Method for determining surface roughness of sample surface of sample

Abstract

The present disclosure relates to a method (300) for determining a surface roughness of a sample surface of a sample (1), the method (300) comprising:-obtaining a number of measurement data based on an optical three-dimensional measurement of the sample surface by an image sensor, each of the measurement data being indicative of a surface topology of the sample surface, each of the measurement data is associated with a different brightness level of the light source illuminating the sample surface or with a different exposure of the image sensor; obtaining, for each of the measurement data, first calculation data indicative of a surface roughness of the sample surface; and-determining, based on the first calculation data, second calculation data of the sample surface indicative of the surface roughness for all the measurement data.

Description

TECHNICAL FIELD

[0001] The present invention generally relates to the field of determining a surface roughness of a sample surface of a sample, in particular a semiconductor wafer having an etched wafer surface. In particular, the present invention relates to a method, a computer program product, a data processing system and a sample processing system for determining a surface roughness of a sample surface of a sample. BACKGROUND

[0002] For quality control purposes or other purposes, it can be useful to measure a surface roughness of a sample surface of a sample or in other words a substrate surface from a substrate as further described herein below. Such a sample can be a semiconductor wafer. In particular, the sample or wafer can have been etched by a chemical liquid or in other words by a wet chemical etching, which can comprise one or more chemical etchants. For example, the etching of the sample or wafer can be done by immersing the sample into a bath containing the chemical liquid or by dispensing the chemical liquid onto the surface of the wafer. For a semiconductor wafer as a sample, a wet etching process is typically used for or within a wafer thickness reduction, in particular on the backside of the wafer but not on the frontside of the wafer. A result of the wet chemical etching can be a change of the surface roughness of the sample surface, in particular in a controlled manner such that it is within a target or target range of the surface roughness.

[0003] The wet etching can be performed during a back end of line (BEOL) phase of a semiconductor manufacturing process. In an exemplary BEOL process for power semiconductor devices employing wafers, the wet etching can be used for a wet chemical surface processing of the wafer. Typically, a tape bonding or a use of a glass carrier wafer and a wafer backside grinding is performed before the wet etching. During a typical BEOL process of semiconductor manufacturing, a contact formation, an annealing and a backside metallization are performed after the wet etching. Thus, the surface roughness can play an important role in the quality of the sample and thus in the quality of a device employing the sample, e.g. a (power) semiconductor device.

[0004] For measuring a surface roughness of a sample surface of a sample, it is known to process images of the sample surface, in particular real-time images. For obtaining accurate results, it can be necessary to adjust parameters of a camera device capturing the images to eliminate external disturbances. For example, reflection characteristics of a particular sample surface and / or material, e.g. a silicon wafer, can be considered for adjusting or calibrating the camera device parameters. However, an accurate determination of the surface roughness is still challenging, but it can be desirable to determine the surface roughness as accurate, fast and reliable as possible, possibly of different kinds of samples, in particular or at least in terms of size, material and / or reflection characteristics. SUMMARY

[0005] The above-mentioned problems are at least partially solved or alleviated by the subject matter of the present disclosure.

[0006] According to a first aspect of the present disclosure, there is provided a method for determining a surface roughness of a sample surface of a sample, the method comprising:

[0007] - obtaining a number of measurement data based on an optical three-dimensional measurement of the sample surface by an image sensor, each of the measurement data being indicative of a surface topology of the sample surface, wherein each of the measurement data is associated with a different brightness level of a light source illuminating the sample surface or with a different exposure of the image sensor;

[0008] - obtaining, for each of the measurement data, first calculation data indicative of the surface roughness of the sample surface; and

[0009] - determining, based on the first calculation data, second calculation data indicative of the surface roughness of the sample surface for all of the (number of) measurement data.

[0010] The method of the present disclosure provides for accurately, quickly and reliably determining a surface roughness of a sample surface of a sample by using several measurement data of several measurements, the several measurements being different in a measurement parameter of the optical three-dimensional measurement, i.e. a brightness level of the used light source or an exposure of the image sensor, and the several measurement data being calculated from the several measurements such that an accurate surface roughness of the surface of all measurements or all measured samples is determined, which can reflect a single accurate value of the surface roughness as a result of the method. In other words, first, several measurements of the sample surface can be performed by an image sensor, which employs an optical three-dimensional measurement of the sample surface and provides measurement data indicative of a surface topology of the sample surface as a result of the optical three-dimensional measurement. For example, each of the measurement data can indicate or comprise surface topology data, e.g. in form of a three-dimensional (surface topology) image or cloud point data. For each of the several measurements and thus for each of the several measurement data, a different brightness level of a light source illuminating the sample surface during the measurement, i.e. during capturing of an image of the sample surface by the image sensor, can be used. Alternatively, for each of the several measurements and thus for each of the several measurement data, a different exposure of the image sensor can be used. Second, a first calculation data can be obtained, in particular determined or calculated, more particularly by a data processing system, the first calculation data being indicative of a surface roughness, in particular a value of the surface roughness, of the sample surface for each of the several measurements or the several measurement data. In particular, each of the surface roughness or the value of the surface roughness can be different based on the observation of different surface roughness values resulting from different brightness levels or different exposures. Third, based on the first calculation data reflecting the surface roughness, in particular the value of the surface roughness, a second calculation data representing all measurements or measurement data can be determined, in particular calculated, more particularly by the data processing system based on the first calculation data, the second calculation data can be an accurate single surface roughness or value of the surface roughness of the entire sample surface. The method is reliable because when performing the method on several samples, by using measurement data with different brightness levels of the light source or different exposures of the image sensor, the method produces reproducible results, in particular independent of the size, material and reflective properties (e.g. shiny or rough sample surfaces) of different samples.

[0011] The method of the first aspect can in particular be at least partially or fully computer-implemented. This means that at least one, several or all of the steps of the method can be performed by a data processing system, which can comprise one or more data processing devices or computers or computing units, which can be part of a system for performing a wet etching process or in other words a wet etching processing system. Different steps can be performed by the same or different computers. A computer is understood herein as a data processing device, which can perform some, several or all of the steps defined by the method. The one or more computers can be configured as or inside one or more sensor units, control units and / or other units of the sample processing system or separate from but as part of the sample processing system. The one or more sensor units can be sensor units with image sensors. For example, the sensor units can be configured as camera units with image sensors and / or light sources.

[0012] For example, the obtaining of the several measurement data can be performed by the data processing system. Alternatively or additionally, the obtaining of the several measurement data can be performed by a sensor unit or camera unit, which can send the several measurement data to the data processing system. Alternatively or additionally, the method of the present disclosure can comprise measuring the measurement data, for example by a sensor unit or camera unit of the sample processing system, in addition to obtaining the several measurement data. For example, the measurement data can be or comprise image data, in particular image data showing a three-dimensional surface topology in a coordinate system, and / or a point cloud of points representing the three-dimensional surface topology.

[0013] For example, the obtaining of the first calculation data and / or the determining of the second calculation data can be performed by the data processing system. In particular, the first calculation data and / or the second calculation data can be based on a calculation of the data processing system, wherein the calculation of the first calculation data is based on the several measurement data as input and / or the calculation of the second calculation data is based on the first calculation data.

[0014] To obtain, in particular to determine, the first calculation data, for example, a calculation method, a simulation or a formula can be utilized, using each of the measurement data as input to determine a surface roughness or a surface roughness value of the sample surface. The method, simulation or formula can be configured such that the surface roughness is determined from physical properties or based on a consideration of the physics of the sample surface. The mathematical method or formula can vary depending on the value representing the surface roughness to be calculated or calculated. For example, an average or an arithmetic mean of the profile height deviations from the mean line, commonly referred to as Ra, Raa or Ryni, can be used as the value of the surface roughness. Such an average or arithmetic mean Ra can be used, for example, for any surface roughness indicated by the first calculation data or the second calculation data. Additionally or alternatively, other values or measures representing the surface roughness can be used, for example, but not limited to, a quadratic mean or root mean square mean of the profile height deviations from the mean line, commonly referred to as Rq or RMs, a maximum depth of valleys below the mean line, commonly referred to as Rv, a maximum height of peaks above the mean line, commonly referred to as Rp, a maximum height of peaks to valleys of the profile, skewness, kurtosis, an average distance between the highest peaks and the lowest valleys, a value based on a number (e.g. five) of the highest peaks and / or the lowest valleys, an ISO grade number and / or any other value. The calculation method, simulation or formula can vary for each of the examples of the values or measures mentioned in the foregoing.

[0015] To determine the second calculation data, the surface roughness of each of the number of measurement data can be combined with each other in any of the different ways as further described below.

[0016] The sample can be, for example, a wafer, in particular a semiconductor wafer. The semiconductor wafer can be used for manufacturing an integrated circuit. In particular, the wafer can be etched at a backside thereof opposite to a frontside thereof. The wafer can have any reflective or reflectivity properties. The wafer can comprise silicon, in particular crystalline silicon, or any other semiconductor material, for example, but not limited to, germanium, gallium arsenide, indium phosphide, silicon carbide or gallium nitride or sapphire. The sample can have any size and geometry. The sample can be, for example, disc-shaped. The sample can alternatively be referred to as a substrate, in particular a disc-shaped substrate. The sample can alternatively be any other substrate than a wafer, for example, a metal substrate or a glass substrate.

[0017] The optical three-dimensional measurement can be, for example, based on white light interferometry. In other words, white light interferometry can be used for the optical three-dimensional measurement. The camera having the image sensor can be part of a device for white light interferometry. For example, the image sensor can be a charge-coupled device (CCD) image sensor. The light source can be, for example, a white light source. White light interferometry is particularly accurate in case of a surface varying in the nanometer range, for example, 50 nm to 500 nm, for example, in case the surface can be a wafer surface.

[0018] Each of the measurement data can be associated with a different brightness level or a different exposure that is increased or decreased in increments between successive measurements of the image sensor. Thus, for example, several measurements or several measurement data can be obtained in succession by changing the brightness level or the exposure in successive increasing or decreasing increments. The increments can be predetermined or predefined. For example, the increments can be predetermined or predefined as absolute and / or relative increments, e.g. in % of a nominal brightness level or a nominal exposure. For example, the increments can be fixed, in particular a fixed value in all measurements. Alternatively, the increments can vary throughout the measurements, e.g. with a smaller or larger increment in the first measurements compared to later measurements, or in any other way.

[0019] For example, the increments (size or magnitude thereof) can be in the range of 0.1 % to 8 %, in particular in the range of 0.5 % to 6 %, more particularly in the range of 1 % to 4 % of a nominal brightness level or a nominal exposure. For example, the nominal brightness level or the nominal exposure can be defined by technical limitations of the light source and / or the image sensor. The nominal brightness level or the nominal exposure can be a maximum brightness level or a maximum exposure. The exposure can also be referred to as exposure ratio or exposure value. The exposure may, for example, define the amount of light per unit area (e.g. mm 2 ) of the surface of the image sensor that reaches. The nominal exposure or the maximum exposure may, for example, be the maximum amount of light per unit area that the image sensor can record or utilize. It has been found that increments in this range provide accurate results for the surface roughness indicated by the second calculation data with at least acceptable or fast determination times.

[0020] Alternatively or additionally, for example, the increments can be between 5 % or more, in particular 10 % or more, and 80 % or more, in particular 90 % or more, more particularly approximately or exactly 100 % of a nominal brightness level or a nominal exposure (increased or decreased, in particular in the magnitude of the increments). It has been found that thereby a substantially complete useful or sensible range of different brightness levels or exposures can be employed to provide accurate results for the surface roughness indicated by the second calculation data with at least acceptable or fast determination times.

[0021] By defining the size of the increments and the relative range in which the nominal brightness levels or nominal exposures are increased or decreased, the number of measurements or measurement data, in particular the number of images of the sample surface captured by the image sensor, can be defined. For example, the number of measurements, measurement data and / or images can be in the range of 10 to 900, in particular in the range of 20 to 900, more particularly in the range of 20 to 180, and even more particularly in the range of 40 to 120, which number can be for example 90, the increments being for example 1% of the nominal brightness level or nominal exposure between 10% and 100% of the nominal brightness level or nominal exposure. It has been found that these numbers are advantageous, as the data obtained thereby are sufficient to obtain accurate second calculation data, while the method can be relatively quickly performed.

[0022] One of the brightness levels and the exposure can for example remain substantially constant or approximately constant between successive measurements of the image sensor. In other words, when one of the brightness levels and the exposure is increased or decreased in successive measurements, the other one can remain constant. It has been found that it is sufficient to vary only one of the aforementioned measurement parameters to produce a set of several measurement values for determining an accurate single surface roughness value. This simplifies the method in comparison to when both measurement parameters would be varied (however, this can be a possibility, for example successively, simultaneously or randomly), and provides a very fast determination of the roughness value for all several measurement data.

[0023] The method can (also) comprise:

[0024] filtering each of the measurement data by one or more of the following: removing data points outside the sample surface, removing noise, cropping the image representing the surface topography indicated by the measurement data, and levelling the image;

[0025] The first calculation data can be based on each of the filtered measurement data. In other words, the filtered measurement data of each of the measurement data can be generated before obtaining the first calculation data, and then the first calculation data is obtained based on the filtered measurement data. The filtering improves the accuracy of the first calculation data, and thus of the second calculation data, because filtering the values, data points or similar from several measurement data would otherwise lead to inaccurate results of the second calculation data, for example, because they are based on noise, outliers or otherwise inaccurately reflect the sample surface. For example, when removing data points outside the sample surface, for example, within the image or point cloud, spikes can be removed from the image or point cloud, for example, line by line. In addition or alternatively, for example, when removing noise, the surface represented by the image or point cloud can be smoothed, for example, by mean filtering. In addition or alternatively, for example, by cropping the image representing the surface topology, image padding on the borders of the image can be avoided. In addition or alternatively, for example, by leveling the image, rough surfaces in the image can be separated from the rest of the surface, whereby waviness of the image can be removed. For example, for the filtering of each of the measurement data as described herein or as an alternative, at least partially or completely, the ISO 25178 specification can be used, in particular with regard to all the filtering measures mentioned herein.

[0026] For example, determining the second calculation data can comprise calculating a density function for each of the surface roughnesses of the sample surface for each of the measurement data, and determining the surface roughness of the sample surface for all the measurement data based on the density functions. In particular, the density function can be based on the several measurement data indicating a probability of a different surface roughness value from the first calculation data. In particular, the density function can be a probability density function based on the surface roughness values of the first calculation data indicating a probability of a surface roughness value within a range of surface roughness values. For example, the density function can be plotted as a probability (for example, in % or point values) over the surface roughness (for example, in nm). Interestingly, it has been found that by calculating a density function of the surface roughness of each of the several measurement data, a distinct maximum can be observed within a range of different brightness levels or different exposures, or in other words, or when the density function is represented graphically, a peak can be observed.

[0027] Thus, for example, the surface roughness of the sample surface for all the measurement data can be determined based on the maximum of the density function, or as the maximum of the density function. The surface roughness, in particular the single surface roughness value, for all the measurement data can be the maximum or peak of the density function, or approximate or close to the maximum or peak of the density function, for example, a mean value or similar value around the peak.

[0028] Determining the second calculation data can for example comprise repeating obtaining several measurement data, the first calculation data and determining the second calculation data, if the calculated density function indicates two peaks for the surface roughness of the sample surface for all measurement data. More specifically, the previously mentioned steps of the method can be repeated, for example, if the two peaks fulfill a peak threshold and / or the size of the two peaks within the peak threshold differ from each other. Two or even more peaks, in particular when fulfilling the peak threshold and thus having a similar or sufficient size, can be interpreted as a signal for repeating the method for determining the surface roughness of the sample surface. For example, but not limited to, dust particles or similar can be the underlying reason for the two peaks or maxima in the density function. If after repeating the previously mentioned steps, there are still two peaks, the measurement or the sample can be rejected, for example, the sample is considered as a scrap part.

[0029] It is noted that the determination of the second calculation data can alternatively or additionally be performed in a different way than using the density function or in a different way than selecting the maximum or peak of the density function. Any other function or method, for example, determining an average or arithmetic value or other value from the surface roughness of the sample surface for each of the measurement data or the density function, is an example for such a different way.

[0030] For example, the sample surface can be an etched sample surface. Further, the method can comprise:

[0031] - obtaining, based on the second calculation data, control data for controlling one or more settings of a wet etching process to be performed on one or more further samples.

[0032] Hence, the method can provide control of the wet etching process by controlling one or more settings of the wet etching process based on second calculation data that accurately reflects the measurement data. In particular, the control data can be obtained for controlling one or more settings of the wet etching process for etching further samples after having etched one or more already etched samples that have been measured previously by the same wet etching process, in particular with the same container that accommodates the chemical liquid that has been used for etching the previous samples. Hence, the method does not rely on statistical methods that can not be accurate to perform the wet etching process (e.g. wet chemistry) of the samples as fast as possible and with as few resources as required, eliminates premature exchange thereof and has a constant quality, e.g. with a substantially constant target surface roughness range. In contrast, the method uses actual measurement data of one or more parameters, in particular target parameters of the wet etching process related to the target dimensions of the etched samples or target parameters before and after etching the samples and / or quality parameters of the wet etching process associated with the quality of the etched samples, the quality in particular being related to the dimensions or dimensional tolerances or accuracies of all etched samples with respect to the one or more parameters. However, in addition to using the surface roughness indicated by the second calculation data, alternative or additional measurement data of one or more other parameters (e.g. measured thickness or material removal of the samples) can be used to determine the control data. In other words, measurement data indicating the thickness and / or material removal of the samples by the wet etching can alternatively or additionally be used as a basis for obtaining the control data.

[0033] For example, the obtaining of the control data can be performed by a data processing system. Alternatively or additionally, the obtaining of the control data can be performed by one or more control units and / or one or more operation units configured to perform one or more control settings, the units being units of the wet etching processing system. In the aforementioned additional variant, the data processing system can provide the control data to the one or more control units and / or the one or more operation units for obtaining and thus performing by the one or more control units and / or the one or more operation units. For example, the one or more control units and / or operation units can be configured for at least partially exchanging the chemical liquid, e.g. by adding one or more chemical etchants to the chemical liquid to change the composition of the chemical liquid, and / or for controlling the etching duration of the samples. For example, the operation units can be or comprise any one of a dispenser or dispensing unit for dispensing the chemical liquid onto the surface of the samples, a pump fluidically connected to the dispenser and the container, a feed line into the container of the wet etching processing system, a container accommodating the chemical liquid, and the like, but are not limited thereto.

[0034] Alternatively or additionally, in addition to obtaining control data, the method of the present disclosure can comprise executing control data, i.e. one or more settings controlled by one or more control units and / or one or more operation units of the wet-etching process system, for example. The obtaining of control data can be the determination of control data, in particular by the data processing system. As further described below, the obtaining of control data can also be the updating of control data, in particular the updating of already obtained or existing control data.

[0035] In this context, the control of one or more settings can for example mean the determination or setting of one or more settings, such as the lifetime of a wet chemical substance or in other words a chemical liquid. Alternatively or additionally, for example, the control of one or more settings can mean the adjustment of a currently set or currently set setting, such as a setting related to the lifetime of a chemical liquid for exchanging, by adjusting the lifetime, for example reducing or extending the lifetime, so that the exchange of the chemical liquid in the container can be triggered earlier or later in accordance with the second calculation data. Further examples of the control of settings are given below, and the control in the examples of the determination or setting and adjustment as described can be applied to these settings.

[0036] The wet-etching process can be a single-sample etching process, in which a single sample can be etched continuously by dispensing a chemical liquid onto a sample surface of the sample. For example, the chemical liquid can be dispensed (e.g. dropped, sprayed or in a similar manner) onto a sample surface of the sample, in particular onto the side, more particularly the backside, of a wafer, by means of a nozzle, a spray system or a similar dispensing unit of the wet-etching process system. In order to better distribute the chemical liquid on the surface of the sample, the sample can optionally be rotated during the dispensing of the chemical liquid or the wet-etching process. The opposite surface can not need or have to be subjected to the chemical liquid, in which case an air flow or the like can be supplied to or at that side, preventing the chemical liquid from reaching that side, in particular the front side of the wafer. The single-sample etching process can be performed by a wet-etching process system, which can be referred to as a single-sample wet-etching process system. In contrast to the case of etching a plurality of samples, for example by means of batch etching, in which a plurality of samples can be placed into a carrier and immersed in a bath of chemical liquid, at least within one process chamber or device for etching, only one sample can be etched at a time. However, batch etching or other forms in addition to single-sample etching can alternatively be implemented.

[0037] The second calculation data can be determined continuously for the samples etched by the wet etching process, and the control data can be obtained or updated based on the second calculation data, in particular continuously. For example, every single continuous sample or every few continuous samples can be measured to obtain the second calculation data. In particular, a sampling or a sampling pattern can be used according to which a predetermined number of samples and / or a sample order are used to obtain the second calculation data of the samples according to the number of samples and / or the sample order. The number of samples can indicate, for example, a number of samples per chemical liquid, a number of samples to be measured, for example, 100 and / or the like. The sample order can indicate samples to be measured within the continuous samples, for example, every few continuous samples, such as, for example, every 2, 5 or 10 samples, or a varying (e.g., fixed variation or dynamically adopted) number of continuous samples. The sampling, in particular the number of samples and / or the sample order, can depend, for example, on the type of wafer (e.g., material and / or size), on the type and / or composition of the chemical liquid used, on the second calculation data from previously measured etching samples and / or on the (previously) obtained control data. By obtaining or updating the control data based on each of these second calculation data, the wet etching process can be constantly monitored during the wet etching process of the samples. In particular, the wet etching process can be monitored such that when the second calculation data indicates a change in quality of one or more continuous samples, for example, when an etched sample deviates from a target range of one or more of the target parameters or approaches a threshold value of the target range, the control data can be updated to control one or more settings, for example, by adjusting the settings and / or determining or setting new settings to counteract the change in quality, in particular a decrease in quality, for example, by at least partially or substantially completely exchanging the chemical liquid in the container (meaning that some remnants or residues of the previous chemical liquid can still be contained in the container, but a large part of the chemical liquid can be replaced).

[0038] For example, at least one of the one or more settings can relate to an at least partial exchange of the chemical liquid. The at least partial exchange of the chemical liquid can also be a complete or substantially complete exchange of the chemical liquid contained in the vessel of the wet-etching processing system (meaning that some remnants or residues of the previous chemical liquid can still be contained in the vessel, but a major part of the chemical liquid can be replaced). For example, the setting relating to the exchange of the chemical liquid can indicate a time, in particular a lifetime, after which the chemical liquid is to be at least partially replaced, in particular with a chemical liquid of the same type and / or composition. Additionally or alternatively, for example, the setting relating to the exchange of the chemical liquid can indicate an amount or substance of the chemical liquid to be exchanged, e.g. one or more chemical etchants. By providing a new or fresh chemical liquid or wet-chemical substance, e.g. as a bath within the vessel, active chemical substances or substances, e.g. one or more chemical etchants, re-appear and / or are able to etch a sample within one or more target parameters to fulfill quality requirements of the sample set thereby.

[0039] In addition or alternatively to the at least partial exchange of the chemical liquid, for example, at least one of the one or more settings can relate to a change of the etching duration. The etching duration can refer to the (total) duration of the etching of the sample in the wet-etching process and can be determined or correspond or substantially correspond to the dispensing time and / or amount of the chemical liquid to be dispensed per sample, for example. Thus, for example, by adjusting, determining and / or setting the dispensing time and / or amount of the chemical liquid to be dispensed per sample, the etching quality can be kept constant within the target parameters. For example, the dispensing time can be increased during the lifetime of the wet-chemical substance, such that the wet-chemical substance, which is chemically weaker or less reactive in terms of etching rate, can still deliver a sample with the target parameters within the target range, but at the cost of an increased etching duration and, thus, an increased processing time per sample. However, these costs can be tolerated due to the trade-off, for example, before the exchange of the chemical liquid, and in order to maintain quality control of the etched samples.

[0040] In addition or in alternative to the at least partial exchange of the chemical liquid and / or the change of the etching duration, at least one of the one or more settings can involve a change of a composition of the chemical liquid. For example, one or more chemical etchants, other chemicals and / or additional etchants (in addition to the one or more chemical etchants in the chemical liquid) can be added to the chemical liquid to change the composition of the chemical liquid. This can also be referred to as spiking or buffering with the respective chemical (e.g. etchant). Thus, before triggering a substantially complete exchange of the chemical liquid or increasing the etching duration to an undesired level, less effective or ineffective chemical etchants (such as but not limited to e.g. hydrofluoric acid (HF)) that have already reacted (e.g. oxidized) with the sample can be filled into the container holding the chemical liquid. Additionally or alternatively, the proportion or amount of water in the chemical liquid can be determined.

[0041] In addition or in alternative to the at least partial exchange of the chemical liquid, the change of the etching duration and / or the change of the composition of the chemical liquid, at least one of the one or more settings can involve a change of a distribution of the chemical liquid on the sample. For example, a dispensing profile of dispensing the chemical liquid on the sample surface can be adjusted to change the distribution of the chemical liquid on the sample. For example, the dispensing profile can comprise a pattern of the chemical liquid per dispensing. Alternatively or additionally, a dispensing direction, a rotation speed and / or direction of the sample or the like can be adjusted to change the distribution of the chemical liquid on the sample. Based on the second calculation data, the change of the distribution can thereby be used, for example, to provide a more uniform thickness and / or surface roughness distribution on the surface of the sample.

[0042] The method can further comprise, for example:

[0043] - obtaining second measurement data indicative of a composition of the chemical liquid,

[0044] The control data is further based on second measurement data. In particular, the amount of one or more chemical etching agents in the chemical liquid can be indicated by the second measurement data. The second measurement data can be obtained or determined based on a measurement unit (e.g. a spectrometer) of the wet etching processing system. Thus, the measurement data indicating the surface topology of the sample surface based on the optical three-dimensional measurement of the sample surface by the image sensor can also be referred to herein as first measurement data. By having the second measurement data and based thereon the control data can be obtained such that it takes into account the composition of the chemical liquid, e.g. the amount of different chemical substances such as chemical etching agents and other surface, e.g. including chemical etching agents (e.g. oxidizing etching agents) within the chemical liquid that occur chemical reactions or are less or not effective. This can be useful because the first measurement data can be associated with the composition of the chemical liquid and, e.g., if the amount of chemically active or effective (e.g. oxidizing) chemical etching agents in the chemical liquid is low, the deviation of one or more of the target parameters from the target range can be attributed to the composition and the control data can be obtained or updated accordingly, e.g. by adding one or more chemical etching agents changing the composition of the chemical liquid.

[0045] The control data can be further based on threshold data indicating a threshold for the surface roughness of the sample. The threshold can indicate or provide or be associated with a target or target range for the respective target parameter of the surface roughness. Thus, it can be ensured that the target parameter can be kept within the desired target range. For example, when the target parameter is outside the threshold, e.g. exceeds or is below the threshold (depending on the threshold definition), the control data can be obtained or updated to control the one or more settings. The control data can depend on the amount by which the target parameter exceeds or is below the one or more thresholds (i.e. targets or target ranges). For example, the one or more settings (e.g. etching duration) can be controlled in relation (e.g. in proportion) to the amount by which the threshold is exceeded or is below.

[0046] Alternatively or additionally, the control data can be obtained at least partially or completely as an output of a machine learning algorithm trained at least with second calculation data and / or control data from a previous wet-etch process. The previous wet-etch process can have used a different chemical liquid or wet-chemical substance, e.g., not necessarily in terms of composition, but having the same composition, but in terms of reactivity of the etching treatment during the previous wet-etch process, chemically depleted and exchanged by fresh chemical liquid. Thus, the machine learning algorithm that can be executed by the data processing system can have learned or have been trained based on at least the second calculation data and / or control data to obtain or update the control data as an output of the machine learning algorithm in an optimized manner based on previous historical data of the previous wet-etch process. For example, in the previous wet-etch process, different and / or same types and / or sizes of samples can have been used, and the machine learning algorithm can have learned an optimal or near-optimal control of one or more settings of the control data based on the different samples. Further, or alternatively, the previous wet-etch process can have controlled different settings and / or different numbers of settings, e.g., an etching duration or an amount of etchant added to fill a chemical liquid container can have been used, and for certain measurement data, e.g., a specific total thickness variation range, the machine learning algorithm can have learned an optimal or near-optimal setting to control in terms of determining or setting the settings and / or the number of settings, so that the machine learning algorithm knows and delivers as an output one or more settings to control in an optimal way to handle certain measurement data, e.g., a specific total thickness variation range.

[0047] Note that the control data based on threshold data, which can be based on a deterministic method as opposed to a machine learning method, does not necessarily exclude the machine learning algorithm method. Rather, both can be used in combination, e.g., by both obtaining control data and selecting from it, or combining both, or in any other way. Further, other or additional ways of obtaining control data can be employed, e.g., neural networks or other artificial intelligence methods.

[0048] The method can be configured for controlling two or more wet-etching processes, in particular each wet-etching process using a different chemical liquid, and wherein the method comprises obtaining control data for each of the two or more wet-etching processes. Further, the second calculation data can be determined for each of the two or more wet-etching processes. By the two or more wet-etching processes, the etching of the sample can be improved. The two or more wet-etching processes are in particular performed consecutively for each of the samples. For example, one of the wet-etching processes can be used for preparing the surface of the sample to be etched. For example, for this wet-etching process, HF can be used as chemical liquid. Then, or alternatively, one of the wet-etching processes can be used for a polishing etching of the surface of the sample. Here, for example, a different chemical liquid can be used (in terms of its composition), for example comprising HNO3, HF, H2SO4, and H3PO4. Then, for example, a wet-etching process can be used for a rough etching of the surface of the sample. Here, again, a different chemical liquid can be used, for example comprising HNO3, HF, H2SO4. Thus, each wet-etching process differently treats the surface of the sample based on the chemical liquid or wet-chemical composition used, and can be attributed to the aforementioned intentions, namely preparation, polishing, and rough etching. For each of the different chemical liquids, using the method for controlling each of the two or more, in particular consecutive, wet-etching processes enables to control one or more settings in each of the two or more wet-etching processes based on the second calculation data according to each of the wet-etching processes or the second calculation data after each of the wet-etching processes to optimize the quality of the sample. Thus, it can be said that the method is suitable for each consecutive wet-etching treatment with different or the same chemical liquid composition of the same sample surface.

[0049] According to a second aspect of the present disclosure, a computer program product comprising instructions which, when the program is executed by a computer or data processing device, cause the computer or data processing device to carry out the method according to the first aspect of the present disclosure is provided.

[0050] The computer program product can be a computer program, in particular meaning a computer program consisting of or comprising program code to be executed by the computer or data processing device. Alternatively, the computer program product can be a product such as a data storage medium, in particular a computer-readable data storage medium, on which the computer program can be at least temporarily stored.

[0051] According to a third aspect of the present disclosure, a data processing system configured to carry out the method according to the first aspect of the present disclosure is provided.

[0052] The data processing system can comprise one or more computers or data processing devices as described before, and optionally, the computer program product of the second aspect of the disclosure.

[0053] According to a fourth aspect of the disclosure, a sample processing system is provided, the sample processing system comprising a data processing system of the third aspect of the disclosure, a light source for illuminating a sample surface, and an image sensor for obtaining a number of measurement data.

[0054] The sample processing system can in particular be a wafer processing system configured for processing a wafer, in particular a wet etching system, or in other words, a system configured for performing a wet etching process.

[0055] For example, the sample processing system can comprise a container for containing a chemical liquid for wet etching a sample, and a dispenser fluidly connected to the container for dispensing the chemical liquid from the container onto a sample surface of the sample.

[0056] The image sensor and the light source can be part of a measurement system of the sample processing system. Further, the measurement system can comprise a measurement unit for obtaining the second measurement data, e.g. in the form of a spectrometer. Further, the wet etching processing system can comprise a chamber or device for containing the sample during dispensing of the chemical liquid onto the sample surface. Further, a rotation unit can be provided in the wet etching processing system for rotating the sample during dispensing of the chemical liquid. Further, the wet etching processing system can comprise a feed line, a pump and / or the like fluidly connecting the dispenser with the container. Similarly, a drain line, a pump and / or the like can be provided in the wet etching processing system for fluidly connecting a drain portion of the chamber or device with the container to enable the chemical liquid for etching the sample in the chamber or device to drain therefrom and to be recirculated to the container.

[0057] If two or more different wet etching processes are used, in particular each using a different chemical liquid, the wet etching processing system can comprise two or more containers for each of the different chemical liquids. Further, the wet etching processing system can comprise separate chambers or drain portions within one chamber or device for draining and recirculating each of the different chemical liquids into their respective containers. Further, the wet etching processing system can comprise an actuator for moving the sample between at least two chambers or drain portions, e.g. in the form of a linearly movable axis between two chambers or drain portions, which actuator can also be rotatable or rotatably connected to a rotation unit.

[0058] It is noted that the above-described aspects, examples and features can be combined with each other, irrespective of the aspects involved.

[0059] The above and other aspects of the disclosure will be apparent from and elucidated with reference to the drawings described hereinafter. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Exemplary embodiments will be further described with reference to the accompanying drawings, in which:

[0061] Figure 1 A perspective view of a sample processing system is shown according to an example.

[0062] Figure 2 Shown Figure 1 Schematic diagram of the sample processing system and its components.

[0063] Figure 3 Shows the etching process of the wafer Figure 1 and Figure 2 A perspective view of the processing chamber of the sample processing system.

[0064] Figure 4 A schematic diagram illustrating the BEOL process of a semiconductor manufacturing process.

[0065] Figure 5 and Figure 6 The quality of the wafer as defined herein is shown in FIG. Figure 4 Schematic diagram showing the results of different settings controlled during different etching processes.

[0066] Figure 7 The method for controlling the quality of the wafer as defined herein is shown. Figure 4 Schematic diagram of the wet etching process method and its results.

[0067] Figure 8 Shown for determining Figure 1 and Figure 2 Schematic diagram of the method for measuring the surface roughness of a sample surface within a sample processing system.

[0068] Figure 9 and Figure 10 Schematic diagram showing the results of optical 3D measurement of a sample surface with different brightness levels.

[0069] Figure 11 Schematic diagram showing the calculated roughness of a sample surface for multiple optical 3D measurements at different brightness levels.

[0070] Figure 12 Schematic diagram showing the calculated roughness of the sample surface for multiple optical 3D measurements at different exposure ratios.

[0071] Figure 13 A schematic diagram showing the calculation of surface roughness using kernel density estimation.

[0072] Figure 14 A schematic diagram of a density function for optical three-dimensional measurement at different exposure ratios is shown. Figure 11

[0073] Figure 15 A schematic diagram of a density function for optical three-dimensional measurement at different exposure ratios is shown. Figure 12

[0074] The drawings are merely schematic and are not drawn to scale. Identical or similar elements, components, and / or steps are provided with identical or similar reference signs in the figures. DETAILED DESCRIPTION

[0075] Figure 1 A perspective view of a sample processing system 10 is shown, which is exemplarily embodied as a wet etching processing system 10 in this context, or in other words, as a system 10 for performing a wet etching process according to the example. However, alternatively or additionally, any other processing of samples 1 can be provided by the system 10. The sample processing system 10 of the example comprises a housing 11 and an obtaining section 12 for obtaining samples 1, which are in this exemplary case semiconductor wafers 1 (see Figure 3 ).

[0076] As indicated in Figure 1 , the wafers 1 can be obtained from individual containers 40 (as indicated in Figure 1 ) containing the wafers 1. Only as an example, two containers 40 are shown in this context, however, the number of containers 40 can be less or more. For example, one or more of the containers 40 can contain wafers 1 which have not yet been processed by the system 10, in particular not yet wet etched, and one or more other containers 40 can obtain or receive the wafers 1 after they have been processed or wet etched by the system 10.

[0077] In addition, the system 10 comprises a data processing system 20, which is exemplarily shown in this context as having an interface and a monitor for receiving input from a human operator. The data processing system 20 is exemplarily shown outside of the housing 11, however, can alternatively also be positioned inside of the housing 11 and for example without the monitor and the interface.

[0078] Figure 2 ​​A sample processing system 10 is shown in a schematic view. Generally, any system, parts and the like as shown in the system 10 are shown herein only schematically with regard to position, size and number and can differ from shown in position, size or number. Wafer 1 to be etched is received from one or more of the shown containers 40 via an intake 12, e.g. an opening within a housing 11, and in particular via a processing section 13. The processing section 13 can comprise one or more handling devices 14, such as one, two or more robotic arms, e.g. for handling the wafer 1. In particular, the handling devices 14 can provide the wafer 1 to be etched to a processing section 15, in which a chamber 16 or a device can be located for etching the wafer 1. In particular, there can be several processing sections 15 and / or chambers 16 or devices. For example, the wafers 1 can be processed in parallel by the respective sections 15 and / or chambers 16. Similarly, once the wafers 1 have been etched, the one or more handling devices 14 can receive the wafers 1 again and provide them inside one or more other containers 40 for receiving the processed wafers 1.

[0079] The chamber 16 or the device can be supplied with a chemical liquid 18, which comprises one or more chemical etchants for etching the wafer 1. The chemical liquid 18 can be contained within one or more containers 17, or in other words, within a tank for containing the chemical liquid 18. The containers 17 can for example be in a range of one to four. The containers 17 can be located inside the system 10, in particular the housing 11, or for example outside the system 10 and connected to the system 10, e.g. via a hose. The chemical liquid 18 can also be referred to herein as a bath or a bath of chemical liquid 18. In particular, as outlined below with regard to Figure 4 Exemplarily explained, different chemical liquid compositions can be provided within two or as exemplarily shown three or more containers 17 for different chemical etching processes 131, 132, 133.

[0080] The sample processing system 10, e.g. in the processing section 15, can further comprise one or more measurement systems 30, which can comprise one or more sensor units, including one or more camera units, in particular one or more image sensors and one or more light sources, for obtaining first measurement data indicative of material removal, thickness and / or surface roughness of one or more wafers 1 etched by the chemical liquid 18 after one or more or each of the wet etching processes 131, 132, 133. Optionally, the measurement system 30 can further comprise a measurement unit for obtaining second measurement data indicative of a composition of the chemical liquid 18 within the container 17, e.g. in the form of a spectrometer.

[0081] Further, asFigure 2 As shown, the data processing system 20 can comprise a data processing device 21, e.g. in the form of one or more computers or computing units. Further, the data processing system 20 can comprise a computer program product 22, e.g. in the form of a computer-readable storage medium 22, on which a computer program 23, e.g. in the form of a computer program product 23, can be stored. When the instructions of the computer program 23 are executed by the data processing device 21, the method 200 as shown and explained in the following can be performed. Figure 7 As shown and will be explained in the following, the method 200 can be performed. Alternatively or additionally, when the instructions of the computer program 23 are executed by the data processing device 21, the method 300 as shown and will be explained in the following can be performed. Figure 8 As shown and will be explained in the following, the method 300 can be performed. Alternatively or additionally, when the instructions of the computer program 23 are executed by the data processing device 21, the method 200 as shown and explained in the following can be performed.

[0082] Figure 3 A perspective view of the processing chamber 16 of the sample processing system 10 is shown. In this example, a wet etching is shown as a single wafer etching process, in which a single wafer 1 is etched continuously by dispensing a chemical liquid 18 onto the surface of the single wafer 1. However, alternatively, any other type of wet etching process using the chemical liquid 18 can be used, e.g. a batch etching as described above. In this example, the chemical liquid 18 is delivered, e.g. pumped, to a dispenser 19, e.g. in the form of a nozzle, which dispenses the chemical liquid 18 onto the surface of the wafer 1, in particular the front side, which is arranged within the processing chamber 16. Thus, a feed line, a pump and / or the like can be arranged within the processing section 15 and connect the container 17 with the chamber 16, in particular the dispenser 19 therein. Further, a discharge line for discharging the chemical liquid 18 from the container 17 can be arranged at the container 17. For example, the wafer 1 can be rotated during the dispensing of the chemical liquid 18 by a rotation unit (not shown), which can be arranged, e.g. below the wafer 1 and driven by an actuator, e.g. an electric motor. Further, the wafer 1 can be lifted from the processing chamber 16, e.g. for cleaning, by a lifting unit (not shown), which can be arranged, e.g. below the wafer 1 and driven by an actuator, e.g. an electric motor. Figure 3 As can be seen, the wafer 1 can be lifted to different levels or discharge sections of the processing chamber 16, e.g. for successive wet etchings using different chemical liquids 18, e.g. also by a lifting such as an electric motor or the same actuator.

[0083] Figure 4A production line back end (BEOL) process 100 of a semiconductor manufacturing process is schematically shown. In the exemplary shown BEOL process for power semiconductor devices employing a wafer 1, a wet etching can be used for a wet chemical surface processing 130 of the wafer 1. Typically, a tape bonding or a glass carrier wafer 110 and a wafer backside grinding 120 are performed prior to the wet etching surface processing 130. During a typical BEOL process 100 of semiconductor manufacturing, a contact formation and annealing 140 and a backside metallization 150 can follow the wet etching.

[0084] Furthermore, as shown by the wet chemical surface processing 130, for example, three different etching processes 131, 132, 133 can be performed consecutively, wherein each of the three different chemical liquids 18 as shown in Figure 2 may be used, thereby distinguishing the wet etching processes 131, 132, 133 from each other. For example, a first wet etching process 131 can be used for preparing the surface of the wafer 1 to be etched. For example, for this wet etching process, HF can be used as chemical liquid 18. A second wet etching process 132 can be used for a polishing etch of the surface of the wafer 1. Here, for example, a different chemical liquid 18 can be used (in terms of its composition), for example, comprising HNO3, HF, H2SO4, and H3PO4. A third wet etching process can be used for a rough etch of the surface of the wafer 1. Here, again, a different chemical liquid 18 can be used, for example, comprising HNO3, HF, H2SO4. Thus, each wet etching process 131, 132, 133 differently processes the surface of the wafer 1 based on the chemical liquid 18 or wet chemical composition used, and can be attributed to the aforementioned intentions, i.e., surface preparation, polishing, and rough etching.

[0085] Figure 5 A schematic diagram of the etching results based on the settings named fixed time correction of the time controlled during the wet etching process 133 as shown in Figure 4 is shown. Specifically, Figure 5The left figure in FIG shows that as the bath of the chemical liquid 18 in the corresponding container 17 for the rough etching of silicon for surface roughening becomes older over time, the removal of silicon (Si) in μm and the roughness Ra in nm become smaller with each wet etched wafer 1, in particular in a linearly decreasing manner. In this context, the roughness Ra is exemplarily selected as the average or arithmetic mean of the profile height deviation relative to the average line. This is because during the wet etching process 133 of the wafer 1, the chemical liquid 18 changes over its lifetime, in particular due to the chemical reaction of the chemical liquid 18 with the material of the wafer 1 (e.g., Si), which actually consumes one or more etchants within the chemical liquid 18 or makes them less effective or ineffective. When the same chemical liquid 18 is used during the wet etching process 131, the changes in the wet chemistry over its lifetime can change the etching results of the wafers 1 that are continuously etched over the lifetime of the wet chemistry.

[0086] Therefore, it may be necessary to replace the bath of chemical liquid 18 in order to maintain the desired consistency of Si removal and roughness in wafers 1 etched by the same bath of chemical liquid 18. However, an alternative action may be a fixed time correction based on time. The control setting of this action may be to change the etching duration, thereby correcting the time based on the usage time of the bath of chemical liquid 18 to date. For example, as the usage time of the bath increases, the time that chemical liquid 18 is dispensed onto each wafer 1 may increase, thereby increasing the time that chemical liquid 18 is able to etch the surface of the wafer 1. Figure 5 As shown in the right figure of , this effectively reduces Si removal and roughness degradation over time of the bath, and thereby allows control of the etching quality, i.e., the consistency of etching results, of wafers 1 etched over time using the same bath.

[0087] Figure 6 Shown in Figure 4 During the wet etching process 132 shown, the fixed time correction setting (as described above with reference to Figure 5 Schematic diagram of etching results for a setup with a chemical liquid 18 buffered or spiked with a chemical etchant (HF here). Figure 6 The left figure in FIG. 1 shows that as the bath of the chemical liquid 18 in the corresponding container 17 for the rough etching of silicon for surface roughening becomes older over time, the Si removal in μm becomes less with each wet etched wafer 1, in particular in a linearly decreasing manner. Therefore, it is necessary to replace the bath of the chemical liquid 18 in order to maintain the desired quality of Si removal and roughness. However, as shown in the middle figure and referred to above, Figure 5The alternative action to be explained can be a time-based fixed time correction. The control setting of this action can be a change of the etching duration, thereby correcting the time based on the usage time of the bath of chemical liquid 18 so far. In particular, the time of chemical liquid 18 dispensed onto each wafer 1 can be increased with increasing usage time of the bath, thereby increasing the time of which chemical liquid 18 can etch the surface of wafer 1. As Figure 6 illustrated in the middle diagram of Fig. 1 1, this effectively reduces the decrease of Si removal and roughness with usage time of the bath and thereby allows controlling the quality of wafers 1 etched over time with the same bath. As Figure 6 illustrated in the right diagram of Fig. 1 1, an alternative control action can be a buffering or doping of the chemical etchant (here exemplarily HF). The control setting based thereon can be a change of the composition of chemical liquid 18, e.g. by adding HF as chemical etchant, thereby buffering or doping chemical liquid 18 with HF. As illustrated in the right diagram, this can even enhance the Si removal consistency over the usage time of the bath of chemical liquid 18.

[0088] Figure 7 A schematic diagram of a method 200 for controlling any, multiple or all of the wet etching processes 131, 132, 133 of Fig. 1 1 and their etching results of Fig. 1 2 is shown (on the left side of Fig. 1 3) and its etching results (on the right side of Fig. 1 4). For example, the method 200 mentioned in Fig. 1 1 is to be used for the wet etching processes 132 and 133, which can be performed consecutively. Figure 4 Figure 7 Figure 7 Figure 7

[0089] In a first step 210 of the method 200, measurement data is obtained, which is indicative of the material removal (e.g. Si in pm), thickness (e.g. wafer thickness in mm, etc.) and / or surface roughness (e.g. Ra in nm) of the last wafer 1 etched by the respective chemical liquid 18 used for this wet etching process 132 or 133. This step can in particular be performed by the data processing system 20 and / or the measurement system 30. For example, the measurement system 30 can obtain the measurement data by measurement and forward it to the data processing system 20, thereby obtaining the measurement data in the data processing system 20 and can further process it, in particular for the second step 220 which can follow the first step 210.

[0090] ​​​​In a second step 220, based on the measurement data, control data for controlling one or more settings of the respective wet etching process 132, 133 are obtained, in particular determined, by the data processing system 20, after the measurement data for the wafer 1 to be etched thereafter have been obtained. For example, the one or more settings can be a change of the etching duration, e.g. a fixed time correction as explained above, a change of the composition of the chemical liquid 18, e.g. a buffering or spiking with HF as explained above, and / or an at least partial or complete exchange of the chemical liquid 18, i.e. a change of a part or all of the bath of the chemical liquid 18 within the vessel 17 for the respective wet etching process 132, 133.

[0091] In particular, the method 200 can be performed twice, once for performing after the wet etching process 132 and once for performing after the wet etching process 133 on the wafer 1, thereby obtaining control data for controlling one or more settings of each of the wet etching processes 132, 133. Thus, as Figure 7 shown in the right part of the figure, after each wet etching process 132, 133, its settings can be controlled such that the results are optimized. Therein, it is shown that by controlling the wet etching processes 132, 133, the Si removal and the roughness can be kept constant or substantially constant over a very long bath usage period, and that this quality control can even be enhanced, in particular by using a mix of the mentioned settings, e.g. by first changing the etching duration, then changing the composition of the chemical liquid 18, and finally changing the chemical liquid 18, or in other words, the bath as indicated with the star in the figure.

[0092] Further, as Figure 7 shown, the method steps 210 and 220 can be repeated, e.g. for each or every few wafers 1 processed by the wet etching process 132 and / or the wet etching process 133, thereby continuously monitoring the bath or the chemical liquid 18 by means of the measurement data of the wafers 1, and updating the control data when necessary or beneficial.

[0093] When the measurement data obtained from the measurement system 30 are used for the method 200 or any other purpose, e.g. for any other method of quality control assurance, the measurement data received directly from the measurement system 30 can not be accurate enough to provide a high etching quality as Figure 7 shown, or at least it can be desirable to increase the accuracy of the measurement data. This is because the measurement data, e.g. the surface roughness indicated thereby, can not be an accurate or reproducible measurement for different types of wafers 1, e.g. with shiny or rough surfaces.

[0094] For measuring the surface roughness of the sample 1, an image of the treated sample surface, in particular a real-time image, is known. For obtaining accurate results, it can be necessary to adjust the parameters of the camera capturing the image to eliminate external disturbances. For example, the reflection characteristics of the particular sample surface and / or material can be taken into account for adjusting or calibrating the camera parameters. However, it is still challenging to determine the surface roughness accurately, but it is highly desirable to determine the surface roughness as accurately, quickly and reliably as possible, possibly of different kinds, in particular or at least in terms of size, material and / or reflection characteristics, of the sample 1, such that the method 200 provides results of high etching quality, for example.

[0095] For this purpose, for example, Figure 8 The method 300, which is schematically shown in Fig. 3, can be performed, in particular, Figure 7 separately from the method 200 of the system 10, as Figure 7 part of or in addition to the method 200 of the system 10. The method 300 is configured for determining the surface roughness of the sample surface of the sample 1, in particular of the wafer 1, inside the system 10.

[0096] The measurement system 30 and / or the data processing system 20 is configured to obtain several measurement data based on the optical three-dimensional measurement of the wafer surface, in particular by the three-dimensional optical measurement of the wafer surface by the same image sensor, each of the measurement data being indicative of the surface topology of the wafer surface, wherein each of the measurement data is associated with a different brightness level of the light source illuminating the wafer surface or with a different exposure of the image sensor. For obtaining the several measurement data, the steps 310, 320, 330 and 340 of the method 300 are repeated several times.

[0097] In particular, in step 310, the optical three-dimensional measurement of the sample surface by the image sensor can be performed at a particular brightness level of the light source or a particular exposure of the image sensor. The optical three-dimensional measurement can be based on white light interferometry. For example, the method 300 can start with a 10% or 11% brightness level of the light source (compared to a nominal, e.g. maximum brightness level) or a 10% or 11% of the exposure ratio of the image sensor (compared to a nominal, e.g. maximum exposure ratio). In Figure 9 Results of the optical three-dimensional measurement at 11% brightness level are exemplarily shown in Fig. 3, showing the surface in three dimensions, i.e. height (in pm), x-axis and y-axis (in pixels). Similar results can be obtained for an exposure ratio of 11% (not shown).

[0098] Then, optionally, in step 320, the measurement data obtained from step 310, i.e. the optical three-dimensional measurement indicative or comprising the surface topography at a certain brightness level or exposure ratio, can be filtered, e.g. according to the ISO 25178 standard. For example, in sub-step 321, data points outside the sample surface can be removed. Further, for example, in sub-step 322, noise can be removed. Further, for example, in sub-step 323, the image representing the surface topography as shown in Fig. 1 1 can be cropped. Further, for example, the image can be leveled in sub-step 324. Figure 9

[0099] Then, in step 330, it is determined whether the brightness level or exposure ratio is at a predetermined threshold or level. If not, the method 300 continues with step 340, in which the brightness level or exposure ratio is increased by a predefined increment, e.g. 1 % or less or more, and steps 310 to 330 and / or 340 are repeated. At the same time, the respective other parameter, i.e. the brightness level or exposure ratio, can remain constant, e.g. at 100% or any other value. Thus, several measurement data are thereby obtained in association with different brightness levels or exposures increased by the increment until the predefined threshold or limit is reached, e.g. 100% of the brightness level or exposure, as exemplarily shown in Fig. 1 1. Thus, if the result of step 330 is that the threshold or level is reached, the method 300 continues with step 350 and step 360. Figure 10

[0100] Generally, after determining the result of step 330 to be “yes”, or at each step 330 or any other step, or between any steps of the method 300, the method 300 can comprise obtaining, in particular by the data processing system 20, for each of the measurement data a first calculated data indicative of a surface roughness of the sample surface. In other words, a surface roughness value, e.g. as the average or arithmetic mean of the profile height deviations with respect to the mean line (Ra), can be determined, in particular calculated, for each of the several measurement data, i.e. the surface topography from the optical three-dimensional measurement at a certain brightness level or exposure. Thus, for each of the measurements, there can be one calculated surface roughness value associated with the measurement.

[0101] Figure 11 The calculated roughness values with increasing brightness levels in % are shown in Fig. 1 1. The repetition of steps 310 to 330 and / or 340, i.e. the measuring of the surface topography and filtering of the measurement data and potentially increasing the brightness level or exposure by an increment, is also referred to herein as a scan, in particular a brightness scan for increasing brightness levels or an exposure ratio scan for increasing exposure ratios. Figure 12 ​​It is shown that the roughness values calculated when measuring the same sample surface at different exposure ratios, but not at different brightness levels, fluctuate significantly depending on the used brightness level or exposure ratio. It is to be noted that the results also depend on the reflection characteristics of the measured sample or wafer 1, i.e. a rather shiny wafer 1 will have different reflection characteristics than a less shiny or rough wafer 1 and, thus, it is not possible to simply calibrate the image sensor to a certain brightness level or exposure ratio at which the results will be comparable to each other for different wafer surfaces.

[0102] Furthermore, as shown in Figure 11 and Figure 12 the brightness and exposure ratio scans eventually lead to almost identical sample roughness results. The relevant difference between brightness and exposure ratio is the measurement duration. For the exposure ratio scan, the measurement duration was found to be about 2.5 minutes, while the measurement duration for the brightness level scan was found to be about 52 seconds. The reason behind this is that brightness can be updated dynamically during the measurement acquisition, while the exposure ratio needs to reconfigure the entire image sensor or camera again, which takes almost 3 times longer than the brightness approach.

[0103] After obtaining the first calculation data, a second calculation data indicative of the surface roughness of the sample surface for all measurement data can typically be determined, in particular by the data processing system 20. In other words, the surface roughness values of each single measurement data are combined into a single surface roughness value representing the accurate surface roughness value of the sample surface.

[0104] For determining the second calculation data, the method 300 can comprise, at step 350, calculating a density function of each of the surface roughnesses of the sample surface for each of the measurement data, and, at step 360, determining the surface roughness of the sample surface for all measurement data based on the density function. For calculating the density function, for example, a Kernel Density Estimation (KDE) as exemplarily shown in Figure 13 may be used.

[0105] In particular, the KDE can be applied to the entire list of calculated roughness values collected to calculate the sample roughness for all measurement data. The KDE is a statistical method for estimating the probability density function (PDF) of a random variable. Unlike a histogram, which bins data, the KDE can produce a smoother representation of the data distribution.

[0106] For each data point x i , e.g. the taken measurement, a kernel function K(x-x i), which can generally be a smooth and symmetric function, such as a Gaussian function. The kernel function is then placed at the center of each data point. The width of the kernel function is then determined by choosing a bandwidth "h". The larger the bandwidth, the smoother the estimate, while a narrower bandwidth yields a more accurate but possibly a bit noisier estimate. The final step is to sum up these kernel values for all observed data points. This yields the contribution of all data points to the density estimate at a point "x", as shown in Figure 13

[0107] Thus, it can be concluded that the density estimate at x (peak) is where n is the number of observed data points, K is the kernel function, and h is the bandwidth.

[0108] Figure 14 and Figure 15 The results of the method 300 are shown in the form of a plot of the density function of the luminance scan Figure 14 ) and the exposure ratio scan Figure 15 ) versus the sample roughness value. Both the luminance scan and the exposure ratio scan yield similar results for the surface roughness of the sample surface, namely about 289 nm and about 299 nm. Specifically, for all measured data as indicated or included by the second calculated data, the peak of the plot can be determined as the surface roughness of the sample surface.

[0109] Optionally, three regions of interest can be observed: a left side region of the peak, a region below the peak, and a right side region of the peak. First, the left side region of the peak can be considered as an underexposed region, where the light is not enough for sample 1, then the light is increased until a second region is reached. The second region is the region just below the peak, which can be considered as a well-exposed region, where all valid calculation results are captured in this region. Then, the light is still increased until a third region of overexposure is reached, where the light is more than what is needed for sample 1. The higher the accuracy of the roughness calculation, the higher the density peak in the well-exposed range.

[0110] Finally, there is no longer a need to adjust the parameters that can be used for the roughness calculation. The method 300 is applicable to any kind of wafer surface (whether shiny or rough) by either the luminance or the exposure ratio scan. Regardless of the reflectivity of the sample, the peak will be detected and thus an accurate surface roughness is obtained.

[0111] While the application has been illustrated and described in detail in the drawings and foregoing description, such illustration and description is to be considered illustrative or exemplary only; the application is not limited to the disclosed embodiments. Other variations of the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed application, from an study of the drawings, the disclosure, and the claims. ​

[0112] As used herein, the word "comprising" does not exclude other elements or steps, and the phrases "at least one", or similar, as used herein in relation to a list of one or more entities should be understood to mean at least one entity selected from the list of entities, but not necessarily including at least one of each and every entity specifically listed within the list of entities and not excluding any combinations of entities in the list of entities. This definition also allows that entities can optionally be present other than the entities specifically identified within the list of entities to which the phrase "at least one" or the like applies, whether related or unrelated to those entities specifically identified within the list of entities to which the phrases "at least one" or the like applies. Thus, as a non-limiting example, "at least one of A and B" (or, equivalently, "at least one of A or B" or, equivalently "at least one of A and / or B" or, equivalently "at least one of A, B or C, or any combination thereof") can refer, in one example, to at least one A, optionally including more than one A, while excluding B; in another example, to at least one B, optionally including more than one B, while excluding A; in yet another example, to at least one A, or at least one B, or optionally both A and B, etc. In other words, the phrases "at least one of A and B", or the like, as used herein, are open-ended expressions that are intended to be given their plain and ordinary meaning and thus can be applicable to multiple entities of A and B, comprise one, all, or none of A and B, etc.

[0113] As used herein, the phrase "indicates" can mean, for example, "reflects" and / or "comprises". Thus, entities, elements and / or steps referred to herein as "indicative of" can be used herein synonymously with, or interchangeably with, said entities, elements and / or steps "comprising of" and said entities, elements and / or steps "reflecting".

[0114] Furthermore, unless otherwise indicated, the phrase “based on” shall not be construed as a reference to an entity, element or step being “based on” only one or another entity, element or step, unless explicitly stated otherwise. Rather, the phrase “based on” shall be construed in a manner that encompasses both an entity, element or step being “based on” one or more entities, elements or steps by virtue of being based on them directly or as processed by another entity, element or step, and / or an entity, element or step being “based on” one or more entities, elements or steps by virtue of being based on them indirectly via the processing by another entity, element or step.

[0115] The designation of methods and steps as first, second, etc. provided herein is merely intended to differentiate among different methods and steps. The designation of methods and steps does not in any way limit the scope of the present disclosure. For example, when the present disclosure describes a third step of a method, the first or second step of the method does not need to be performed prior to the third step to be performed separately, unless they are explicitly referred to as necessary or prior to the third step. Furthermore, the presentation of methods or steps in a certain order merely is intended to promote ease of understanding the present disclosure and is in no way intended to limit the scope of the present disclosure. Generally, the methods and steps can be performed in any feasible order, unless an explicit order is mentioned. Specifically, the terms first, second, third or (a), (b), (c) etc. are used merely to identify similar elements, and are not necessarily intended to describe a sequential or chronological order. It is to be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the application described herein are capable of operating in other sequences than the one described or illustrated herein.

[0116] In the context of the present application, any numerical values indicated are generally associated with an interval of accuracy that will be understood by the skilled person to still ensure the technical effect of the feature in question. As used herein, a deviation from the indicated numerical value is within the range of ±10%, and preferably within the range of ±5%. The aforementioned deviation of ±10%, and preferably ±5%, from the indicated numerical value interval is also indicated by the terms “about” and “approximately” used herein in connection with numerical values.

[0117] Any reference signs in the claims should not be construed as limiting the scope.

Claims

1. A method (300) for determining the surface roughness of a sample surface of a sample (1), the method (300) comprising: - obtaining a plurality of measurement data based on an optical three-dimensional measurement of the sample surface by an image sensor, each of the measurement data indicating a surface topology of the sample surface, wherein each of the measurement data is associated with a different brightness level of a light source illuminating the sample surface or with a different exposure of the image sensor; - obtaining first calculated data indicative of the surface roughness of the sample surface for each of the measurement data; and - determining second calculated data indicative of the surface roughness of the sample surface for all measurement data based on the first calculated data.

2. The method (300) of claim 1, wherein: The sample (1) is a wafer (1).

3. The method (300) according to claim 1 or 2, wherein: The optical three-dimensional measurement is based on white light interferometry.

4. The method (300) according to any one of the preceding claims, wherein: Each of the measurement data is associated with a different brightness level or a different exposure that is incrementally increased or decreased between consecutive measurements made by the image sensor.

5. The method (300) according to claim 4, wherein: The increments are: ○ The size is within the range of 0.1% to 8% of the nominal brightness level or nominal exposure, and / or o Between 5% or more of the nominal brightness level or the nominal exposure and 80% or more of the nominal brightness level or the nominal exposure.

6. The method (300) according to claim 4 or 5, wherein: One of the brightness level and the exposure remains substantially constant between the successive measurements made by the image sensor.

7. The method (300) according to any one of the preceding claims, wherein: The method (300) comprises: - filtering each of the measurement data by one or more of: removing data points outside the sample surface, removing noise, cropping an image representing the surface topology indicated by the measurement data, and leveling the image; The first calculated data is based on each of the filtered measurement data.

8. The method (300) according to any one of the preceding claims, wherein Determining the second calculation data includes calculating a density function for each of the surface roughnesses of the sample surface for each of the measurement data, and determining the surface roughnesses of the sample surface for all the measurement data based on the density function.

9. The method (300) of claim 8, wherein: The surface roughness of the sample surface for all measurement data is determined based on the maximum value of the density function, or the surface roughness of the sample surface for all measurement data is determined as the maximum value of the density function.

10. The method (300) according to claim 8 or 9, wherein: Determining the second calculated data includes repeatedly obtaining the number of measurement data, the first calculated data, and determining the second calculated data if the calculated density function indicates two peaks in the surface roughness of the sample surface for all measurement data.

11. The method (300) according to any one of the preceding claims, wherein: The sample surface is an etched sample surface, and wherein the method comprises: - based on the second calculated data, obtaining control data for controlling one or more settings of a wet etching process (131, 132, 133) to be performed on one or more further samples (1).

12. A computer program product (22, 23) which, when executed by a data processing device (21), instructs the data processing device (21) to perform the method (300) according to any one of the preceding claims.

13. A data processing system (20) configured to perform the method (300) according to any one of claims 1 to 11.

14. A sample processing system (10), comprising a data processing system (20) according to claim 13, a light source for illuminating the sample surface, and an image sensor for obtaining the plurality of measurement data.

15. The sample processing system (10) of claim 14, wherein: The sample processing system (10) includes a container (17) for containing a chemical liquid (18) for wet etching a sample (1), and a dispenser (19) fluidically connected to the container (17) for dispensing the chemical liquid (18) from the container (18) onto a sample surface of the sample (1).

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