Journal of Spectroscopy

Volume 2016 (2016), Article ID 1617063, 14 pages

http://dx.doi.org/10.1155/2016/1617063

## Depth-Sensitive Raman Investigation of Metal-Oxide-Semiconductor Structures: Absorption as a Tool for Variation of Exciting Light Penetration Depth

^{1}Institute of Electron Technology, Aleja Lotników 36/42, 02-668 Warsaw, Poland^{2}Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland

Received 27 September 2015; Accepted 10 November 2015

Academic Editor: Christoph Krafft

Copyright © 2016 Paweł Borowicz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Presented work focuses the attention on two regions of MOS structure placed in the vicinity of the semiconductor/dielectric interface, in particular: on part of dielectric layer and thin layer of the substrate. In the presented work the application of absorption as a tool that can vary the absorption depth of excitation light into the semiconductor substrate is discussed. The changes of the absorption depth of visible light allows to obtain Raman signal from places in the substrate placed at different distances from the dielectric/semiconductor interface. The series of Raman spectra obtained from visible excitation in the case of varying absorption depth allowed to analyze the structure of the substrate as a function of distance from the interface. Deep ultraviolet Raman study regarding part of silicon dioxide layer placed directly at the interface is not discussed so far which makes the analysis of the structure of this part of dielectric layer possible. Comparison of reported in this work Raman data with structure of silicon/silicon dioxide interface obtained from other experimental techniques proves the applicability of proposed methodology.

#### 1. Introduction

The progress in miniaturization of Metal-oxide-semiconductor- (MOS-) type electronic devices results in limitation of active area of semiconductor substrate to the thin layer placed in the vicinity of interface between semiconductor substrate and dielectric layer. An example of such device is High Electron Mobility Transistors (HEMTs). The thickness of active area in this device is limited to several dozen nanometers [1].

Raman spectroscopy detects small shifts in frequencies of normal modes caused by small differences between parameters of crystal or molecular structure like bond lengths or bond angles. This accuracy makes from this experimental technique a very efficient tool for structural study. An example of this type of application of Raman spectroscopy is delivered by study of changes in semiconductor structure caused by implantation [2].

Optical microscopy is the experimental technique which offers high spatial resolution. The transverse resolution is determined by diffraction limit of microscopic objective. The diameter of Airy spot can be calculated according to Rayleigh or Sparrow criteria [3]. In the case of the microscopic lenses with high numerical aperture (), = 0.55, the dimension of Airy spot is placed in the range between 500 nm and 700 nm [3]. Spatial resolution of Raman microscopy was applied in the investigation of spatial distribution of such parameters like mechanical stress in semiconductor substrate [4, 5] or channel temperate in HEMTs [6, 7]. The thermal effect observed in HEMTs is caused by self-heating present in the case of current flow between source and drain of the transistor.

The axial dimension of the focus depends also on . The distribution of the intensity across the laser beam can be described by Gaussian function. The axial dimension of the laser beam focus in the case of confocal microscopes is not smaller than 1 *μ*m [8]. The thickness of active area in today’s electronic devices is at the least order of magnitude smaller than axial dimension of laser beam focus determined from geometrical optics. Because of this it is necessary to introduce the procedure that can avoid the limitation coming from geometrical optics.

The most important property that can help to overcome the limitation of axial diameter of laser beam focus is absorption. Absorption coefficient of each material is a function of wavelength of incident light. It means that one can change the penetration depth of the light into the material by choice of the irradiation wavelength. The dependence between wavelength and absorption of the material was applied for investigation of ohmic contacts with additional carbon layer formed at different temperatures [9]. Silicide film mixed with carbon atoms is transparent for visible light, because this visible irradiation of the ohmic contact through silicide layer causes the Raman scattering in carbon layer placed between silicide film and silicon carbide substrate. The deep-ultraviolet excitation applied in the same configuration cannot reach the above-mentioned carbon layer due to strong absorption of the silicide layer mixed with carbon structures. Therefore Raman scattering excited in deep-ultraviolet spectral range delivers information about two types of carbon species:(i)carbon layer which is built on the free surface of silicides due to carbon atom diffusion;(ii)carbon clusters placed inside of silicide layer [9].

The other problem which was investigated by means of extraction of signal generated in thin layer from large background is related to properties of the interface between silicon carbide (SiC) and dielectric layer. The Near Interface Traps (NITs) in the MOS-type structures can decrease the mobility of charge carriers even by two orders of magnitude. Extensive study of the properties of SiC/SiO_{2} interface showed that carbon plays very important role in formation of the defects that can be candidates for NITs [10–13]. The most important Raman bands generated by species built from carbon atoms [14] are placed in the same range of Raman shift as two-phonon spectrum of different polytypes of SiC [15, 16]. Application of two different excitation wavelengths, in particular visible and ultraviolet, made the extraction of the scattering coming from the interface from background which is formed by two-phonon Raman scattering in SiC substrate possible. The extraction was possible due to significantly different penetration depths of exciting radiation from both used spectral ranges [17].

The other area where the decreasing of two-phonon Raman scattering plays a key role is related to Raman study of properties of dielectric layer. The problem was discussed in the literature for the system composed of Si substrate and SiO_{2} layer. Standard configuration of Raman apparatus includes excitation in visible spectral range. In this case significant two-phonon signal generated in Si substrate is observed [18]. The intensity of this second-order Raman scattering is strong enough even to mask the signal form SiO_{2} layer [19]. Application of deep-ultraviolet excitation makes possible the observation of Raman scattering generated in SiO_{2} layer [20]. The increase of Si absorption due to change of the excitation wavelength from visible spectral range to deep-ultraviolet results in reduction of radiation penetration depth by about 30 times. In turn, the intensity of two-phonon Raman scattering coming from Si substrate becomes negligible and the signal from silicon oxide layer becomes detectable. This was shown for ~50 nm thick SiO_{2} layer placed on Si substrate by comparison with bulk material which was commercially available quartz glass Suprasil I [20]. The price to pay for this advantage is long irradiation time. The reason for this “price” is small efficiency of Raman effect in the case of SiO_{2} combined with small thickness of investigated material. The typical thickness of SiO_{2} layer of today’s electronic structures is about two orders of magnitude smaller than the axial dimension of the focus of laser beam.

This work focuses the attention on the properties of thin layer of semiconductor substrate in the vicinity of semiconductor/dielectric interface. The Si/SiO_{2} system is used as an example. The change of the power density of exciting light on the sample results in change of* effective absorption depth*.* Effective absorption depth* is the thickness of the investigated material which is active from the point of view of measured Raman signal under certain power density. Since the definition of the* effective absorption depth* is a crucial point in the interpretation of experimental data it will be discussed in detail in the next chapter* Experimental* where also the methodology of data analysis is described. The systematic change of power density makes possible to record Raman signal from material with different thickness. As a result one can get depth profile of structural properties of investigated material.

Another point that will be discussed here is the appearance of crystal-like structures of silicon dioxide that should be placed at the Si/SiO_{2} interface [21]. As was mentioned above application of deep-ultraviolet excitation in order to reduce two-phonon signal from Si substrate was discussed for amorphous part of SiO_{2} layer [20]. However, Raman signal observed for this type of excitation contains also traces of narrow lines. These traces will be compared here with Raman spectra reported for crystalline forms of silicon dioxide.

The paper is organized according to the following outline. Section 2 presents method of sample preparation and their characterization, Raman apparatus, and methodologies of data analysis and measurements. The special attention was paid to two aspects:(i)the description of the mathematical model which links the power density of irradiation with thickness of the layer of material from which the Raman scattering is recorded;(ii)the discussion of two experimental parameters which are changed if the power density of exciting light is varied: half-angle of the maximum cone of light collected by microscope objective and the dimension of the laser-beam spot.Section 3 presents the measured data. The results of the investigation are discussed in Section 4.

#### 2. Experimental

##### 2.1. Samples Preparation and Characterization

Silicon dioxide films were manufactured in Division of Silicon Microsystem and Nanostructure Technology (Institute of Electron Technology, Warsaw, Poland). Three-inch diameter p-type silicon wafers were used as substrates. Samples were characterized by means of spectroscopic ellipsometry, transmission electron microscopy, and transmission/reflection spectroscopy. Details of sample preparation and characterization were already presented in the literature [20].

##### 2.2. Raman Apparatus

Raman spectra were measured with micro-Raman spectrometer MonoVista 2750i (Spectroscopy & Imaging GmbH, Germany).

Microscopy part of the spectrometer is based on fluorescence microscope type BX-51 (Olympus, Japan). The microscope is equipped with four objectives:(i)three of them (magnification: 100x, 50x and 20x) are working in visible (VIS) spectral range;(ii)one objective (magnification 40x) is designed for deep-ultraviolet (deep-UV) spectral range.Images from microscope are recorded with imaging camera TM 2040 GE (JAI, Japan). Motorized stage (Ludl Electronic, USA) makes the following types of spatially resolved measurements possible:(i)line scanning along each coordinate: , , and ;(ii)two-dimensional mapping: , , and ;(iii)three-dimensional mapping .

Spectroscopy part of the setup is based on imaging spectrograph SpectraPro 2750i equipped with liquid nitrogen cooled spectroscopy CCD camera LN/2048 × 512B/IUVAR, Spec-10 System (Princeton Instruments USA). The camera has maximum efficiency in UV spectral range. The spectrograph has three diffraction gratings:(i)two of them (1800 grooves/mm and 2400 grooves/mm) are blazed in visible spectral range;(ii)one grating (3600 grooves/mm) is blazed in ultraviolet.Large focal length of the spectrograph (750 mm) allows high spectral resolution combined with single pass of the radiation through the spectrograph. The spectral resolution of the apparatus is equal to about 0.1 cm^{−1} for VIS spectral range and about 1 cm^{−1} in deep-UV.

In the case of visible excitation the combination of objective with magnification equal to 100x and grating with 2400 grooves/mm was used. The combination of deep-UV objective and grating with 3600 grooves/mm was applied to record the spectra excited in deep-UV.

As excitation sources two continuous work (CW) lasers were used. Raman scattering in VIS spectral range was excited with Ar^{+} laser INNOVA 90C FRED (Coherent Inc., USA). In particular the line 488 nm was used. Deep-UV excitation was done by means of semiconductor laser FQCW-266-10 (CryLas GmbH, Germany). The wavelength of laser line was equal to 266 nm.

The power of the excitation light was not larger than 1 mW on the sample for each excitation wavelength. The position of one-phonon Si line depends on the temperature; in particular it is shifted by about 2 cm^{−1} towards smaller values of Raman shift if the temperature increases from room temperature to 100°C [22]. The power of exciting light should be set within the range which makes it possible to avoid local heating of the sample caused by absorption of the exciting light. Applied in this work power of exciting light is adjusted within the range used for investigation of the stress in semiconductors. For example, the power of the exciting light on the sample used for stress mapping in porous Si microcapsules was equal to 1 mW [23]. The power of laser line on the sample used in investigation of self-heating effect in electronic devices is equal even to 5 mW [7, 24, 25].

##### 2.3. Model

As was mentioned in Introduction variation of the power density results in changes of thickness of the material from which the scattering is collected. The type of measurement called* line scan z* allows to record the series of Raman spectra for different power density of irradiation light on Si/SiO_{2} interface. This set of different values of power density is reflected in variation of thickness of material from which Raman signal is collected. This thickness will be called* effective absorption depth*, .

The concept of tuning of the thickness of material from which Raman signal is collected is based on the fluorescence measurement in reflection. This concept was applied in Multifunctional Spectrofluorimetric System designed by Jasny (“focusing and collimating system type A”) [26]. In this configuration angle between optical axes of exciting and analyzing setup was equal to 30°. It means that the luminescence was measured in the configuration similar to the back scattering. Measurements were performed in solutions. The thickness of the layer where the excitation light was effectively absorbed was determined by concentration of absorbing agent, because the intensity of exciting light was constant. In the case of high concentration of absorbing species the thickness absorbing layer was tended to monomolecular film.

In the case of Raman scattering in solid material (i.e., Si) excited with laser line the absorption is determined by the wavelength of exciting light and it is constant for each wavelength. In order to tune the* effective absorption depth* the power density of the irradiation light must be varied. Tuning of the power density of exciting light in the case of constant absorption results in the same effect as tuning of the absorption for constant power density. In particular the thickness of the material where the incoming light is effectively absorbed is changed. Important is the question about the lower limit of the thickness of the film where all photons from incoming light should be absorbed. This layer should have the same properties as whole material. In the case of crystalline media the smallest part of material which has the same properties as large crystals is defined by unit cell. It means that in the case of small density of irradiation light the thickness of absorbing layer should be compared with dimension of unit cell of the investigated material. In the case of crystalline silicon this dimension is equal to about 0.5 nm.

The crucial problem in quantitative data analysis is the development of the model which allows to calculate values of* effective absorption depth* resulting from changes of power density of irradiation light on the sample. The absorption of exciting and scattered light must be taken into account. The model which links the variation of power density of irradiation light with* effective absorption depth* is presented below.

Let us start with short overview of basic knowledge necessary for the development of the announced above mathematical model. The absorption of material is described by Lambert law [27]:where denotes the intensity of incident light, is the optical pathway through the material, is the intensity of the light after the pathway equal to , and is the absorption coefficient of the material. In many applications the base equal to 10 is used instead of exponential function. In such a case the Lambert law has the formwhere quantity is called absorbance and denotes an extinction coefficient. Lambert law can be expressed in terms of imaginary part of complex refractive index. The complex index of refraction has the formwhere and denote real and imaginary parts of complex refractive index, respectively. Both and are functions of wavelength. The sign “−” in (3) results in positive value of damping coefficient of electric field for materials which do not amplify the light. Since the intensity is proportional to the square of electric field amplitude absorption coefficient can be expressed as a function of damping coefficient by the following equation:where denotes the circular frequency and is the velocity of light. Taking into account dependencies between circular frequency , frequency , and wavelength one can present (4) in the following form:Penetration depth is defined as thickness of absorbing material which corresponds to the decrease of the quantity describing electromagnetic wave by times [28]. Since intensity is important for further analysis the attention will be focused on parameters related to intensity of the light. In such a case the penetration depth *δ* is given by following equation:The imaginary part of refractive index used in (6) has the form in order to emphasize the fact that the damping coefficient is a function of wavelength. Taking into account values of Si damping coefficient for green lines of Ar^{+} laser (wavelengths of laser lines usually used in Raman experiments: 488 nm and 514 nm) [29] one obtains penetration depth equal to about 0.7 *μ*m. The application of deep-UV excitation (typical wavelengths of laser lines: 244 nm or 266 nm) reduces the value of to several dozen nanometers [29].

Now we can move to the definition of* effective absorption depth*. This quantity is important in the case of micro-Raman study of semiconductor substrates because it determines the thickness of material which is investigated.* Effective absorption depth* can be calculated from properties of spectral CCD camera used to record the Raman signal and the damping coefficient . The following approximation will be used in calculation of* effective absorption depth*: due to small difference between wavelengths of exciting and scattered light, the value of damping coefficient will be taken equally for excitation and scattering.

Now we focus the attention on crystalline silicon as an example of absorbing material. The first step to determine the* effective absorption depth* is to show that the thickness of Si from which the Raman scattering is collected depends on the number of incident photons. One can express the number of photons reaching the depth equal to by the following equation:where is the number of incident photons for unit area. Value corresponds to the interface between silicon substrate and silicon dioxide layer. The maximal depth corresponds to the thickness of material which is passed* only by one photon*: . It means that one can change by varying the number of incident photons . Equation (7) can be rewritten as a condition for :The condition specified by shows that one can change the thickness of the material which gives the contribution to Raman scattering by varying the number of incident photons per unit area .

Let us move now to the calculation of* effective absorption depth* in the case of Raman scattering. CCD cameras used in spectroscopic measurements have 16-bit analog-digital conversion. It means the maximum intensity of the Raman line that can be accumulated is equal to counts. Further extension of accumulation time results in saturation of line intensity. It means that the maximum cannot be obtained because the upper part of the line (over 65536 counts) is cutoff. The intensity of scattered light as a function of thickness of material is given by following equation:In (8) denotes the intensity of excitation and describes the efficiency of the observed Raman effect. Integration from 0 to gives the intensity of Raman scattering measured from the layer whose thickness is equal to . The expression under the integral described the statistical weight of the contribution of the scattering coming from the material placed at the depth equal to . Factor 2 in the argument of exponential function in (8) was introduced because scattered light is absorbed in the same manner as exciting light. At this point the approximation concerning the equality of damping coefficient for exciting and scattered light is introduced to the model. The intensity reaches its maximal value equal to 65536 when the thickness is equal to . Equation (8) takes in this case the following form:

In practice it is convenient to explain by multiple of value of penetration depth defined by (6). The value of efficiently tends to maximal value of intensity with increase of . In particular the values of ratio are equal: 0.865 for , 0.982 for , and 0.998 for* n* = 3. The standard deviation of the intensity of Raman line can be calculated from Poisson distribution, because photon statistics is based on this distribution. The standard deviation is equal to the square root of the intensity understood as a number of counts obtained for Raman shift equal to maximum position of the line. In the case of maximal value of intensity measurable by 16-bit CCD camera the standard deviation is equal to . This standard deviation is equal to about 0.4% of the maximum measurable intensity. The ratio is equal to 0.996. It means that for is placed within the range .

To sum up, assuming , one obtained the intensity of Raman scattering which differs from by value smaller than standard deviation .

In the case of crystalline Si for excitation wavelength equal to 488 nm the maximum of* effective absorption depth* is equal to 2.2 *μ*m. The change to deep-UV excitation (wavelength 244 nm or 266 nm) reduces for crystalline Si to the value from the range between 100 nm and 200 nm.

The next problem is how to link the* effective absorption depth * with intensity of Raman line if the intensity does not reach value . Replacing by in (8) one obtains the following expression:Dividing by one obtains the intensity ratio :Expanding in power series for and one obtains approximate expression for intensity ratio :From one can obtain the following expression for :In (10) the obtained earlier approximation for maximum of* effective absorption depth * was introduced.

##### 2.4. Measurement Methodology

Two types of measurements were performed. In the case of deep-UV excitation the laser beam was focused on the Si/SiO_{2} interface. Due to small intensity of the signal long time of irradiation was applied. The exposition time of single spectrum accumulation was equal to 1 hour.

The second type of measurement is called* line scan z*. This type of measurement was performed for VIS excitation ( nm). The direction perpendicular to the surface of interface is marked with coordinate. The following sequence of steps was necessary to perform line scan along coordinate. First the laser beam was focused on the Si/SiO_{2} interface. This position was assumed as . Then the measurements of Raman spectra were performed for different values of coordinate. The range of coordinate which was scanned spread from −20 *μ*m to 20 *μ*m. The difference between two subsequent positions, in other words the step of the scan, was equal to 1 *μ*m. The exposition time for single spectrum was equal to 1 minute.

There are two important parameters of the setup which change when the sample is moved along optical axis from the position corresponding to focal spot. These parameters are half-angle of the maximum cone of light collected by microscope objective and the power density of the laser light exciting Raman scattering. Let us now discuss how these parameters change if the sample is moved from focus position by *μ*m.

Figure 1 presents the beam path between microscope objective and the sample. The cone of the light that can be collected by objective is described by hyperboloid. The asymptote of the hyperboloid is defined by numerical aperture of the objective. The numerical aperture is the function of half-angle of the maximum cone of light that can enter the microscope objective. The other important parameters of the objective are as follows:(i): focal length;(ii): working distance;(iii): diameter of the entrance pupil;(iv): diameter of the focal spot.Numerical aperture, half-angle, focal length, and diameter of entrance pupil fulfill the following equation:The diameter of the focal spot can be calculated from Rayleigh or Sparrow [3] criterion for diffraction limit of Airy spot:where in the case of Sparrow criterion or for Rayleigh criterion.