ICE FIELD TRANSISTOR

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ICE FIELD TRANSISTOR

V. Petrenko, N. Maeno

To cite this version:

V. Petrenko, N. Maeno. ICE FIELD TRANSISTOR. Journal de Physique Colloques, 1987, 48 (C1),

pp.C1-115-C1-119. �10.1051/jphyscol:1987117�. �jpa-00226261�

JOURNAL DE PHYSIQUE

Colloque CI, suppl6ment au n o 3 , Tome 48, mars 1987

ICE

FIELD

TRANSISTOR

V.F.

PETRENKO and

N.

MAENO"

Institute of Solid State Physics, The USSR Academy of Sciences, Chernogolovka 142432, USSR, Moscow District

" ~ n s t i t u t e of Low Temperature Sciences, Hokkaido University, Sapporo 060, Japan

Resume

Une nouvelle mgthode est proposke pour la determination de la mobilitk des porteurs de charge dans la glace. Elle est basee sur la mesure de la conductivite de surface sous l'action d'une charge dlectrostatique appliquee perpendiculairement B lasurface.

Une analyse thkorique et les details experimentaux de la methode sont decrits.

Abstract - A new method is proposed for the determination of the charge carrier mo- bility in ice based on the measurement of the surface conductivity of ice under the action of an electrostatic field applied normally to the surface. A theoretical con- sideration and experimental details of the method are described.

To date one of the important and unsolved problems of ice physics is the lack of re- liable experimental methods to measure the mobility of charge carriers. In the pre- sent work a new method is proposed for the determination of the charge carrier mobi- lity in ice based on the measurement of the surface conductivity of ice under-condi- tions when the carrier concentration in the near-surface layer is controlled by the electrostatic field applied normally to the surface. We also present a theoretical substantiation of the method, technical means of its realization and preliminary ex- perimental results on the measurement of the magnitude of the surface conductivity of ice and the mobility of H,O+ and OH-.

1.

THEORETICAL CONSIDERATIONS

Consider the surface of ice (x

= 0 )

with normally applied electrostatic field E(t0)

=

Eo. The surface electric conductivity is described by the formula

*

where E is the component of the alternating field applied along the y surface, j is the xurrent density along the surface and

w

is the cyclic frequency. The chargg carrier concentration distribution ni (i

=

1-4) in the x-axis is determined by the system of Poisson's equations

where

E ,

is a relative dielectric permettivity of ice for high frequencies

(E,:

3.2 1,

E

is dielectric ~ermettivity of vacuum, ei is the carrier charges (i

=

1,2,3,4, res- pgctively, for H,O+, OH-, D and L defects), 9 is the electrical potentia1,n. is the equilibrium concentrations of the carriers away from the surface, beyond th2- actson of the field Eo. The sign

(x')

stands for differentiation with respect to x.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987117

CI-116

JOURNAL

DE

_PHYSIQUE

Equating to zero of the defect flows on the x axis :

Here

vL

is the mobility of defects,

D.

is their diffusion coefficient, jl is the con-

f

igurational vector [ 3 , 4 ,

(5)

j. is the flux of the i-th type of defect, $

- ^3.85

^KBT

^r

^{oo 1 2 )}

^,

^{roo= 2.76 A}

^.

^{is the}

siacing between oxygen atoms in the lattice of ice,

The system of equations ( 1 )

- ⁽⁵⁾

has no general analytical solution, but it can be found in each particular case. Consider some most important examples, (we omit in- termediate elementary transformations and present only the final results) :

a) Great potential difference between the surface and the bulk

In this case inside the space charge region, responsible for the excessive surface conductivity n. >> n. for the carriers attracted to the surface (for example for OH- and L de$ects)'%nd n.<< n. for those repelled by the field (for example, for H,O* and

D

defects). Besidks, wkmassume all the carrier charges equal in the absolute value

In this approximation

Em€, 4, T

n, -- ^{n, -}

(1 0 )

Fig.1 : Frequency dependence on the real part of the sur- face conductivity X

.

Figure

1

presents the frequency dependence of the real part X

.

The formula (10) has very simple frequency asymptotics :

with w + 0 :

5-

E O ~ L / " 4 / ~ / " ~ %og'*)'

f

^.o E0 b;*(~Ll/l] (1 2)

W +

h o - > E o € e ~ o / / l r ~ + ~ + ) ~ ~ o ~ ~ E ~ ~ a r { / t , / ( l + f

(13)

So, the measurement of the frequency dependences X ( w ) for two polarities of

E

enables one to determine all the four p . mobilities. Disadvantage of the conside2 red approximation is the assumption on the equality of /e./. Inasmuch as inside the space charge region near the surface

KL

= hi

f- ^{=: ye=LL; $ 5}

^'T)

where

Z

is the configurational potential

do

~ = J f i ~ r

F

Therefore the charges of the ion concentrations

(lei

^{$ 2}

1

^z 0.62 e) can exceed those of Bjerrum defects

(1

^{es,s (}

-

^{0.38 e)}

b) One can easily calculate a partial excess surface electric conductivity AXi of the defects that form the space charge near the surface. Let

4

2 e , ( n ~ - h ; , ) = e . ( h ; - n ' - )

4

Then from (2)

since

E

(m) = 0.

Subsequently, for the calculation of

Xs

_{and X,} one should take into account whe- ther i-th charge carriers are majority carriers or not.

C1-118 J O U R N A L

DE

PHYSIQUE

c) Finally, we shall consider the case when the space charge is formed by one carrier type- by the majority carriers (L-defects, for example, that is nk), and to determine 1 we have to determine a change of

A

Xs of the minority carriers (H,o+-ions, for certainty, that is n 1 ) . In case that, as before,

1

eiyl

>>

KBT,

nL

>>

n

where RSC is the screening length in nonlinear approximation

In the space-charge region, in this case,

A

n, z -n

.

The solution of the system (1)-(5) can easily be obtained in all the other particular cases of the relationship between n.

1 m and kT and

]

ei

Y" .

2. THE EXPERIMENT& REALIZATION OF THE METHOD

Figure 2 shows a measuring cell for measuring the electric conductivity of the sur- face of ice with the electrostatic field applied perpendicular to it. The field is produced by the battery V. The potential difference of V is distributed between the dielectric SiO, layer, the space charge region in Si and the space charge region in ice near to SiO,. As can easily be shown in this case

Fig.2 : Experimental

I

^{set up}

where C is the capacity between the "combs" electrodes and Si-plate,S is the area of the "combs" electrodes. The field Eo is determined from the eq.(20). In our case S=2.5

lo-'

m Z

,

C = (2.2-3.3).103 pF. Here if V )/ 1 V t h e first term in the eq.(20) is determining and some uncertainty in n. (with n > 10"n1-~) is of no consequence.

The dielectric layer of SiO, and gold elictrodesi& it were produced by one of the standard techniques of microelectronics : the electrodes in the form of two "combs"

inserted into one another were prepared with the help of photolithography, the inter- electrode gaps and the "tooth" width being

'

50pm (Faculty of Engineering,Hokkaido University), by the computer-controlled ion-beam etching we obtained

"

^{30 D m}

(Institute of Solid State Physics). The SiO, thickness was about 0.1 pm, the thick- ness of the Au electrodes about 1 pm. In the measurements the ice samplesused, were obtained at a slow (about 2 h) freezing of a deionized and degassed water drop placed on the Si-SiO,.plate surface. At temperatures T

>

-25OC the measurements of the elec- trical properties of the ice surface were distorted by the presence of a "quasiliquid"

layer on it. Therefore the results cited pertain to lower temperatures.

Figure 3 presents the time diagram of the surface conductivity and the potential dif- ference applied between the Si-plate and the ground. The figure shows that the appli- cation of the potential difference between the surface and the ice bulk alters the surface conductivity by two orders of magnitude, this alteration being dependent on the polarity of the applied voltage. A greater conductivity (-1.55V on the Si-plate) corresponds to a greater mobility of

H,O+

ions as compared with OH- -ions since it is these ions that determine the AC conductivity at this frequency. The estimations of

the mobility using eq(17) yield

/ , = J . L . . ~ o - ~ ~ ~ / ( l l i ) ~ )jL = 2 . 7 . - / 0 - * ~ ~ / ( 1/51

Fig.3 : Time diagram of the surface AC conductivity of ice, measured at frequency f = 10 HzT=-33.1°C. The lower curve represents the po-

tential difference between the Si plate and the ground.

These estimations are close to the values obtained by other methods for the ion mo- bility [5-71. Finally, figure 4 shows the frequency dependences of G with the field E and without it. As seen from this figure, with the field applied, the dispersion

'of C, nearly vanishes which indicates comparability of U I , ~ and u s , , ,

.

We are, therefore, not confident in the vali- dity of using the eq(17), obtained in the ap- proximation nl + n 2

<<

ns + ns ,in determi- ning p, and P 4.

Fig.4 :Frequency dependence of the real part of the surface conductivity G with T = -33.1°C The upper curve V = -1.55 V the lower curve

v

= 0.

One of the authors (V.F. Petrenko) wishes to thank the Japan Society for the Promo- tion of Science for providing him the JSPS Fellowship, which enabled him to stay and carry out the present work at the Institute of Low Temperature Science, Hokkaido University, in 1984.

References

1. Hobbs P.V. Ice Physics, Clarendon Press, Oxford (1974).

2. Hubman

M.

Z.Phys. B32,(1979) 141-146.

3. Jaccard C., Helv.Phys.Acta

2,

(1959) 89-128.

4. Jaccard C., Phys.Condens.Mater.3, (19641, 99-118.

5. Petrenko V.F., R.W. Whitworth and J.Glen, Phil.Mag.(~)s,(1983) 259-278.

6.

Petrenko V.F. and I.A. Ryzhkin, JETF,

87,

(1984) 558

7. Zaretskii A.V., V.F. Petrenko, I.A. Ryzhkin and

A.V.

~rukhanov (this symposium)