction in polyimide films, J. Appl. Phys. 60 (1986) 318326, doi: 10.1063/1.337646.]
v = 1018cm
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Some examples of the resistivity
Apical® type 200NP film, 50 µm:V ≥ 1012 cm at 200 °C
Kapton® type 100 CR film, 25 µm:V = 2.3 × 1016 cm ASTM D25778S = 3.6 × 1016 / ASTM D25778
Kapton® types KN and E, 50 µm:V = 2.4 – 3.6 1017 cm 10% RHV = 1.3 – 1.8 1017 cm 50% RHS = 8.9 – 13.0 1017 / 10% RH S = 0.1 – 3.1 1017 / 50% RH
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Evacuation of avalanche surface charge
Owing to the high resistivity of polyimide, surface charge evacuation is a slow process.Mobility measurement: deposit positive corona [ion+], negative corona [ion, e], charged liquids [positive] on polyimide metallised on one side only: Broadly similar results suggest charge is transferred onto the internal charge carriers, at first the initial charge carriers, later the steadystate carriers.Virtually no lateral spread is observed: evacuation appears to proceed via the bulk.
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Surface charge evacuation
The measurements of the mobility diverge:Andrés Aragoneses A. et al.:
µ+ = 0.22 1012 cm2/V.sµ = 0.20 1012 cm2/V.spresumed to include the charge transfer phase.
Z. Ziari et al.:µ+ = 0.9 1012 cm2/V.sµ = 1.2 1012 cm2/V.smeasurements start after ~30 s.
G.M. Sessler et al.:µ+ = 510 1012 cm2/V.s
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Charge transit times
Charges need ~104 s to move across a GEM tip, if µ = 2 1012 cm2/V.s.
During GEM operation, equilibrium is therefore likely come from ion+/e cancellation.
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Summary
Conductivity in polyimide consists of 2 phases:initial resistivity of 1016 cm presumably with protons and other ions as carrier e.g. from residual polyamic acid;steadystate resistivity of 1018 cm, with electrons as (one of several) candidate carriers.
Initial carriers may cause minor field distortions when accumulated on polyimidegas interfaces.
Surface charge evacuation thought to be carried out by the internal carriers, in a process which takes hours.
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Spare material
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Dielectric constant
Apical® type 200NP film, 50 µm ≤ 3.9 at 1 kHz
Kapton® type 100 CR film, 25 µm = 3.9 ASTM D15081
Other sources: = 3.1 at 100 kHz, 10% RH other Kapton®, 50 µm = 3.4 3.6 at 100 kHz, 50% RH idem = 3.62 at 1 kHz Azom = 3.5 at 1 Mhz Wikipedia = 3.2 3.3 at 1 Mhz = 2.88 3.48 at 1 Hz