Field Emission-Driven Microdischarges

Transcription

1 small scale transport research laboratory Field Emission-Driven Microdischarges Prof. David B. Go Aerospace and Mechanical Engineering 03/16/2012

2 Microplasmas and Microdischarges Microplasmas/discharges gas discharges with a characteristic dimension less than 1 mm advantageous pd scaling enables stable operation at high p (1 atm) high pressure leads to new chemical pathways new applications Lighting Medical and Dental Effects of Confinement* decreased electrode spacing affects charge density distribution & Debye length increased surface-to-volume ratio affects energy balance and distribution Environmental and Chemical Analysis Nanomaterial Synthesis Harper et al., Anal. Chem., 2009 *Mariotti & Sankaran, J. Phys D: Appl. Phys., 2010 As surfaces begin to play a dominant role, it is necessary to establish a better understanding of plasma/surface interactions slide 2

3 Plasma/Surface Interactions Plasma/surface interactions important for applications liquid/flesh/sputtering/cells/etc. electrochemistry/biological/environmental Plasma/electrode damage important for device development device lifetime/robustness/design Plasma/electrode coupling important for fundamental understanding emission processes (secondary/photo/thermionic/field) charging processes (dielectric barriers) slide 3

4 Outline Field Emission and Microscale Breakdown Theory for Modified Paschen s Curve applied dc voltage (V) Experimental Evidence of Field Emission-Driven Microdischarges 50 Fluid Models for Field Emission-Driven Microdischarges electrode spacing (μm) μm E ion, V m Conclusions and Future Work μm Applied Potential, V slide 4

5 Outline Field Emission and Microscale Breakdown Theory for Modified Paschen s Curve applied dc voltage (V) Experimental Evidence of Field Emission-Driven Microdischarges 50 Fluid Models for Field Emission-Driven Microdischarges electrode spacing (μm) μm E ion, V m Conclusions and Future Work μm Applied Potential, V slide 5

6 History on Microscale Breakdown Microscale breakdown was originally studied in the 1950s in a series of papers out of IBM Rejuvenated in 1990s by surge of interest in MEMS devices preventing sparks and device failure Near universal deviation from the classic Paschen s breakdown curve modified Paschen s curve Go and Pohlman, J. Appl. Phys. (2010) slide 6

7 Deviation from Paschen s Curve Deviation from Paschen s curve occurs because either secondary emission is a function of the electric field alternative charge creation processes are at play cathode electron impact ionization (-process) e e e e ion-induced secondary emission ( i -process) e field emitted electrons ( -process) anode At the microscale, the electric field can be very high (~ V/μm) such that electrons tunnel from the cathode electron field emission acts as an additional charge source and it is also a function of the electric field At pressure, ions in the electrode gap affect the electric field ion-enhanced field emission ~1-10 μm Boyle & Kisliuk Phys. Rev. Lett slide 7

8 PIC/MCC Simulations of Breakdown Zhang, Fisher, Garimella J. Appl. Phys., 2004 Radmilovi-Radjenovi, Lee, Iza, Park, J. Phys. D. Appl. Phys., 2005 Radmilovi-Radjenovi, Radjenovi, IEEE Trans. Plasma Sci., 2007 PIC/MCC simulations confirmed the role of field emission slide 8

9 Remaining Questions Is there a basis for a theory to describe the deviation from Paschen s curve? What is the nature of the interaction between field emission and the discharge? Can field emission play any other role in the discharge? Implications? slide 9

10 Outline Field Emission and Microscale Breakdown Theory for Modified Paschen s Curve applied dc voltage (V) Experimental Evidence of Field Emission-Driven Microdischarges 50 Fluid Models for Field Emission-Driven Microdischarges electrode spacing (μm) μm E ion, V m Conclusions and Future Work μm Applied Potential, V slide 10

11 Classic Breakdown Theory Volumetric breakdown characterized by Paschen s curve Pre-Breakdown Current j j prebreakdown = o e d 1 ( i e d 1) Breakdown Condition Townsend Criterion e d ( 1+1 ) i balance of multiplication and secondary emission Traditional exponential form for ionization coefficient, = Ape Bpd V A & B coefficients p pressure d electrode gap V - voltage V b = Breakdown Voltage: pd scaling Bpd A ln( pd)+ ln ln 1 i +1 ( ) = f( pd) slide 11

12 Ion-Enhanced Field Emission work function work function Fermi energy F e Fermi energy F e f() solid vacuum f() solid Fowler-Nordheim Equation (1928) [ ] 2 ( ) j = A FN E 2 y ( ) exp B FN 32 vy E *theoretically require fields ~1000 V/μm but practically as low as V/μm 0 th -order ion enhanced field emission j = A FN [ E + E ion ] 2 2 ( y) ( ) exp B FN 32 vy E + E ion *the ion s potential thins the potential barrier making it easier for an electron to tunnel from the cathode Can use 0 th -order approximation to derive theory for field emission s role in breakdown slide 12

13 Field Emission Breakdown From a 0 th order perspective, superposition can be used to account for the ion-enhanced effect j field = C FN E 2 exp D FN E j field + = C FN D FN ( E A + E ion ) 2 exp ( ) E A + E ion Can derive relationship for ion-enhanced field emission j field+ = j field e Mj n field+ ( ) = j field+ j ion = Ke D FN d V effective secondary emission coefficient Boyle & Kisluik, J. Appl. Phys, 1955 Recall the Townsend criterion i e d 1 ( )=1 replace i by This formulation reproduces linear deviation from Paschen s curve Ke D FN d V b ( e d 1)=1 Radmilovi-Radjenovi & Radjenovi, Plasma Sources Sci. Technol., 2008 slide 13

14 Semi-Empirical Modified Paschen s Generally, secondary emission coefficients can be added linearly ion-induced, metastable-induced, photoemission Townsend Criterion: e d ( 1+1 ) Semi-empirical analytical formulation for modified Paschen s curve net = i + i + Ke Dd V ( e d 1)=1 K is an ill-defined parameter that is a combination of a number of other parameters essentially a fitting factor Go and Pohlman, J. Appl. Phys. (2010) slide 14

15 Semi-Empirical Modified Paschen s Paschen s curve i + Ke Dd V ( e d 1)=1 field emission only combined equation: modified Paschen s curve Go and Pohlman, J. Appl. Phys. (2010) slide 15

16 Semi-Empirical Modified Paschen s K~ physical interpretation? some arguably questionable assumptions in derivation of Can a more complete ab initio formulation be derived? Go and Pohlman, J. Appl. Phys. (2010) slide 16

17 Ion-Enhanced Field Emission Revisit 0 th order perspective, j = A FN ( E A + E ion ) 2 2 ( y) ( ) exp B FN 32 vy E A + E ion explicit form for E ion using a single ion and method of images The number of electrons field emitted because of the presence of a single ion is the integration of the current density over area and ion s time of flight N emit = 1 q T A s je ( )da s dt '= N emit N ion cathode surface area influenced by single ion time of flight of ion Substitute into breakdown condition ( i + )( e d 1)=1 Tirumala and Go, Appl. Phys. Lett. (2010) slide 17

18 Analytical Modified Paschen s Curve Fully Analytical Model i + 1 R T (2rdr) dt Er,t q 0 t 2 0 y ( ) ( ) exp B FN 3/2 v( f ) Er,t ( ) ( exp Bpd V eapd ( ) 1)=1 where E(r,t) = (E A ) + q 2 0 L 0 be A t (( L 0 be A t) 2 + r 2 ) 3/2 T = lifetime of ion R = radius of interaction b = ion mobility Since E A = V/d Numerically solve for breakdown potential V b Effective emission coefficients < 1 effect of ion on the field averaged over time of flight is fairly small but not insignificant slide 18

19 Analytical Modified Paschen s Curve applied dc voltage (V) modified Paschen s curve Paschen s curve Experimental Breakdown Curve: Slade and Taylor (2002) Simulated Breakdown Curve: Zhang et al. (2004) Semi-empirical breakdown model: Go and Pohlman, (2010) Analytical breakdown model: Tirumala and Go, (2010) electrode spacing (μm) Tirumala and Go, Appl. Phys. Lett. (2010) slide 19

20 Implications: pd vs. d Scaling Tirumala and Go, Appl. Phys. Lett. (2010) slide 20

21 Implications: pd vs. d Scaling At the microscale, scaling no longer pressuredistance Tirumala and Go, Appl. Phys. Lett. (2010) slide 21

22 Remaining Questions Is there a basis for a theory to describe the deviation from Paschen s curve? What is the nature of the interaction and/or coupling between field emission and the discharge? Can field emission play any other role in the discharge? Implications? slide 22

23 PIC/MCC Simulations of Breakdown Simulated Breakdown Curves of Argon for 3 Cases: (a) No field emission, secondary emission only (b) Field emission as a function of applied field only (native field emission) (c) Field emission as a function of applied field and space charge (ion-enhanced field emission) j FE = 0 j FE = f( V A d) j FE = f V A ( ) d + E SC native field emission ion-enhanced field emission slide 23

24 Cathode Coupling to Discharge (b) Field emission as a function of applied field only (native field emission) (c) Field emission as a function of applied field and space charge (ion-enhanced field emission) cathode emission vs. time at the breakdown voltage d = 3 μm; p = 760 torr j FE = f( V A d) j FE = f V A ( ) d + E SC native field emission ion-enhanced field emission slide 24

25 Positive Feedback Mechanism Breakdown requires a positive feedback mechanism cathode emission must respond to the discharge Ion-enhanced field emission responds to positive build up of space charge in the discharge mobility difference in the pre-quasi neutral regime ionization e emitted electron e- E ion enhances electric field slide 25

26 Remaining Questions Is there a basis for a theory to describe the deviation from Paschen s curve? What is the nature of the interaction and/or coupling between field emission and the discharge? Can field emission play any other role in the discharge? Implications? slide 26

27 Outline Field Emission and Microscale Breakdown Theory for Modified Paschen s Curve applied dc voltage (V) Experimental Evidence of Field Emission-Driven Microdischarges 50 Fluid Models for Field Emission-Driven Microdischarges electrode spacing (μm) μm E ion, V m Conclusions and Future Work μm Applied Potential, V slide 27

28 Glow Discharge-Type Experiments breakdown At what point does this canonical i-v curve become invalid? pre-breakdown glow discharge tube micropositioner stage tungsten cathode nickel anode slide 28

29 Representative Glow Results 500 breakdown Plasma Voltage, V p (Volts) pre-breakdown 5 μ m 7 μ m 10 μ m 20 μ m 50 μ m 100 μ m 500 μ m 1 mm Argon, 100 Torr glow Current, i(a) From 1000 to 5 μm the typical transition to glow was observed Townsend discharge current ~pa Rumbach and Go, 2011 Gaseous Electronics Conference slide 29

30 Field Emission Results 200 Current-Voltage Response 28 Fowler-Nordheim Plot N 2, 100 Torr, 4 μm Plasma Voltage, V p (Volts) N 2, 100 Torr, 4 μm steady current increase without breakdown ln(i / V 2 ) ln( iv 2 )1 V N 2 d=4μ m, p=100torr Ar d=4μ m, p=200torr Argon, 200 Torr, 4 μm Current, i(a) x /V Below 5 μm, growth in current was anomalous (~na rather than ~pa) and consistent with field emission Rumbach and Go, 2011 Gaseous Electronics Conference slide 30

31 Field Emission Exotic Materials Planar microscale devices operated in open, atmospheric air 5-20 μm gap active region Electrodes fabricated out of plasma-enhanced chemical vapor deposited diamond diamond electrode diamond electrode etched gap diamond electrode etched gap 10 m 2 m Go, Fisher, Garimella & Bahadur, Plasma Sources Sci. Tech (2009) slide 31

32 Field Emission Exotic Materials steady current increase (~μa) without breakdown Fowler-Nordheim Plot ln( iv 2 )1 V Using materials with favorable field emission properties can obtain Townsend discharge ~μa due to field emission Go, Fisher, Garimella, & Bahadur, Plasma Sources Sci. Tech (2009) slide 32

33 Field Emission in the Literature Peterson, Zhang, Fisher, Garimella Plasma Sources Sci. Technol., 2005 Venkattraman, Garg, Peroulis, Alexeenko Appl. Phys. Lett., 2012 diamond & CNTs; open air; μm Kim J. Phys. D. Appl. Phys., 2006 nickel; open air; ~3 μm CNTs; ~1-100 mtorr; ~500 μm Additional evidence in literature of field emissiondriven discharges slide 33

34 Field-Emission Driven Discharges Operation Below Breakdown Plasma-based Photodiodes Peterson, Zhang, Fisher, Garimella Plasma Sources Sci. Technol., 2005 Tchertchian, Wagner, Houlahan, Li, Sievers, Eden Contrib. Plasma Phys., 2011 Opportunity to develop field-emission driven discharges: moderate current (~μa), high-pressure Townsend discharges modulate cathode electron production slide 34

35 Outline Field Emission and Microscale Breakdown Theory for Modified Paschen s Curve applied dc voltage (V) Experimental Evidence of Field Emission-Driven Microdischarges 50 Fluid Models for Field Emission-Driven Microdischarges electrode spacing (μm) μm E ion, V m Conclusions and Future Work μm Applied Potential, V slide 35

36 Fluid Model A self-consistent 1-D Townsend fluid model that includes ion-enhanced field emission. dj e dx = J e dj + dx = dj e dx E = de dx = + e 0 electron conservation ion conservation Poisson s Equation Cathode boundary condition J e (x = 0) = J FE (E 0 ) + J + (x = 0) + j 0 Incorporate Fowler-Nordheim field emission in the BC Electric Field B.C. V = J + (d) = 0 d 0 E(x)dx Solution Paths: Analytical solution possible by using simplifications for the more complex relationships semi- self consistent Numerical solution using standard integration procedures fully self consistent slide 36

37 Fluid Model Breakdown Analytical assumptions lead to a transcendental equation that only has a subset of voltages that are solutions Breakdown Voltage, V B, Volts Ar, 760 torr Paschen Numeric Fluid Go/Tirumala PIC/MCC Fluid Solvability solvability condition = breakdown condition Gap distance, d, μm Prediction of breakdown consistent with both theory and PIC/MCC model. slide 37

38 Scaling Relationships If we make the assumption that the field due to space charge is much smaller than the applied field E SC < V A /d obtain analytical relationships for critical properties E SC = J V A FE ( d )+ j 0 1 (e d 1) AV,d, p A e d e x n + (x) = V eb A + ( d )1 (e d 1) e d ( ) ( ) [ ] J V [ A FE ( d )+ j 0 ] [ ] J tot = 1 (e d 1) J V FE( d )+ j 0 where 1 1 A(V A,P,d) = (1 e d ) + d 2 V A 0 b 2 + [ 2 ed + d ] E ion, V m μm electric field due to ions can approach 10 7 V/μm as d 1 μm N 2, 760 torr Applied Potential, V Primary Insights: Virtually all the relationships scale as ~ e d V J FE ( A d ) experimental confirmation? Field due to space charge becomes very large (~10 7 V/μm!) analytical approximation incomplete 20μm slide 38

39 Numeric vs. Analytical J tot / J FE Total current divided by native field emission Numeric Approx. (Avalanche) N 2, 760 torr, d = 3 μm breakdown E ions, V / m 2.5 x 106 Field due to ions, N 2, d =3e06 m, S = Numeric Approximate N 2, 760 torr, d = 3 μm Electric field due to space charge breakdown Applied potential, V Applied Potential, V Analytical solution accurate for most of Townsend discharge strong divergence within ~10 % of breakdown voltage as feedback mechanism begins to dominate slide 39

40 Impact of Ion-Enhancement Current density, A / m x 105 Total current, N 2, d =3e06 m, S = Numeric Approximate Native FE breakdown Applied potential, V The ion enhancement (space charge) effect only becomes prominent within ~30% of breakdown voltage slide 40

41 Comparison to PIC/MCC Ion and electron concentrations AP Electrons Ions Number density, cm Position, x, m x 10 6 Qualitatively, numerical model matches well with PIC/MCC simulations slide 41

42 Outline Field Emission and Microscale Breakdown Theory for Modified Paschen s Curve applied dc voltage (V) Experimental Evidence of Field Emission-Driven Microdischarges Conclusions and Future Work 50 electrode spacing (μm) Fluid Models for Field Emission-Driven Microdischarges μm E ion, V m μm Applied Potential, V slide 42

43 Conclusions Electron field emission can play a critical role in microscale discharges modified breakdown condition field emission-driven Townsend discharges Field emission inherently coupled to the ionization in the electrode gap (discharge/cathode coupling) ion-enhanced field emission Opportunities for new types of devices that capitalize on field emission phenomenon tuning field emission properties understanding/measuring discharge properties slide 43

44 Future Work Extending the theory 0 th order more accurate (resolving quantum mechanics) incorporation of enhanced theory into PIC and fluid models AC fields comprehensive emission theory secondary + field + thermal Experiments controlling discharge properties with cathode materials (nanoparticles, nanostructured surfaces, semi-conductors) pushing the envelope on scalability below 1 μm slide 44

45 Acknowledgements Current Students Rakshit Tirumala theoretical Jay Li PIC/MCC Paul Rumbach experiments/fluid model Danny Taller Ben Rollin (u) Matt Goedke (u) Collaborators Prof. Hsueh-Chia Chang Prof. Mihir Sen Prof. Aimee Buccellato Dr. Paul Brenner Prof. Norm Dovichi Dr. Carlos Gartner Prof. Mohan Sanakran (CWRU) Former Visitors/Post-Docs/Students Dr. Jenny Ho (visiting scientist) Dr. Ming Tan (post-doc) Dr. Nishant Chetwani (post-doc) Dr. Alejandro Guajardo-Cuéllar (Ph.D.) Katie Isbell (M.S.) Sajanish Balagopal (M.S.) 15+ undergrads Funding Air Force Office of Scientific Research Young Investigator Award (AFOSR Grant FA ) Intel Corporation Notre Dame Faculty Scholarship Award slide 45

46 Acknowledgements slide 46