Patent Description:
The advent of ultrafast pulsed laser sources (with pulse durations <<NUM> ps) enabled laser welding technologies for selectively bonding two workpieces in the spatial region around the interface between the two workpieces. Typical materials involved in such laser welding technologies are transparent materials:.

However, to date no laser welding involving a semiconductor material and an opaque material - especially silicon on metal - has been demonstrated. Such a laser welding technology would pave the way for three-dimensional (3D), fast and contactless fabrication of a broad range of devices in microelectronics, micromechanics, photovoltaics, Internet-of-Things (IoT) sensors, etc..

Two main reasons can be identified for the fact that such a welding technology does not exist until today. A first reason is that most semiconductor materials are transparent in the near- and mid- infrared region of the electromagnetic spectrum only. High-power ultrashort pulse lasers emitting light in this spectral region have emerged only very recently with the development of, e.g., optical parametric amplifiers, and fiber lasers (e.g., Er-doped, Tm-doped). Secondly, unlike for transparent materials, recent investigations have demonstrated that inducing permanent modifications with ultrashort pulses inside semiconductors or at their exit surface is extremely challenging (see for example <NPL>). This uncommon material behavior mainly results from the competition between the Kerr-induced self-focusing effect on the one hand, and plasma absorption and defocusing effects on the other hand (see for example M. As a consequence, the maximum energy deposited in the material is not only saturated but also strongly delocalized (see for example <NPL>).

<CIT> discloses a system for laser welding of two workpieces, in which the focus of the laser beam is varied along the beam direction. A measuring unit is provided that measures a displacement of the focus. On this basis, the laser beam passing through one of the workpieces is controlled to have its focal point in the common surface of the two workpieces. The energy of the laser beam thus melts material of the two workpieces, and the two workpieces are welded together.

From the foregoing it is readily appreciated that there is a need for an improved laser welding technique. It is an object of the invention to provide a reliable, repeatable and reproducible approach for laser welding of two workpieces one of which consists of a semiconductor material.

In accordance with the invention, a method for welding a first workpiece to a second workpiece by means of a laser is disclosed. The method comprises the steps of:.

A permanent modification at the interface between the two workpieces is achieved by the approach of the invention with the exit surface of the semiconductor workpiece being mechanically and/or optically in contact with the second workpiece. The laser flux is absorbed to a maximum extent at the interface between the two workpieces as a re-localization procedure of the intensity maximum is performed so as to compensate for the nonlinear propagation of the laser beam through the semiconductor workpiece. The laser welding process is optimized by this approach in terms of bonding strength.

The method of the invention is divided into two main sections. In the first, preparatory section, the first workpiece is irradiated with the pulsed laser radiation with the radiation being focused at the exit surface of the first workpiece, which is to form the interface with the second workpiece. Due to the nonlinear interaction of the laser pulses with the transparent semiconductor material an intensity delocalization occurs, i.e., a shift of the intensity maximum along the beam path to a position upstream of the actual geometric focus at the exit surface. This delocalization is determined in the first section of the method of the invention, e.g. by measuring the variation of the intensity of the irradiated laser radiation along the beam path to find the position of maximum intensity within the first workpiece. In the second section, the actual welding process takes place. To this end the second workpiece is placed against the first workpiece at its exit surface. The two workpieces may be maintained in position either with or without a suitable assembling method such as optical contact or mechanical fixture (e.g., glue). The focus of the laser beam is re-positioned along the beam path taking the measured delocalization into account such that the intensity maximum is located precisely in the plane of the interface between the two workpieces. The assembly of the two workpieces is then irradiated in this corrected configuration such that the delocalization is compensated for, and the two workpieces are firmly bonded.

The term "welding" within the meaning of the invention refers to any process providing a laser-induced bond between the two workpieces, i.e. a force maintaining the two workpieces in mechanical contact.

According to a preferred embodiment, the laser radiation is formed by a single pulse or a pulse train with a pulse duration between <NUM> fs and <NUM> ns. A pulse train is defined as a group of several individual pulses temporally separated. For simplicity, the term "pulse" is used herein both for a laser irradiation constituted by a single laser pulse or a train of laser pulses. The intensity of a single pulse is defined as I=2E/[τπ(w<NUM>)<NUM>], where E in the pulse energy, τ is the pulse duration taken at full-width at half-maximum, w<NUM> is the beam radius at the focus (taken at an intensity drop of <NUM>/e<NUM>) in the case of a bell-shaped beam (e.g., a Gaussian beam). If the laser irradiation is constituted by a pulse train, the duration of the irradiation corresponds to the time interval starting with the maximum intensity of the first laser pulse and ending with the maximum intensity of the last laser pulse; and the pulse energy is defined as the average power during the train multiplied by the duration of the train.

According to another preferred embodiment, the parameters of the laser radiation, specifically the spectrum, the pulse duration, the beam size, as well as the pulse energy, are identical during the determination of the delocalization and during welding the first workpiece to the second workpiece. By choosing identical parameters during the first (preparatory) and second (welding) section of the method of the invention it is made sure that the determined delocalization of the intensity maximum corresponds to the delocalization during the actual welding procedure. In other words, the selection of identical radiation parameters during both sections ensures that the intensity maximum of the laser radiation is located precisely at the interface between the two workpieces so as to obtain an optimal bond.

According to yet another preferred embodiment, the material of the second workpiece is opaque at the wavelength of the laser radiation. The method of the invention is particularly well suited for welding a transparent semiconductor material to material (e.g. a metal) that is opaque at the wavelength of the laser radiation. In this case, the laser radiation is absorbed at the interface between the two workpieces and thus induces a material modification during the welding process. Transparency and opacity of a workpiece are defined by comparing the photon energy of the laser radiation (at a given wavelength) with the band gap of the material of the respective workpiece. The term "semiconductor" refers to a band gap material, i.e., a material with a valence band and a conduction band separated by an energy range where no electron state exists (in the ideal case of defect-free semiconductor) and where the Fermi level is located. Both the valence and the conduction band are close enough to this level so they are populated with electrons or holes. Defining the photon energy hc/λ of the laser radiation employed for the laser welding process, where h≈<NUM>×<NUM>-<NUM> J·s is the Planck's constant, c=<NUM>×<NUM><NUM> m/s is the speed of light in vacuum, and λ is the laser wavelength (expressed in meters), the band gap of the semiconductor material Δ<NUM> (expressed in Joules), and the band gap of the opaque material Δ<NUM> (expressed the same units as Δ<NUM>), the wavelength λ of the laser radiation is preferably selected in the interval satisfying: <MAT>.

In the following, for sake of convenience, the band gap values are given in electron-volts (<NUM> eV ≈ <NUM>,<NUM> ×<NUM>-<NUM> J). The method of the invention can advantageously be applied, for example, for welding a silicon workpiece (Δ<NUM>=<NUM> eV) to a copper workpiece (Δ<NUM>=<NUM> eV) at λ=<NUM>, or for welding a silicon workpiece (Δ<NUM>=<NUM> eV) to a germanium workpiece (Δ<NUM>=<NUM> eV) at λ=<NUM>.

The placing of the second workpiece against the first workpiece may involve an optical contact, a loose stacking, or a mechanical fixturing, as appropriate in terms of workpiece condition, i.e., surface roughness, workpiece size etc..

Preferably, the assembly formed by the two workpieces is relatively moved in a plane perpendicular with respect to the laser beam during the welding process to create a welding pattern. The number of laser pulses per welding point of the welding pattern may be controlled by controlling the repetition rate of the laser and/or the speed of the relative movement of the laser beam and the workpieces during welding. Moreover, the beam size at the interface between the two workpieces and the laser intensity per pulse may be varied for optimizing the bonding force between the two workpieces. For example, a gradual increase of the laser intensity at the interface between the two workpieces starting from a predetermined value may be useful to obtain a maximum bonding force. A multi-scan welding procedure may be useful, with or without a variation of the laser intensity between different scans of the same zone at the interface between the two workpieces.

More generally, the focus of the laser radiation is moved along the interface between the two workpieces to create a welding pattern. This may involve a simultaneous relative movement of the laser beam and the assembly of the two workpieces along the optical axis as well as along the axes perpendicular thereto.

The method of the invention described thus far can be carried out by means of a system for welding a first workpiece to a second workpiece, comprising:.

The positioning device enables the intensity maximum of the laser radiation to be positioned at the interface between the two workpieces based on the determined delocalization of the focus. The positioning device further enables the relative movement of the assembly of the two workpieces in the plane perpendicular to the laser beam during welding, e.g. for generating a suitable welding pattern by scanning the laser beam across the assembly formed by the two workpieces. The positioning device may comprise galvanometer mirrors, scanning mirrors, a beam steering phased array, a translation stage, a rotation stage and/or a piezoelectric stage.

The measuring device comprises a microscope arranged on the side of the exit surface of the first workpiece, the observation direction of the microscope being essentially opposite (anti-parallel) to the propagation direction of the laser beam. This also includes a variant in which a small angle (e.g., in the range of <NUM>-<NUM>°) is introduced between the observation direction of the microscope and the propagation direction of the laser beam). The microscope may comprise an objective lens and a camera. The intensity variation along the beam path can be imaged/scanned by moving relatively the focal plane of the microscope along the beam path within the material of the first workpiece to determine the position of maximum intensity.

According to a preferred embodiment, the beam controlling device is configured to control the parameters of the laser radiation, specifically the spectrum, the pulse duration, the temporal pulse shape, the beam size, the polarization and/or the pulse energy. In possible embodiments, the beam controlling device is constituted by a number of sub-modules. A sub-module used for focusing the laser radiation may comprise objective lenses, spherical lenses, aspherical lenses, F-Theta lenses, cylindrical lenses, and/or parabolic mirrors. Moreover, a further sub-module of the beam controlling device may comprise an optical parametric amplifier, an optical parametric oscillator, a frequency converting crystal for controlling the wavelength of the laser radiation. Yet another sub-module may comprise a stretcher based on a combination of dispersive elements such as gratings or prisms for controlling the pulse duration. A sub-module comprising a spatial light modulator may be employed for controlling the spatial distribution of the laser beam, a Keplerian or a Galilean telescope made of a combination of lenses and/or parabolic mirrors may be used as a further sub-module for controlling the beam size. A sub-module comprising a combination of polarizers and/or waveplates may be employed for controlling the polarization of the laser beam, and/or a combination of waveplates, polarizers and/or neutral density filters may constitute a sub-module for controlling the pulse energy. The pulse energy, polarization and repetition rate may be controlled using an acousto-optic modulator (AOM) or an electro-optic modulator (EOM).

According to yet another preferred embodiment, the system further comprises an observation device configured to inspect the entrance surface of the first workpiece. The observation device makes it possible, e.g., to observe concomitance of the entrance surface of the first workpiece with the geometric focus of the laser beam such that the precise relative position of the workpiece and the focus can be determined. The observation device may comprise a dark-field or a bright-field microscope or a phase-contrast microscope working either in transmission or reflection.

According to a further preferred embodiment, the system comprises a conditioning device configured to control the ambient conditions of the assembly of the two workpieces. The conditioning device controls the environment of the welding process in terms of chemical composition, pressure and temperature. It may include a gas-tight chamber in which the assembly of the two workpieces is arranged, wherein the chamber can be connected to a vacuum pump and to one or more gas reservoirs to establish a desired gas composition within the chamber. A heating device (an oven) may be used to control the ambient temperature during welding.

It should be noted that the two workpieces are subject to the welding process carried out by the system of the invention and are therefore not part or component of the system itself.

The enclosed drawings disclose preferred embodiments of the present invention. It should be understood, however, that the drawings are designed for the purpose of illustration only and not as a definition of the limits of the invention. In the drawings:.

With reference to <FIG>, a system <NUM> for welding a first workpiece <NUM> to a second workpiece <NUM> is shown as a block diagram. The first workpiece <NUM> consists of a semiconductor material, e.g. silicon. The material of the second workpiece is a metal, e.g. copper. The two workpieces <NUM>, <NUM> may or may not be in optical contact at their common interface. The optional optical contact can be established by introducing a suitable fluid within the gap between the two workpieces <NUM>, <NUM>, such as, e.g., methanol, ethanol, etc. The workpieces <NUM>, <NUM> can be maintained in contact by means of any common mechanical fixturing method.

The laser welding system <NUM> includes in particular a laser device <NUM>, e.g. a mode locked fiber laser in combination with one or more optical amplification stages, which emits pulsed laser radiation <NUM> with given properties in terms of spatial and temporal distribution, polarization, energy, spectrum, repetition rate, etc. A beam controlling device <NUM> is provided for controlling the characteristics of the laser pulses <NUM> in terms of wavelength, pulse duration, temporal pulse shape, repetition rate, spatial distribution of the beam, beam size, pulse energy, and polarization before being directed through the first workpiece <NUM>. The beam controlling device <NUM> comprises several sub-modules <NUM>-<NUM> for controlling the pulse characteristics and a focusing optics <NUM> to focus the laser beam, which enters through an entrance surface of the workpiece <NUM> and leaves it through an exit surface forming the interface between the two workpieces <NUM>, <NUM>, with the geometric focus being set at a location along the beam path. The focusing optics <NUM> can include, e.g., an objective lens, a convex single lens, a parabolic mirror, an aspherical lens, an F-Theta lens, a cylindrical lens, etc..

The relative position of the assembly <NUM> of the two workpieces <NUM>, <NUM> with respect to the incoming focused beam is adjusted by a positioning device <NUM> (e.g., a translation stage, a rotation stage, a piezoelectric stage, or a combination of these) enabling the displacement of the assembly <NUM> in the direction of the laser beam (in order to adapt the position of the geometric focus) as well as in the plane perpendicular thereto. For adapting the focus position further components may be used, such as an F-Theta lens, galvanometer mirrors, a beam steering phased array etc. (not depicted). The three-dimensional control of the relative position of the beam with respect to the assembly <NUM> makes it possible to carry out the welding procedure along a predefined welding pattern. The welding pattern is determined by a scanning strategy to obtain, e.g., a point-by-point pattern, a line-by-line pattern, a concentric circle pattern, a spiral pattern, single-scan, multi-scan with or without increase in laser intensity between the scans, etc. Ideally, the scanning speed during welding is between <NUM>/s and <NUM>/s. The welding pattern can be chosen as a function of the amount of energy deposited per point of the welding pattern at the interface between the two workpieces <NUM>, <NUM> which mainly depends on the laser repetition rate, pulse energy, and beam size.

The system <NUM> further comprises an observation device <NUM> for inspecting at least one of the surfaces of the first workpiece <NUM>. The observation device <NUM> can be, e.g., an optical bright-field or dark-field microscope either working in transmission or in reflection, with or without phase contrast. The observation device <NUM> enables monitoring of the interaction of the laser radiation at the respective surface of the first workpiece <NUM> for precise calibration of the positioning of the geometric focus of the laser beam relative to the surfaces of the workpiece <NUM>. The system <NUM> further includes a conditioning device <NUM> for controlling the ambient conditions of the welding process in terms of chemical composition, pressure, and temperature. The conditioning device <NUM> includes, for example, a chamber with a valve for gas injection, a vacuum chamber connected to vacuum pumps, an oven, etc..

As mentioned above, the beam controlling device <NUM> includes optional sub-modules <NUM>-<NUM> for tailoring the laser pulse properties. The first optional sub-module <NUM> is provided for controlling the wavelength, and, more generally, the spectral characteristics of the pulses. Module <NUM> can be, for example, an optical parametric amplifier (OPA), an optical parametric oscillator (OPO), a frequency doubling crystal, etc. The wavelength of the pulses <NUM> at the output of module <NUM> has to be adjusted so that workpiece <NUM> is transparent at this wavelength, whereas workpiece <NUM> is opaque at this wavelength. As an example, an adjusted wavelength of <NUM> is appropriate if the material of workpiece sample <NUM> is crystalline silicon, and the material of workpiece <NUM> is a metal (e.g., copper, gold, silver, aluminum, etc.). The second optional module <NUM> is provided for controlling the temporal shape of the laser pulses, in accordance with a predefined welding pattern. For an irradiation composed of single-pulses, or a pulse train, the module <NUM> can decrease the repetition rate of the pulses <NUM>, and can be, for example, an optical beam shutter, an optical chopper, a Pockels cell, an acousto-optic modulator (AOM), etc. Secondly, the module <NUM> gives access to the control of the pulse duration, and can be, for example, a stretcher or a compressor composed of a combination of various dispersive elements such as diffraction gratings or prisms, or a pulse stretcher based on group velocity dispersion in a given material. The third optional module <NUM> is provided for controlling the spatial distribution of the beam. It can increase or decrease the beam size, e.g., by means of a Galilean or a Keplerian telescope, and, more generally, any afocal system. Secondly, module <NUM> can change the beam profile (i.e., the spatial beam distribution) from the beam at the input <NUM> to the output <NUM>. , module <NUM> can be able to generate Gaussian, tophat (i.e., uniform in intensity), Bessel or vortex beams. Module <NUM> can include an axicon, phase plates, a spatial light modulator, etc. The fourth optional module <NUM> enables the control of the polarization of the laser beam, i.e., the direction of the electric field of the laser. Module <NUM> can include, for example, wave plates (half-wave plate, quarter-wave plate), polarizers (e.g., linear polarizer, radial polarizer, electro-optic modulator), etc. The fifth and last optional module <NUM> is provided for the control of the pulse energy by decreasing the beam power from the entrance <NUM> to the exit <NUM> of this module. The attenuation in pulse energy can be carried out with, for example, an optical attenuator, neutral density filters, the combination of a half-wave plate and a polarizer (the control of the energy is achieved by rotating the half-wave plate in this case), etc. If all the aforementioned optional modules <NUM>-<NUM> of the beam controlling device <NUM> are used, the spectral, temporal, spatial, polarization and energy characteristics of the beam <NUM> can be optimally tailored. The sequence of the sub-modules <NUM>-<NUM> may be modified as required.

The laser pulse energy can be estimated by applying an energy calibration procedure. This procedure consists of measuring the average power of the laser radiation, e.g. using a power meter, between the focusing optics <NUM> and the workpiece <NUM>. The corresponding pulse energy can be easily determined by calculating the ratio between the measured average power value (in Watts) and the repetition rate of the laser (i.e., the number of laser pulses per second, in Hertz). Furthermore, the energy after propagation through the entrance surface of the workpiece <NUM> can be estimated by multiplying the pulse energy with the Fresnel transmission coefficient calculated from the refractive indices of the environment and the workpiece <NUM>, the laser polarization and the angle of incidence of the laser beam.

<FIG> shows a depiction of the measuring device <NUM> of the system <NUM>. The measuring device <NUM> is used to measure the variation of the intensity of the laser radiation along the beam path within the first workpiece <NUM> to determine a delocalization of the focus caused by nonlinear interaction of the laser radiation with the semiconductor material of workpiece <NUM>. This measuring procedure is carried out before the actual welding. The measuring procedure includes the focusing of the laser beam with identical beam parameters as used in welding (in terms of spectrum, temporal profile, pulse duration, spatial distribution of the beam, beam size, polarization, and pulse energy). The laser beam is initially focused on the exit surface of the first workpiece <NUM> that has to be laser welded to the second workpiece <NUM> (<FIG>) afterwards. The measuring device <NUM>, a microscope collinear to the optical axis Z and directed oppositely to the laser beam direction, enables imaging of the exit surface of the workpiece <NUM>. Due to the fact that the imaging system <NUM> is also centered on the beam focused by the focusing system <NUM>, the measuring device <NUM> is able to image the spatial distribution of the beam intensity at the exit surface of workpiece <NUM>. In the depicted embodiment, the measuring device <NUM> is composed of a collecting optics <NUM> whose numerical aperture (NA) is ideally higher than the one of the focusing optics <NUM> for ensuring to collect all angular components of the incoming light. The collecting optics <NUM> can be, for example, an infinity-corrected objective lens. In this way, the beam is collimated after being collected by the focusing optics <NUM>. An optional tube optics <NUM> is provided to refocus the collimated light onto a camera <NUM> that can be equipped, for example, with a bandpass filter for ensuring that only the light at the wavelength of the laser radiation is detected. This filter can be particularly relevant in the case of third-harmonic generation in the material, as well as for blocking most of the ambient light. When a finite-corrected objective lens is employed in the collecting optics <NUM>, the tube optics <NUM> can be bypassed and the beam is directly refocused on the camera <NUM>. Ideally, for optimized dynamic range, the camera <NUM> has a linear response at the wavelength of the incoming laser. Moreover, the image on the camera <NUM> should not show any saturated pixels during measurement. The system <NUM> further includes a linear translation stage <NUM> enabling relative displacement of the focusing optics <NUM> only along the optical axis Z, upstream as well as downstream along the laser beam path. In a possible alternative embodiment (not depicted), the translation stage <NUM> enables the workpiece <NUM> and the measuring device <NUM> to move together along the optical axis Z, with a fixed position of the focusing optics <NUM>. The arrangement shown in <FIG> enables to image the spatial distribution of the incoming laser light in the (X,Y) plane for various relative positions of the focus along the optical axis Z with respect to the exit surface of the workpiece <NUM>. By repeated alternating movements of the focusing optics <NUM> and image acquisitions using the measuring device <NUM> the intensity variation of the laser beam propagating through the first workpiece <NUM> can be determined in the (X,Z) and (Y,Z) planes.

A first beam propagation imaging procedure can be carried out at a pulse energy for which the beam propagation is linear, i.e. without nonlinear interaction of the laser radiation with the semiconductor material of the first workpiece <NUM> (typically at a pulse energy between <NUM> fJ and <NUM> pJ, depending on the sensitivity of the camera <NUM>). The energy can be attenuated to such a low level by means of, for example, neutral density filters of module <NUM> (see <FIG>). Then, the same measurement is performed at the pulse energy at which the welding procedure is to be carried out. The intensity corresponding to this pulse energy has to be sufficient for inducing a material modification at the interface between the two workpieces <NUM>, <NUM> during the laser welding procedure. Due to the fact that this increased intensity will not be sufficient for inducing a modification of the material of the first workpiece <NUM> (being transparent at the wavelength of the laser radiation), neither at the exit surface nor in the bulk material, the measurement of the intensity variation under nonlinear propagation of the laser beam at the higher pulse energy is reliable and repeatable. The linear and the nonlinear propagation images acquired by measuring device <NUM> can be analyzed to determine the position of maximum pixel amplitude along the optical axis Z (which is related to the maximum fluence and intensity of the laser beam). The difference between the positions of maximum intensity along the optical axis Z in the linear and nonlinear propagation cases (designated herein below as ΔZ) can be derived from a comparison of the two images. At pulse energies required for welding, the position of the maximum intensity is strongly shifted upstream along the beam path, i.e., in the pre-focal region of the bulk semiconductor material. This is physically related to soliton formation provoked by the competition of nonlinear phenomena such as Kerr-induced self-focusing, plasma formation (due to, e.g., multi-photon absorption, avalanche ionization, tunnel ionization, etc.), and plasma defocusing.

<FIG> illustrates an experimental quantification of the evolution of the nonlinear propagation-induced shift ΔZ along the optical axis as a function of the pulse energy (measured in air before the entrance surface of the first workpiece <NUM>). It can be seen from the diagram of <FIG> that, for <NUM>-ps pulses at low energy (i.e., <<NUM> nJ), ΔZ is close to zero, showing the linear propagation of the laser radiation at these energies. In the energy range <NUM>-<NUM> nJ, ΔZ monotonically increases with increasing pulse energy, indicating that nonlinear propagation phenomena start to become prominent. A similar behavior is observed for <NUM>-ps duration pulses, but shifted toward higher pulse energies. These results demonstrate that, for maximizing the intensity at the exit surface of the semiconductor workpiece <NUM>, i.e. at the interface between the two workpieces <NUM>, <NUM>, simply positioning the geometric beam focus at the interface is not appropriate. The shift ΔZ along the optical axis has to be taken into account for optimizing the energy deposition at the interface between the semiconductor material of the first workpiece <NUM> and the opaque material (metal) of the second workpiece <NUM>. To this end, the focus of the laser radiation is (re-)positioned according to the invention during welding so that the intensity maximum is located precisely at the interface such that the two workpieces <NUM>, <NUM> are optimally bonded.

Claim 1:
Method for welding a first workpiece (<NUM>) to a second workpiece (<NUM>) by means of a laser, comprising the steps of:
- irradiating the first workpiece (<NUM>) with a beam of pulsed laser radiation, wherein the first workpiece (<NUM>) consists of a semiconductor material which is transparent at the wavelength of the laser radiation, so that the beam enters the first workpiece (<NUM>) through an entrance surface and leaves it through an exit surface, the geometric focus of the beam being positioned in the plane of the exit surface;
- determining a delocalization of the focus caused by nonlinear interaction of the laser radiation with the semiconductor material;
- placing the second workpiece (<NUM>) against the first workpiece (<NUM>); and
- again irradiating the first workpiece (<NUM>) with the laser beam of pulsed laser radiation, the focus of the laser radiation being positioned along the beam direction taking into account the determined delocalization so that the intensity maximum is located in the plane of the exit surface forming the interface of the two workpieces (<NUM>, <NUM>), whereby the first workpiece (<NUM>) is welded to the second workpiece (<NUM>).