Method for dividing of monocrystalline layers, disks or wafers

0001The invention relates to a method for separating single-crystal wafers or parts thereof. In particular, the invention relates to a method for separating single crystals with self-adjusting crack propagation.

0002Single-crystalline wafers made of semiconducting materials are used as substrates for the production of microelectronic components such as field effect and heterobipolar transistors or optoelectronic components such as laser and luminescent diodes. The functional layers are deposited on these substrates by various methods such as CVD, MOCVD, LPE, MBE and optionally reworked or produced in the substrate by ion implantation. You then go through complex structuring processes using multiple exposure masks.

0003The substrate has a so-called orientation flat (OF) and an identification flat (IF) offset by 90 ° counterclockwise or counterclockwise for the alignment (adjustment) of the exposure masks and the necessary differentiation between front and back. The wafer normal and the surface normal of the flats are generally perpendicular to one another. Conventional manufacturing processes for wafers with flats involve creating the flats by means of grinding. The orientation accuracy of the orientation flat with respect to the crystallographic <110> direction is ± 1 ° for conventional wafer production, ± 5 ° for the identification flat, but this way it is also possible to reach ± ​​0.02 ° for the orientation flat. Flats produced by grinding can have disorientations and breakouts that structure along the flats and impair their function as a reference for the adjustment of exposure masks. This applies above all to the manufacture of laser diodes, to the highly precise and, moreover, trouble-free, sharp-edged flats with an orientation accuracy of ≤ | 0.02 ° | measured over a length relevant to this technology.

0004It is known that the orientation accuracy of the flats can be increased if they are produced instead of by grinding by splitting the generally brittle semiconductor materials using the natural splitting planes. For example, in III-V semiconductors, the {110} surfaces are natural gap surfaces. From the<patcit id="pcit0001" dnum="US5279077A"><text>US 5,279,077</text></patcit> and the <patcit id="pcit0002" dnum="US5439723A"><text>US 5,439,723</text></patcit> are known wafers with such flats produced by cleavage. From the<patcit id="pcit0003" dnum="US5154333A"><text>US 5,154,333</text></patcit> a device is known with which the cleavage is carried out over a defined bending stress of a wafer in which there is a crack germ produced by scratching. A disadvantage of a mechanical splitting device, however, is that the crack propagation cannot be controlled and a complex break mode is realized by the initialization of the break by a break germ on the wafer edge.

0005Alternatively, there are thermal separation processes that work with a combination of local heating and adjacent local cooling. A basic process is in<patcit id="pcit0004" dnum="DE2813302"><text>DE 28 13 302</text></patcit> described method for cutting flat glass using thermally induced stresses. In this method, glass is heated in one area on at least one of the two main surfaces within two areas that are sharply delimited and symmetrical to the cutting line, one after the other on the intended straight cutting line, and is cooled in the other area. The temperature gradients in the glass resulting from the thickness of the glass and in the direction of the cutting line cause thermal stresses which, starting from the edge marking, drive a crack perpendicular to the main surfaces along the intended straight cutting line, the crack propagation speed being controlled by regulating the applied temperatures and the advance of the heating / Cooling device is checked.

0006Out <patcit id="pcit0005" dnum="WO9320015A"><text>WO 93/20015</text></patcit> a method for separating semiconductor components is known. In this, a break is initiated by the formation of tensile stresses in an area between a heating laser beam and a subsequent cooling. The method is intended to control the shape, direction, depth, speed and accuracy of the fracture caused by thermal stresses.

0007Out <nplcit id="ncit0001" npl-type="s"><text>BELSINGER HE JR ET AL: "A fracture criterion for gallium arsenide wafers", ENGINEERING FRACTURE MECHANICS UK, Vol. 48, No. 2, May 1994 (1994-05), pages 199-205, XP002518266, ISSN: 0013-7944</text></nplcit>a method for separating semiconductor devices is known, wherein conditions for the separation of GaAs wafers are disclosed.

0008A feature of the known methods for separating brittle materials by crack propagation is the generation or the presence of an initial crack. A stress field is then generated in the vicinity of the crack tip using a suitable method, such as the mechanical bending stress mentioned above or with thermal action. This stress field leads to a complex stress on the crack front, which is characterized by the stress intensity factor K. If the field of tension is chosen that applies <maths id="math0001" num="(1.1)"><math display="block"><mi mathvariant="normal">K</mi><mo mathvariant="normal">></mo><msub><mi mathvariant="normal">K</mi><mi mathvariant="normal">C.</mi></msub><mo>,</mo></math><img file="EP2106331B1_D0001.tif" /></maths> where K_C. is the material-specific stress intensity factor, the crack length increases until the condition <maths id="math0002" num="(1.2)"><math display="block"><mi mathvariant="normal">K</mi><mo>≤</mo><msub><mi mathvariant="normal">K</mi><mi mathvariant="normal">C.</mi></msub></math><img file="EP2106331B1_D0002.tif" /></maths> is satisfied. K> K_C. is the progress condition for the separation process, which must be maintained continuously or at intervals until complete separation is achieved.

0009The crack propagation follows the principle of minimizing the free energy of the body to be separated. This means that the crack spreads in such a way that the mechanical energy release rate G is maximum in isotropic materials. In anisotropic materials, the principle of minimizing the effective surface energy 2γ competes in minimizing the total energy of the system during crack propagation_e of the separated areas with the principle of maximizing the mechanical energy release rate. <maths id="math0003" num="(1.3)"><math display="block"><mfrac><mi mathvariant="italic">you</mi><mi mathvariant="italic">dC</mi></mfrac><mo>=</mo><mn>2</mn><mo>⁢</mo><msub><mi>γ</mi><mi>e</mi></msub><mo>-</mo><mi>G</mi><mo>→</mo><mi mathvariant="italic">Min</mi></math><img file="EP2106331B1_D0003.tif" /></maths>where U is the total energy of the system and C is the area generated by crack propagation.

0010For the methods mentioned above, this means that with isotropic materials, the time and location-dependent stress fields control the course of the crack. In the presence of crystallographic fissure planes that are characterized by minimal effective surface energy, the crack propagation direction (G → max) forced by the stress fields compete with the directions of these crystallographic fissure planes that have a minimal effective surface energy. In practice, therefore, it is only possible to produce gap levels with steps and jumps into the neighboring network levels. This has a disadvantageous effect on technologically relevant gap areas, such as resonator areas of laser components and deviations in the orientation of split flats.

0011Theoretically, the production of absolutely flat gap surfaces would succeed if a flat tensile field is generated perpendicular to the desired gap plane. In this case, the stress fields and the splitting levels would be coordinated so that they do not compete with each other. These conditions cannot be met in practice. For the splitting of laser components, for example, it would require that the wafer be oriented with high precision to the splitting device in order to achieve sufficient quality of the splitting plane at least over the length of a laser component. Even with the smallest deviations in the wafer orientation with respect to the generated stress fields, steps at the slit level are unavoidable.

0012It is an object of the invention to provide a method for separating single crystals which avoids the disadvantages mentioned above and ensures exact splitting planes over the entire distance until the desired parts are completely separated.

0013The object is achieved by a method according to claim 1. Further developments of the invention are specified in the subclaims.

0014The method has the advantage that the previous determination and adjustment of the crystallographic splitting planes to the splitting device is only required with the usual accuracies. The exact orientation of the propagating crack is ensured by the process conditions according to the invention, which force a self-adjustment of the crack propagation direction in exactly one of the crystallographic fissure planes without steps and jumps.

0015Due to the invention, gap areas with accuracies in the range of ≤ [0.02 ° |, | 0.01 ° |, | 0.005 ° | or even | 0.001 ° | - measured over the extent of the technologically relevant area or a large number of partial areas thereof - achievable. The respectively technologically relevant area corresponds in the case of laser diodes to the length of a laser resonator, for example, or in the case of integrated circuits to the edge length of the chip to be separated. When the wafer is split off to form flats, it corresponds to the flat length. The production of a natural gap surface is also possible due to the self-adjusted gap proposed here.

0016The orientation accuracy of a separating surface with respect to a crystallographic network plane is measured by placing the crystal on a reference surface, with at least 2 points of the separating surface being used. The orientation of the crystallographic network plane with respect to this reference surface can then be determined with an X-ray goniometer. The network plane alignment is now related to the reference stop surface, which results in an angle difference, which represents the accuracy here.

0017The alignment of the separating surface with respect to the reference surface of the method used to determine the alignment of the network plane can be done in other ways besides by mechanical stop. B. done by optical methods.

0018In addition to determining the global orientation deviation of the gap surface of technologically relevant length produced in accordance with the method, a local orientation deviation can also be determined by dividing the technologically relevant length in partial lengths of z. B. 2 mm is divided and their alignment z. B. by means of an optical microscope, a miniature interferometer, a white light interferometer or an autocollimator. The orientation accuracy of the interface then corresponds to the largest of these measured local deviations.

0019The gap areas achieved by the invention are z. B. distinguishable by the LEED method as such from surfaces of a semiconductor wafer with a different orientation. , see. For this<nplcit id="ncit0002" npl-type="s"><text>Qian, GX, Martin, RM, Chadi, DJ, in Phys. Rev. B, Vol. 37, p.1303. (1988</text></nplcit>) or <nplcit id="ncit0003" npl-type="b"><text>Bechstedt, F. "Principles of Surface Physics", Springer Verlag; ISBN 978-3-540-00635-0, chapter 1.2.4; Pages 16-18</text></nplcit>. It is exploited that natural gap surfaces of III-V semiconductors only show a relaxed, but not a reconstructed arrangement of the near-surface atoms, as is the case for other orientations.

0020Further advantages and expediencies result from the description of an embodiment with reference to the figures. From the figures show:<dl id="dl0001"><dt>Fig. 1</dt><dd>is a schematic plan view of a wafer to be split;</dd><dt>Fig. 2</dt><dd>the energy release rate G and effective surface energy 2γ_e if a first condition is met;</dd><dt>Fig. 3</dt><dd>the energy release rate G and effective surface energy 2γ_e if a second condition is met;</dd><dt>Fig. 4</dt><dd>the energy release rate G and effective surface energy 2γ_e if a third condition is met;</dd><dt>Fig. 5</dt><dd>the energy release rate G and effective surface energy 2γ_e in compliance with his fourth condition;</dd><dt>Fig. 6</dt><dd>a first phase of crack propagation;</dd><dt>Fig. 7</dt><dd>a second phase of crack propagation, which is controlled by the relative movement of the stress fields (e.g. in isotropic materials);</dd><dt>Fig. 8</dt><dd>a phase of crack propagation in the event of a deviation from the desired splitting direction in the presence of a crystallographic splitting plane and asymmetrical adjustment of the stress fields to this;</dd><dt>Fig. 9</dt><dd>a phase of crack propagation in the desired splitting direction with ideally symmetrical adjustment of the stress fields to the splitting plane;</dd><dt>Fig. 10</dt><dd>a schematic representation of the orientation of the wafer in the splitting device;</dd><dt>Fig. 11</dt><dd>an example of the maximum error between the position and direction of the desired column plane for the direction of movement and the generated voltage fields in the start area;</dd><dt>Fig. 12</dt><dd>an example of the maximum error between position and direction of the desired column plane for the direction of movement and the generated tension fields in the target area;</dd><dt>Fig. 13</dt><dd>the energy release rate G_- and G₊ in the start or in the finish area depending on the angle α; and</dd><dt>Fig. 14</dt><dd>a phase of crack propagation in compliance with the conditions according to the invention.</dd></dl>

0021The invention is described below using the exemplary embodiment of cleaving a GaAs wafer by means of thermally induced voltage fields. First, the wafer is placed in a splitting device. The wafer is aligned with the splitting device on a previously applied marking, for example a short flat, which is sharpened, for example with the aid of X-ray diffractometry. In practice, an accuracy of the flat orientation to the {110} column plane of 0.1 ° can be achieved. Other markings or short flats perpendicular or in a specific relation to the splitting planes are also conceivable as a pre-adjustment aid. The pre-adjustment to the direction of movement can be carried out using stops or using optical methods.

0022How schematic out <figref idref="f0001">Fig. 1</figref> can be seen, an initial crack 2 is made in the GaAs wafer 1 in a {110} slit plane. Ideally, the initial crack 2 is introduced into a split plane that runs parallel to the preferred sliding direction of the α dislocations.

0023The initial crack 2 is generated, for example, by indentation using an indenter with a defined geometry (Vickers, Knoop-Indenter). Other geometries or scoring are also possible. By choosing the impression load and geometry, the formation of B cracks perpendicular to it can be avoided.

0024By means of thermally induced stress fields, a flat edge crack is produced in the {110} gap plane from the impression-induced crack, which serves as a flat initial crack for the further crack propagation or the desired gap direction or gap plane 2 '. In this phase, the thermally induced stress fields are dimensioned in such a way that the initial crack cannot spread any further.

0025A stress intensity K is then generated for crack propagation and the size G (α) is determined, which is the energy release rate for further crack propagation as a function of a deflection of the crack from the splitting plane by the angle α. The crack propagation can be viewed as a superposition of a twist (twist configuration) by the angle φ around an axis perpendicular to the crack front of the initial crack and a rotation by the angle θ around the crack front of the initial crack (tilt configuration). Both cases can be considered separately. The described method according to the invention applies to both cases, so that further reference to a deflection angle α is sufficient (with α = θ for tilt and α = φ for twist configuration). The exemplary embodiment is explained using the example of the tilt configuration without restricting the validity for the general case. The voltage intensity K is determined using known methods, such as the method according to FIG<patcit id="pcit0006" dnum="DE2813302"><text>DE 28 13 302</text></patcit> or the procedure of <patcit id="pcit0007" dnum="WO9320015A"><text>WO 93/20015</text></patcit> generated. One or more heat sources 4 and one or more heat sinks 3 (cf.<figref idref="f0006">Fig. 11</figref>, <figref idref="f0007">12</figref>, <figref idref="f0008">14</figref>) applied to one or both sides of the wafer, so that ideally there are symmetrical stress fields with regard to the wafer thickness and the desired splitting direction. The heat sources can e.g. B. by absorption of laser beams and the heat sinks by targeted application of cooling aerosols, such as in the<patcit id="pcit0008" dnum="WO9320015A"><text>WO 93/20015</text></patcit> is described. But other variants are also possible. The heat sources and sinks are controlled and positioned in such a way that crack propagation is made possible.

0026The dimensioning or control - or also regulation - of the stress fields takes place in such a way that the crack progresses continuously or at intervals, which is determined by G (0) ≥ 2 γ_e(0) is marked. According to the invention, the voltage fields are dimensioned or controlled in such a way that at least one of the following conditions is additionally present:<maths id="math0004" num="(2.1)"><math display="block"><msub><mfenced open="|" close="|"><mfrac><mrow><mo>∂</mo><mi>G</mi></mrow><mrow><mo>∂</mo><mi>α</mi></mrow></mfrac></mfenced><mrow><mi>α</mi><mo>=</mo><mn>0</mn></mrow></msub><mo>≤</mo><mn>2</mn><mo>⁢</mo><mfrac><msub><mi>β</mi><mi>e</mi></msub><mi>H</mi></mfrac><mspace width="1em" /><mi>if</mi><mspace width="1em" /><mfrac><mrow><msup><mo>∂</mo><mn>2</mn></msup><mo>⁢</mo><mi>G</mi></mrow><mrow><mo>∂</mo><msup><mi>α</mi><mn>2</mn></msup></mrow></mfrac><mo>≤</mo><mn>0</mn></math><img file="EP2106331B1_D0004.tif" /></maths> or <maths id="math0005" num="(2.2)"><math display="block"><mfenced open="|" close="|"><mfrac><mrow><mo>∂</mo><mi>G</mi></mrow><mrow><mo>∂</mo><mi>α</mi></mrow></mfrac></mfenced><mo>≤</mo><mn>2</mn><mo>⁢</mo><mfrac><msub><mi>β</mi><mi>e</mi></msub><mi>H</mi></mfrac><mspace width="3em" /><mo>∀</mo><mi>α</mi><mo>:</mo><msub><mi>α</mi><mn>1</mn></msub><mo>&lt;</mo><mi>α</mi><mo>&lt;</mo><msub><mi>α</mi><mn>2</mn></msub></math><img file="EP2106331B1_D0005.tif" /></maths> are fulfilled.

0027There are<dl id="dl0002" compact="compact"><dt>α</dt><dd>Possible deflection angle when the crack progresses from the splitting plane</dd><dt>α₁, α₂</dt><dd>Angular range in which the necessary condition for crack propagation (1.1) is guaranteed</dd><dt>G (α)</dt><dd>Energy release rate as a function of a deflection of the crack from the splitting plane by the angle α.</dd><dt>γ_e(0)</dt><dd>effective surface energy of the gap surface</dd><dt>γ_e</dt><dd>directional effective surface energy</dd><dt>β_e</dt><dd>effective step energy (material-specific)</dd><dt>H</dt><dd>Step height (material-specific).</dd></dl>

0028The effective free surface energy γ_e, which is known from fracture mechanics, is determined in fracture experiments from the relationship between fracture strength and crack length. It contains γ compared to the intrinsic surface energy_s also energy components of dissipative processes. These include, for example, the formation of dislocations in the process or plastic zone, the emission of sound energy or the occurrence of dissipative structures (fracture structures) on the fracture surfaces. It is therefore larger than the intrinsic surface energy γ_s.

0029For the specific free step energy one finds the following approximation in the thermodynamic equilibrium: <maths id="math0006"><math display="block"><msub><mi>β</mi><mi>e</mi></msub><mo>=</mo><mo>-</mo><mi>n</mi><mo>⁢</mo><msub><mi>k</mi><mi>B</mi></msub><mo>⁢</mo><mi>T</mi><mspace width="1em" /><mi>ln</mi><mo>⁢</mo><mi>η</mi><mo>⁢</mo><mfenced><mn>1</mn><mo>+</mo><mn>2</mn><mo>⁢</mo><mi>η</mi></mfenced><mo>,</mo><mspace width="2em" /><mi>η</mi><mo>=</mo><mi>exp</mi><mfenced><mo>-</mo><mi>ε</mi><mo>/</mo><msub><mi>k</mi><mi>B</mi></msub><mo>⁢</mo><mi>T</mi></mfenced><mn>.</mn></math><img file="EP2106331B1_D0006.tif" /></maths> In it mean: n - step density with n = 1 / a, k_B - Boltzmann constant, ε - binding energy between nearest neighbors in the crystal lattice, a - distance of the building blocks in the step.

0030The binding energy ε can be derived from the sublimation energy ΔH_sub(T) of the crystal ("congruent evaporation") and the coordination number Z of the crystal under consideration: <maths id="math0007"><math display="block"><mi mathvariant="normal">ε</mi><mo mathvariant="normal">≈</mo><msub><mi mathvariant="normal">ΔH</mi><mi>sub</mi></msub><mo mathvariant="normal">/</mo><mi mathvariant="normal">Z.</mi><mo>,</mo></math><img file="EP2106331B1_D0007.tif" /></maths> ΔH_sub(T) is obtained from a calculation of the thermodynamic equilibrium X_s ⇔ X_G with the thermodynamic data of the solid (s) and gaseous (g) phase X.

0031The free step energy can also be determined experimentally.

0032The following values ​​can be assumed for GaAs:

0033The effective free surface energy of GaAs {110} cleavage surfaces results from fracture experiments on γ_e(0) ≈ (0.86 ± 0.15) J / m². Known investigations in the area of ​​the crack front ensured that dissipative processes can be neglected, i.e. the measured effective free surface energy, i.e. the intrinsic surface energy γ_s(0) ≈ 0.82 J / m², which results from crystal growth.

0034For GaAs {110} / <001>, ie <001> oriented steps on a {110} gap surface with a tilt axis parallel to <001>, the step energy was estimated with the following data: ΔH_sub(300 K) = 451.4 kJ / mol, Z = 4 ⇒ ε ≈ 1.17 eV and for T = 300 K η ≈ 45.25.

0035The distance between the atoms in a <001> parallel step is a_O = 0.565325 nm, the height of a double step is h = a_O/ √2 = 0.399 nm. This gives the free step energy from the above formula: <maths id="math0008"><math display="block"><msub><mi mathvariant="normal">β</mi><mi mathvariant="normal">e</mi></msub><mo>≈</mo><mn mathvariant="normal">3</mn><mo mathvariant="normal">,</mo><mn mathvariant="normal">31</mn><mo>⁢</mo><mi mathvariant="normal">x</mi><mo>⁢</mo><msup><mn mathvariant="normal">10</mn><mrow><mo mathvariant="normal">-</mo><mn mathvariant="normal">10</mn></mrow></msup><mspace width="1em" /><mi mathvariant="normal">J</mi><mo mathvariant="normal">/</mo><mi mathvariant="normal">m</mi></math><img file="EP2106331B1_D0008.tif" /></maths> and <maths id="math0009"><math display="block"><msub><mi mathvariant="normal">β</mi><mi mathvariant="normal">e</mi></msub><mo>/</mo><mi mathvariant="normal">H</mi><mo mathvariant="normal">≈</mo><mn>0.83</mn><mspace width="1em" /><mi mathvariant="normal">J</mi><mo mathvariant="normal">/</mo><msup><mi mathvariant="normal">m</mi><mn>2</mn></msup></math><img file="EP2106331B1_D0009.tif" /></maths>

0036This value is roughly in line with the intrinsic free surface energy γ_s ≈ 0.82 J / m² a {110} gap surface.

0037The same statement applies to the free step energy as to the surface energy. The experimental effective step energy can be larger than that estimated here due to dissipative components. With the specification of the theoretically determined step energy, the right side is known in conditions (2.1) and (2.2),

0038The stress fields under the selected conditions of the heat sources and sinks are calculated by simulation calculations. However, the voltages can also be measured directly, for example by means of stress birefringence, ultrasound microscopy or micro-Raman spectroscopy. From this, the energy release rate is calculated for the given stress field depending on possible deflections of the crack by the angle α. By controlling and positioning the heat sources and sinks, the voltage fields are set so that the above-mentioned conditions according to the invention are met.

0039There is an angular range α₁ &lt;α &lt;α₂, in which the condition G ≥ 2γ_e is satisfied. This range depends on the stress fields and the material properties as well as the misalignment of the splitting device used from the splitting plane to be separated. In the angular range between α₁ and α₂ the necessary condition (1.1) for crack propagation is fulfilled. The control or dimensioning of the stress intensity K according to the invention to ensure compliance with the conditions (2.1) or (2.2) ensures that the crack is nevertheless not in the region α₁ &lt;α &lt;α₂ is deflected, but runs over the entire distance to be separated in the desired column plane.

0040The unavoidable misalignment of the splitting device, or a tension intensity K with mixed crack opening modes K_I. + K_II + K_III, generates a curve of the energy release rate G (α) which is asymmetrical with respect to the desired crack propagation direction in the splitting plane α = 0 as a function of possible deflection angles α. Furthermore, the crack spreads in the direction where the size<i>G</i> = <i>G</i> - 2γ_e maximum. The control or dimensioning of the stress intensity K according to the invention to ensure compliance with conditions (2.1) or (2.2) ensures that even when the splitting device is misaligned, or a stress intensity K with mixed crack opening modes K_I. + K_II + K_III the maximum of size g is always α = 0. As a result, the crack propagation in the desired network level is forced by self-adjustment of the crack propagation direction. This enables crystallographic slit surfaces with high orientation accuracy in the range of at least ≤ | 0.01 ° |, ≤ | 0.005 ° | or even generate ≤ | 0.001 ° |. Furthermore, crystallographic gap areas with a minimum step density, ideally without steps, can be generated over the entire technologically relevant area (flats, resonator areas, etc.).

0041Two situations in which the conditions according to the invention are met are in <figref idref="f0002">2 and 3</figref> shown.

0042<figref idref="f0002">Fig. 2</figref> shows the energy release rate G and effective surface energy 2γ_e and g = G - 2γ_e if the condition is met <maths id="math0010"><math display="inline"><msub><mfenced open="|" close="|"><mfrac><mrow><mo>∂</mo><mi>G</mi></mrow><mrow><mo>∂</mo><mi>α</mi></mrow></mfrac></mfenced><mrow><mi>α</mi><mo>=</mo><mn>0</mn></mrow></msub><mo>≤</mo><mn>2</mn><mo>⁢</mo><mfrac><msub><mi>β</mi><mi>e</mi></msub><mi>H</mi></mfrac></math><img file="EP2106331B1_D0010.tif" /></maths> and <maths id="math0011"><math display="inline"><mfrac><mrow><msup><mo>∂</mo><mn>2</mn></msup><mo>⁢</mo><mi>G</mi></mrow><mrow><mo>∂</mo><msup><mi>α</mi><mn>2</mn></msup></mrow></mfrac><mo>≤</mo><mn>0</mn><mspace width="1em" /><mo>∀</mo><mi>α</mi><mo>:</mo><msub><mi>α</mi><mn>1</mn></msub><mo>&lt;</mo><mi>α</mi><mo>&lt;</mo><msub><mi>α</mi><mn>2</mn></msub></math><img file="EP2106331B1_D0011.tif" /></maths>.

0043<figref idref="f0002">Fig. 3</figref> shows the energy release rate G and effective surface energy 2γ_e and g = G - 2γ_e if the condition is met <maths id="math0012"><math display="inline"><mfenced open="|" close="|"><mfrac><mrow><mo>∂</mo><mi>G</mi></mrow><mrow><mo>∂</mo><mi>α</mi></mrow></mfrac></mfenced><mo>≤</mo><mn>2</mn><mo>⁢</mo><mfrac><msub><mi>β</mi><mi>e</mi></msub><mi>H</mi></mfrac><mspace width="1em" /><mo>∀</mo><mi>α</mi><mo>:</mo><msub><mi>α</mi><mn>1</mn></msub><mo>&lt;</mo><mi>α</mi><mo>&lt;</mo><msub><mi>α</mi><mn>2</mn></msub></math><img file="EP2106331B1_D0012.tif" /></maths>.

0044With the method, surfaces such as flats with an orientation accuracy of 0.01 ° - measured over lengths of the respective technologically relevant surfaces - can be attached to the wafer, ie the accuracy that can be achieved in practice by a grinding process is reduced by increased an order of magnitude. The method ensures that the adjustment accuracy between the direction of movement and the splitting plane of 0.1 ° is sufficient to force the crack propagation in the splitting plane with an accuracy of ≤ 0.01 °. Initial results show that accuracies of ≤ 0.005 ° or even ≤ 0.001 ° are possible. Finally, the completely step-free, ideal gap area is also possible, which then extends along the natural crystallographic plane.

0045<figref idref="f0003">4 and 5</figref> show situations in which there is a misalignment of the splitting device or a stress intensity K with mixed crack opening modes and the conditions according to the invention are not met.

0046<figref idref="f0003">Fig. 4</figref> shows the energy release rate G and effective surface energy 2γ_e and g = G - 2γ_e With <maths id="math0013"><math display="inline"><msub><mfenced open="|" close="|"><mfrac><mrow><mo>∂</mo><mi>G</mi></mrow><mrow><mo>∂</mo><mi>α</mi></mrow></mfrac></mfenced><mrow><mi>α</mi><mo>=</mo><mn>0</mn></mrow></msub><mo>></mo><mn>2</mn><mo>⁢</mo><mfrac><msub><mi>β</mi><mi>e</mi></msub><mi>H</mi></mfrac></math><img file="EP2106331B1_D0013.tif" /></maths>. In<figref idref="f0003">Fig. 4</figref> crack propagation occurs at α = <i>α_f</i> ie the crack deviates from the desired splitting direction α = 0. Steps or curved surfaces are created on the generated surface. The technologically relevant surfaces (flats, resonator surfaces) do not have the desired orientation accuracy or quality.

0047<figref idref="f0003">Fig. 5</figref> shows the energy release rate G and effective surface energy 2γ_e and g = G - 2γ_e With <maths id="math0014"><math display="inline"><mfenced open="|" close="|"><mfrac><mrow><mo>∂</mo><mi>G</mi></mrow><mrow><mo>∂</mo><mi>α</mi></mrow></mfrac></mfenced><mo>></mo><mn>2</mn><mo>⁢</mo><mfrac><msub><mi>β</mi><mi>e</mi></msub><mi>H</mi></mfrac><mspace width="1em" /><mi>f</mi><mo>⁢</mo><mover><mi mathvariant="normal">u</mi><mo>¨</mo></mover><mo>⁢</mo><mi>r</mi><mspace width="1em" /><mi>α</mi><mo>></mo><msub><mi>α</mi><mi>G</mi></msub></math><img file="EP2106331B1_D0014.tif" /></maths>. In<figref idref="f0003">Fig. 5</figref> the crack progression is not stable at α = 0. If the angle α ≥ α is exceeded<i>_G</i> the course of the crack deviates from the desired plane α = 0.

0048The <figref idref="f0004 f0005">Figures 6 to 9</figref> show different cases of crack propagation in the wafer. By controlling and positioning the heat sources and heat sinks, a compressive stress maximum 4 'and a tensile stress maximum 3' are generated. The heat sources and sinks are positioned such that the compressive stress maximum 4 'in front of the crack tip 5 is positioned in the direction of propagation and the tensile stress maximum 3' behind the crack tip 5, as in FIG<figref idref="f0004">Fig. 6</figref> is shown. In the area between tensile and compressive stress maxima at time t = t₀ at a certain position P (0) the condition <i>K</i> = <i>K_c</i> or. <i>G</i> = 2γ<i>_e</i> Fulfills. By relative movement between temperature fields and wafers, which in<figref idref="f0004">Fig. 7</figref> is indicated by arrow 6, the conditions (1.1) <i>K</i> > <i>K_c</i> or. <i>G</i> > 2γ<i>_e</i> or (1.2) <i>K</i> ≤ <i>K_C.</i> or. <i>G</i> ≤ 2γ<i>_e</i> can be checked, ie the crack tip 5 can be felt, stopped in a targeted manner or moved on. The relative movement can take place through the movement of the heat sources and sinks (laser focus and cooling nozzles) or else through a movement of the wafer or a combination of both. Dissipative or dynamic effects can be avoided by controlling the speed of propagation. The speed of propagation can be chosen to be sufficiently low that quasi-static crack propagation and thermodynamic equilibrium can be assumed (v «1/3 of the speed of sound). The course of the crack follows the relative movement 6 between the stress fields and the wafer 1. This is used in the prior art to cut even complicated geometries, which can be straight or curvilinear.

0049In the presence of crystallographic cleavage planes, during the relative movement 6 between the stress fields and the wafer, as described above, the influence of the cleavage planes with that of the stress fields 3 'and 4' or the cleavage direction 2 'compete with the direction of movement 6 of the device during crack growth together. This situation is in<figref idref="f0005">Fig. 8</figref> shown. With an infinitesimal relative movement 6 µm<i>dr̅</i> due to the energy principle (1.3), the crack is generally around the angle α_f distracted. That corresponds to the situation in<figref idref="f0003">Fig. 4</figref>. The crack tip is at position P (t₀+ dt) where the condition <i>G</i>(α<i>_f</i>) = 2γ<i>_e</i> (α<i>_f</i>) after a time t = t₀+ dt is reached (quasi-static crack propagation). In this way, undesirable steps are generally generated on the splitting levels or deviations from the desired splitting direction occur.

0050In order to avoid competition between the splitting direction and the stress fields, the maximum tensile stresses should ideally be perpendicular to the desired splitting plane according to known fracture mechanics principles. In order to best achieve this situation, an ideally symmetrical adjustment of the voltage fields 4 'and 3' (ie heat source or sink) to the splitting plane would have to be carried out, which also during the entire separation process, ie over distances of the diameter of a GaAs wafer must be maintained. This means that the direction of movement 6 of the device must also be adjusted ideally parallel to the splitting plane 2 'and to the line of symmetry of the voltage fields. This situation is in<figref idref="f0005">Fig. 9</figref> shown. After a relative move around<i>dr̅</i> the crack tip remains at position P (t₀+ dt) on which the condition <i>G</i>(0) = 2γ<i>_e</i> (0) after a time t = t₀+ dt is reached. That means the crack runs in the crevice level. However, this ideal situation cannot be achieved in practice. This would require the measurement and adjustment of the splitting plane to the heat sources and sinks as well as to the direction of movement of the device with very high precision, which cannot be achieved from a production and economic point of view. With the help of the invention, however, an area is generated which is oriented with very high accuracy.

0051<figref idref="f0006">Fig. 10</figref> shows the orientation of the wafer 1 in the splitting device. As described above, there is usually a marking or a short flat 7, which is ground with a certain orientation tolerance to the crystallographic directions. Under practical conditions, an accuracy of the flat orientation 8 to the {110} column planes of 0.1 can be achieved with reasonable effort. The flat 7 is pre-adjusted to the direction of movement 6 of the relative movement between the voltage fields and the wafer. With the separation method according to the invention, a surface (flat) with an orientation accuracy of ≤ | 0.01 ° | attached, ie the accuracy that can be achieved in practice by a grinding process increased by an order of magnitude. The method according to the invention ensures that the adjustment accuracy between the direction of movement 6 and the splitting plane 2 'of 0.1 ° is sufficient to force the crack propagation in the splitting plane with an accuracy of at least ± 0.01 °. This can happen from the wafer edge 9 to the opposite wafer edge 9 or there can be a certain area 10 within which the requirement of the orientation accuracy of the flat 11 to be produced must be met. The size and geometry of this area 10 can vary and depends on different technological requirements. Accuracies of ≤ | 0.005 ° | or even ≤ | 0.001 ° | are also possible, as well as exactly stepless splitting along the crystallographic level.

0052Using simulation calculations in advance, the stress fields are preferably calculated under the selected conditions of the heat sources and sinks. The simulation is carried out in the areas at the intended start and end point of the separation process. This can happen, for example, at the edges of the technologically used area 10 in areas 12 and 13. The initial crack 2 introduced by the above-described method is present in the column plane at the edge of the start area 12, preferably outside the area 10. However, other positions are also possible. The proportions in<figref idref="f0006">Fig. 10</figref> are not to scale and are exaggerated to illustrate the situation. The known measuring accuracies (for example in X-ray diffractometry), the known tolerances during grinding and the known positioning accuracies determine the maximum possible error during the pre-adjustment of the wafer. For example, with the aid of simple geometric relationships, it is possible to determine the maximum error between the position and direction of the desired slit plane with respect to the direction of movement 6 and the generated voltage fields 3 'and 4' in the start and target area of ​​the separation process 12 and 13. <figref idref="f0006">Fig. 11</figref> shows an example of the maximum error in the start area 12. <figref idref="f0007">Fig. 12</figref> shows an example of the maximum error in the target area 13. But mirrored positions are also possible.

0053With the given stress fields in the start position 12 of the crack tip 5 of the initial crack, the energy release rate for the case of infinitesimal crack propagation can be calculated depending on possible deflections by the angle α. The same can be calculated in the planned target area 13 on the assumption that the crack has not left the gap level 2 '. This creates two functions G_-(α) and G₊(α), which are given by the known maximum errors in the start and target positions. The true function G (α) is not known, but it represents a state between G_-(α) and G₊(α).

0054By dimensioning and positioning the heat sources and sinks, the voltage fields are now set so that the conditions according to the invention <maths id="math0015" num="(3.1.)"><math display="block"><msub><mfenced open="|" close="|"><mfrac><mrow><mo>∂</mo><mi>G</mi></mrow><mrow><mo>∂</mo><mi>α</mi></mrow></mfrac></mfenced><mrow><mi>α</mi><mo>=</mo><mn>0</mn></mrow></msub><mo>≤</mo><mn>2</mn><mo>⁢</mo><mfrac><msub><mi>β</mi><mi>e</mi></msub><mi>H</mi></mfrac></math><img file="EP2106331B1_D0015.tif" /></maths> and <maths id="math0016" num="(3.2)"><math display="block"><mfrac><mrow><msup><mo>∂</mo><mn>2</mn></msup><mo>⁢</mo><mi>G</mi></mrow><mrow><mo>∂</mo><msup><mi>α</mi><mn>2</mn></msup></mrow></mfrac><mo>≤</mo><mn>0</mn></math><img file="EP2106331B1_D0016.tif" /></maths> for both functions G_-(α) and G₊(α) are satisfied. This ensures that the conditions according to the invention are also fulfilled for each intermediate state G (α) and that the crack remains in its splitting plane during the entire separation process.

0055<figref idref="f0007">Fig. 13</figref> shows an example of a balanced situation. With compliance with the condition according to the invention for both functions G_-(α) and G₊(α) the function g also has its maximum at α = 0 in all possible (unknown) intermediate states during the separation process and a self-adjustment of the crack in the splitting plane is guaranteed for the entire separation process between the start and the target position. A deflection of the crack as in<figref idref="f0004">Fig. 7</figref> is shown is suppressed and the crack tip moves t = t at every point in time of the separation process_n+ dt in the splitting direction α = 0, as in <figref idref="f0008">Fig. 14</figref> is shown.

0056The calculation of the functions G_-(α) and G₊(α) and the comparison of the voltage fields is also iterative and possible for all possible combinations of known maximum errors in the pre-adjustment. The control and dimensioning of the voltage fields is easily possible with the known methods, for example by controlling the laser power and / or varying the laser focus and / or arranging the cooling nozzles to form the laser spot. But other possibilities are also conceivable.

0057The method can also be carried out in such a way that in the step of checking the conditions (2.1) or (2.2) a maximum permissible angular range α₁ &lt;α &lt;α₂ is determined. The following must apply in this area:<maths id="math0017"><math display="inline"><mfrac><mrow><msup><mo>∂</mo><mn>2</mn></msup><mo>⁢</mo><mi>G</mi></mrow><mrow><mo>∂</mo><msup><mi>α</mi><mn>2</mn></msup></mrow></mfrac><mo>≤</mo><mn>0</mn></math><img file="EP2106331B1_D0017.tif" /></maths> in the case of condition (2.1) or <i>G</i>(α) ≥ 2γ<i>_e</i>(α) in the case of condition (2.2). The angular range determined is compared with a previously known and now predefined possible adjustment error of an alignment of the crystallographic column plane (2 ') relative to the separating device. The control of the voltage fields (3 ', 4') and / or the adaptation of the pre-adjustment is then carried out as a function of the comparison.

0058The invention is not limited to the separation of GaAs wafers, which is described as an exemplary embodiment. It is applicable to all single crystals. Approximate numerical values ​​for CaF₂ (111) area are for example γ_s ≈ 0.47 J / m² (<i>from initio</i> Hartree-Fock calculations) and β_e ≈ (3.31 - 6.8) x10^-10 J / m and with h = 0.32 nm: β_e/ h ≈ (1.03 - 2.13) J / m².

0059Furthermore, the invention relates not only to the cutting of slices, wafers or parts thereof to form flats. In particular, the separation of single crystals is also included in the invention, which has previously been coated, for example epitaxially or as part of deposition processes, and, if appropriate, were structured lithographically, and / or from which integrated circuits or opto-electronic components, in particular laser or luminescent diodes, were / are then produced.

0060Furthermore, the invention is also applicable to single crystals which have been formed as single-crystal layers on a single-crystal substrate. The layer and the substrate can be made of the same or a different material.

0061In the exemplary embodiment, a special arrangement of the stress fields was described, namely the crack front was held in the stress field between the temperature sink and the temperature source. However, the invention is not limited to this special arrangement. For example, stress fields can also be provided only by a temperature source or only by a temperature sink, and / or the crack front is not behind but in front of this sink or source.

0062The invention can also be implemented as a computer program product which is set up to carry out and control the steps according to one of the attached method claims.