Method for separating substrates

1. A method for separating a substrate made of brittle-hard material, comprising:

introducing defects into the substrate at a spacing from one another along a separation line using at least one pulsed laser beam;

setting a first reference stress (σ R1 ) according to a formula σ R1 ≤C R1 ·α·E·(T g −100° C.) and a second reference stress (σ R2 ) according to a formula σ R2 ≥C R2 ·α·E·(T g −100° C.),

wherein C R1 and C R2 are reference stress coefficients with C R1 =0.5/k and C R2 =0.5·k,

wherein k is 1.5,

wherein α is the coefficient of thermal expansion of the material of the substrate,

wherein E is the Young's modulus of the material of the substrate, and

wherein T g is the glass transition temperature of the material of the substrate;

selecting an average spacing between neighboring defects that is at least 3 μm and a number of laser pulses for generating a respective defect such that a breaking stress (σ B ) for separating the substrate along the separation line is smaller than the first reference stress of the substrate and such that an edge strength (σ K ) of the separation edge obtained after separation is greater than the second reference stress of the substrate; and

separating the substrate after introducing the defects by applying a stress along the separation line so as to provide resulting broken edges of the substrate along the separation line with an average roughness R a of less than 0.5 μm.

2. The method of claim 1 , setting the first reference stress (σ R1 ) and the second reference stress (σ R2 ) identical to one another and to a maximum thermal stress (σ th ) that depends on a material of the substrate.

3. The method of claim 2 , further comprising determining the maximum thermal stress (σ th ) according to a formula σ th =0.5·α·E·(T g −100° C.), wherein α is the coefficient of thermal expansion of the material of the substrate, E is the Young's modulus of the material of the substrate, and T g is the glass transition temperature of the material of the substrate.

4. The method of claim 1 , wherein, when the substrate is a chemically toughened substrate, the method comprises:

setting the first reference stress (σ R1 ) and the second reference stress (σ R2 ) identical to one another and to an inner tensile stress (σ CT ) that depends on properties of the chemically toughened substrate; and

determining the inner tensile stress (σ CT ) according to the formula σ CT =(σ CS ·d L )/(d−2d L ),

wherein σ cs denotes a surface compressive stress of the chemically toughened substrate, d L is a penetration depth of a preliminary stress, and d is a thickness of the chemically toughened substrate.

5. The method of claim 1 , wherein, when the substrate is a thermally toughened substrate, the method comprises:

setting the first reference stress (σ R1 ) and the second reference stress (σ R2 ) identical to one another and to an inner tensile stress (σ CT ) that depends on properties of the thermally toughened substrate; and

determining the inner tensile stress σ CT according to the formula σ CT =σ CS /2,

wherein σ cs denotes a surface compressive stress of the thermally toughened substrate.

6. The method of claim 1 , wherein the step of separating the substrate comprises moving a point of incidence of a laser radiation over the substrate along the separation line to cause the stress to be applied along the separation line.

7. The method of claim 1 , wherein the step of selecting the average spacing between neighboring defects comprises selecting the spacing of at most 10 μm.

8. The method of claim 1 , wherein the step of selecting the number of laser pulses comprises selecting from an interval [1, 20] or from an interval [2, 8].

9. The method of claim 1 , wherein, when the substrate is made of a material with a coefficient of thermal expansion in an interval [3·10 −6 K −1 , 4·10 −6 K −1 ], a Young's modulus in an interval [69 kN/mm 2 , 76 kN/mm 2 ], and/or a glass transition temperature in an interval [700° C., 800° C.], the step of selecting the average spacing and the number of laser pulses comprises selecting the average spacing from an interval [6 μm, 8 μm] and the number of laser pulses from an interval [7, 9].

10. The method of claim 1 , wherein, when the substrate is made of a material with a coefficient of thermal expansion in an interval [7·10 −6 K −1 , 8·10 −6 K −1 ], a Young's modulus in an interval [69 kN/mm 2 , 76 kN/mm 2 ], and/or a glass transition temperature in an interval [500° C., 600° C.], the step of selecting the average spacing and the number of laser pulses comprises selecting the average spacing from an interval [6 μm, 8 μm] and the number of laser pulses from an interval [1, 3].

11. The method of claim 1 , wherein, when the substrate is made of a material with a coefficient of thermal expansion in an interval [3·10 −6 K −1 , 4·10 −6 K −1 ], a Young's modulus in an interval [60 kN/mm 2 , 68 kN/mm 2 ], and/or a glass transition temperature in an interval [500° C., 600° C.], the step of selecting the average spacing and the number of laser pulses comprises selecting the average spacing from an interval [4 μm, 8 μm] and the number of laser pulses from an interval [7, 9].

12. The method of claim 1 , wherein, when the substrate is made of a material with a coefficient of thermal expansion in an interval [3·10 −6 K −1 , 4·10 −6 K −1 ], a Young's modulus in an interval [60 kN/mm 2 , 68 kN/mm 2 ], and/or a glass transition temperature in an interval [500° C., 600° C.], the step of selecting the average spacing and the number of laser pulses comprises selecting the average spacing from an interval [6 μm, 8 μm] and the number of laser pulses from an interval [3, 5].

13. The method of claim 1 , wherein the step of selecting the average spacing between neighboring defects comprises selecting the spacing to at most 8 μm.

14. The method of claim 1 , wherein the step of selecting the average spacing between neighboring defects comprises selecting the spacing from at least 5 μm to at most 8 μm.

15. The method of claim 1 , wherein the step of selecting the average spacing between neighboring defects comprises selecting the spacing from at least 7 μm and at most 8 μm.

16. A method for separating an untoughened substrate made of brittle-hard material, comprising:

introducing defects into the untoughened substrate at a spacing from one another along a separation line using a pulsed laser beam;

selecting an average spacing between neighboring defects and a number of laser pulses for generating the defects such that a breaking stress (σ B ) for separating the untoughened substrate along the separation line is smaller than a first reference stress (σ R1 ) of the untoughened substrate and such that an edge strength (σ K ) of the separation edge obtained after separation is greater than a second reference stress (σ R2 ) of the untoughened substrate;

setting the first reference stress (σ R1 ) and the second reference stress (σ R2 ) identical to one another and to a maximum thermal stress (σ th ), wherein the maximum thermal stress (σ th ) depends on a material of the untoughened substrate and is determined according to a formula σ th =0.5·α·E·(T g −100° C.), wherein α is a coefficient of thermal expansion of the material, E is a Young's modulus of the material, and T g is a glass transition temperature of the material; and

separating the untoughened substrate after introducing the defects by applying a stress along the separation line.

17. A method for separating a substrate made of brittle-hard material, comprising:

introducing defects into the substrate at a spacing from one another along a separation line using a pulsed laser beam, wherein the substrate is chemically toughened;

selecting an average spacing between neighboring defects and a number of laser pulses for generating the defects such that a breaking stress (σ B ) for separating the substrate along the separation line is smaller than a first reference stress (σ R1 ) of the substrate and such that an edge strength (σ K ) of the separation edge obtained after separation is greater than a second reference stress (σ R2 ) of the substrate;

setting the first reference stress (σ R1 ) and the second reference stress (σ R2 ) identical to one another and to an inner tensile stress (σ CT ), wherein the inner tensile stress (σ CT ) depends on properties of the substrate and is determined according to the formula σ CT =(σ CS ·d L )/(d−2d L ), wherein σ CS denotes a surface compressive stress of the substrate, d L is a penetration depth of a preliminary stress, and d is a thickness of the substrate; and

separating the substrate after introducing the defects by applying a stress along the separation line.