the following description is provided to enable any person skilled in the art to make and use the invention and sets forth the best modes contemplated by the inventor of carrying out his invention . various modifications , however , will remain readily apparent to those skilled in the art , since the generic principles of the present invention have been defined herein specifically to provide a method and apparatus for isothermal capacitance transient spectroscopy . the preferred embodiments of the present invention will be described below . according to a first preferred embodiment , in an isothermal capacitance transient spectroscopy , a pulse voltage having an appointed magnitude is applied to a semiconductor sample , which is held at a constant temperature , to analyze a resultant capacitance - change of the semiconductor sample . the quantity of impurities and the like contained in the semiconductor sample can be determined by an expression defined by the following equation ( 4 ): ## equ9 ## a differential coefficient obtained by differentiating k ( t ) defined by equation ( 4 ) is used as the icts spectrum , and this is expressed by the following equation ( 8 ): ## equ10 ## in this case , the concentration of impurities , n t , and the thermal emission time constant , τ , are expressed by the following equation ( 9 ) on the basis of equation ( 2 ): ## equ11 ## equation ( 9 ) will be further described below with reference to fig3 . as shown in fig3 ( a ), c ( t ) is the actual measured sample capacitance , and it has a time dependence after the initial and predetermined bias voltage pulse is applied to the sample for a predetermined time . the term &# 34 ; c o &# 34 ; is the equilibrium capacitance established in the sample after the application of the bias voltage pulse . provided that a capacitance transient waveform c ( t ) is as shown in fig3 ( a ), the k ( t ) obtained according to equation ( 4 ) ( that is , an integrated capacitance transient waveform ) is as shown in fig3 ( b ). as understood from fig3 ( b ), the integrated capacitance transient waveform k ( t ) is improved in s / n . this k ( t ) is differentiated to use the obtained differential coefficient as the icts spectrum . this icts spectrum has a waveform as shown in fig3 ( c ) and is improved in s / n 10 times or more , as compared with the above - described conventional method . accordingly , an accuracy of measurement of the concentration of impurities and thermal emission time constant can be improved . thus , impurities of low concentration 1 / 10 times or less , as compared with that in the conventional method , can be detected . the present invention is not limited by the above - described first preferred embodiment . a differential coefficient obtained by differentiating an expression defined by the following equation ( 5 ) may also be used as the icts spectrum : ## equ12 ## a concentration of unknown impurities , n t , and a thermal emission time constant , τ , in this second preferred embodiment are expressed by the following equation ( 10 ): ## equ13 ## in this second preferred embodiment , an expression which is approximate as compared with that in the above - described first preferred embodiment is used , so that the accuracy is slightly inferior , but the expression is comparatively simple . thus , an advantage occurs in that the calculation can also be conducted , if desired , by an analog circuit . in addition , in the case where the capacitance transient waveform c ( t ) includes an invariable fraction , c n , as shown in fig4 the following equation ( 6 ) may be used as k ( t ) in the above - described first and second preferred embodiments . c n is the nullbalance capacitance , which can be determined either manually by the operator from a display screen , or can be determined automatically by the computer system . if a capacitance meter directly measures c ( t ), then a relatively larger capacitance range ( e . g . 1 , 000 pf ) must be used . if the capacitance meter measures c ( t )-- c n , then a small capacitance range ( e . g . 100 pf ) can be used . generally , the smaller capacitance range has a higher capacitance resolution capability so that c n is important in enabling such resolution . thus , a differential coefficient obtained by differentiating equation ( 6 ) may be used as the icts spectrum . ## equ14 ## a concentration of impurities , n t , and a thermal emission constant , τ , in this third preferred embodiment are expressed by the following equation ( 11 ): ## equ15 ## in this third preferred embodiment , an effective number of figures in a signal processing operation by the computer is increased , so that there is the possibility that the accuracy of the calculation is improved . in addition , a differential coefficient obtained by differentiating an expression defined by the following equation ( 7 ) may be used as the icts spectrum : ## equ16 ## a concentration of impurities , n t , and a thermal emission time constant , τ , in this fourth preferred embodiment are expressed by the following equation ( 12 ): ## equ17 ## in this fourth preferred embodiment , an expression which is approximate as compared with that in the above - described third preferred embodiment is used , so that the accuracy is slightly inferior , but the expression is comparatively simple . thus , calculations can also be conducted by an analog circuit and , at the same time , an effective number of figures in an operation by the computer is increased . thus , there is still the possibility that the accuracy of calculations can be improved . in the preferred embodiments , a digital signal processing is performed with a computer program . the selected mathematical equation for the particular embodiment is implemented in a software algorithm program in a manner well known in the art so that the operator can prepare the sample to achieve an isothermal state by inserting it into a constant temperature bath . the sample is permitted to equalize to the environment , and probes 7 and 8 can be applied to the desired test area of the sample . a predetermined bias voltage is applied as a pulse for a set time period . the measurement time cycle is then started and the data representing c ( t ) is collected and then converted to binary information and stored , for example , in a register to be assigned to a ram memory . the data can then be processed pursuant to the desired mathematical equation , depending on the particular embodiment to be implemented , to provide an output of measured impurities . as described above , according to the present invention , the icts spectrum is improved in s / n 10 times or more , as compared with the conventional method . thus , an accuracy of measurement of concentration of impurities and thermal emission time constant can be improved . thus , impurities of low concentration 1 / 10 times or less , as compared with that in the conventional method , can be detected . those skilled in the art will appreciate that various adaptations and modifications of the just - described preferred embodiment can be configured without departing from the scope and spirit of the invention . therefore , it is to be understood that , within the scope of the appended claims , the invention may be practiced other than as specifically described herein .