Patent Description:
Two-dimensional materials such as graphene and TMDC materials (transition metal dichalcogenide), have been under intense study for the past several years due to their unique mechanical and electrical properties. Of particular interest are the 2D semiconductor materials, i.e. 2D materials which exhibit a bandgap. The TMDC materials MoS<NUM> and WS<NUM> are examples of such 2D semiconductor materials. One of the factors that can strongly influence the performance of 2D semiconductor materials is the trap density which is dependent on intrinsic or contamination- related material properties of the 2D material, and on the substrate onto which the 2D layers are placed. Defects within the material or at the interface with the support substrate may generate electron or hole traps in the bandgap.

For both graphene and TMDCs, it has been shown that traditional support substrates such as SiO<NUM> can cause increased scattering, while enhanced performance is achieved when atomically flat 2D dielectrics, such as hexagonal boron nitride (hBN), are employed as support substrates. Performance, however, is often measured in terms of carrier mobility, which requires full device processing before the metric can be acquired. Device processing can however introduce non-idealities in the material which are difficult to deconvolute from electrical measurements.

The use of photoluminescence-based techniques has been explored for studying the properties of the interface between 2D TDMC materials and different support substrates. The direct photoluminescence peak of one monolayer of MoS<NUM>, around <NUM>. 8eV, contains information on thickness, doping and strain. Also, direct exciton lifetime measurements can give insights on interface scattering.

However, at this time there is no practical non-invasive technique that allows to measure the trap density in a 2D semiconductor material. Such a technique is crucial for the in-line measurements of the trap density in a semiconductor production process.

Document "<NPL> reports an anomalous photoluminescence quenching with decreasing temperature for multilayer WSe<NUM>. This document discloses the transition routes of a multilayer Wse<NUM> including direct transition and indirect transition, and the photoluminescence (PL) spectra as a function of the wavelength obtained using an excitation laser at <NUM>, obtained by varying the temperature.

Document "<NPL> discloses the exciton dynamics in transition metal dichalcogenide monolayers using time-resolved photoluminescence experiments performed with optimized time resolution.

Document "<NPL> discloses carrier recombination dynamics in MoS2 monolayers. The authors present a model for carrier recombination dynamics that quantitatively explains all features of the obtained data for different temperatures and pump fluences. The theoretical estimates for the rate constants for Auger carrier capture are in good agreement with the experimentally determined values.

Document "<NPL> discloses results on photoexcited carrier lifetimes in few-layer transition metal dichalcogenide MoS<NUM> using nondegenerate ultrafast optical pump-probe technique. The results show a sharp increase of the carrier lifetimes with the number of layers in the sample and suggest that carrier lifetimes in few-layer samples are surface recombination limited due to the much larger defect densities at surface layers compared with the inner layers.

Document "<NPL> discloses that the relative intensities of the A- and B- emission features can be used to qualitatively asses the non-radiative recombination, and thus the quality of the sample.

The invention aims to provide a solution to the above-described problems. This aim is achieved by the method according to independent claim <NUM>.

The invention is equally related to an apparatus configured to perform the method of claim <NUM>, defined in independent claim <NUM>.

According to an embodiment, the carrier concentration is modulated by illuminating the spot with a laser and by modulating the output power of the laser.

According to an embodiment, the layer of 2D semiconductor material is deposited on a dielectric layer that is itself deposited on an electrically conductive substrate, and wherein the carrier concentration is modulated by changing a bias voltage between the layer of 2D semiconductor material and the conductive substrate.

According to an embodiment, the layer of 2D semiconductor material consists of at least two monolayers of a transition metal dichalcogenide material, hereafter abbreviated as a TMDC material. Said TMDC material may be MoS<NUM> or WS<NUM>.

According to an embodiment, the theoretical model linking the ratio Iind/Idir, the carrier concentration and the trap density is the following : <MAT> wherein <MAT> (in seconds) is the radiative lifetime of the excitons in the indirect bandgap, B is the Auger rate constant I, N is the carrier concentration (in cm-<NUM>), nd the trap density (in cm-<NUM>), Fd the defect occupancy state, and a and b are correction terms which account for experimental uncertainties.

The invention is equally related to an apparatus for performing the method of claim <NUM>, defined in independent claim <NUM>.

According to an embodiment, the light source is a laser configured to produce a laser beam, the output power of which may be incremented within in a given range.

According to an embodiment, the light source is a laser and the apparatus further comprises a voltage probe configured to apply a bias voltage to the layer of 2D semiconductor material.

According to an embodiment, the apparatus is integrated in an apparatus for producing the layer of 2D semiconductor material on the support substrate.

The invention is equally related to the use of the method for performing in-line measurements of the trap density in a semiconductor production process, according to claim <NUM>.

The invention is equally related to the use of the apparatus for performing in-line measurements of the trap density in a semiconductor production process, according to claim <NUM>.

The invention is equally related to a computer program product configured to run on a processing and calculation unit of the apparatus of claim <NUM> and execute the following steps :.

As stated above, the direct photoluminescence peak of TMDC semiconductor materials has been used for characterizing a monolayer of the material. However, when multilayer TMDC is considered, the material transitions from a direct bandgap material to an indirect bandgap material, i.e. the material exhibits both direct and indirect bandgap. The band gap is the energy gap between the valence band and the conduction band of the material. For a direct bandgap, the crystal momentum is the same at the maximum energy level of the valence band and at the minimum energy level of the conduction band, whereas for an indirect bandgap, there is a shift in the crystal momentum between the maximum energy of the valence band and the minimum level of the conduction band. This results in differences in terms of the dominant recombination mechanism occurring in the material.

When light is irradiated on a 2D semiconductor material, electron-hole pairs - excitons - are generated by an electron being excited from the valence band to the conduction band, provided that the photon energy of the light source is in excess of the bandgap of the material. Once generated, the electron-hole pair can recombine again through <NUM> mechanisms: Radiative, Shockley-Read-Hall (SRH) or defect-assisted Auger recombination. Radiative recombination occurs through the emission of a photon, which is detectable and which contributes to a specific peak in the photoluminescence (hereafter abbreviated as PL) spectrum, hereafter referred to as the 'direct peak'. Non-radiative recombination, i.e. SRH or defect-assisted Auger recombination, occurs when the exciton combines with a defect-generated trap state.

Radiative recombination is the dominant mechanism for direct bandgaps, even when the trap density is high, as only a photon is needed for the excitons to decay, but for indirect bandgaps, both photons and phonons are needed for radiative recombination, the phonons being required for compensating the difference in crystal momentum. Therefore, non-radiative recombination mechanisms become more important in the case of indirect bandgaps, and in the presence of a sufficiently high trap density. However, with low enough trap density, radiative recombination still occurs also for indirect bandgaps, leading to the appearance of an indirect peak in the PL spectrum, at a lower photon energy compared to the direct peak. The intensity of the indirect peak decreases when the trap density becomes higher. However, the indirect peak is also an inverse function of the carrier concentration in the material. The higher the number of charge carriers, the higher the number of carriers which can recombine with trap states, hence the lower the indirect peak.

The method of the invention uses the above-described relations for determining the trap density through a series of PL measurements at different carrier concentrations, in a 2D semiconductor material that exhibits both direct and indirect bandgaps, like for example a WS<NUM> or MoS<NUM> layer thicker than <NUM> monolayers. The ratio of the PL intensity (i.e. the photon count) of the indirect peak, Iind, to the PL intensity of the direct peak, Idir, is recorded as a function of the carrier concentration. The relation between Iind/Idir and the carrier concentration is then fitted to a theoretical model of the interaction between the carrier concentration and the trap density, taking into account the different recombination mechanisms. According to this model, the inverse relation between the ratio Iind/Idir and the carrier concentration is different for each value of the trap density. So by fitting the measured relation to one of the theoretical relations, the trap density is obtained.

It has been found in prior research that for TMDC 2D-semiconductor materials, the dominant non-radiative recombination mechanism is the defect-assisted Auger mechanism. Taking into account this knowledge, i.e. neglecting the influence of SRH recombination in favour of radiative and Auger recombination, the inventors have developed a theoretical model that links the ratio Iind/Idir to the carrier concentration and the trap density according to the following equation : <MAT> wherein <MAT> (in seconds) is the radiative lifetime of the excitons in the indirect bandgap. <MAT> can be measured or if a measured value is not available it can be used as a fitting parameter (see further). B is the Auger rate constant which can be measured or of which a value or at least an applicable range can be taken from literature for each 2D-semiconductor material. In the last case, B can be used as a fitting parameter within said range (see further). N is the carrier concentration (in cm-<NUM>), nd the trap density in the band gap (in cm-<NUM>) and Fd the defect occupancy state. Fd is related to the Fermi level of the material, and obtainable from literature. The variables a and b are correction terms which account for experimental uncertainties. The terms a and b can be set to zero or used as fitting parameters if the zero value of a and b does not allow to fit the experimental data to the theoretical model. The '∝' symbol indicates 'is proportional to'.

The method of the invention is performed on a sample comprising a support substrate carrying on its surface a layer of a 2D semiconductor material produced thereon, the layer exhibiting both direct and indirect bandgaps. The layer may for example be a TMDC <NUM>-D semiconductor material, such as MoS<NUM> or WS<NUM>, with thickness greater than two monolayers. The layer is then illuminated by a light beam configured to generate a plurality of excitons. This is preferably a laser beam directed to a spot of the layer. The spot may have a diameter in the order of micrometres, for example about <NUM>. For MoS<NUM> or WS<NUM>, a laser beam with a wavelength of <NUM> is suitable. Photons emitted from the spot are detected by a detector configured to obtain the photoluminescence spectrum of the illuminated spot, i.e. the number of the detected photons as a function of their energy. This measurement may be performed using laser and detector tools which are known as such in the prior art for performing photoluminescence measurements.

According to a preferred embodiment, the carrier concentration is modulated by incrementally changing the output power of the laser within a given range. A conceptual view of the required measurement setup is shown in <FIG>. A laser <NUM> is oriented perpendicularly to a sample (other angles of the laser are also possible however), which comprises the base substrate <NUM> carrying a layer <NUM> of the 2D semiconductor material under investigation. A detector <NUM> is mounted laterally with respect to the laser, and is configured to detect photons <NUM> emitted from the irradiated surface of the layer <NUM>.

<FIG> shows the spectra measured on a WS<NUM> flake having a surface of a few square micrometers, present on a SiO<NUM> substrate. The flake has a uniform thickness of <NUM>, i.e. the flake consists of several monolayers of WS<NUM>. The spectra labelled <NUM>, <NUM> and <NUM> are respectively related to measurements obtained at <NUM>%, <NUM>% and <NUM>% of the maximum available laser power of <NUM>. 34MW/cm<NUM> using a <NUM> wavelength laser beam of <NUM> in diameter. The image shows that the indirect peak, at about <NUM>. 55eV, significantly reduces when the laser power increases. This is caused by an increase in non-radiative defect-assisted Auger recombination as the photogenerated carrier concentration increases. Due to the momentum conservation requirement, the indirect peak is more sensitive to nonradiative recombination, explaining the experimental observations. The direct peak remains the same in amplitude but shifts along the X-axis in the range of <NUM> to <NUM> eV, likely from a combination of heating-induced strain and a small degree of local oxidation.

A similar set of spectra is illustrated in <FIG>, measured on MoS<NUM>. The spectra <NUM> through <NUM> corresponding respectively to <NUM>%, <NUM>%, <NUM>% and <NUM>% of the maximum laser power.

The measurements illustrated in <FIG> and <FIG> were obtained under the following conditions. Photoluminescence (PL) spectra were collected in a confocal Raman microscopic system, using exciting lasers with primary wavelength of <NUM> (green). The laser radiation is focused onto the 2D material using a 100x objective lens with a spot-size around <NUM>. Photoluminescence spectra were resolved by a spectrometer using gratings of <NUM>-<NUM> and acquired by a CCD (charge-coupled device) detector. Measurements were performed at room temperature, in air.

The laser power is correlated to the carrier density through the following equation : <MAT> Wherein Plaser is the laser power (in W/cm<NUM>), Aspot is the excitation area (in cm<NUM>), hv the excitation photon energy (in J), R the Fresnel reflection coefficient and α the absorption coefficient of the 2D material. R and α are known from literature. For example for WS<NUM>, R = <NUM> and α = <NUM> τcarrier is the carrier lifetime (in s), which can be measured using known techniques, such as time resolved photoluminescence, or a value or at least an applicable range can be found in literature. In the latter case, τcarrier can be used as a fitting parameter.

<FIG> shows a number of curves which reflect the theoretical relation (<NUM>) for WS<NUM> and for different values of the trap density, ranging from <NUM> x <NUM><NUM> cm-<NUM> for the upper curve <NUM> to <NUM> x <NUM><NUM> cm-<NUM> for the lower curve <NUM>. Superimposed on these curves are the measured values of the ratio Iind/Idir as a function of the carrier concentration, taking into account the relation (<NUM>), and measured on two similar WS<NUM> flakes, as indicated by the two different symbols '▲' and '•'. The correction factors a and b were set to zero. The lifetime of the indirect transition <MAT> is treated as a fitting parameter, since a precise determination of this value is yet unavailable for WS<NUM> and MoS<NUM>. All other parameters were determined from literature. The fitting process involved searching for the value of <MAT> for which the measured data correspond as close as possible to one of the theoretical curves, within reasonable bounds. For the data points measured on WS<NUM>, it was found that when <MAT> is <NUM> nanosecond, the measured data fit to the theoretical curve <NUM> corresponding to a trap density of <NUM> x <NUM><NUM> cm-<NUM>. This illustrates how the trap density can be obtained by the method of the invention.

The example of the measured data points obtained on WS<NUM> and shown in <FIG> was successful for obtaining the trap density using only <MAT> as a fitting parameter, while all the other parameters were either measured or taken from literature, and with correction terms a and b set to zero. However, the method is applicable also when additional parameters are not known or only known within a given range. For example, if measured values of B and τcarrier are not available, nor good estimates of the correction terms a and b, the method may use a fitting algorithm that starts from estimated values for the unknown parameters, possibly lying within predetermined ranges obtained from literature. The fitting process is then performed by iterative steps until a closest match is found between the measured data and the theoretical model, yielding the trap density. Such algorithms are known as such in the art.

According to another embodiment, the carrier concentration is modulated by using a constant laser power, and applying a variable back bias voltage to the substrate onto which the 2D semiconductor material is present. A conceptual view of the required measurement setup is shown in <FIG>. In this case, it is necessary that the 2D material <NUM> is deposited on a dielectric material <NUM>, which is itself deposited on an electrically conductive substrate <NUM>, such as a metal or a highly doped semiconductor. The conductive substrate <NUM> may be grounded, and the bias voltage may be applied by contacting the 2D material <NUM> with a probe needle <NUM> placed at the bias voltage level V relative to the conductive substrate <NUM>. The relation between the bias voltage and the carrier concentration is known from literature, for example from the document "<NPL>. This paper takes into account the influence of the quantum capacitance of the dielectric layer <NUM>, which is however only necessary in the case of very thin dielectric layers. In practice however, the method according to this embodiment does not require such thin layers. A thicker layer <NUM> can thus be used wherein the quantum capacitance is negligable. In this case the carrier concentration can be calculated as the product of the applied bias voltage and the capacitance of the dielectric layer <NUM>. The laser <NUM> and detector <NUM> are the same as in the setup shown in <FIG>. By measuring the PL spectrum at different levels of the bias voltage, the measured relation between the ratio Iind/Idir can thus also be determined, and the above-described fitting process yields the value of the trap density.

The equation (<NUM>) is valid also for other TMDC 2D-semiconductor materials besides WS<NUM>. The invention is however not limited to these materials nor to the equation (<NUM>) for describing the theoretical model. For other materials, the balance between the different recombination mechanisms may require a different theoretical model to be developed. The method of the invention is applicable also in combination with such alternative models.

The method of the invention may be used in-situ or in-line. In situ refers to the measurement of the trap density in the same tool as the one used for producing the 2D semiconductor material on its support substrate. In-line refers to the integration of the method into a semiconductor production process. The latter application is particularly useful as the method of the invention is non-invasive and may be executed quickly without slowing down or disrupting a production line. The method of the invention does not require the fabrication of a test device, and thereby avoids material defects induced by such device fabrication.

The invention is equally related to an apparatus configured to perform the method of the invention. Such an apparatus may be devised for measurements in-situ or for measurements in-line, and the precise details of the apparatus may be slightly different according to these conditions. However, and as illustrated in <FIG> for an apparatus <NUM> suitable for performing the method according to the embodiment of <FIG>, the basic components of any apparatus according to the invention are the following :.

The processing and calculation unit <NUM> may be a computer programmed to determine the measured relation between Iind/Idir and the carrier concentration and further comprising the theoretical relation, for example equation (<NUM>) and an algorithm for performing the fitting process and the determination of the trap density. The invention is also related to a computer program configured to perform the above three steps, when the program is run on the processing and calculation unit <NUM>.

Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, and the disclosure.

Claim 1:
A method for determining a trap density in a layer of a <NUM>-dimensional (2D) semiconductor material, said material exhibiting direct and indirect bandgaps between the valence band and the conduction band, the method comprising the steps of :
- providing a sample comprising a support substrate (<NUM>;<NUM>,<NUM>) carrying on its surface said layer (<NUM>) of 2D semiconductor material,
- illuminating a spot of the layer (<NUM>) with a light beam, thereby generating electron-hole pairs,
- detecting emitted photons (<NUM>) generated by direct and indirect bandgap transitions generated by radiative recombination of the electron-hole pairs, and determining a direct photoluminescence intensity Idir and an indirect photoluminescence intensity Iind,
- repeating the two preceding steps at different values of the charge carrier concentration in the layer (<NUM>) by modulating the charge carrier concentration,
characterized in that the method further comprises the steps of:
- obtaining measured values of the ratio Iind/Idir and the corresponding carrier concentration,
- fitting the measured values to a theoretical model linking the ratio to the carrier concentration and the trap density, the model taking into account both radiative and non-radiative recombination mechanisms,
- calculating the trap density from the fitting step.