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INFORMATION SYSTEM FOR MEASURING DEFORMATIONS OF SEMICONDUCTOR DEVICES
GAAS WAFERS
Oksanich I.,
Kremenchuk Mykhailo Ostrohradskyi National University, Prof.
Shevchenko I.,
Kremenchuk Mykhailo Ostrohradskyi National University, Prof.
Palagin V.,
Kremenchuk Mykhailo Ostrohradskyi National University, Prof.
Kohdas M.,
Kremenchuk Mykhailo Ostrohradskyi National University, assist. Professor
Belska V.,
Kremenchuk Mykhailo Ostrohradskyi National University, Senior Lecturer
Bahno V.
Kremenchuk Mykhailo Ostrohradskyi National University, Student
DOI: 10.5281/zenodo.6532885
ABSTRACT
The work is devoted to solving the actual problem of automating the measurement of deformation of semiconductor wafers. The GaAs semiconductor wafer quality control method has been further developed, which is characterized by the use of a non-contact method for measuring complex forms of deformations, considering crystallographic directions, which makes it possible to reduce the absolute measurement error from ± 5% to ± 2%. Keywords: GaAs, deformations, semiconductor.
INTRODUCTION
The main trends in the development of electronics are related to higher functional complexity of electrical devices with increased speed and sensitivity. These requirements influence the direction of work on the searching for new materials and new technological processes that will provide necessary qualitative indexes [1-3].
In this regard, the problem of increasing the structural perfection of grown galli-um arsenide ingots by the Chokhralsky method (reducing the dislocation density, the level of internal tensions and deformations) becomes particularly urgent. Cur-rently, it is proved that when the temperature distribution is uneven along the length and cross-section of gallium arsenide single crystals, an internal tension oc-curs in it. Its value, besides to the radial temperature difference, depends on the me-chanical characteristics of single crystals and the thermal expansion coefficient [4]. In turn, the radial temperature difference increases with increasing diameter of the sin-gle crystal. It is also known that in the process of making semiconductor devices and integrated circuits, gallium arsenide wafers are subjected to various mechanical and thermal influences: grinding and polishing, diffusion of impurities, separation into blanks, etc. At the same time, defects occur in gallium arsenide wafers that re-duce their mechanical strength and worsen the electrical parameters of devices.
Wafer deformation also leads to distortion of the shape and size of integrated circuit (IC) topology elements and affects one of the important parameters - the to-tal deviation from parallelism and flatness. In this way, wafer deformation can complicate technological steps such as photolithography, diffusion, epitaxy, etc., can change the electrical characteristics of finished semiconductor devices and chips [5-8].
The purpose of the work is to improve the deformation measurements of GaAs semiconductor wafers.
To achieve this goal the following tasks have been set and solved:
- Analyze the requirements of optical methods for measuring the deformation and dislocation of semiconductor wafers;
- Develop a computerized system for the optical deformation measurement and quality control of GaAs semiconductor wafers;
- Develop an automated computer device for measuring the results of defor-mations;
- Analyze the results of the automated control system for semiconductor wafers quality.
1. PURPOSE AND OBJECTIVES OF THE RESEARCH
The relevance of the work is to solve the problem of increasing the structural perfection of grown gallium arsenide ingots by the Chokhralsky method (reducing the dislocation density, the level of internal tensions and deformations).
The solution of this problem allows us to determine the conditions for obtaining ingots with a low dislocation density, as well as create conditions for purposeful changes in the temperature conditions of growth.
At the same time, defects occur in gallium arsenide wafers that reduce their mechanical strength and worsen the electrical parameters of devices. The study of plastic deformation is of great practical importance for improving the efficiency of production of semiconductor devices and integrated circuits, as it helps to improve the parameters and increase the reliability of these most important electronic products.
Wafer deformation also leads to distortion of the shape and size of integrated circuit (IC) topology elements, which can complicate technological steps such as photolithography, diffusion, epitaxy, etc., can change the electrical characteristics of finished semiconductor devices and chips [9-12].
Considering the above, it can be argued that the task of developing a computerized system for optical measurement of deformations of GaAs semiconductor wafers, in order to increase their structural uniformity and perfection, is relevant both from a scientific and practical point of view.
The aim of the work is to improve the deformation measurements of GaAs semiconductor wafers.
To achieve this goal the following tasks have been set and solved:
- Analyze the requirements of optical measurement methods for the control system;
- Develop a computerized system for optical measurement and quality control of GaAs semiconductor wafers;
- Develop an automated computer device for measuring the results of deformations;
- Analyze the results of the automated quality control system for semiconductor wafers.
2. ANALYSIS AND DEVELOPMENT OF A METHOD FOR QUALITY CONTROL OF SEMICONDUCTOR WAFERS
In general, measuring deformations in the micrometer range poses serious metrological tasks, and reference measuring complexes are expensive equipment. However, in some cases, it is possible to use a highresolution interference microscope for rapid measurement. In this case measurements in the vertical direction are carried out by processing interference images of the sample surface when it is illuminated with white light.
The use of any contact sensors to determine the deformation of the wafer does not give high measurement accuracy due to errors in the devices themselves. Therefore, to solve this problem, we chose a non-contact method for measuring the interference pattern.
This method consists in the following: that the resulting interference pattern in the upper part of the sample is processed using an CCD camera and centered along the middle of the white line of the interference pattern, the deviation from the surface is measured using an inductive sensor.
This approach to solving the problem of automating the deformation measurement process allowed us to increase the accuracy of the results obtained, as well as new tasks related to processing images obtained using a CCD camera (contour selection, binarization, etc.).
The quality of the video image is affected by dust-iness of the lens, changes in the brightness of lighting,
etc. To minimize these factors, it is necessary to process the received video image, which consists in contrast, filtering and highlighting the borders.
Linear filtering or a nonlinear transformation operator is usually used to contrast an image. To take into account the kind of the image, the most optimal method is to increase the contrast of the image with a nonlinear transformation operator, which is represented as a static function (1) for 0<k < and (2) for s<k < 1.
vi = (G -1)
r-1
v
= (G-1)
1 -
(1 - k )r
(1 - - )r -1
(1)
(2)
where G - is the image level value equal to 255 for a grayscale image;
k=f(x,y)/(G-1) - standardized value of the input image function;
v=f/(x,y)/(G-1) - standardized value of the output image function; s=S/(G-1) - standardized value of the inflection point of the image characteristic; S - inflection point of the image characteristic equal to 112 (determined experimentally);
r - exponential function which equal to 3. To select borders, use the gradient capture operation. The researches have shown that the best results were achieved by calculating the second derivative by The Laplace operator, which is represented as (4):
Д7( x, y) = f 2( X y) + sin в
-2,
dx
2
dy
2
(3)
and which is calculated using an approximate formula (4)
A2f ( X, y) = f ( X, y) + 4f(x, y) - 0,25[f( x +1, y) + f(x -1, y) + f (x, y +1) + f (x, y -1)]}
(4)
Applying this operator (4) enhances the boundary by adding high-frequency components to them and subtracting laplacians from the original image, which reduces the focus of the image.
After these tasks, binarization is applied to the image, which allows you to finally distinguish interference lines from the background. There are various implementations of image binarization. Our task is to identify interference lines that do not have a high level of contrast compared to the surrounding area.
Let's create a binarization task. First, let's introduce the concept of an image.
Image - is standardized function
f : D ^ [0,1], where D с M2,M с N -
image selection area.
It is need to find the function
g(x f, p) ^ [0Д] where
x e D; O(x) e D
v y - some contour, х - image, p-some parameter or group of parameters.
Global threshold binarization can be used to isolate interference lines. It can be described by a function of the form (5).
Z f (y)
h{O{ x), f) = yeO( x)
\\0( x)||
(5)
This function shows how much the area around the selected pixel differs from its color and adjusts the preset cut-off threshold. In fig. 1 (a) shows the resulting image of interference lines, and fig. 1 (b) result of the global threshold binarization method.
a) image received b) image after processing
with a CCD camera global threshold binarization
Figure 1. Image of interference lines before and after binarization The video image is entered into a computer and of interest are determined. The installation algorithm is converted into a video array, after which the image is shown in fig.2 in manual mode and 3 in automatic examined line by line, basic brightness levels and areas mode.
r
Figure 2. Algorithm of operation of the installation in manual mode
Figure 3. Algorithm of operation of the installation in automatic mode
The physics of plasticity and strength of semiconductor materials is one of the fundamental branches of physical materials science and solid-state physics. the regularities of plastic deformation are of considerable theoretical and practical interest. Plastic deformation leads to a change in the shape of semiconductor substrates, to a change in their structure and, accordingly, the properties of GaAs substrates. Problems of the influence of deformation on changes in shape and properties are often solved simultaneously.
Deviation from the flatness of semiconductor devices can cause both positive and negative effects. Deformation in semiconductors can be caused intentionally, in order to obtain new or improve existing properties of semiconductor devices, and manifest itself as an unintentional process that leads to tensions relaxation caused by a temperature gradient or friction forces, different coefficients of thermal expansion and specific volumes of phases, etc.
In [8], it is shown that plastic deformation of wafers during high-temperature processing occurs as a consequence of the temperature gradient between the edge and the center of the wafer. In [9], the influence of dislocations on the value of mechanical strength is shown.
Deviation from the flatness of the substrate also leads to distortion of the form and dimensions of elements of the IC topology and affects one of the important parameters-a useless deviation from parallelism and flatness.
The problem of determining the amount of deformation and deviation from parallelism and flatness for semiconductor wafers and structures consists in a wide range of values of deviations from flatness, which must be controlled (from one to hundreds of microns) with a wafer thickness of several microns, requirements for non-contact and non-destructive testing.
Currently, there are quite a few experimental
methods for measuring deviations from flatness in various materials. These methods include tenso-metric methods for measuring flatness deviation, electrotenzo-metric methods, and optical effects-based methods such as moire band method, optically sensitive coating method, and holographic interferometry.
To study the surfaces of solid bodies, there are techniques used depending on the task at hand. In [1], a method and device for non-destructive testing of deviation from the flatness of silicon structures using microsilicon comparators is described. However, existing methods either do not provide the necessary measurement accuracy, or are contact methods.
As shown in [2], the substrate is deformed by small forces, has a flat shape and a stable equilibrium, which are maintained up to a certain value of forces. If the forces applied to the wafer exceed the critical values, the wafer passes to a new stable shape with a curved surface in the form of a bend, deflection, or with two radii of curvature in the opposite direction (anti-classical bending). The transition of the wafer to this
state can occur as a result of minimal effort.
Taking into account the fact that semiconductor materials have a crystal structure, the bending value directly depends on the crystallographic orientation. It can be concluded that the method developed in this paper should allow measuring deviations from flatness of semiconductor wafers and structures that have almost all types of bending, including anti-classical bending, and also allow measuring deviations from flatness in various crystal-graphic directions.
In recent years, interferometry methods have been intensively developed to control the microrelief and surface purity of semiconductor materials. The in-terferometry method makes it possible to estimate the size of micro-bends due to the high sensitivity and accuracy of interference devices.
The principle of light interference is based on the addition of light wave fields from two or more sources. Let's consider our proposed scheme of a non-contact method for measuring deviation from flatness, which is shown in fig. 4.
Cr ,
I1
I. v d I,
Figure 4. Diagram of a non-contact deviation measurement method
from flatness
As can be seen from the diagram, the movement difference AS = S2 - Si between rays coming from sources Ii i I2 to the point fi with the x coordinate, you can find as:
Si2 = L2
= L2 + (x + ^)2
(5)
(6)
where d - distance between light sources, and L - distance from light sources Ii i I2 to the focal surface of the lens O, x - moving of the interference band formation site from the main axis of the optical system, therefore, we can write:
= (x + Î)2 -(x-i)2 =2xxd (7)
Or
52 = (52 + Si)2 x (52
51)2 = 2L XAS (8)
Then the difference in the optical path of the Rays will have the following form:
xx d
AS = — (9)
Moving the lens O leads to a change in the ratio li/l2. If the focal surface of the lens coincides with the plane of the wafer, interference bands will be observed on it at the point fi.
In the event that the wafer has a deviation from
flatness in the form of a deflection by an amount of k, then moving the wafer along the optical system in the direction of y will cause the focus of the lens to shift to the point f2 by a distance of x, and therefore, accordingly, the interference pattern will also shift. Changing the ratio li/h caused by moving the lens in the vertical direction, the focus will shift to the f3 point, and as a result, the interference image will shift in the opposite direction.
The amount of lens displacement by the amount k until the interference image coincides with the base one, for which a point with zero deformation is selected located near the support P, it will correspond to the amount of deviation from the flatness of the wafer.
Turning the test wafer by an angle y makes it possible to measure the deviation from the flatness of the wafer in various crystallographic directions.
3. DEVELOPMENT OF ELEMENTS OF A INFORMATION SYSTEM FOR CONTROLLING THE DEFORMATION OF SEMICONDUCTOR WAFERS
The functional diagram of the developed automated complex "Micron-1" is shown in fig. 5. this complex is based on the "MHH-4" microinterferometer.
Ç2
1
Figure 5. Functional diagram of the automated complex "Micron-1"
Ml - motor for moving the coordinate table along the X-axis. M2 - motor for moving the coordinate table along the Y-axis. ECXA - engine control unit X axis movement of the coordinate plane. ECYA - engine control unit Y axis movement of the coordinate plane. PWM 1, 2 - pulse width modulators, they are used to set the speed of rotation of engines. ADC - analog-to-digital converter. DAC - digital-to-analog converter. IDS - inductive displacement sensor. UM - unit for measuring data from an induction displacement sensor. VC - video camera. IPU - image processing unit. IC -industrial computer, processes data received from the motion sensor and video camera.
The developed installation can operate in two modes: manual and automatic.
In manual mode, the operator moves the table with the wafer using the Ml motor (fig.5, the movement of the interference pattern from the center of the image is controlled using the VC CCD-camera, the operator can move interference lines vertically across the screen using Ml, which rotates the micrometer screw. The
movement of the «MHH-4» is controlled by an inductive sensor IDS, the operator can write the values obtained from the UM to a file and display them on the IC monitor as a 3D image or topogram. The operator can rotate the wafer by 45 degrees either manually or using a vacuum gripper manipulator.
To perform measurements in automatic mode, the operator just needs to set the diameter of the wafer under study, as well as the X-axis measurement step in mm. The wafer is moved automatically using the M1 motor, which moves the table on which the wafer is located. The program processes the data received from the CCD-camera and uses the M2 motor to monitor the state of interference lines in the center of the image. Data from the inductive sensor IDS is recorded in a file and displayed on the screen in the form of a 3D image. After scanning, the table moves to its initial position. Rotation by 45 is carried out using a manipulator.
The user interface is shown in fig. 6, this figure also shows the result of the program in a 3D image.
Режим работы
(• Автоматический ;(. Ручной
Диаметр пластины 90 мм V {
т
3D модель Изображение
Figure 6. User interface. Front panel oof the "Micron" program.
We carried out metrological certification of the "Micron-1" installation, measurements were carried out on two PI-120 type interference verification wafers. the deformation measurement was checked using an inductive displacement sensor and an CCD camera. The absolute error when using an inductive sensor was about ±10%, and when using a CCD camera, about ±2%.
4. RESEARCHING COMPLEX FORMS OF DEFORMATIONS OF SEMICONDUCTOR WAFERS
After cutting, GaAs wafers were subjected to double-sided mechanical and chemical polishing to a thickness of 1.2 mm. Measurements of complex forms of deformations were carried out at the "Micron-1" installation developed by us.
Five gallium arsenide wafers with orientation (100) were measured: one from the upper part of the ingot (table 1., A), three wafers were cut from the middle part of the ingot (table. 1 B-D) and one wafer from the lower part of the ingot (table. 1, E) doped with chromium, with an impurity concentration of 5*1014 cm-3, resistivity of 107 Ohm*cm, diameter of 92 mm.
Based on the measurement results, bend plots and 3D images of deformations were constructed depending on the crystallographic direction (table. 3.1, A-D). Curvature plots (table. 1, fig. A-E) have the form of a "socket", in most cases drawn along one of the directions <001>. Directions with a "positive" bend are selected according to [001], and directions with a "negative" bend are selected according to [010].
It is worth noting that the wafers bent uniformly in both the [001] and [010] directions. After bending in one "weak" direction along the upper structure, it is most possible to continue bending in this direction. At the same time, the wafer bends in the direction perpendicular to the previous one, due to the dependence of the Poisson's coefficient.
It can also be noted that the wafers have a complex bending character, and two zones with a maximum bend <001> and two zones with a minimum bend <011>are determined from the wafer plane. These zones are located at an angle of 900 degrees between each other.
As can be seen from the table.1, on a wafer cut from the upper part of the ingot, deformations are reduced, since the internal tensions are reduced by half relative to the lower part of the ingot.
Table 1
Bend plots and 3D images of deformations depending on the crystallographic direction
Plots
3D image
Explanation
A) Bends of GaAs plate №1 (upper part of the ingot) in the plane (100) depending on the crystallo-graphic direction
B) Bends of the GaAs plate №2 (middle part of the ingot) in the plane (100) depending on the crystallographic direction
C) Bends of GaAs plate №5 (middle part of the ingot) in the plane (100) depending on the crystallo-graphic direction
D) Bends of the GaAs plate №4 B (middle part of the ingot) in the plane (100) depending on the crystallographic direction
E) Bends of GaAs plate №5 (lower part of the ingot) in the plane (100) depending on the crystallo-graphic direction
CONCLUSIONS
The scientific work presents a new solution to an actual scientific and applied problem, which consists in improving the quality control method of GaAs semiconductor wafers, which is characterized by the use of a non-contact method for measuring complex forms of deformations, considering crystallographic directions, which made it possible to reduce the absolute measurement error from ± 5 microns to ± 2 microns.
Based on the results of the conducted research it is possible to say the following:
— methods, techniques and installations for studying complex forms of deformation have been analyzed.
— the model has been compiled based on the method of paired comparisons, which makes it possible to determine the overall quality indicator, which takes into account such parameters as: tension, dislocation and deformation;
— the structure of optical deformation measurement and quality control of semiconductor wafers has been developed;
— the automatic computerized system for optical deformation measurement and quality control of semiconductor wafers has been developed;
— calculation tables, plots and images have been obtained that allow us to determine the overall quality indicator of semiconductor wafers;
— hardware for the computerized system for optical measurement of deformations and quality control of semiconductor wafers has been developed that allows us to determine the quality indexes;
— software implementation of the graphical operator interface, a computerized system for optical deformation measurement and quality control of semiconductor wafers has been performed.
— It has been found out that when processing large-diameter GaAs wafers with an orientation of (100), a complex bend occurs, the plots of which have extremes in one of the crystallographic directions <001>.
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CLASSIFICATION OF LOESS TYPE SOILS OF CENTRAL MONGOLIA BY INDIRECT SIGNS AND
FOUNDATION DESIGNING ISSUES
Nyamdorj S.
Mongolian State University of Science and Technology
Ulaanbaatar. Mongolia DOI: 10.5281/zenodo.6532889
ABSTRACT
Quality assessment of Physical and mechanical properties of the loess type of sandy loam and loamy sand soil distributed in the Orkhon-Selenge region is growing to be more vital. In this region, the distribution of loess type soil in the top layer of soil is relatively low with a thickness of 4.0-10m and it shows subsiding effects due to techno genic saturation. With an intention to assess the saturated properties of soil, many linear regression equations are iterated in numerous laboratories and in the field. Furthermore, the cause of deformation of buildings constructed in the region was identified. The efficient use of structures of optimal foundation types in the region were recommended and conclusion has been made.
Keywords: construction site, lithological cutting, technogenic saturation, base soil subsiding, pile foundation, soil solidification, optimal use.
Introduction. Estimation of subsidence properties of deluvial-proluvial clayey soils in Central Mongolia is a top priority since these soils serve as the basis for most of the buildings and structures under construction. They are common in wide intermountain valleys and in the middle and lower parts of the gentle slopes of local uplands. It is these areas that are primarily subject to construction development. The Darkhan-Seleng and Erdenet-Orkhon regions have well-developed road, rail and other structures, industrial and agricultural sectors.
Engineering-geological research. Most researchers studying loess rocks see the characteristic features of their appearance in the increased content of silt particles (more than 50%), low natural humidity (up to 15%) and significant porosity (more than 42%-45%) [2:4:5]. With these parameters, regulatory documents [1] associate indirect indicators by which soils can be classified as subsiding. It should be noted that some sandy-loamy varieties common in the Central regions
of Mongolia, although they do not fit into the above criteria, often have subsidence, both under domestic and additional loads [2]. The predisposition to subsidence, along with other features of the composition and properties, make it possible, with a certain conventionality, to classify these soils as loess type deposits.
Studies of physical and mechanical properties based on the results of 782 laboratory experiments found that clay soils are characterized by subsidence properties when soaked under a pressure of 0.2-0.3 MPa [2]. These are the most common loads in the foundations of buildings under construction, so the assessment of subsidence in the range of given pressures is of paramount importance. For the territory of the above named regions, it was found that the dependence of subsidence with other physical properties of rocks (porosity, humidity, etc.) weak, which limits the prospects for using indirect methods in surveys and building design. This is explained by the fact that subsidence does not depend on one indicator, but is a function of many
