Influence of the surface electron processes on the kinetics of silicon etching by fluorine atoms

Vacuum/volume 41/numbers 4-6/pages 902 to 905/1990 Printed in Great Britain

0042-207X/90S3.00 + .00 © 1990 Pergamon Press plc

Influence of the surface electron processes on the kinetics of silicon etching by fluorine atoms Yu E Babanov, A V Prokaznikov and V B Svetovoy, Institute of Microelectronics, Academy of Sciences of the USSR, Universitetskaya, 21, Yaroslavl, 150007, USSR

The m o d e / o f silicon etching by fluorine atoms is presented. It is shown that the dielectric SiFx film formed on the surface plays an important part in the etching. As a consequence of high heat of adsorption for fluorine atoms on this film its penetration under the surface by thermal activation is difficult. A specific mechanism explaining the origin of the electric field in the film is proposed. The process of electric field formation is connected with valence electrons tunneling from silicon to adsorbed fluorine. The analysis of the electron processes in the S i - S i F x - F system results in non-linear equations which can be used to calculate the electric field strength and etch rate in a stationary regime. In the proposed model non-activated fluorine penetration into the SiF× film is provided and essential experimental results can be explained.

Introduction The development of plasma etching technology of different materials has a great importance for the purposes of microelectronics. Gas phase reactions taking place in plasma are complex and many studies are devoted to their investigation. At the same time plasma only supplies active particles but the interactions of these particles with a solid play a key role in the etching. At present there is a lack of understanding of the mechanisms governing the reactions on the surface. However, the knowledge of these mechanisms is necessary to control technological processes. A lot of experimental and theoretical works are devoted to investigation of silicon etching by different fluorine-containing gases. Most researchers believe that atomic fluorine generated either in plasma or by dissociative chemisorption of molecules plays a principal role in the etching. The other components of the etchants can activate or passivate the surface. To exclude the influence of the minor phenomena on the reaction of fluorine atoms with silicon the most simple etchants were chosen: gaseous XeF2,1 F 2 plasma 2'3 and atomic fluorine4. Their main feature is absence of any active components besides atomic fluorine. The etching mechanisms discussed in the literature are often contradictory or not supported by numerical estimations. For example, in the picture proposed in ref 2, fluorine atoms react right on the silicon surface. At the same time there are obvious experimental proofs that a stationary SiF:, film (x = 1, 2, 3) with thickness of h ~ 10 A 3'5'6 is formed on the etched surface. This film can play a principal role in the etching. Its composition was studied 7-9 by XPS method where it was found that it is amorphous mixture of SiF, SiF 2 and SiF 3. The fluorine atom is adsorbed on the SiF x surface and then penetrates into the film where it forms volatile SiF4 molecules with a definite probability. Taking into account the fact that the barrier for dissociative chemisorption of XeF 2 molecules is 902

low 5 we found ~° the adsorption heat restriction for fluorine atom on the SiF x surface (Q ~> 1.2 eV). As a consequence of high heat of adsorption of chemisorbed fluorine its penetration into the film is difficult. The field-assisted diffusion mechanism for the fluorine penetration was suggested in ref 6. The similar idea was proposed by Cabrera and Mott ~' to explain the initial stage of metal oxidation. A number of authors ~2' ~3 discussed this proposal but no estimation supporting its validity was made. The field effect was considered in more detail 14 in context of the investigation of silicon etch rate dependence on doping level. In this article the model of silicon etching by fluorine atoms is developed. It is taken into account the influence of the surface electron processes on fluorine adsorption and its interaction with silicon. The non-linear kinetic equations allow calculation of the electric field strength and the etch rate. It is shown that electric field arising in the SiFx film provides the barrier lowering necessary for fluorine penetration into the film. This process proceeds without thermal activation. The basic ideas of this work were discussed briefly in refs 15, 16.

Fluorine penetration into the SiFx film The experiments on the silicon etching in F 2 plasma carried out by different groups give essentially different etching probability. This problem was analysed in ref 3, where it was concluded that atomic oxygen generated in discharge f r o ~ residual gases and by plasma interactions with the reactor walls passivates the surface reducing the etching probability. The strong passivation of the surface by oxygen in experiment 2 carried out at high pressure was assumed. The etching probability found in this experiment is much less than at low pressures in F 2 plasma 3 or in gaseous XeF21"17 where there is no surface passivation by atomic oxygen. Authors assumed t°. ts that the surface passivation by oxygen with SiO2 layer formation reduces the heat of adsorption of

Yu E Babanov et al: Kinetics of silicon etching by fluorine atoms

fluorine on this surface so that its penetration into the film is quite possible by thermal activation. On the basis of this assumption we have explained the reduction of the etching probability and have correctly predicted the temperature dependence of it. If the passivation of the etched surface by atomic oxygen can be excluded, then the heat of adsorption of fluorine Q ~> 1.2 eW ° is too high for fluorine penetration into the film by thermal activation. Moreover, atoms should overcome the surface barrier Es which can be more than Q. The adsorption potential for fluorine atom on the SiFx surface is illustrated schematically in Figure 1. According to ref 11 we can suppose that the lowering of the surface barrier from E s to E~ can be explained by arising of electric field in the SiFx film. As a result of electron tunneling through the thin dielectric film, negative ions ( F - ) are created on the SiFx surface while the holes are accumulated on the semiconductor-dielectric interface. The field of this double layer makes the barrier lower. If a is the distance from the adsorbed particle to the SiF x surface and ~ is double-layer field strength, then the barrier for ions F - penetration is E~ = E~ - e~a

( l)

The charge exchange between adsorbed particles and silicon occurs through the dielectric film which plays the role of the effective reaction layer. Fluorine ions having overcome the surface barrier diffuse into the film depth reacting on their way either with Si or with one of SiF x components. The volatile product created as a result of the interaction with SiF 3 diffuses to the surface and desorbs from it. Starting points of our model are quite similar to those in ref 14, but we believe that in steady-state etching the fluorine ions overcoming of the surface barrier is more important than the processes in the film (i.e. field-assisted diffusion). Below we give the proofs of this statement. The etch rate probability are defined by the SiF4 molecules flux Js~v, desorbing from the surface. In general case this flux is proportional to the fluorine flux Jv going under the surface,

u(x)

J'siF 4 = ~JF"

(2)

The factor ~ is determined by the processes in the film and depends on SiF x molecules distribution in the film depth. If the film is stationary this distribution must be that for each 4 atoms going under the surface, one SiF 4 molecule should be formed, i.e. ~t = 1/4. The flux jv is determined by the surface processes. Therefore the etch rate depends only on processes on the SiF x surface. The detailed description of fluorine diffusion and its interactions in the film is useful for calculation of SiFx molecule distribution in the depth, and the time of reaching the steadystate of the etching. Concentration of neutral and charged atoms on the surface

Let us assume for simplicity that silicon doping level is not so high and all band bending is determined by the amount of ions on the surface. This bending is characterised by

V,=~s-e,

(3)

where q and G are the distance from the Fermi level to the bottom of the conduction band near the surface, and in bulk of semiconductor, respectively. Supposing Vs>>kT, for ~band bending we have the following expression ~9

V~= kT In(N/N*):,

(4)

where

N*

( ~kT n* ) \ 2 roe-

"

~( is the silicon dielectric constant, n* is the bulk concentration of the majority carriers in the crystal depth, N is the ion concentration on the SiFx surface. The field strength in dielectric is connected with the surface ions concentration by the fiat capacitor formula

= 4 heN~e,

\ Figure 1. Adsorption potential for fluorine atom on the SiFx surface.

(6)

where e is the SiF, dielectric constant. Electron energy diagram of the semiconductor-dielectricadsorbed fluorine system is shown in Figure 2. From silicon, electrons are tunneling to the electron level of adsorbed atoms. When the field is zero this level is determined by the sum of the heat of adsorption Q and the affinity level E~ for fluorine Vo = Q + Ea ~>4.65 eV.

ES

(5)

(7)

The band bending in silicon and the restriction (7) give us a chance to assume that the level in adsorbed fluorine is located below or slightly higher than the edge of the valence band near the Si-SiF:, interface. That is why we believe that the field formation is determined by valence electron tunneling to adsorbed fluorine. We hold the Wolkenstein's opinion 19, who considered an adsorbed atom like a semiconductor defect. In such description an electron level is a part of the crystal quantum system. The presence of the SiFx film Which is transparent for electrons increases only the time of the electron equilibrium reaching and does not change the essence of the matter. Let z R be the time of electron resonance tunnel transition from silicon to the electron level of adsorbed fluorine. The electron equilibrium in semiconductor is reached fast enough and we can use the Fermi distribution for electrons and holes in silicon. The probability of direct (opposite) transition is proportional to the probability to find an electron (hole) in the 903

Yu E Babanov et al:

Kinetics of silicon etching by fluorine atoms Vacuum level

Si

Now we can obtain the kinetic equations for the concentration of adsorbed fluorine atoms and ions on the surface

SiFx

VO

J

Ec

•*----- h

-~

£

EF

Vs ~

Ev

F

Figure 2. Electron energy diagram of the semiconductor-dielectricadsorbed fluorine system.

state with energy E = V0 + ega. For the time of direct opposite (Z~r) processes we have =zR[l+exp(

(TT) and

dN F - N d t = Vr

N ~r

dF

Ft - F

N

dt

TA

(15)

~'s'

Ts

(16)

(8)

where Ek is the Fermi level in silicon without the field. The time of resonance tunneling is defined by the probability of passing the barrier shown in Figure 2. In semi-classical approximation it is2° 2 ~ - - ~ [ ( I + fl)3/2_ 11} . z~=r°exp {H

(14)

Here F is the surface fluorine concentration (atoms and ions), Ft is the concentration of active adsorption centers. In the right part of equation (14) the first addend is a number of ions created per unit time as a result of electrons tunneling; the second addend is a number of ions losing an electron as a result of reverse process and the third one is the ion flux going into the SiF x film. It is supposed here that the charge accumulating in the film can be neglected in comparison with surface charge. The equation (15) is similar concerning its form to the Langmuir's equation 19,21 where it is taken into account that only F - ions go away from the surface. It is so because the desorption can be ignored and the barrier for neutral particle penetration is too high. Let us emphasize that equations (14), (15) are non-linear since the time parameters zx, Z;r and z, depend on the field strength. The stationary solution of this equations corresponding to time independent etch rate can be expressed formally as

V°--E'F

/ Vo- e~ V1 Z~r=Z~ l + e x p ~ k T ) J '

N zs'

uF = Ft

(17)

Introducing d' into (16) in accordance with (6) we find the non-linear equation on the field strength in the film.

(9) Analysis of solution

Here the parameters H and fl are connected with the barrier characteristics 2 H=-~(2mVo)l/2h, f=eSh/V o

(10)

where h is the barrier width, m is the effective mass of tunneling particle. The precise calculation of the prefactor in (9) is rather difficult but for the estimation we can take a frequency characterizing electron movement in semiconductor ('c°) - t ~ 10 is S-1.

(11)

Besides the time of electron transitions ZT and Z;r the problem is described by the adsorption time of a neutral atoms ~A and the time of overcoming the surface barrier for fluorine ions z,. The adsorption time is determined by cross-section of fluorine atom capture by the surface (~r ~ 10/~2) and impinging fluorine

In general case the equation (16) should be solved numerically but in some interesting limit cases it allows analytical approximate solutions. Detailed analysis of this equation solutions for different ranges of parameters will be made elsewhere. Let us consider here only one specific case being of special interest for the present experimental data interpretation. If the electron level in adsorbed fluorine lies below the Fermi level in silicon, then Z~r>>zT. First we shall suppose that ZA >> ZT' This is true in the range of low fluxes at least when the adsorption time is long. In this case equation (16) can be written as

E,~=E~+kTIn(~)+kT

(12)

The time of the surface barrier overcoming according to (1) is z'=~°exp(E'-e°~a)kT ' where z ° ~ 10-f2 s is the time of molecular vibration. 904

(13)

(18)

where

flux JF

ZA = (aJF) - l

ln(~E~),

E¢=e~fa,

4 ne2Fta Et = -

(19)

The quantity E t is the highest energy of the field confined between the adsorbed particles layer and the surface when all adsorption centers are occupied by ions. If E,r is not so close to E t, then the equation can be solved by iterations since the last term is small in comparison with the others. To estimate

Yu E Babanov et al: Kinetics of silicon etching by fluorine atoms

the field strength it is enough to take zero approximation E ~ ' ~ Es + kT ln(~°~

(20)

Supposing here a = 2 A, Es = 1.5 eV, ZA = 0.1 S (it is equivalent to impinging fluorine flux JF ~ 1016cm-2 s - l ) at room temperature we have g ~ 4 × 1 0 7 V c m - 1 . At the same values of the parameters we can estimate the band bending in silicon. According to relations (4) and (5) we have Vs ~ 0.5 eV. It supports our assumption that the valence electrons tunnel to the adsorbed fluorine. To calculate the time of ion penetration into the film depth we should take the solution of equation (18) with the first correction. It gives E~ zs "~ Et ~ - ) E~ rA'

(21)

It is interesting to note that the initial exponential temperature dependence of zs disappears and the etching mechanism provides nonactivated fluorine penetration into the film. The analysis of experimental data concerning etch rate temperature dependence in the absence of the surface passivation was carried out in ref 22. It was concluded that nonactivated character of the silicon interaction with atomic fluorine does not contradict to this data. In the stationary regime the flux of SiF4 molecules desorbing from the surface is JSiF4 = N/(4rs) (see equation (2) and the etch rate is aft

[-

Es

k T l n ( Z ° ' ]]

(22)

where nsi is the bulk concentration of silicon atoms. The important feature of this relation is a nearly linear dependence of the etch rate on the fluorine flux. It is a non-trivial consequence of the initial non-linear equation solution. Linear dependence on fluorine flux was clearly established experimentally 1-3. The influence of the logarithmic term in equation (22) can not be fixed in experiments because it is too small. When fluorine flux increases the adsorption time decreases and TT increases. Therefore, the condition TA >>ZT is broken at some fluorine flux. In the opposite limit the etch rate does not depend on ,Iv. In principle the calculation of the flux value corresponding to the saturated etch rate can be done. However, it is difficult to make reliable numerical estimation because we do not know the thickness of the SiFx film exactly. Really, according to equation (9) even a small change of h gives a substantial change of the tunnel time. Conclusion

The model of silicon etching by fluorine atoms is presented. It is based on the propositions which are discussed in refs 14, 15.

(i) the thin film of SiFx being an effective reaction layer is created on the silicon surface; (ii) electrons from silicon valence band are tunneling to fluorine atoms adsorbed on the surface of this film resulting in the strong electric field arises in the film; (iii) the field makes lower the potential barrier for penetration of fluorine ions into the film depth. It is shown that processes taking place in SiFx layer do not influence on the etch rate in stationary regime. The kinetics of the surface processes taking into account the electrons transitions through the SiFx film is analysed. The non-linear kinetic equations giving all necessary information about etching process are obtained. The most interesting limit case allowing analytical solution of the kinetic equations is examined. It is found out that the etch rate depends nearly linearly on impinging fluorine flux in agreement with the experiment. The temperature dependence of the etch rate has nonactivated character. The estimation of the electric field strength in the film has been done. References

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