the present invention discloses an automatic metrology , e . g . thickness calculation method , for each and all deposition / doped layers of a finfet or an led . an electronic image of a semiconductor device taken by tem , fib , afm , or xrd is processed to extract the boundaries between different material layers ; each of the non - continuous boundaries is than modified before mapping onto an excel spreadsheet . each of the physical parameters interested over the devices , such as thickness or width of a deposition layer , average value of thickness or width , deviation and / or root - mean - square ( rms ) for a statistics , fin angle , radius of a curvature . . . etc ., can be calculated automatically by a macro - instruction written over the excel spreadsheet . the statistics can be selected to output to a printer and / or displayed on a display screen . fig2 shows a dimension calculation method according to the present invention . fig2 shows that the calculation method includes the following steps : ( 1 ) image providing ; an electronic image of tem , fib , afm , or xrd is prepared ; ( 2 ) edge detecting and noise removing ; an edge detection filter such as gaussian blur and canny algorithm or equivalent is applied over the image to extract the boundaries between different deposition layers . noise removing is then processed to remove unwanted dots or spots . the edge lines extracted are always non - continuous due to the image quality and the intrinsic property of the software to be used . ( 3 ) edge modifying ; either a polynomial interpolation or a linear interpolation is adopted to modify the non - continuous edge lines and make each of them continuous . ( 4 ) data exporting to excel spreadsheet ; the edge lines are then mapping onto an excel spreadsheet for data calculation . ( 5 ) data outputting ; user can select one or more of the physical parameters including but not limited to the following to output to a printer or display on a display screen : ( a ) thickness or width at a selected location of a deposition layer . ( b ) average of the thickness or width for the deposition layer . ( c ) deviation for the thickness or width . ( d ) root - mean - square for the thickness or width . ( e ) fin angle ; and / or ( f ) radius of a curvature . fig3 - 8 shows a first embodiment according to the present invention . fig3 shows an electronic image or picture of a finfet taken by tem to be analyzed , a similar image taken by fib , afm , or xrd can also be analyzed here in similar method . the finfet has a fin - type silicon ( si ) configured in a center of the device ; a layer of silicon dioxide ( sio2 ) is deposited to cover the top surface of the fin - type silicon ; a layer of hafnium oxide ( hfox ) is deposited to cover the top surface of the silicon dioxide . a layer of titanium aluminide / titanium nitride ( ti — al / tin ) is deposited to cover the top surface of the hafnium oxide . a layer of tungsten ( w ) is deposited to cover the top surface of the titanium aluminide / titanium nitride ( ti — al / tin ). there are four boundaries or edge lines e 1 , e 2 , e 3 , e 4 between neighboring deposition layers in the image of fig3 . e 1 indicates an edge line between si — sio2 ; e 2 indicates an edge line between hfox and siox ; e 3 indicates an edge line between ti — al / tin and hfox ; and e 4 indicates an edge line between w and ti — al / tin . fig4 shows the extracted edge lines from the image of fig3 due to the intrinsic property of the software used and the quality uncertainty of the electronic image , each of the extracted edge lines is usually non - continuous as shown in fig4 . an edge modifying process is then needs to be performed . a polynomial interpolation is adopted to modify the non - continuous curved lines . while a linear interpolation can be selected to modify a linear or a linear approximate line . fig5 shows a modified edge lines over the non - continuous edge lines of fig4 a polynomial interpolation software is chosen here to modify the curve for the image of fig4 . fig5 shows that each of the edge lines is a continuous one after the modification . fig6 shows the continuous edge lines mapped on an excel spreadsheet and thickness measurement exemplified . the physical parameters can be obtained by macro - instruction written based on the commercialized excel application software . referring to fig6 . thickness for three layers is exemplified at a randomly selected vertical line xn . e 3 - e 4 is 3 . 03 nm for the thickness of ti — al / tin layer at the position of the vertical line xn . e 2 - e 3 is 1 . 56 nm for the thickness of hfox layer at the position of the vertical line xn . e 1 - e 2 is 0 . 53 nm for the thickness of sio2 layer at the position of the vertical line xn . fig7 shows the continuous edge lines mapped on an excel spreadsheet and width measurement exemplified . referring to fig7 . width or thickness for three layers is exemplified at a randomly selected horizontal line yn . e 1 - e 2 is 1 . 31 nm which represents the width or thickness of sio2 layer at the position of the horizontal line yn . e 2 - e 3 is 1 . 01 nm which represents the thickness of hfox layer at the position of the horizontal line yn . e 3 - e 4 is 2 . 36 nm which represents the thickness of ti — al / tin layer at the position of the horizontal line yn . fig8 shows the continuous edge lines mapped on an excel spreadsheet and fin angle and fin radius of curvature exemplified . a randomly selected vertical line xn is made on the figure and a tangent line l is made over a randomly selected point p on the edge line e 1 . a fin angle θ is formed between the tangent line l and the vertical line xn . the fin angle θ is 30 . 15 degree at point p shown in fig8 . a radius of curvature is 6 . 78 nm at a randomly selected curvature on the right side of edge line e 1 . fig9 - 15 shows a second embodiment according to the present invention . the similar metrology described above for the finfet can also be applied on the epitaxial layers of a led device . the accurate measurement with least uncertainty and quantification of the local change in the width of the epitaxial layers including super lattices and multiple quantum wells ( mqws ) in a led device is critical for its performance and optimization of the device . fig9 shows a section view of a typical led device . fig9 shows a section view of a typical led device . there are several different deposition layers . please see the dashed square in fig9 , where a superlattice structure and quantum well structure are located . the structure in the dashed square is then enlarged in fig1 . fig1 shows an electronic image of the superlattice structure and the quantum well structure . fig1 shows an electronic image of the superlattice structure and the quantum well structure of an led taken by tem to be analyzed , a similar image taken by fib , afm , or xrd can also be analyzed here . it can be seen that the superlattice structure is configured on the top , and the multiple quantum well structure is configured on the bottom with reference to the superlattice structure . the superlattice structure is composed of interleaved wells and barriers , each of the wells and barriers is in the form of nanometer thin layer ; and the multiple quantum well is also composed of interleaved wells and barriers , each of the wells and barriers is in the form of nanometer thin layer . fig1 shows the edge lines extracted the image of fig1 and only the multiple quantum wells and multiple quantum barriers are exemplified in the fig1 . due to the intrinsic property of the software used and the quality uncertainty of the image , each of the extracted edge lines is usually non - continuous . an edge modifying process needs to be performed . a linear interpolation is adopted to modify the linear or linear approximate line . fig1 shows a modified edge lines over the non - continuous edge lines of fig1 a linear interpolation software is chosen here to modify the edge lines for the image of fig1 . fig1 shows that each of the edge lines between quantum well and quantum barrier is a continuous one after the modification . fig1 shows the continuous edge lines mapped on an excel spreadsheet and thickness measurement exemplified . the physical parameters can be obtained by macro - instruction written based on the commercialized excel application software . thickness t 1 , t 2 , t 3 for each of the three quantum wells is exemplified at a randomly selected vertical line xm ; and thickness t 2 , t 4 , t 6 for each of the three quantum barriers is exemplified at a randomly selected vertical line xm . similarly , thickness for each and all the quantum wells and / or the quantum barriers can be obtained at any designated vertical line . additional statistic such as mean value , deviation , rms . . . etc ., can be made automatically for each and all of the quantum wells and / or the quantum barriers . fig1 shows typical physical parameters determined for the superlattice and quantum well . fig1 shows layer width ( mean ) distribution for the superlattice and multiple quantum well . the x - coordinate shows the number of layers and the y - coordinate shows the width in nanometer ( nm ). where “ solid diamond ” represents the superlattice wells ( sl wells ), “ solid square ” represents superlattice barriers ( sl barriers ), “ solid triangle ” represents multiple quantum wells ( mqws ), and “ cross ” represents multiple quantum barriers ( mqbs ). the average thickness of sl wells is between 2 ˜ 3 nm . the average thickness of mqws is between 2 . 5 ˜ 3 . 5 nm . the average thickness of sl barriers is around 5 . 5 ˜ 6 . 5 nm ; and the average thickness of mqbs is mostly between 10 ˜ 11 nm . fig1 shows layers data statistics for the multiple quantum wells and multiple quantum barriers . fig1 shows multiple quantum barrier layers in the first column ; multiple quantum well layers in the second column ; mean value in the third column ; distribution range in the fourth column ; rms in the fifth column ; and standard deviation in the sixth column . while several embodiments have been described by way of example , it will be apparent to those skilled in the art that various modifications may be configured without departs from the spirit of the present invention . such modifications are all within the scope of the present invention , as defined by the appended claims .