LAPPD Collaborative Meeting, June 10-11, 2010LAPPD Collaborative Meeting, June 10-11, 2010

Muons, Inc.

1

Comparison & Discussion of Secondary Electron Emission (SEE)

Materials - TheoryZ.Insepov, V. Ivanov, S. Jokela

2Muons, Inc.

OutlineOutline• Simulation chart• SEE Yields for various materials• Future SEE tasks• Charge relaxation time• Future simulation plans• Summary

3Muons, Inc.

Simulation work chartSimulation work chart

MCPExperiments

Macro-scopicGain, Rt,

saturation simulations

Micro-scopicSEE, PE

SaturationHeating & Aging

simulations

MacroscopicFringe-field

Comsolsimulations

SEE = f(E)SEE = g()

– relax. time

SEE = f(E)SEE = g()

– relax. time

T = f(z)T = f(z)

Gain, RtGain, Rt

SEE, PEEscape lengthMater. properties

SEE, PEEscape lengthMater. properties

Map of electric fringe fieldRelaxation times

Map of electric fringe fieldRelaxation times

Materials properties

Materials properties

Materials propertiesRelaxation times

Materials propertiesRelaxation times

4Muons, Inc.

Low-Energy Monte Carlo codesLow-Energy Monte Carlo codes• Algorithm of SEE calculations

)./exp()(

,)1()(1

),(

,

,104.3

,1024

511

1

41021.5

,5.58

76.9

,)85.0(166.1

log**500,78

67.03

22

2

221

19.0

xAxp

kEkEExn

cmN

AE

Z

atomcmE

E

E

Z

eVZ

ZJ

J

JE

AE

Z

ds

dE

Ea

E

e

J– the mean ionization potential – energy for production of SE – mean free path, escape length - screening factor

Casino simulation

Al2O3, D. Joy (1995)Al2O3, D. Joy (1995)

Inelastic, Bethe-Joy (1989)Inelastic, Bethe-Joy (1989)

Elastic,Rutherford

Elastic,Rutherford

Berger-Seltzer (1970)Berger-Seltzer (1970)

= 20 eV = 60 Å

Insulators, Kanaya (1978)Insulators, Kanaya (1978)

5Muons, Inc.

SEE yield calculation via MCSEE yield calculation via MCMonte Carlo algorithm• Initial electrons are created, E = 0.1 - 4 keV, = 0-89• New electron, new trajectory, similar to previous

– The process continued until the electron E < E0

• 1-10K trajectories computed for each sample (error 1/N)

• h=102-104 Å samples were simulated (100Å - 1 m)

Experimental data from literature• Experimental SEE yields were compared with our

calculations

6Muons, Inc.

SEE Yield calculationsSEE Yield calculations

• MgOMgO• Al2O3Al2O3• ZnOZnO• CopperCopper• GoldGold• MolybdenumMolybdenum

Target

SEE

h

E, ev

Nel=103-104

7Muons, Inc.

Simulation Group paperSimulation Group paper• Z. Insepov, V. Ivanov, H. Frisch, Comparison of Candidate Secondary Electron

Emission Materials (accepted for publication in NIMB)

8Muons, Inc.

Why Monte-Carlo ?Why Monte-Carlo ?Empirical, semi-empirical SEE Models are too bad• Specific material, bulk, flat surface, one element, no angular dependence

Monte Carlo simulation algorithm is simple• Search for high SEE materials -- Gain/TTS critical to SEE at first strikeSearch for high SEE materials -- Gain/TTS critical to SEE at first strike

• Higher QE PC for thin films, ML, nanostructured coatingsHigher QE PC for thin films, ML, nanostructured coatings

• Mixture of materials (Alumina+ZnO)Mixture of materials (Alumina+ZnO)

• Surface roughness can be studiedSurface roughness can be studied

• Materials aware MCP simulation – against blind experimentationMaterials aware MCP simulation – against blind experimentation

Experimental data from literature are not good• SEE for E-dependence, no angular

Experimental data at ArgonneExperimental data at Argonne• ANL characterization experiments are in progressANL characterization experiments are in progress

9Muons, Inc.

Empirical ModelsEmpirical Models

.

cos

,cos1exp

,1

4,

0

0

2

i

mim

imim

imiim

imiii

• No space charge effect, no surface charging effectNo space charge effect, no surface charging effect• Poisson distribution for the SEEPoisson distribution for the SEE• Maxwellian energy and Cosine angular distributionsMaxwellian energy and Cosine angular distributions• Bulk material, flat surface, no temperature effectsBulk material, flat surface, no temperature effects

cos1cos1expcos0mmm

• Guest (1971)

– adjustable parameter

AZ

m

m

m285.1

00

00

1

2

• Ito (1984)• Yakobson (1966)

• Agarwal (1958)

10Muons, Inc.

Comparison of SEE- modelsComparison of SEE- models

11Muons, Inc.

Alumina SEE Yield: MC vs ExperimentAlumina SEE Yield: MC vs Experiment

12Muons, Inc.

ZnO SEE Yields: MC vs ExperimentZnO SEE Yields: MC vs Experiment

13Muons, Inc.

Metal SEE Yields: MC vs ExperimentMetal SEE Yields: MC vs Experiment

14Muons, Inc.

MgO SEE Yields: MC vs ExperimentMgO SEE Yields: MC vs Experiment

15Muons, Inc.

MgO SEE Yield vs MgO SEE Yield vs ((E-differentE-different))

16Muons, Inc.

Charge relaxation timeCharge relaxation time

17Muons, Inc.

Electric fieldGain

Shape function

.1)(

,)(1)(1ln)(1lnln

ln),(

,

exp1),(1

),(),(

),,(),(

/0

00

0

0

0

t

R

zE

ppE

E

Ezz

eI

Itc

etCMtCtCM

Mtzh

Tttzh

tzhMtzM

tzhEtzE

E0z, M0 – electric field and a gain for non-saturated modeI0 – initial current of photo electrons, IR – resistance currentτ – relaxation time for induced positive charges

Analytical model of saturation effectsAnalytical model of saturation effects

[Berkin et al, Tech. Phys. Lett.(2007) 75][Berkin et al, Tech. Phys. Lett.(2007) 75]

18Muons, Inc.

9.6

)(10)25.038.1(

).(104.03)-(0.725

,101.6

1029.1 10500)-(90

110

10

3-

2912

cm

cm

m

m

l

SR

AZO Maxwell relaxation timesAZO Maxwell relaxation times

Channel Resistive Channel Resistive Layer MaterialLayer Material

70% Zn/(Zn+Al)70% Zn/(Zn+Al)

Maxwell relaxation Maxwell relaxation timetime

111010-6-6 sec sec

Channel Resistive Channel Resistive Layer MaterialLayer Material

60% Zn/(Zn+Al)60% Zn/(Zn+Al)

Maxwell relaxation Maxwell relaxation timetime

111010-3-3 sec sec

.10)10020(/

,10)50090(

).(104.03)-(0.725

31

91

7

NRR

R

cm

19Muons, Inc.

DD-Model of charge relaxationDD-Model of charge relaxation

.,

),(

states ofdensity ,)()/2(2

[7] eV 4.3-3.2),/exp(

,)(/1

),(/1

,,

,

,

,,,,,

0

2

4

3

2

32

B2

0

0

0

eTkDne

nne

mmhkTNN

ETkENNn

t

nnnennDJ

qt

n

nnennDJqt

n

nnEdiv

EneneDJ

EneneDJ

Bhehehehehe

he

hevc

ggvci

Auger

hehhhhhh

h

eheeeeee

eh

hhhhh

eeeee

[1] A.K. Jonscher, Principles of semiconductor device operations, Wiley (1960).[2] A.H. Marshak, Proc. IEEE 72, 148-164 (1984).[3] A.G. Chynoweth, J. Appl. Phys. 31, 1161-1165 (1960).[4] R. Van Overstraeten, Solid St. Electronics 13 (1970) 583-608. [5] L.M. Biberman, Proc. IEEE 59, 555-572 (1972).[6] Z. Insepov et al, Phys.Rev. A (2008)[7] I. Costina et al, Appl. Phys. Lett.78 (2001)

r

rz

r = 20 mr = 10 nmAspect ratio 40

A. Spherical symmetry

B. Cylindrical symmetry

D– diffusion coefficient, - mobility, n - density of carriers (= e, h)

z

rr = 10 nmAl2O3+ZnO

Primaryelectron SEE

20Muons, Inc.

Input parameters for DDMInput parameters for DDM• Diffusion coefficients of amorphous alumina are unknownDiffusion coefficients of amorphous alumina are unknown• Carrier mobilities for alumina are known for limited mixture contentCarrier mobilities for alumina are known for limited mixture content

[1] Ruske, Electrical transport in Al-doped zinc oxide, J. Appl. Phys. (2010).

• ZnO with 1% of Al2O3 was measured: =40 cm2/Vs, =1.410−4(cm) [1]

• Conductivity of AZO with 20% Al: = 107 ( cm), mobility unknown.

• Assuming linear dependence between conductivity and mobility, mobility of a mixture Al2O3+ZnO was extrapolated from low Al-content to high.

• Diffusion coefficients via Einstein relation: D = kBT/e.

21Muons, Inc.

Proposed material constantsProposed material constants• Mobility and diffusion constants of carriers were extrapolated from low Al-content to high [1]

SiO2, Dapor

[Dapor, Surf. Interface Anal. 26, 531È533 (1998)][Dapor, Surf. Interface Anal. 26, 531È533 (1998)]

22Muons, Inc.

Charge dissipation in Al2O3+ZnOCharge dissipation in Al2O3+ZnOSet of equations for the drift-diffusion model were numerically solved for several values of material constraints and the relaxationtimes were obtained.

23Muons, Inc.

Internal Electric fieldInternal Electric field

24Muons, Inc.

Hole densities vs time, AlHole densities vs time, Al22OO33+ZnO+ZnO

Dh=1.2e-11 cm2/s Dh=1.2e-10 cm2/s

Dh=1.2e-9 cm2/s Dh=1.2e-8 cm2/s

• Variable – diffusion coefficients, Dh

25Muons, Inc.

Relaxation times via DDMRelaxation times via DDM

• Relaxation time vs diffusion coefficients

Dh=1.2x10-11 cm2/sDh=1.2x10-10 cm2/sDh=1.2x10-8 cm2/s

Maxwell relaxationtime

SiO2, Dapor (1998)

26Muons, Inc.

Status of relaxation timeStatus of relaxation time• Experimental verification of relaxation time model Experimental verification of relaxation time model

– under progress (APS/HEP)– under progress (APS/HEP)• Our calculations will be extended to electrons and

two types of holes – to be compared to Auger• Different local nano-structures of the mixtureDifferent local nano-structures of the mixture• Two types of geometries: plane and cylindrical • Ambipolar drift-diffusion model is essential• Relaxation time is obtained via numerical solution

of the kinetics of charge carriers• Impact ionization model will be addedImpact ionization model will be added

27Muons, Inc.

Relaxation time measurementRelaxation time measurement• Continuous delay within 5m (15 ns)Continuous delay within 5m (15 ns)• Laser flashing (Ed May) – 1 Laser flashing (Ed May) – 1 ss

B. AdamsB. Adams

28Muons, Inc.

Future simulation workFuture simulation work Photo-electron bunch formationPhoto-electron bunch formation• Microscopic model of the photo-electron emission (Zeke, Klaus, Bernard);• Angular and energy distribution for the photo-emitted electrons (Zeke);• Bunch formation for electron optical calculations (Valentin);

• Systematic study the charge relaxation time vs. the material properties (Zeke);• Continue study how saturation phenomena affect on the gain & time resolution for real

devices, comparison the simulations and experiment (Valentin).

Saturation effectsSaturation effects

Heating effectsHeating effectsAging effectsAging effectsRoughness effectsRoughness effectsMixing and multilayer effectsMixing and multilayer effects