Surface conductivity of the insulator of an MIS or MIM device

Thin Solid Films, 17 (1973) 253-264 © Elsevier Sequoia S.A., Lausanne---Printed in Switzerland

253

S U R F A C E C O N D U C T I V I T Y OF T H E I N S U L A T O R OF A N MIS OR MIM DEVICE

R. CASTAGNE, P. HESTO AND A. VAPAILLE

Laboratoire d'Electronique Fondamentale, UniversitO Paris XI, 91 405 Orsay (France) (Received February 19, 1973: accepted April 14, 1973)

A method for measuring the surface resistivity of the insulator of an MIS or an M I M device is described. The variation of the surface resistivity with relative humidity has been studied for various insulators. The results obtained are explained through the B.E.T. adsorption theory, and a model of conduction in the adsorbed layer is proposed.

1. INTRODUCTION When the metallic gate of an MIS or an M I M device is polarized, there is a migration of electric charge either through the insulator or on its surface. In this work, we have mainly investigated the motion of charge on the surface of insulators used in semiconductor device technology. In order to do this, we have developed a method which gives the value of the volume resistivity p (f~ cm) and the surface resistivity R[] ( ~ / [ ] ) of the insulating film from the current through the MIS or M I M capacitor under a very low frequency sine-wave voltage (5 x 10- 4_ 10 3 Hz). We have studied particularly the well-known and important effect of the relative humidity on the insulator surface resistivity 1-4, and have tried to explain our experimental results with the aid of the B.E.T. adsorption theory. 2. INFLUENCE OF THE CONDUCTIVITY ON THE FREQUENCY RESPONSE OF AN MIS OR MIM DEVICE Consider an insulating film with a thickness el deposited onto a conducting substrate (semiconductor or metal). We assume that the substrate and the film have infinite dimensions in the x and y directions. A metallic gate is evaporated onto the insulator. The gate dimensions are considered to be infinite along the y axis and finite along the x axis. When the gate is polarized, charges can move into the volume or over the surface of the insulator (see Fig. 1). The charge motion in the insulator volume is characterized by a volume resistivity p (f~ cm) and that on the insulator surface by a surface resistivity R[] (f~/[-]). When a sine-wave voltage vexp(jo0t) is applied to the structure, the charge current of the device includes: (1) the current il through the insulator film under the electrode;

254

R . C A S T A G N E , P. H E S T O , A. V A P A I L L E

Fig. 1. P o l a r i z e d M I M device.

(2) the current o f charge i2 o f the gate-substrate capacitance: and (3) the current i3 due to charges m o v i n g outside the gate. The first two currents are easy to calculate: S i x = - - v exp (jcot)

(1)

Pei • gig 0 S

i2 = J - ei

(jco t)

o91) e x p

(2)

where S is the electrode area and s i the permittivity of the insulator film. In order to estimate the current i3 we used the equivalent circuit o f the device, shown in Fig. 2 3. Using this circuit, we can calculate the potential v(x,t) on the surface o f the insulator as a function o f x and time t from the equation

Ov(x,t)

xg ~2v (x,t) v (x,t)

~t

z

Ox 2

(3)

77

with

(4)

x 2 = p el/Rf 3

(5)

l" = /0 8i8 0

x o is the characteristic length o f the m o t i o n of charges outside the metallic gate. K n o w i n g v(x,t) we can calculate i3: P

i3

-

-

(6)

~v (x,t)

RVq

~

x=O

where P is the perimeter of the metallic gate. W h e n a sine-wave voltage is applied to the gate and a steady state is reached, it is easy to integrate eqn. (3), and then the current i3 can be calculated using eqn. (6):

~ \ ~ ,

IZ ??

i

Y

/

i

v(x)

, ~ / ~

"?/}/??

Fig. 2. E q u i v a l e n t c i r c u i t o f the M I M device.

v(x-dx)

SURFACE CONDUCTIVITY

i3 -

P~

R~ Xo

OF THE INSULATOR OF AN

MIS

v exp (j cot)

OR

MIM

DEVICE

255

(7)

with ~2 ---- 1 +jcoz

(8)

The admittance of the device is obtained from the expressions for the three currents it, i2 and i3:

Y= C~° ( O~2+Px°

(9)

Co = eo ei S/ei is the high frequency capacitance due to the gate. In eqn. (9) the first term in parentheses accounts for what happens under the gate and the second one shows the charge spreading. The device admittance modulus I Y! as a function of the signal frequency applied to the gate is shown in Fig. 3. We used reduced coordinates, with the modulus of Y/Coco as ordinate and cot as abscisse. The family of curves has ( P / S ) x o as parameter, which is characteristic of the charge spreading. The charge moving on the insulator surface follows the applied signal better when the frequency is lower; thus an increase in the admittance is observed at low frequency, which is larger when the spreading is larger. 1

lC

3 5

3 G

i

1 F i g . 3. M o d u l u s o f 7, x o = 180.

3.

"",,,,,,a_ 10

10 2

Y vs. o): 1, x o =

10 3

10 4

WT

0; 2, x o = 0 . 7 3 ; 3, x o = 2.2: 4, x o = 6.7; 5. x o = 19.7; 6, x o = 60;

EXPERIMENTAL TECHNIQUE

The device admittance was measured for frequencies ranging from 5 x 10 -4 to 5 x 105 Hz. Since this range is very broad two different measurement techniques were used: (a) at high frequencies ( > 103 Hz), the capacity and the losses of the device were measured using a Boonton 75C capacitance bridge; and

256

R. CASTAGNE, P. HESTO, A. VAPAILLE

(b) at low frequencies, the charge current of the device when a sine-wave voltage was applied to the gate was measured using a Lemouzy PA 16 coulombmeter; from this the modulus of the admittance was obtained. The experimental system has been described previously 5' 6 Since the relative humidity of the atmosphere around the sample is a very important parameter with regard to motion of the charges on the insulator surface, it was necessary to keep the sample in well-defined conditions of temperature and relative humidity. The sample was therefore placed in a container entirely immersed in a thermostatic water bath at a temperature T1, and subjected to a flow of air saturated with water vapour at a temperature T2 < 7"1. By adjusting the temperatures T1 and T 2, the temperature and the relative humidity of the container holding the sample could be established simultaneously. 4. EXPLOITATION OF EXPERIMENTAL RESULTS The problem was to obtain the values of the volume resistivity p and the surface resistivity R from the experimental curve [Y(o~)]. (1) The sample was first vacuum outgassed and then its temperature was brought back to the desired temperature. Still in the same vacuum, the admittance of the device was measured as a function of the applied signal frequency. A curve like the one shown in Fig. 4 was obtained. Because the measurements were made in vacuum, there was no charge spreading in the curve. At low frequencies the shape of the response curve of a parallel RC dipole can be recognized.

15

3

10

!

I

I

I

10 -2

10 "1

1

10 f(H z)

Fig. 4. Modulus of Y r s . ~o: organic monomolecular layers.

For frequencies higher than 0.5 Hz, with some devices we observed a slow decrease of Y(o3) v e r s u s ~ . This decrease occurred without any variation of the phase shift between the applied signal and the charge current, so it was due to a change of e~ and we could find el(m).

S U R F A C E C O N D U C T I V I T Y OF T H E I N S U L A T O R OF A N

MIS

OR

MIM

DEVICE

257

For frequencies lower than 0.5 Hz, the increase of Y(co) was due to conduction through the insulator under the metallic electrode: Y(co) = S ( -p -e1+i j

~oei(co)co)

(10)

ei

Knowing ~i(o)) and ei, we could then deduce the value of p for the sample in the vacuum (for this example, p was taken as 2 × l013 ~ cm approximately). (2) The relative humidity in the container holding the sample was adjusted as described in Section 3. The sample was left in this environment for several hours and sometimes for as long as a day in order to achieve equilibrium between the humid air and the sample. The admittance of the device was then measured as a function of the applied signal frequency. The results were plotted as i Y(co)/Cocol dB versus co. Using the empirically determined value of ei(co), we adjusted the values of the surface resistivity R~ and the volume resistivity p in order to fit the theoretical curve given by eqn. (9) with the experimental curve. The fitting was done as follows. (i) The value of x o (i.e. p/RL~) was adjusted to give the same shape to both the theoretical and the experimental curves. (ii) The value of z (i.e. p) was chosen to superpose the theoretical and experimental curves by translation. Thus we obtained the values of R~ and p corresponding to the relative humidity of the air around the sample. 5. EXPERIMENTAL RESULTS

We studied the insulator films normally used for surface passivation in semiconductor technology. These films were therefore deposited onto silicon substrates. The substrate, heavily n-doped ( p < 1 0 -2 ~ cm), was etched before film deposition to select out the natural oxide layer as much as possible. Two types o f insulator were deposited: (1) silicone varnishes--the insulator was 2 jam thick and was deposited by centrifugation and then polymerized; (2) inorganic glasses--the insulator was 3.4 jam thick and was deposited by centrifugation, and then sintered. A metallic gate was evaporated after film deposition to make an MIS device. In addition, we studied organic monomolecular layers. Five layers of orthophenanthroline with three stearic chains, of a total thickness of 80 ,~, were deposited by pulling out according to the Langmuir-Blodgett method 7. These layers were deposited onto a metallic substrate and a metallic gate was evaporated onto the film to make an M I M device. For each type of device and for each temperature studied we plotted a family of curves showing ] Y(co)/CocoldB as a function of frequency with relative humidity as parameter. An example of such curves is given in Fig. 5. Using the method described in Section 4, we related each curve to a value of the surface resistivity R~. In Fig. 6 the values of R~2 obtained by this method for the different insulators

258

R. CASTAGNE, P. HESTO, A. VAPAILLE

I

\

I I

\

\

I

\

~t

\

\

\

1

\ \ \ \ \

47%

H.R.

~ 56~..R. , 6T~,.,.

\ \ \ ,

¢O

10 -7

10 "1

1

10

10 ~ f(Hz)

Fig. 5. Modu]us of Y t's, {o: silicone varnishes.

v ca 1018

1016

1014

1012

3 10 ~o

; I 0

i 20

i

t

40

!

I 60

| I

i 80

I H.R. (%)

Fig. 6. Surface resistivity vs. relative humidity: 1, silicon dioxide3: 2, passivation glasses: 3, silicone varnishes: 4. organic m o n o m o l e c u l a r layers.

studied have been plotted against relative humidity, and for comparison we have given the results of Ho et al. 3 for thermal silicon dioxide. It can be seen that the curves for the varnishes and the glasses are parallel to the curve for silicon dioxide, but the order of magnitude of the surface resistivities is much lower. For these three insulators one notices a large variation of R s w i t h relative humidity, spreading over five orders of magnitude. The behaviour of the organic mono-

SURFACE CONDUCTIVITY OF THE INSULATOR OF AN

MIS

OR

MIM

DEVICE

259

molecular layers is completely different: R[] has a smaller relative humidity dependence and the surface conductivity is larger. The values of the volume resistivity found for the various types of films were: silicone varnishes p-~2 x 1014 f~ cm; inorganic glasses p-~ 1015 f~ cm; organic monomolecular layers p-~2 x 1013 f~ cm. The dependence of the volume resistivity p on the relative humidity h cannot be determined; in fact, when h is large, the admittance of the device is only a function of R D (see eqn. (9)). 6.

DISCUSSION OF THE RESULTS

The experimental results presented in the previous section show that relative humidity has a very strong effect on the motion of charges in the insulator surface. Thus we must assume (1) that atmospheric water is adsorbed on the surface of the insulator and that this adsorption may or may not be followed by diffusion throughout the volume of the layer; and (2) that transport of electric charges is made possible by the adsorbed layer. In order to interpret the shape of the experimental curves of R[] versus relative humidity, we have used the B.E.T. theory of adsorption s to characterize the sorbed layer and we suggest a model for conduction in this sorbed layer.

6.1. B.E.T. theorv of adsorption In the B.E.T. theory it is assumed that adsorption does not occur uniformly, i.e. there are parts of the surface without any adsorbed molecules, parts coated with only one layer of molecules and parts covered with i layers of molecules. Let us call the corresponding areas So, sl ..... si,.... The specific area, meaning the area on which adsorption occurs, is equal to Sm =

(11)

~, Si i=O

In fact we consider a model in which the number of adsorbed layers is limited 9 by n (n is independent of the relative humidity). When a steady state is reached, the areas s o, s 1, s~ are constant. For the surface s o, without any adsorbed molecules, the balance can be written

alp So = bl sl exp ( - E1/RT)

(12)

where a 1 and bl are constants, p is the partial pressure of the gas, R the perlect gas constant, T the temperature of the sample and E1 the heat of adsorption for the first adsorbed layer. In eqn. (12), the left-hand side expresses the rate of condensation on the bare surface, and the right-hand side shows the rate of evaporation of the molecules of the first adsorbed layer, which is the exposure rate of the bare surface. F o r the surface s~, the balance can be written

a~+lPsi+bls~exp ( - ~ T ) = a ~ p s i - l + b ~ + l S i + l e x p

(-~)

(13)

260

R. C A S T A G N E , P. HESTO, A. V A P A I L L E

where ai and bi are constants and E~ is the heat of vaporization of the ith adsorbed liquid layer. The left-hand side of this equation shows the effect of the mechanisms leading to a diminution of s~ (the condensation on si and the evaporation from s~). whilst the right-hand side shows the effect of the mechanism leading to an increase in si (the condensation on si_ 1 and the evaporation from s~+l). It is assumed that all heats of vaporization are equal except for the first layer:

EI~E2=~

.....

E~

EI.

~14)

Further. it is assumed that all the quantities bi/a i are equal except for the first layer: bl @ b2

-

b3

-...-

bi

-g

(15)

al a2 a3 ai F r o m these data, we can calculate the ratio of the surface s o, where there are no adsorbed molecules, to the surface Sm, where adsorption is possible: So 1-h Sm - 1-~-(C- l) h

(16)

with al C=~gexp\

(Ex - EL~ RT /

(17)

and where h is the relative humidity. Brunauer, E m m e t and Teller s assumed that (al/ba) g is practically equal to unity, from which it follows that C ~ e x p {(E, - EL)/RT }. Depending on the relative values of E~ and E L, the structure of the adsorbed layer can be completely different. (a) When E l > E L . then C > 1 and So is smaller than S m (e.g. if C = 10 and h = 60/o, o / only 1/16 of the surface has no adsorbed molecules). The adsorbed film is practically continuous, although its thickness is variable: the average thickness is given by W

Ch (1 - h") A ( 1 - h ) { I + ( C - 1) h}

(18)

where A is the thickness of one adsorbed monomolecular layer. It can be seen that only when 17 is near unity does the value of W depend on n. (b) When E L > E 1, then C < I and So is not very different from Sm (e.g. if C = 0.04 and 17 = 60 o./only 6 % of the surface is covered by adsorbed molecules). The adsorption occurs on spots surrounded by bare regions. On the spots. molecules pile up. If b is the average diameter of a spot and et the average interval between two spots, the ratio (b/d) 2 is practically equal to (Sin--So)/Sm; thus, when C is small

b / d~/

Ch 1-h

(19)

SURFACE CONDUCTIVITY OF THE INSULATOR OF AN

MIS OR M I M DEVICE

261

As was pointed out in Section 5, the variation of R~ is completely different for organic monomolecular layers and for the other insulators. We suggest that this difference of behaviour may be interpreted by a difference in the structure of the adsorbed layers.

6.2. Organic monomolecular layers For the organic monomolecular layers we assume that a continuous adsorbed layer is formed (case (a) of Section 6.1). The adsorption occurs on the hydrophile end of the organic molecules which are nearest to the surface (see Fig. 7). Let us call Ps the volume resistivity of the adsorbed layer. The surface conductivity is given by W A Ch(1-h") (2o) Ps Ps ( l - h ) { 1 + ( C - 1) h} .

.

.

.

In Fig. 8, it can be seen that by fitting together the values of A/ps, C and n we get a good agreement between the computed values of G[] (from eqn. (20))

~1 Dql D I

IDql

,l~q

DI

/D= IqDIDI I D I D q l DLI D I I | 1

DII DII bl DI

Dql D I

Fig. 7. Adsorption on organic monomolecular layers:* adsorbed layer. G=(o)

6 . 1 0 I(

4 . 1 0 -11

2 . 1 0 1c

0

I 0

I 20

!

I 40

!

I 60

i

i 80

,

H.R.(%) 100

Fig. 8. Surface conductivity vs. relative humidity for organic monomolecular layers.

262

R. CASTAGNE, P. HESTO, A. VAPAILLE

and the experimental values of G{~ (the best fit is obtained for C = l0 and n - 6). If we assume that the order of magnitude of the thickness of one adsorbed layer is 1 A, we find Ps = 75 ~ cm. This value is much smaller than the value of the resistivity of water (-~ 1 M ~ cm). However, this result is acceptable because the physical structure of an adsorbed layer is fundamentally different from a liquid structure.

6.3. Other insulators For the other insulators studied, we consider an inhomogeneous adsorption on the surface (case (b) of Section 6.2) characterized by areas of adsorbed molecules isolated by bare regions of the surface. We assume that conduction is due to the hopping of electrons from one spot where there is adsorption to another one. The diffusion factor associated with such a mechanism is given by 1°

D =Is d2

(21)

where d is the distance between two spots where there is adsorption and Fs is the average frequency of hops between two such spots. Let us assume that these spots constitute potential wells. An electron bound to one of these spots occupies an energy level E 0. If we consider two neighbouring spots, we observe a splitting of the energy level with a possible hop of the electron from one well to another. The hopping frequency is given by 11

a/2

-a/2 where a is the distance between the edge o f the spots and is equal to d-b (d and b were defined in Section 6.2), h is the reduced Planck constant, ]Pl = {2m ( U - E)} 1/2 is the modulus of the moment in the classically forbidden region, m is the electron mass, U the potential outside the well and E the particle energy. Assuming that IPl is roughly constant, we have F s ~ exp

(-IPl a/h)

(23)

Using eqn. (19) we can calculate a:

a=d-b~b{(~hh) l/2-1}

(24)

Then

If b is independent of h, the spot areas, we have

i.e. if only the

R[]oc exp { -]~] - b (~hh) 1/2}

number of spots increases with h and not

(26)

SURFACE CONDUCTIVITY OF THE INSULATOR OF AN MIS OR M I M

DEVICE

263

If we plot R[] versus {(1-h)/h} 1/2 for silicon dioxide 3, the passivation glasses and the silicone varnishes (our measurements) (Fig. 9), we see that eqn. (26) gives a good representation of the variation of the surface resistivity R[] with relative humidity h.

R, (o)

1018

.//

1016

10 I'

1012

101°

/

I 0,5

(~a)',2 I 1

I 1,5

Fig. 9. Surface conductivity ~s. {(1-h)/h}l/2: 1, silicon dioxide3; 2, passivation glasses; 3, silicone varnishes.

The slope of the straight line in Fig. 9 gives the value of ]l~b/hC 1/2. If we estimate b to be equal to 2 A (order of magnitude of a molecule diameter) and U - E to be equal to 2 eV, then C-~0.04 and a ~- 13 A for h = 30%, and a-~5 A for h = 70~o. These values are reasonable. 7. CONCLUSION The very low frequency measurement of the admittance of an MIS or an M I M device can be used to determine the volume and surface resistivities of the insulator film. We have studied the variations of surface resistivity with relative humidity for various insulating films. For the passivation glasses, silicone varnishes and silicon dioxide the very steep variation of R D with relative humidity can be explained by a conduction due to a hopping process of electrons between places where adsorption occurs. For the organic monomolecular layers, R[] changes more slowly with relative humidity: this can be explained by a conduction in a uniform adsorbed layer.

264

R. CASTAGNE, P. HESTO, A. VAPAILLE

REFERENCES

1 2 3 4 5 6 7 8 9 10 I1

E.S. Schlegel, G. L. Schnable, B. F. Schwarz and J-P. Spratt. IEEE Trans. Electron Devices, ED-15 (1968) 973. G. Sawa and J. H. Calderwood, J. Phys. C. 4 (1971) 2313. P. Ho. K. Lehovec and L. Fedotowski, Surface Sci., 6 (1967) 440. Y. Awakuni and J. H. Calderwood, J. Phys. D, 5 (1972) 1038. P. Hesto, ThOse, Orsay, 1972. R. Castagne, P. Hesto and A. Vapaille, C.R. Acad. Sci. (Paris), 272 (1971) 885. R. Castagne and A. Vapaille. Surface Sci.. 28 (1971) 157. A. Barraud, J. Messier, A. Rosilio and J. Tanguy, Communication A VISEM, Versailles. 1971. E.A. Flood, The S o l i ~ G a s Interlace, Marcel Dekker, New York, 1967. R. Dellyes, J. Chim. Phys., 60 (1963) 1008. Y. Adda and J. Philibert. La diffusion clans les Solides, P.U.F.. Paris, 1966. L. Landau and E. Lifchitz, M~;canique Quantique, M.I.R., Moscow. 1966.