WO1999031305A1 - Device for measuring and controlling the solidification of an electrically conductive material - Google Patents

Abstract

The invention concerns a device for solidifying an electrically conductive material, characterised in that it comprises means (26, 28, 30, 32) for differential measurement of the conducting material load resistance, between a first point located in a solid portion (22) of the load and a second point (30) located in a liquid portion (20), and between a third point (28) located in another solid portion of the load and the second point (30).

Description

DEVICE FOR MEASURING AND MONITORING THE SOLIDIFICATION OF AN ELECTRICALLY CONDUCTIVE MATERIAL

Technical field and prior art

The present invention relates to a measuring device and method suitable for controlling the solidification of a single crystal, obtained for example according to the Czochralski, Bridgman or Stockbarger methods both in their terrestrial and spatial realization. This device and this method are compatible with the solidification systems of an electrically conductive doped material, described in documents EP-246,340 and EP-549,449. The device relating to the invention can either replace the instrumentation existing, or be grafted to it. The compatibility and the complementarity of the systems make it possible to favor the diagnosis concerning the developed structure. The existing devices described in the documents cited above do not mention the measurement or control of the characteristic that is the resistivity of the crystal formed.

A precise measurement of this characteristic provides information on the structure being formed and especially on its anomalies. Several existing systems exploit this characteristic (on a separate sample) to know the position and the speed of movement of the mobile interface. However, this characteristic is not used in structure analysis. The Bridgman zone (or solidification zone) changes in temperature as the crystal is formed. But the resistivity of this area also changes with the structure formed. For a linear displacement of the furnace one obtains a quasi-linear evolution of the resistance.

The conventional measurement method is relatively simple. A stabilized current flows through the charge which is being solidified. By a so-called "four-wire" method, the voltage across it is recovered. This voltage is directly proportional to the resistance of the load. During solidification, the variation in resistance is approximately 10 to 15%, at most, of the overall value of the load.

Figure 1 illustrates a block diagram of a method of the prior art. This is an example of a filler used for the formation of any metal alloy. The load has an approximate diameter of approximately 6 mm and a length of 1 m.

It is located inside a device comprising, for example, two ovens, a stationary oven and a mobile, as described in document EP-246 940. This assembly of the ovens is not shown in FIG. 1.

Four distinct zones 2, 4, 6, 8 are shown in this figure. The two zones 2, 4 at the ends of the load represent the parts still remaining solid. The central zone 6 represents the zone melted by the fixed and mobile ovens. Finally, zone 8 known as "Bridgman", corresponds to the zone subjected to one or more successive solidifications by virtue of the movement of the mobile oven which will, depending on the direction of movement, either melt the Bridgman zone or solidify it.

An alternating supply 16 supplies an alternating current I = I _m sinωt which flows between two current input and output points 12 and 14 located on the external faces of the two solid zones 2, 4.

The overall load resistance is the result of the sum of the various resistive zones subjected to the thermal gradient of the ovens.

The overall measurement of the resistance according to the procedure described does not make it possible to obtain sufficient sensitivity to be able to judge the structure formed.

Statement of the invention

In order to increase the sensitivity of the measurement, the invention proposes to carry out a differential resistance measurement between two parts of the sample, for example between two halves of the sample.

To this end, the subject of the invention is a device for solidifying an electrically conductive material, characterized in that it comprises means for differential measurement of resistance of a charge of conductive material, between a first point located in a solid portion of the charge and a second point located in a liquid portion, and between a third point located in another solid portion of the charge and the second point.

Such a device makes it possible to extract the variation of the resistance, independently of the absolute value of the load resistance. However, the latter is much greater than the variations themselves. The device according to the invention therefore improves the accuracy with regard to variations which may be small.

According to one embodiment, the differential measurement means include means for measuring a first voltage Vi, between the first and second points, and a second voltage V ₂ , between the second and third points.

The first voltage is for example measured between a first electrode, applied to the first point and a second electrode, called recovery electrode and applied to the second point. The second voltage is then taken between the recovery electrode and a third electrode applied to the third point.

The voltage measurement means comprise for example a differential transformer.

In a symmetrical configuration, the second point is located halfway between the two ends of the liquid part of the charge.

For a non-symmetrical configuration, the differential transformer has first and second primary windings having respectively a number of turns ki, k ₂ , the voltages V _τ and V ₂ being, for a zero differential resistance, such that k ₁ V ₁ - k ₂ V ₂ = 0.

According to another embodiment, the device further comprises a potentiometer arranged in series between a first and a second primary winding of the transformer and electrically connected to the second voltage measurement point.

Finally, it is possible to provide means for measuring the total resistance of the load.

By simultaneously measuring the total resistance and the differential resistance, one can know the interface (the variable resistance or the fixed resistance serving as a reference) which causes a variation. Brief description of the figures

In any case, the characteristics and advantages of the invention will appear better in the light of the description which follows. This description relates to the exemplary embodiments, given by way of explanation and without limitation, with reference to the appended drawings in which:

- Figure 1 shows a device known from the prior art, - Figure 2 shows a differential resistance measurement diagram, according to the invention.

Figure 3 shows another embodiment of the invention.

- Figure 4 shows an electrical assembly of a device according to the invention.

- Figure 5 illustrates an example of load for a measurement according to the invention.

- Figures 6 and 7 show the change in sensitivity as a function of the value of the resistance of the load.

Detailed description of embodiments of the invention

An embodiment of the invention is shown in Figure 2. In this figure, a charge comprises, inside a crucible 23, a liquid part 20 and two solid side parts 22, 24. A source 16 allows supplying alternating current to a circuit closed by the load 20, 22, 24. Three electrodes 26, 28, 30 make it possible to take two voltages Vi and V ₂ . One of them, called recovery electrode 30, is introduced into the liquid part of the load. The other two are in contact with the solid part of the load. This arrangement separates the overall resistance of the load into two parts. The Vj. is, for example, the reflection of the part of the resistance which evolves with the movement of the furnace, the sample V ₂ then being the reflection of the part of the fixed resistance, the latter serving as a reference. The use of a differential transformer 32 makes it possible to recover the voltage V _s , which has the expression:

V _s = K (Vι-V ₂ ) where K is a coefficient depending on the transformer used.

Such a device makes it possible to extract the variation of the resistance alone, and thereby eliminates the absolute value of the resistance of the load. Since the latter is much greater than the variations themselves, direct measurement greatly limits the accuracy of the variations. For example if R (load) has the value 20 mΩ, a measurement to 10 ^{~ 4} makes it possible to obtain the true value to within 2 μΩ. If the variations due to the movement of the mobile oven are around 1 mΩ, we obtain a real precision of 2.10 ^"3 for this variation. On the other hand, if only the variation of 1 mΩ can be taken into account, then we find the precision of 10 ^{" 4} and the value of the variation from 1 mΩ to 0.1 μΩ is obtained.

This example illustrates the advantage of such a device, which improves the precision with regard to variations which may be very small.

The means for measuring the voltage V _s can be connected to means 33 for calculating the resistance which are themselves connected to display and / or storage means.

In particular, these means can allow the transmission of data relating to the differential resistance to a microcomputer 37, for example for piloting or controlling the solidification device.

The configuration described above is suitable for perfectly symmetrical loads. This is not always the case. Indeed, in some cases, the crucible filling tube is the only possible place to install the sampling electrode. However, this tube can be off-center, to allow the mobile oven a maximum displacement (for example of the order of 120 mm).

To overcome this asymmetry, obtain a device which is compatible with the principle described, and succeed in achieving the objective of starting a cycle, with a zero resistance value, it is for example possible to set different multiplicative coefficients for each of the voltages Vj . and V ₂ ; thus, the windings 27, 29 on the transformer can be adapted to obtain:

(k ₁ V ₁ -k ₂ V ₂ ) = 0 where ki and k ₂ are proportional to the ratio of the number of secondary / primary turns (ki (respectively k ₂ ) is equal to the ratio of the number of turns of the secondary winding / number of turns of the primary coil 27 (respectively 29)). This solution presents difficulties in achieving the fact that an entire ratio of the number of turns is easier to achieve. In addition, a specific transformer is to be adapted for each loads carried out, knowing that not all of them are the same size.

The practical solution, illustrated in FIG. 3, is to add a potentiometer 34 in series with the two windings 36, 38 of the transformer primary and to connect its cursor 40 to the recovery electrode 30. With this configuration, in the hypothesis of an ideal transformer and under the condition jωL "(rι + r ₂ ), where r _: and r ₂ represent the two parts of the resistance as a potentiometer, on either side of the cursor,

avec : N_s = nombre de spires au secondaire.

with: N _s = number of turns in secondary school.

N = number of turns in the primary, knowing that Lι = L ₂ = kN ² = L

Vi = RiXl

V ₂ = R ₂ xl. The potentiometer 34 catches the potential differences between Vi and V ₂ due to the mechanical off-center of point 40.

This relation (1) is established in the following way, by considering the diagram and the notations of figure 4. Let M be the mutual inductance of the coils

36, 38, Mi and M ₂ the mutual inductances, of the secondary coil (of inductance L _s ) and, respectively, of the primary coil 36 (of inductance L _x ) and of the primary coil 38 (of inductance L ₂ ). If we set the conditions ls = 0, Lι = L ₂ = L, we can then write: eι = -jωMxI ₂ and e ₂ = -jωMxIι In addition:

(Vi - jωMxI ₂ ) (~ V ₂ - jωMxIi)

Il = r and I ₂ = r

(ιωL + ri) (; jωL + r ₂ )

Or :

et -V₂(jωL + ∑ι) - jωMxV_}

and -V ₂ (jωL + ∑ι) - jωMxV _}

12 =

(jωL + r) (jωL + r ₂ ) + ω 2 ^' M „2

=kL et sous l'hypothèse K≡l (transformateur idéal), il vient :Knowing of

= kL and under the assumption K≡l (ideal transformer), it comes:

Vι (jωL + r ₂ ) + jωLxV ₂ II = T -; r JCÛL + rι jωL + r ₂ ) + ω ₂ L ₂ and:

As I _s = 0, and that we impose, by construction of mutual inductances Mi and M ₂ equal or similar, the voltage V _s is equal to:

V _s = ± jωM _s x (Iι + I ₂ ) with M _s = Mι = M ₂

V ^" ι (jωL + r) + jωLxV ₂ - V ₂ (jωL + r) - jωLxV V _S = ± jωM _s x -

(jωL + η ωL + r ₂ ) + ω L Finally, knowing that jωL ”(rι + r ₂ ):

avec :So we get

with:

N _s = number of turns in secondary school,

N = number of turns in the primary (number of turns of Ni and N ₂ , with the condition Nι = N ₂ = N, because Lι = L ₂ = L), I = excitation current of the load, Ri = resistance variable to be measured, R ₂ = fixed resistance serving as a reference. We can therefore easily adjust the multiplying coefficients for Vi and V ₂ . These will depend on the ratio (rι / r).

This solution makes it possible to cancel V _s , whatever the asymmetry of the load and, therefore, allows to obtain the maximum sensitivity for all displacements.

Once balancing has been carried out (V _s = 0), there is insensitivity to variations in current I, and the change in ambient temperature is then also fully compensated.

By simultaneously measuring the total resistance and the differential resistance, one can know the interface causing the variation. A positive variation of the total resistance will have the same sign on the differential measurement if R _: is the source of the variation, and will have a contrary sign if it is R ₂ which is the cause of the variation.

On the other hand, the sensitivity depends on the setting. But, as the following numerical example will show, the setting has little influence.

EXAMPLE We consider the geometry illustrated in Figure 5. The load has a total length 1 = 960 mm and two partial lengths (on either side of the filling tube and, therefore, of the sampling electrode) 1 ₁ = 508 mm and 1 ₂ = 380 mm. Consider a eutectic charge SnCu 0.94 at% Cu.

The resistance of the load at room temperature before the temperature rise is

11.47 mΩ. This value corresponds to the lengths of 508 mm (mobile side) and 380 mm (fixed side) which turn out to be lengths used for resistance measurement. The length of 508 mm corresponds to Ri, the length of 380 mm corresponds to R ₂ .

^ 11.47x508 ^ 1 _{^ ^ Λ}

R ^, _{= =} 6.56mΩ (moving dimension

V 888 ^

(1.47x380 ^ R = - = 4.91mΩ (fixed side)

V 888 J

These values are those of the charge at ambient temperature, before the temperature rise.

At 600 ° C, the oven having returned (dimension 0), the total resistance of the load reaches 21.6 mΩ after having carried out the melting F ₀ and the solidification Si. The oven brought to dimension 120 mm, the resistance reaches the 24.96 mΩ value.

The melted area, oven returned (dimension 0), is: 131x2 = 262 mm (from interface to interface). Compared to the ambient, this molten zone increases R _ι + R ₂ by approximately 10 mΩ (volume compensation included).

The lengths of the solid areas of interest for the measurement then have the following values: - 380-131 = 249 mm (fixed side), - 508-131 = 377 mm (mobile side).

The gradient zones are the same, fixed side and mobile side. The additional solid length (mobile side) is very close to that at room temperature, since it is located after the cold well. If we neglect, at first, the slight increase in cross-section in the 120 mm zone, we can estimate the maximum possible difference between Ri and R ₂ . (The increase in section reduces the gap). The difference in length of the zones is: 377-

249 = 128 mm.

The resistance of a piece of 128 mm load at room temperature is:

11.47x127, _ _,. = 1.65mΩ (departure difference).

888 The values of the retracted oven resistance (dimension

0) for R ₂ and Ri are:

^{2 6 ~ X65} = 9.975mΩ = R ₂

R ₂ + 21.65 = ll, 625mΩ _n = Ri

The mobile oven having returned to dimension 0, the resistance difference between the two halves is relatively smaller when the ovens are raised in temperature than when the temperature is room temperature.

The compensation for canceling the voltage V _s gives, for the value of ri and r ₂ :

As Vι = IRι and V ₂ = IR ₂ , then:

En prenant par exemple (rι+r₂)=lΩ (condition (jωL>> (rι+r₂) vérifiée), on obtient : r_ι=0,5382Ω (coefficient multiplicateur pour R₂) , r₂=0,4618Ω (coefficient multiplicateur pour Ri). Ces valeurs de r_x et r₂ représentent les coefficients multiplicateurs pour chaque côté. La variation de tension pour un "delta" de résistance donné ne sera pas équivalent selon le coté concerné. Par exemple, pour une variation de ΔR=lmΩ côté mobile, la tension correspondante ΔV est :

By taking for example (rι + r ₂ ) = lΩ (condition (jωL >> (rι + r ₂ ) verified), we obtain: r _ι = 0.5382Ω (multiplying coefficient for R ₂ ), r ₂ = 0.4618Ω (multiplier coefficient for Ri) These values of r _x and r ₂ represent the multiplier coefficients for each side. The voltage variation for a given resistance "delta" will not be equivalent depending on the side concerned. For example, for a variation of ΔR = lmΩ on the mobile side, the corresponding voltage ΔV is:

Nς ΔRxIx —≥- x0.4618 = 166μV = ΔV / ΔR = 166μV / mΩ N and ΔR / ΔV ≈ (6μΩ / μv) with:

I = 30 niA, N _s / N = 12.

For the fixed side, it comes:

N ΔRxIx - χ0.5382 + 193μV ΔV / ΔR = 193μV / mΩ N and Δr / Δv ≈ (5.2μΩ / μv)

When the mobile oven is moving (120 mm maximum), RI is the cause of all the variation. In the present example, the variation is 3.36mΩ.

This value is to be compared with the absolute value of R which is 7 times greater. We can therefore gain a factor of 7 in sensitivity over the entire variation of R if we opt for a differential measurement instead of an absolute measurement. For small movements of the oven, using the potentiometer settings you can obtain a maximum sensitivity whatever the place of the variation. Sensitivity can be improved a very important factor compared to an absolute measure of resistance.

However, the sensitivity depends on the setting, and the new position of the balancing potentiometer can be recalculated to compensate for the maximum variation, namely:

- R ₂ remains fixed and is worth 9.975mΩ,

- Ri goes from ll, 625mΩ to 14.985mΩ.

To balance, you need:

R _{2 value}

9.975

0.3996Ω

14.985 + 9.975

R _{x value}

¹⁴⁹⁸⁵ = C600 Ω

14.985 + 9.975 The corresponding sensitivity for each of the interfaces will then be:

No.

ΔRxIx —≥- x0.3996 = 144μV = ΔV / ΔR = 144μV / mΩ N and ΔR / ΔV ≈ (6.94μΩ / μv) (mobile interface)

Born

ΔRxIx - χ0.6004 = 2166μV => ΔV / ΔR = 2166μV / mΩ N and ΔR / ΔV ≈ (4.62μΩ / μv) (fixed interface)

With balancing redone, the sensitivity concerning the two interfaces (S _m and S _f ) will evolve in the range: 144μV / mΩ <Sm <166μV / mΩ, or 7μΩ / μV <Sm <6μΩ / μV

216μV / mΩ>Sf> 193μV / mΩ, or 4.6μV / μV>Sf> 5.2μΩ / μV We can also trace the theoretical evolution of the sensitivity S (in μV / mΩ) for the two interfaces according to the value of the resistance R of the load (in Ω), and readjust the position of the mobile oven accordingly. This development is shown in Figure 6, where curve I corresponds to S mobile and curve II to S fixed.

A range D of displacement D of the mobile oven (120 mm) corresponds to the range of variation of the resistance indicated by ΔR _D in FIG. 6. FIG. 7 is an enlarged representation of the curves I and II over this range.

The arrows A, B, C represent the settings at dimensions 0 mm, 60 mm and 120 mm. The values Si and S ₂ are the sensitivities obtained for a balancing performed at the 0 mm dimension, the values S ₃ and S are the sensitivities obtained for a balancing performed at the 120 mm dimension.

If balancing is carried out between the two dimensions (0 mm and 120 mm), the respective sensitivities of S _m and S _f will change according to the curves (S _fixed , S _mob iie), the dimension varying in a completely linear fashion. For example, the sensitivities obtained at the 60 mm dimension will be those found between the 0 mm dimension and the 120 mm dimension.

An interesting solution is to adjust the dimension 60 mm. This provides the variation of Ri in ± l, 68mΩ. The measurement scale chosen for the voltmeter or synchronous detection which processes V _s can correspond to the equivalent of ± 2mW. This scale is much more interesting than the scale necessary for the total absolute value of the load which will be practically equivalent to 50 mΩ, because the calibers on the voltmeters or the synchronous detections are thus made. The precision thus obtained for all the variation of Ri is directly improved by a factor greater than 10 compared to the direct and absolute measurement of the load. The adjustment can only be made once at the start of the measurement, and it does not normally need to be touched up. The sensitivities to be taken into account for the two interfaces are those obtained for setting the dimension 60, i.e. 155μV / mΩ (or 6.45μΩ / μV) for the mobile interface.

To further increase the sensitivity, just make reduced movements of the mobile oven and touch up the potentiometer settings for each starting dimension. The choice of a scale adapted to the expected variation makes it possible to obtain the greatest possible precision. The limit of precision is imposed by the electronic noise of the amplification, and not by the caliber of the measuring device as it is the case today.

Claims

1. Device for solidifying an electrically conductive material, characterized in that it comprises means (26, 28, 30, 32; 36, 38) for differential measurement of resistance of a charge of conductive material, between a first point located in a solid portion (22) of the load and a second point located in a liquid portion (20), and between a third point (28) located in another solid portion of the load and the second point ( 30) . 2. Device according to claim 1, the differential measurement means comprising means (22, 30, 36) for measuring a first voltage Vi, between the first and second points, and means (28, 30, 38) for measuring a second voltage V ₂ , between the second and third points. 3. Device according to claim 2, the differential measurement means further comprising a differential transformer (32). 4. Device according to one of claims 1 to 3, the second point (30) being located halfway between the two ends of the liquid part of the load. 5. Device according to claim 3, the differential transformer (32) having a first and a second primary winding (36, 38) having respectively a number of turns ki, k ₂ , the voltages Vi and V ₂ being, for a differential resistance zero, such as kιVι-k ₂ V ₂ = 0. 6. Device according to claim 3, further comprising a potentiometer (34) arranged in series between a first and a second primary windings (36, 38) of the transformer (32), and connected electrically at the second voltage measurement point (40). 7. Device according to one of the preceding claims, further comprising means (33, 35, 37) for measuring the total resistance of the load.