Charge relaxation times

Z. Insepov, V. Ivanov

Glass conductivity

Materials propertiesPore structure• Pore diameters – 20 m• Al2O3+ZnO coatings – 1 m and 5 m• Aspect ratio -- 40

Materials parameters:• Glass: = 110-17 S/m, =5.8• Al2O3+ZnO: = 110-8 S/m, =6.9• Air: = 110-17 S/m, =1

Al2O3 + ZnO coating resistivity

h

z

rd

r = 20 md = 1 mh = 1.6 mm

29

21222

1029.1

1041

m

mrRS

R1 = N R

MCP resistance: R = 18-100 M

N = 5106 pores

R1=RN = (18-100 M) 5106 = (90-500)1012

Microscopic model of charge relaxation

.,

),(

,)()/2(2

),/exp(

,)(/1

),(/1

,,

,

,

,,,,,

0

2

4

3

2

32

B2

0

0

0

eTkDNe

NNe

mmhkTNN

TkENNN

t

NNNeNNDJ

qt

N

NNeNNDJqt

N

NNEdiv

ENeNeDJ

ENeNeDJ

Bhehehehehe

he

hevc

gvci

Auger

hehhhhhh

h

eheeeeee

eh

hhhhh

eeeee

A.K. Jonscher, Principles of semiconductor device operations, Wiley (1960).A.H. Marshak, Proc. IEEE 72, 148-164 (1984).A.G. Chynoweth, J. Appl. Phys. 31, 1161-1165 (1960).R. Van Overstraeten, Solid St. Electronics 13 (1970) 583-608. L.M. Biberman, Proc. IEEE 59, 555-572 (1972).Z. Insepov et al, Phys.Rev. A (2008)

r

rz

r = 20 mr = 1 mAspect ratio 40

A. Spherical symmetry

B. Cylindrical symmetry

z rr = 1 mAl2O3

D,,N – diffusion coeff., mobility, density of carriers (= e,h)

110

10

3-

2912

)(10)25.038.1(

).(104.03)-(0.725

,101.6

1029.1 10500)-(90

cm

cm

m

m

l

SR

ZnO/Al2O3 alloy relaxation times

Channel Resistive Channel Resistive Layer MaterialLayer Material

30% Al2O3+70% 30% Al2O3+70% ZnOZnO

Relaxation timeRelaxation time(current setting)(current setting)

6.16.11010-6-6 sec sec

Channel Resistive Channel Resistive Layer MaterialLayer Material

40% Al2O3+60% 40% Al2O3+60% ZnOZnO

Relaxation timeRelaxation time(desirable setting)(desirable setting)

6.16.11010-3-3 sec sec

.10)10020(/

,10)50090(

).(104.03)-(0.725

31

91

7

NRR

R

cm

The current set of emissive coating parameters is not acceptable due to very high curent ~ 20 mA!The current set of emissive coating parameters is not acceptable due to very high curent ~ 20 mA!

MCP ParametersAl2O3+ZnOTable 1: Dielectric constants [1] and resistivities [2] for Al2O3/ZnO ALD films

*) DEZ -- Diethylzinc (Zn(CH2CH3)1. Herrmann et al, Proc. of SPIE Vol. 5715 (2005) p.159. 2. Elam et al, J. Electrochem. Soc. 150, pp. G339-G347, 2003.

% DEZ* exposures 0 10 25 33 50

Dielectric Constant 6.8 6.5 6.9 7.2 6.6

  Resistivity( cm) ~1016 5x1015 5x1014 1014 1013

Relaxation times, sec 6x103 2.9x103 305 64 5.8

Bulk Material Borosilicate glass

Dielectric Const 5.8

Conductivity 110-17 S/m

Relaxation time 5.1106 sec