The present invention relates to methods of cutting a substrate by the introduction of thermo- mechanical tensions. The present invention also relates to the precise manufacturing of a substrate shape by the cutting methods specified. The present invention also relates to devices for performing the methods according to the present invention.

PCT application No. PCT/EP2010/005945 describes a method and device for cutting of brittle materials such as glass by the introduction of heat into the material and the subsequent occurring separation of this material by thermo-mechanical tensions. Such non-contact cutting methods using thermally induced tensions for cutting, which also comprises various laser cutting methods, are becoming increasingly important for cutting of high performance materials such as strengthened and ultra-thin glass. Not only do these methods allow for cuts without the typical micro-cracks seen along the cut edge in classical, i.e. mechanical, cutting methods but also prevent the release of micro particles which cause problems and special precautions, respectively, in clean room environments typical for high performance glass processing sites.

The method and device described in PCT/EP2010/005945 provide for a first and very general approach to high frequency - high voltage based electrothermal cutting. In order to achieve cutting performances compatible with current and future industrial requirements, in particular cutting speed and precision, additional methods and devices need to be implemented. Accordingly, it was an object of the present invention to provide for an improved method and device for high performance electrothermal cutting. It was furthermore an object of the present invention to provide for a method and device for electrothermal cutting that allows a high cutting speed and cutting precision.

These objects are solved by a method of cutting a substrate involving

- a) an application, at a frequency in the range of from 1 kHz to 10 GHz, of an AC voltage and an electrical current to a defined region of a substrate by means of one or more electrode(s) connected to an AC voltage source, thereby heating said defined region and generating an electric field inside said substrate, and - b) a movement of said defined region along a path on said substrate by moving

(i) said electrode(s) relative to said substrate,

(ii) or said substrate relative to said electrodes,

(iii) or both said electrode(s) and said substrate relative to each other, wherein step a) involves

- a') maximizing the electric field inside said substrate at said defined region.

In one embodiment a') comprises

(i) providing a conductive plasma or conductive region between said electrode(s) and said substrate, and/or

(ii) providing a region of high permittivity between said electrode(s) and said substrate, and/or

(iii) providing and using an electrode (electrodes) which emits (emit) electrons easily, and/or

(iv) using an electrode (electrodes) having a pointed tip and being made of a material allowing the tip to become sufficiently hot for electron emission, said material providing sufficient heat conduction and heat capacity to prevent a destruction or evaporation or disintegration of the electron tip, and/or

(v) heating a surface layer of the tip(s) of said electrode(s) above the melting temperature of the material from which said electrode(s) is (are) made.

In one embodiment said electrode(s) emitting electrons easily is (are) made of a material which emits electrons at a temperature in the range of from (T _me | _t jng of electrode material - 500°C) to

1 evaporation of electrode material) and/or has a heat conductivity in the range of from 50 W-nf'-K ^-1 to 430 W-m -K ^-1 (at room temperature), and/or said electrode(s) emitting electrons easily are composite electrodes having a core and a cover layer on said core, wherein the cover layer is made of (I) a material preventing a destruction or evaporation or disintegration of the electrode(s), such as a noble metal, and/or (II), a material facilitating the emission of electrons, i.e. having a low work function.

To reach temperatures sufficiently high for the electrode(s) to emit sufficient amounts of electrons, in one embodiment, it is advantageous to surround the electrode(s) with an inert or otherwise protective gas or atmosphere to avoid oxidation or other degradative processes which would lead to a destruction or deterioration of the electrode(s). In one embodiment a') comprises

(i) using a gas composition between the electrode(s) and the substrate allowing the formation of a conductive plasma, and/or

(ii) avoiding significant capacitive plasma sheath layers on the surface(s) of the electrode(s) and/or on the substrate to be cut, and/or

(iii) applying a minimum current to the electrode(s) to make the tip(s) of the electrode(s) sufficiently hot so as to emit electrons so that at least 10% of the voltage applied to the electrodes is present across the substrate, and/or

(iv) selecting a distance between the electrode(s) and the substrate to adjust the current flow from the electrode(s) to the substrate to a current sufficient to heat the electrode tip(s) sufficiently to emit electrons but also to prevent thermal destruction of the electrode tip(s), and heating the space between electrode and substrate surface sufficiently so as to minimize the voltage drop across this space.

In one embodiment step a) involves a") generating a plasma arc by application of said AC voltage and said electrical current to said defined region of said substrate and reducing the area at which said plasma arc touches the substrate surface.

In one embodiment said plasma arc comprises a resistive part, and step a") comprises reducing the area of the resistive part of the plasma touching the substrate surface.

In one embodiment step a") is achieved by reducing the distance between the electrode(s) and the substrate, preferably to a minimum, while maintaining a resistive part of the plasma and while avoiding the plasma entering into a purely capacitively coupled state.

In one embodiment step a') and/or a") is achieved by producing a region of high permittivity between the electrode tip(s) and the substrate surface, with ε _Γ » 1 , wherein said region is produced by direct or indirect heating and/or by a temperature of the electrode tip(s) which is sufficiently high, and/or wherein the region of high permittivity is produced together with a conductive plasma region. In one embodiment, the temperature of the electrode tip(s) is typically » 100°C. 8 _r is the relative permittivity. In one embodiment step a) involves a"') using an impedance matching network, said impedance matching network being an integrated or intrinsic part of the AC voltage source, such as one or several coil inductances and parallel capacitances, to increase the voltage drop across the substrate and/or to reduce the size of a plasma arc generated by the application of an AC voltage and an electrical current to said substrate, on the substrate surface, and/or to modulate resistive and capacitive properties of the plasma arc.

In one embodiment step a) involves a reduction of the surface area electrically or dielectrically connected to the electrode(s) so as to reduce the capacitance across the substrate and the current flowing, thus enabling a higher voltage across the substrate and a stronger confinement/focussing of the heated substrate region, by concurrently reducing voltage drops across all other components including the plasma arc, if present, electrode(s), wiring and the AC voltage source.

In one embodiment the AC voltage source is a self-oscillating resonant transformer circuit, employing a magnetic feedback from the output coil to the active switching element thereby allowing the voltage source to adapt to changing conditions at the substrate site to be cut, such as resistance, capacitance and/or inductance, wherein preferably, the self-oscillating resonant transformer circuit has one or several high Q coils to achieve output voltages > 1000 Vpp (Volts peak-to-peak). In one embodiment, Q is typically >5.

In one embodiment step a) involves heating the substrate in said defined region to a heated state so as to increase the dielectric constant of said substrate, wherein, preferably, a temperature feedback mechanism is used so as to prevent the temperature of the substrate in said defined region from exceeding a defined temperature value or range which, preferably, is the melting temperature of said substrate.

In one embodiment step b) is performed, while said defined region of said substrate is maintained in a heated state, as defined above.

In one embodiment, said substrate to be cut comprises a damping element attached to said substrate, so as to dampen vibrations of the substrate and thus avoid unintentional breakage of the substrate. In one embodiment the method further comprises step c) applying tensile stress on the substrate, e.g. by bending, to facilitate or guide the cutting process and/or applying thermomechanical stress to the substrate so as to correct and/or modify the cutting vector/direction, wherein, preferably, the application of thermomechanical stress is performed by using a laser or an AC voltage source and an electric arc generated thereby and applied to the substrate.

The objects of the present invention are also solved by a device for performing the method according to the present invention comprising:

a) an AC voltage source capable of applying a voltage in the range of from 10 V to 10 ⁷ V at a frequency in the range of from 1 kHz to 10 GHz,

b) a first electrode connected to said AC voltage source,

c) holding means to hold a substrate to be cut and to expose one side of said substrate to said first electrode,

d) means to move the electrode and/or the substrate relative to each other, e) control means to control a) and d),

f) optionally, a counter-electrode placed on the opposite side of the substrate, g) optionally, cooling means arranged at a fixed distance to said electrode, for cooling the substrate, comprising a cooling nozzle directed at the substrate.

The present inventors have surprisingly found that the cutting performance can be improved with respect to cutting speed and cutting precision by optimization of the heat dissipation inside the substrate and the lateral size of the heated area in the substrate. With respect to the first parameter, the heat dissipation inside the substrate must be increased. With respect to the second parameter, i.e. the lateral size of the heated area, this must be reduced so as to achieve a high degree of focusing.

An embodiment of a basic setup used for electrothermal cutting is shown in Figure 1. The material to cut is moved between the two electrodes and a high frequency (HF) high voltage (HV) is applied across the material using the electrodes, leading typically to the formation of an electric arc between the electrodes and the material. If one electrode is omitted an arc can still form while the material itself acts as counter electrode coupling capacitively to the counter electrode/side of the voltage source. Figure 2 shows an embodiment of the equivalent circuit describing the region between the electrodes, which comprises as main components the electric arc and the material to cut.

The invention can be applied to different homogeneous or heterogeneous materials, including glass (borosilicate, float glass, soda lime and other forms, e.g. also hardened glass, ion treated or plasma treated glass, tempered glass), silica, fused silica, sapphire, special glassy materials (hardened glass, ion-treated or tempered) and layered materials, which tend to plastically break. Also substrates having none-flat or irregular surfaces are amenable to the invented method. However, to improve results under these conditions the setup may be adapted in such a way as to have the electrode(s) follow substrate surface having a defined, e.g. constant, distance to the substrate surface. Typical thicknesses of substrate materials vary in the range from 0.01 mm to 5 mm, preferably from 0.1 mm to 2 mm. In one embodiment, the substrate, on one or both sides, has an additional layer of a conductive material, such as indium tin oxide (ITO) or non-conductive material, such as metal oxide, attached.

Moving the substrate and electrode(s) along a linear, i.e. single dimensional, path with respect to each other a straight line cut or separation will be produced. Substrates with complex shapes can be obtained applying the invented method while controlling the electrode(s) position/movement in such a way as to follow the requested shape on the substrate. In the tested configuration, complex shapes were easily obtained, including rectangles with rounded edges and undulating line cuts.

To obtain precisely cut substrates, the relative movement between the electrode and the substrate may be controlled by numerically controlled electromechanical equipment. In a possible configuration, the electrode(s) are moved by the positioning machine over the substrate, or alternatively, the substrate is moved while keeping the electrode(s) in a fixed position; combinations of such two options are also possible. In order to control and adapt the electrical and mechanical parameters in an appropriately short time (typically keeping the corrective intervention time below 100 ms), a feedback loop can be implemented. In this way, basing on measured values of currents, voltages and/or temperatures, it is possible to adjust voltage generator parameters, cooling system, substrate-electrode(s) distance and/or speed in real time to maintain a regular process.

Without wishing to be bound by any theory, analyzing in general terms the electrical power dissipated into heat inside the material by dielectric loss p _in = ε _Γ (Τ)εο tan5(T) ω E ² , where B _r (T) is the temperature dependent dielectric constant of the material, tand(T) the respective temperature dependent loss tangent, ω the applied circular frequency and E the electric field inside the material, the following conclusions can be drawn with respect to the goal of this invention:

1. ω and E should be as large as possible

2. both e _r (T) and tanS(T) should be high; since both are material and temperature dependent, this can only be achieved by increasing the substrate temperature since both are a correlated to the substrate temperature in an exponential fashion, e.g. locally by the HF system itself or additional means such as a laser

For the equivalent circuit given in Figure 2, point (1) leads to conditions for optimized cutting:

3. The voltage drop between the material surface and the electrodes must be minimized As the voltage drop between electrodes and material surface is the sum of the voltage drop inside the electric arc/plasma and the sheath layers forming on the electrodes and the material surface, it follows

4. The voltage drop across the sheath layers must be minimized

5. The voltage drop inside the plasma arc if formed must be minimized

Point (4) and (5) are controlled by various parameters; one very important parameter is the plasma state, the gas temperature and the properties of the electrodes. Two main strategies have been developed to reduce the voltage drop between the electrodes and the material surface:

6. Providing a plasma that is sufficiently conductive and

7. Providing electrodes able to easily provide electrons to the plasma, most notably by thermoionic emission

An alternative strategy, on the other hand, assumes no or partial electric conduction within the space between electrode and material surface but heating of the gas there thus that the dielectric constant of this gas is significantly raised. This way a capacitive voltage divider forms having the capacitance of the space between the electrodes in series with the capacitance of the corresponding material area. As the voltage drop in such a configuration is inverse proportional to the dielectric constant, a high dielectric constant of the space between electrodes and material surface will shift the voltage drop across the material and will lead to high dielectric losses inside the substrate. Hence, a simple condition for a corresponding cutting device and method can be derived: 8. Increase the gas temperature between the electrode tip and material surface and consequently its dielectric constant

Successful implementation of both strategies suggests the following methods.

9. As the voltage drop across the plasma correlates to its length, the electrode should be placed closely to the material

At the same time it should be ensured that the space between electrode tip and material surface is (I) either conductive and the electrode tip emits electrons or (II) the space has a high dielectric constant. For either of these conditions to be met,

10. a minimum electrode tip temperature enabling either electron emission and/or strong heating of the gas between electrode tip and material surface should be provided.

Conditions 9 and 10 usually define some optimum distance of the electrode tip to the material surface.

At too close distances, currents will either be limited or flow over a large electrode area thus the electrode tip will not heat sufficiently, at too large distances the voltage drop outside in the space between material surface and electrode tip becomes too large. The optimum distance can be determined either by monitoring the heating of the material or by comparing cutting performances for different electrode tip distances.

However, heating of the electrode tip also depends strongly on the electrode properties. Ensuring electrode stability, condition 10 demands specific electrode characteristics. The more the electrode tip is pointed, the more it will heat. This is of course compensated by the heat conduction of the electrode material and the shape which defines the effective heat transfer from the tip. It has been experimentally shown that certain combinations of electrode geometry and material lead to optimum electrode tip performances. In one example, a highly thermally conductive electrode of 4 mm diameter Cu rod was made highly pointed over a distance of 8 mm, providing a conical shape. Placing the electrode tips ca. 2 mm from the material surface on both sides provided electrode tip temperatures »800 °C. T at the very tip can reach values above the melting T of the electrode material. Because of the highly thermally conducting electrode material, this molten region is highly confined to the outermost layer of the very tip. Eventually a thermodynamic equilibrium is reached and the tip will not deform or get destroyed. The design formula for optimum electrodes demands Condition 1 1 , i.e. an electrode geometry, in particular tip geometry (electrode diameter, tip diameter, angle of the electrode tip) in combination with an electrode material that allows for very high T of the very electrode tip. Well suited are electrodes made of thermally well conductive materials that are very pointed at the tip.

Due to the very high tip T that can be reached, such a tip may also provide electron emission for materials normally not well suited as electron emitters. The tip may also be designed to provide for a specific current range, thereby controlling the extension of the material surface region heated.

At the same time, designing the tip with respect to heating of the gas between tip and material surface in order to reach a high dielectric constant, it is possible to define the extension of this heated gas zone and therefore the region with highly increased dielectric constant and eventually the material region exposed to high voltage, which defines the region with the highest dielectric loss/internal heating.

In order to enable current conduction between the electrode tip and the material surface, in general, the following conditions 12-14 should be fulfilled:

12. The electrode material should be able to get hot enough at the tip, i.e. without global melting, to emit sufficient amounts of electrons to provide for a highly conductive arc and minimal sheath layers

As the electrode tips define the position of the cut and must therefore be sufficiently pointed to match the required specifications for precise cutting

13. The electrode material must also be suited to provide sufficient heat conductivity into the bulk to avoid excessive melting and evaporation of the electrode tip, this is ideally supported by

14. An electrode geometry and material which allows for an efficient heat transfer and dissipation in the bulk phase, which is usually achieved by a conical electrode design matching the electric currents and material properties.

Optimum conditions for (11-14) may also be achieved by using a hybrid electrode, e.g. consisting of a highly heat conducting base material and a material that emits easily electrons, such as copper or nickel in combination with a Rhenium or BaO/SrO surface layer for easy electron emission. Using noble metals as cover layer also allows to reduce decomposition of the electrode by oxidation and similar chemical processes. In particular if the very tip is heated over its melting T such protective coatings may significantly prolong electrode lifetime.

In order to work with materials emitting electrons at lower temperatures it is necessary for certain materials to work under a protective atmosphere, such as Argon or Nitrogen. Such gases, applied locally or over a larger electrode region, allow to work with electrode materials that otherwise would burn/oxidize under normal air. An example is a tungsten electrode; this electrode may also be covered by a good electron emitter such as thorium oxide.

It is important to note that during cutting different gas and plasma modes may concurrently form between the electrodes and the material surface. The very high voltages at the electrode tips - in combination with the very high frequencies used - may therefore not only lead to a plasma core driven by active/resistive currents, i.e. phenomena similar to arc discharges, but also to purely capacitively coupled plasmas in the vicinity of the electrode tip and glass surface. Such plasmas may e.g. surround the resistive or hot plasma that is formed in a arc discharge processes. Due to the high possible voltage drop inside the capacitive plasma and the associated sheath layers there may be no or only a limited contribution of such plasma to the cutting process and performance.

To achieve a good focusing of the internal power dissipation/heating, providing for precise cutting and reduced source HF power, a local increase in T inside the substrate may also be used:

15. Based on (2) (see above), increasing the (local) material temperature leads to an increase in ίαηδ(Τ), allowing for a reduced voltage for cutting while maintaining /?,„. Both, the reduced voltage as well as the small but dielectrically more lossy region can lead to a strong reduction of the arc spot size on the material surface.

However, implementing method/condition 15 (see previous paragraph) may be difficult. Using a laser for pre-heating requires focused laser radiation sufficiently absorbed inside the material to raise T. Another method is the heating through the HF system itself and then moving the heated spot through the substrate, thereby always staying in a focused mode. While this method has been successfully tested for its focusing ability, the maximum speed may be limited using method (15) alone. A simple schematic embodiment of a T-feedback HF system suitable for (15) is shown in Figure 3A, a practical realization in Figure 3B. It is important to notice that such a system should ensure that the material surface T stays below the melting temperature. As shown in figure 3B, this is achieved by a reduction in the quality factor (Q) of the secondary coil of the resonant transformer due to the increased power dissipation that occurs when the material T approaches the melting T (which leads to a significant increase in the ohmic conductance of the material and therefore ohmic losses) and the concurrent reduction in the signal picked up by the feedback coil, which effectively stops the oscillations. Adapting the coil properties allows to define T at which the HF system stops to oscillate/provide an output voltage, adjusting the gate bias/offset voltage allows to control the off-time, i.e. the time the system requires to start oscillations again once the ohmic load and T has reduced, respectively. There are many other implementations possible for such a T- feedback system. The one shown here is only exemplary. Other simple devices include E-field sensors. With increasing T the substrate increases exponentially, leading consequently to a reduction in E. Using therefore the magnitude of E as a measure for the substrate T allows to turn off oscillations below a minimum E/maximum T.

The methods and devices described rely on a simple abstract model of the actual situation during cutting. Based on this model and its predictions excellent cutting results, even for highly strengthened soda lime glass, have been achieved (Figure 4). However, due to limited data available on the plasma parameters, the formation of sheath layers on electrodes and material as well as other electrical system parameters it can be assumed that electrical parameters and parasitic components currently not part of the above model may also influence cutting performance. To enable an optimal cutting performance under all conditions optionally an impedance matching network can be introduced, adjusting empirically for such hidden and/or undetermined parameters/components (Figure 5). The matching network consists of reactive components (L, C) arranged to provide a maximum power dissipation inside the substrate and/or an adjustment of the size of the material surface region interacting with the plasma arc. These conditions strongly depend on the type (ε _Γ (Τ), ίαηδ(Τ), σ(Τ)) and thickness of the material as well as the electrical characteristics (Voltage, Impedance) of the HF source used. In particular for thin materials an additional matching network appears often not required to meet industry cutting specifications. For materials up to 1 mm tested a simple tuned inductor in the current return path could provide for a more symmetric and better focused electric arc. However, the actual network is usually adapted to the specific HF source and material.

In general, an optimally tuned cutting system will provide for the highest cutting speed and/or precision. Several parameters have been identified to guide such tuning of the cutting system (HF generator, electrodes, etc) and matching network (if used). As described, an important parameter is a small arc spot size, allowing for precise, high speed cutting at relatively low input powers. In general, the better the focusing, the better the cutting performance and the lower the power needed by the cutting system. At the same time it is important to ensure only a minimum voltage drop outside the material to be cut. This can be tuned by the operator by analyzing the wavelength distribution/color and intensity of the electric arc and plasma region, respectively. The formation of sheath layers and/or space charge zones can be analyzed and tuned observing the formation of DC/static potentials between the electrodes. Optimally, such potentials are reduced to zero; the formation of large potentials in the range of tens or hundreds of volts may necessitate a better/tuned matching network, HF source or electrode geometries/materials.

Performances that can be expected under normal operation conditions are shown in Figure 6. Here material and arc are simulated as a simple series circuit consisting of a capacitor (material) and resistive element (arc). Voltages approach and exceed easily 40 000 Vpp. Tuning of the HF generator (Figure 7) is however important for good performance. Tuning of the generator may in particular include a variation of the coupling factor between the inductances, the value and quality factor of primary, secondary and feedback coil, the parallel capacitance in particular of primary and secondary coil, the parasitic capacitive coupling between all three coils. The principle of the generator presented in Figure 7 has been particularly developed for electrothermal cutting, providing for a very high output voltage (tested up to 120 kVpp) at very high frequencies (tested up to 50 MHz). Key to the generator design is a magnetic feedback of the secondary (output) coil L3 provided by LI . This allows for a virtually phase lag free feedback signal, allowing for nearly loss-less switching of the transistor/Mosfet and very high output voltages if coils with high quality factor are used. This generator allows therefore for a very simple but highly efficient (typ. > 70%) transformation and application of the input power. Because of the feedback principle, this HF source will automatically adapt to changing load or resonance conditions. This is important for cutting as both may change during the process due to the temperature dependence of material parameters.

Optimization of the so far shown parameters represents the main path to obtaining a high electrothermal cutting performance. However, a variety of additional methods and devices have been developed to further improve cutting performance.

In particular for work with strengthened glass, the factor that limits the cutting speed is often the tendency of the material to break in an uncontrolled fashion because of the compressive stress in the surface region of the sample. This tendency can be reduced applying a damping material on the surface without covering the region of the cutting path. Such material can be a layer of soft rubber, foam or any element able to absorb the shock wave generated by the propagation of the cut.

Creating a region under tensile stress on the material surface can be helpful to start the separation of the material. This can be obtained on one of the surfaces, by applying a bending stress on the material, unbalancing the tension state increasing the traction on the expanded region, making easier the initiation of the separation in such zone. This method can also be used to temporarily reduce the typical compression of the external regions of strengthened glass that makes difficult the initiation of the cut.

The control of the linearity of the cutting path is normally a very important feature for all cutting methods. For electrothermal cutting, more specifically when a sample needs to be cut not along its symmetry axis, the factor that limits the control over linearity is the deviation of the cutting vector because of asymmetrical tensions in the material. This can be moderated using two possible approaches:

a) correcting the cutting path, following a trajectory that compensates the deviations naturally arising,

b) adding an auxiliary heating spot moving over the sample, preceding the path of the cutting electrode and shifted by an offset, in order to expand the glass and create a balancing tension that corrects the deviation due to the asymmetry of the separation.

In the following, reference is made to the figures, which describe embodiments of the invention. The figures are not intended to limit the present invention, but are merely given for illustrating purposes.

Figure 1 shows schematically an embodiment of a basic setup for electrothermal cutting (ETC). The output of a high voltage high frequency generator (1) is electrically connected to two electrodes (3, 3'). The material to be cut (6) is moved between these two electrodes. The high frequency high voltage applied to the electrodes leads to the formation of an electric arc (4, 4') between the material (6) and the electrodes (3, 3'). Consequently the material is locally heated at the arc contact site, (A) by heat conduction from the arc in the material and (B) by dielectric losses inside the material itself (5). This heat leads to mechanical tensions that separate the (usually brittle) material. The main goal of the presented methods and devices is the promotion of (B) in order to achieve higher cutting speeds and accuracy.

Figure 2 shows a model of the electric circuit of Figure 1 used to simulate and analyze the material heating. The HF HV source (1) is electrically connected to the discharge unit (20). The connection and electrodes (3) between (1) and (20) may show a non negligible inductance, which typically is in the nH-range. Ideally, this inductance is reduced to zero. In this special case, the source consists of a transformer consisting of the primary coil (1 1) and the secondary coil (12). (12) forms a resonant circuit involving its own capacitance (13), the parasitic capacitances (15) which occur through capacitive coupling of (12) to ground, as well as the attached circuit consisting of (3, 3') and (20). The series resistance of (12) is shown as (14). One end of (12) and/or (20) may be referenced to ground (16). Power is coupled into (12) via (1 1) at its resonance frequency, resulting in a very high (typ. » 1000 Vpp) voltage across (2). One goal of the present invention is to transfer this voltage directly across the material. However, the original voltage generated across (12) is reduced by the voltage drop across the electrode and material surface sheath layers (221, 223 and layers on opposite side) and the voltage drop across the electric arc (222, and opposite side). (22) represents the arc (4) in Figure 1, (23) the actual arc (4'). To increase the voltage across the substrate (21, represents capacitive region 5 in Figure 1) it is important to avoid sheath layers as much as possible using e.g. electrodes that provide easily electrons to the plasma arc, a highly conductive plasma, a short distance between the material and the electrodes as well as a small spot size of the arc on the material. The smaller the spot size, the smaller (21) and therefore the current flowing through the substrate and through (14). This strongly reduces unwanted voltage drops inside the transformer and along the discharge circuit. Another strategy to transfer the electrode voltage to region (21)/(5) is the generation of a region of high dielectric constant between the electrodes and (21). That way a capacitive voltage divider is formed and the voltage drop across (22) + (23), which now form a capacitance of a similar order of magnitude as the capacitance across the substrate, will reduce and the voltage drop across (21) increase. Both strategies may possibly be combined.

Figure 3A shows an embodiment of a self-oscillating HF-HV generator using a resonance transformer L2-L3 to produce the HF HV required for electrothermal cutting. Oscillation starts when the gate voltage exceeds a minimum value (typ. 3 - 5 V) leading to a drain current that induces a voltage and eventually current in L3 via L2. The oscillations in L3 are picked up via magnetic coupling using LI and fed-back to the gate. This leads to an auto-oscillation with a frequency given by the resonance frequency of the L3 circuit. Using fast

transistors/Mosfets, such as the IXYS DE275/375 series having only 2 - 4 nsec switching delay, a very efficient and almost phase lag free energy transfer between L2-L3 becomes feasible. Using high Q coils allows consequently for very high output voltages fed to the electrode E2. The sample is placed between the electrodes El - E2, using E2 as counter electrode that provides for a current return path.

Placing a dielectric such as glass between E1-E2 leads to a resonant circuit including L3 and the corresponding parallel coil capacitance C3 (not shown) having the capacitance forming across the material in parallel. In series with this latter C is the resistive electric arc. If the dielectric is significantly below its melting T, the quality factor of this L3 based resonant circuit is high and a high voltage is produced and a strong signal is fed-back to the gate via LI . With increasing substrate T and therefore substrate conductivity, the losses in this resonant circuit become larger, the quality factor as well as voltage and feedback-signal smaller. At a critical T, which is given by the properties of L3, LI and the coupling factor between them, the feedback signal will be too small to switch the transistor/Mosfet, which stops oscillation and therefore voltage/power output. Tuning of these parameters allows to set a specific T at which the systems stops power output. Once oscillations stopped, the gate voltage will raise again via the applied bias voltage. The resistor Roff and the gate

capacitance Cg form a low pass filter having a time constant on the order of Roff x Cg. Once this voltage exceeds the gate threshold voltage, the system will be excited again and oscillations can start if the load has been sufficiently reduced, i.e. the material conductance and T, respectively, have been reduced again. Adjusting the value of Roff allows for a simple adjustment of the off-time and the time it takes for power output again after reaching a pre-set material T, respectively. This system therefore allows for a simple yet efficient T feedback system.

Figure 3B shows a practical implementation of the scheme shown in Figure 3A. This generator oscillates at ca. 10 MHz and produces voltages »1000 Vpp. The self-capacitance of L3 is ca. 2.5 pF, L2 has a parallel capacitance of 250 pF. C6 represents the parasitic capacitance between L2 and L3. Electric arc and substrate are represented by Rl and CI, respectively. Voltages across the substrate/material and the electrode have been simulated. Figure 6 gives shows simulation results. The time constant for the off-time is controlled via R3 and R4. The coupling between the coils is given by the shown coupling factors kl , k2, k3. The transistor used was an IXYS Mosfet DE275, IXZ210N50L.

Figure 4 Left: Scanning Electron Microscope image of 0.7mm thick strengthened glass (central tension = 30 MPa) processed by electrothermal cutting. Right: optical image of the same material cut following a curved path (radius of curvature = 5mm) close to the edge.

Figure 5 shows schematically the use of an impedance matching network to control the complex output impedance of the HF HV generator. As shown, the impedance matching circuit (2) can be a separate circuit from the generator (1), connected by (12). The output of the impedance matching network is then fed to the electrodes (3, 3') that apply the voltage to the material (4). For practical purposes, the impedance matching network may be directly an integral part of the generator itself, e.g. by tuning the capacitance of the primary coil (L2 in figure 3 A, B) or the properties (L, C, Q, Rs) of the secondary coil (L3 in 3 A, B). Also the electrodes may become part of the impedance matching network, as well as the connections between the generator and electrodes. The practical realisation depends on the kind and properties of the HF HV generator used, the electrode design and environment (e.g. ground coupling etc) and distances and the material properties (dielectric properties, thickness, cutting speed).

Figure 6 shows the voltage across the material/substrate using the circuit shown in Figure 3B and Figure 7, assuming an arc resistance of 200 Ohm and a capacitance across the material of 200 fF. Sheath layers have been assumed non existent; the arc conductivity may vary over a relatively large area without reducing the voltage across the material significantly (e.g. a range of 0 - 5000 Ohm will have little effect on the substrate voltage). The voltage is largely defined by the capacitance forming across the substrate. An increase of CI to e.g. 1 pF will significantly reduce the output voltage; as CI is proportional to the material surface area touched by the arc, it is important to keep this area small. Shown is also the drain current which stabilizes at ca. 3 A as well as the arc/substrate current of ca 500 mApp.

Figure 7 shows an embodiment of the generator as it was developed for electrothermal cutting. It resembles the generator shown in Figure 3B but omits the circuit to control the off- time. Instead a high-pass filter is used (C3, R3, R2), producing an initial voltage spike at the gate upon turn-on, to start oscillation and power output. Depending on the cutting task the circuit in Figure 3B or Figure 7 may be chosen. Both circuits present a generic oscillator design that can be adapted to the specific cutting task, mostly by adjusting the supply voltage V2, the transistor Ml , the properties and coupling coefficients of the inductors, the frequency and the combination of electrode, arc and substrate properties (Rl , CI). Shown is also the parasitic capacitive coupling C6 between L3 - LI . Simulations show that this coupling influences the generator output voltage and impedance and therefore my be actively controlled (the same, albeit to a lesser extent, is also true for the other capacitive couplings between the inductors, which are not shown here).

Figure 8 shows the effect of the electrode material on the arc and plasma properties. (A) shows a nearly symmetric arc across a 0.1 mm thick soda lime glass substrate. Because of the high electrical and heat conductivity of the Cu (upper) and Ag (lower) electrode (tip) heat and electron emission from the tip is limited and only a faint arc is visible. In (B) the lower electrode is made of Pd, leading to a molten surface layer at the electrode tip and

consequently a higher temperature and electron emission from the tip. Consequently, the arc appears significantly more intense. The corresponding electrode properties suggests a significantly higher voltage transfer from the electrode tip to the substrate if compared to electrodes shown in (A). A substrate thickness of 0.7 mm was chosen to underline the effect of the electrode material; at 0.1 mm substrate thickness as in (A) the intensity of the arc is even more pronounced. Both setups used an air gap between electrode and substrate, a frequency of 20 MHz and a voltage of ca. 10 000- 30 000 Vpp.

Figure 9 shows the effect of varying the distance between the substrate surface and the electrodes. The substrate is 0.7 mm soda lime glass, the electrodes are made of Cu, f = 50 MHz, Vpp ca 5 000 - 20 000 V. Only one electrode shown, electrode distance to substrate shown to the right of the image. At substrate - electrode distances down to ca. 0.5 mm a significant heating of the electrode tip occurs, visible as an adjacent bright region. At lower distances the heated region moves to the side of the electrode tip. This leads to a reduced cutting performance (speed, occasionally precision) due to the degraded voltage and heat transfer to the substrate. At distances >2.1 mm the performance also decreases due to reduced heat transfer and increased voltage drop inside the arc. For this specific example, the optimum electrode distance for cutting is between ca. 1 - 2 mm. Figure 10 shows the combined effect of electrode distance variation and electrode material. Using highly pointed Pd electrodes (made of 1 mm diameter Pd wire) at 0.3 mm distance on the lower side from the substrate (0.7 mm thick soda lime glass), the very electrode tip still gets very hot and most likely molten thus that a high voltage and heat transfer to substrate surface occurs. To demonstrate the effect of electrode design and electrode distance, the lower Pd electrode was chosen to reach the melting temperature at the tip, while the upper electrode shape and substrate distance were chosen to keep the tip below this temperature. Using an electrode material such as Pd, very close distances between electrode and substrate surface provide for a focussed and effective/fast cutting. The electrode material and design may consequently be chosen according to the cutting requirements such as speed, accuracy, material thickness, electrical and mechanical properties. Choosing electrode materials among materials with lower heat conductivity such as Pd can improve heat and voltage transfer to the substrate.

The features of the present invention disclosed in the specification, the claims and/or in the accompanying drawings, may, both separately, and in any combination thereof, be material for realising the invention in various forms thereof.