referring now to the drawings , wherein fig1 ( a ) and 1 ( b ) show a method for measuring the height of the bumps provided on a semiconductor substrate using x - rays according to the present invention . in the bump detecting method according to this invention , x - rays are irradiated onto the work and the intensity of x - rays which transmit through the work is measured to determine the heights of the bumps . in the measuring method of fig1 ( a ) and 1 ( b ), the measurement results for one sample , wherein a bump 12 is not formed on the land 16 of the substrate 10 , and the measurement results for another sample , wherein a bump 12 is formed on the land 16 of the substrate 10 , are compared to each other to determine the height of bump 12 . as shown in fig1 ( a ), in the case of no bump being formed , if the intensity of incident x - ray is i 0 and the intensity of transmitted x - ray is i 1 , the following relationship between i 0 and i 1 is given . in the following representation , μ 1 is planck &# 39 ; s linear absorption coefficient . on the other hand , as shown in fig1 ( b ), in the case of bump 12 being formed on the land 16 , if the intensity of incident x - rays is i 0 and the intensity of transmitted x - rays is i , the following relationship between i 0 and i is given . in the following representation , μ b is a linear absorption coefficient of the material constituting the bumps and h is the height of bump . i ={ i 0 exp (− μ 1 x )}· exp (− μ b h )= i 1 · exp (− μ b h ) ( 2 ) the relationship between i and i 1 can be deformed as follows . according to this representation , if the intensity i 1 of transmitted x - rays in the state that no bumps 12 are formed on the lands 16 is measured beforehand and , on the other hand , if the linear absorption coefficient μ b of the material constituting the bumps 12 is measured beforehand , the height ( h ) of bumps can be detected by only measuring the intensity of transmitted x - rays in the state that the bumps 12 are formed on the lands 16 . the thickness of the lands 16 formed on the substrate 10 is relatively thin , about 18 μm , the deviation of the thickness is relatively small , and in general the linear absorption coefficient is relatively small . therefore , the lands 16 do not result in a great influence to the measuring results . therefore , it is sufficient to measure the intensity ( i 1 ) of transmitted x - rays with respect to the samples of substrate having no bumps to use the measured results as a reference value . the intensity i 1 of transmitted x - rays with respect to the samples of substrate having no bumps 12 formed on the lands 16 reflects - the intensity of transmitted x - rays through the land 16 as well as the intensity of transmitted x - rays through the base body of the substrate 10 . therefore , the measuring method of this embodiment can be used for detecting the height of bumps 12 , either for a substrate having no inner conductive layer other than the lands 16 , as well as a substrate having such an inner conductive layer . this is because the height of bumps 12 can be determined in such a manner that the intensity of transmitted x - ray with respect to the substrate having no bumps 12 is defined as a reference value and then the difference is determined . the wavelength of the x - rays which transmit through the work can be optionally selected . therefore , depending on the bumps to be measured , the absorption spectrum of x - ray is measured beforehand and the wavelength of x - ray which is the most favorable for measuring can be determined . for example , if the bumps 12 are formed of solder , the absorption spectrum of x - ray with respect to solder is measured beforehand . thus , it is possible to measure using x - rays having such a wavelength of large linear absorption coefficient . since the absorption spectrum may be different depending on the products even if the substrate itself is the same kind , it is effective to measure the absorption spectrum of x - rays to use the optimum wavelength . fig2 shows an example wherein the bumps 12 a and 12 b are provided on the respective surfaces of a substrate 10 . as a product of the semiconductor device , there are many kind of such a substrate having the respective surfaces of a substrate 10 on which the . bumps 12 a and 12 b are formed . if the materials of the bumps 12 a and 12 b formed on the respective surfaces of the substrate are different from each other , such as , if the bumps 12 a on one of the surfaces are formed of tin - lead and the bumps 12 b on the other surface are formed of tin - silver , the respective heights h a and h b of the bumps 12 a and 12 b can be detected . in order to detect the respective heights h a and h b of the bumps 12 a and 12 b formed on the respective surfaces of the substrate , two or more types of x - rays having different wavelength can be used to measure the intensity of the transmitted x - ray . that is to say , if the intensities of x - rays , the wavelength thereof being λ 1 and λ 2 , are i 1 and i 2 respectively ; the linear absorption coefficients of the material constituting the bumps 12 a and 12 b respectively for x - rays , the wavelength thereof being λ 1 and λ 2 , are μ a1 , μ a2 , μ b1 and μ b2 , i 1 and i 2 are given by the following representations . i 1 = i 0 exp (− μ a1 h a )· exp (− μ b1 h b ) ( 4 ) i 2 = i 0 exp (− μ a2 h a )· exp (− μ b2 h b ) ( 5 ) in this representations , μ a1 , μ a2 , μ b1 , and μ b2 are given beforehand by measurements and i 1 and i 2 can be given as the results of measurements . therefore , the heights h a and h b of the bumps 12 a and 12 b can thus be obtained from the above - mentioned representations ( 4 ) and ( 5 ). in order to measure the height of the bumps by detecting the intensity of the transmitted x - rays , it is necessary to measure the respective intensity of the transmitted x - rays for the respective bumps . in this connection , fig3 to 5 show some examples of measuring apparatus for measuring the intensity of the transmitted x - ray . the embodiment shown in fig3 uses an x - ray ccd camera , the embodiment shown in fig4 uses x - ray image intensifier , and the embodiment shown in fig5 is a measuring apparatus using a photomultiplier tube . the bump detecting apparatus shown in fig3 comprises a x - ray generating device for generating x - rays which should be incident to the work 30 and a ccd camera 22 for detecting x - ray transmitted through the work 30 . the image data detected by the x - ray ccd camera 22 is converted to a digital value by an ad converter 24 and detected by a computer 26 as an intensity of transmitted x - ray . the apparatus further includes a stage 28 on which works are set and a stage guide 29 for moving the stage 28 in the direction parallel to the optical axis of the ccd camera to regulate the focus position of the work 30 . as mentioned above , as far as both the linear absorption coefficient ( μ b ) of the material constituting the bumps of the work 30 and the intensity ( i 1 ) of transmitted x - rays of the substrate having no bumps are available in advance , the height of the bumps can be determined by detecting the intensity of transmitted x - rays transmitted through the work 30 . in the computer 26 , the respective intensities ( i ) of x - ray transmitted through the respective bumps of the work 30 and the linear absorption coefficient ( μ b ) and the intensities ( i 1 ) of transmitted x - rays are analyzed to determined the height ( h b ) of bumps . from these detected results , whether the bumps have a predetermined dimension of height or not can be determined to discriminate allowable and non - allowable products . in this embodiment , the ccd camera 22 and the ad converter 24 constitute detecting means and the computer 26 . constitutes an analyzing means . in the embodiment as shown in fig3 a standard sample 32 can be provided for correcting the intensity of x - rays . the standard sample 32 is disposed on the stage 28 and the x - ray transmitted intensity with respect to the standard sample 32 is detected by the x - ray ccd camera 22 , thereby the intensity of the incident x - rays can be regulated . otherwise , the results of measurements can be revised in accordance with the intensity of the incident x - rays . in the embodiment of fig4 x - rays are incident toward the work 30 from the x - ray generating device 20 and the x - rays transmitted through the work 30 are incident on the x - ray image intensifier 34 . the x - ray image intensifier 34 converts the weak x - ray image into a visible image and a digital ccd camera 36 is arranged at the optical output side . thus , the x - ray transmitted image of the work 30 can be output to the computer 26 as a digital image . in the computer , the x - ray permeability of the respective bumps are analyzed from the digital image of the works 30 and the heights of the respective bumps can thus be detected on the basis of these data . since the x - ray image intensifier 34 has a high image quality , even though a large number of fine bumps are highly densely arranged on the work 30 , the bumps can be accurately detected . also , as the x - ray image intensifier 34 can detect a relatively wide image range , if the work itself is small in size , as a semiconductor device , it is possible to measure at all the bumps once . in this embodiment , a standard sample can be used for correcting the intensity of the incident x - rays . in this embodiment , the x - ray image intensifier 34 , the digital ccd camera 36 and the computer 26 constitute a detecting device . fig5 shows a further embodiment of a measuring apparatus for detecting the transmitted x - ray intensity , in which x - rays are incident toward the work 30 from the x - ray generating device 20 , the x - rays transmitted through the work 30 are detected by a photomultiplier tube 38 and thus the intensity of x - rays transmitted through the work can be measured . the photomultiplier tube 38 serves to amplify the photoelectron energized by the x - rays and the data counted by a photon counter 40 is input into the computer 26 . a high voltage power 39 supplies power to actuate the photomultiplier tube 38 . in the measuring method using the photomultiplier tube 38 , the count number of the respective bumps of the work are individually measured to detect the intensity of transmitted x - rays . therefore , the work 30 must be moved for each bump with respect to the photomultiplier tube 38 . in this embodiment , a stage 28 is supported on a movable stage 42 and the position of the movable stage 42 is controlled by the computer 26 . the output ( count number ) from the photomultiplier tube 38 is memorized by the computer for each bump of the work 30 and thus the intensity of transmitted x - rays can be measured for all of the bumps of the work 30 . the process for detecting the height of the individual bumps from the intensity of transmitted x - ray is the same as that of the previous embodiments . although the detecting method using the photomultiplier tube 38 is complicated as the detecting process must be performed for each bump , a more precise measurement can be expected . in this embodiment , the photomultiplier tube 38 , the photon counter 40 and the computer 26 constitute a detecting device . as mentioned above , according to the present invention , since the height of the bumps is measured using x - rays transmitted through the work , the following advantages can be obtained . that is to say , a precise measurement can be effected regardless of the nature of the object , such as the gloss of the bumps . also , as the height of the bumps from the land can be measured by using transmitted x - rays , it is no longer necessary to measure the height of bumps using a protective film , such as a solder resist , as in the prior art . therefore , there are no fluctuations in the measurement results due to deviations in the thickness of protective film . this is particularly advantageous when a semiconductor element is mounted on a substrate by flip - chip connection using bumps densely arranged on the substrate . in addition , according to the measuring method of this invention , any warps of the substrate do not affect the measured heights of bumps . it should be understood by those skilled in the art that the foregoing description relates to only some of the preferred embodiments of the disclosed invention , and that various changes and modifications may be made to the invention without departing the sprit and scope thereof .