text: referring now to fig1 there is shown a semiconductor wafer 11 including a thin layer 13 disposed on a substrate 15 . layer 13 is usually of submicron thickness and formed on the substrate 15 by diffusion or ion implantation . the wafer 11 may be of the type useful as a solar cell or in the fabrication of high frequency transistors , for example . wafer 11 serves as a sample for which the sheet resistivity of the thin film layer 13 is to be measured . there is provided a first probe head 17 which includes four linearly aligned , spaced - apart electrodes 19 , 21 , 23 , and 25 . the ends of the four electrodes serve as probe tips and can be positioned in contact with the top surface of layer 13 . a current source 27 is connected to the outer electrodes 19 and 25 to inject a known current , i s , into the layer 13 . ideally , the current established between electrodes 19 and 25 flows solely through layer 13 ; however , in reality some of the current flow between electrodes 19 and 25 passes through the substrate 15 , and is deemed to be leakage current . leakage current is commonly caused by one or more of three factors : ( 1 ) minority carriers can be injected into the substrate by the electrodes 19 and 25 , particularly in the case where the semiconductor at the probe electrode contact points is heated , pressed and / or carrying a high density current ; ( 2 ) the thin layer 13 can easily be penetrated by the current electrodes , and current may be injected directly from the electrodes to the substrate 15 ; and ( 3 ) there may be defects at the junction between layer 13 and substrate 15 in the region near the current electrodes 19 and 25 . the manner in which the apparatus of the present invention determines the magnitude of the leakage current is described hereinafter . the two inner electrodes 21 and 23 of the first probe head 17 sense the voltage difference on the surface of the layer 13 produced in response to the current flow established by electrodes 19 and 25 . this voltage difference is amplified by a preamplifier 29 . to assure optimum sensitivity , the probe tips 19 , 21 , 23 , and 25 are formed of a high temperature conductive material such as osmium or tungsten carbide . preamplifier 29 has a high input impedance on the order of 10 11 ohms or more , and a high common mode rejection ratio on the order of 100 db or more . preamplifier 29 may be a varactor bridge electrometer for example . the low level output of preamplifier 29 is further amplified by amplifier 31 to produce the output voltage v . current source 27 includes internal circuitry for determining the magnitude of the current injected into the semiconductor wafer 11 . the magnitude of the current is selected by a switch ( not shown ) and indicated by a signal level proportional to the current magnitude on the output line 33 . in combination , the current source 27 and preamplifier 29 and amplifier 31 comprise a first circuit means coupled to the first probe head 17 . wafer 11 is disposed on a platen 35 . on the opposite side of wafer 11 from the first probe head 17 , there is a second probe 36 including two electrodes 37 and 39 . the two electrodes 37 and 39 are movable along an axis perpendicular to the plane of wafer 11 into engagement with the substrate 15 of the wafer . electrodes 37 and 39 of the second probe 36 are spaced apart with a predetermined spacing s and vertically aligned opposite the outer current electrodes 19 and 25 of the first probe head 17 . the two electrodes are preferably formed of osmium , tungsten carbide or stainless steel . movement of electrodes 37 and 39 is achieved by actuation of a piston 41 , as hereinafter described . the two electrodes 37 and 39 of the second probe head 36 are positionable to engage the bottom surface of the substrate 15 of wafer 11 and sense the voltage difference δv between these two electrodes on the surface of the substrate . this voltage difference is applied to second circuit means including a preamplifier 43 , an amplifier 45 and a computation network 47 for determining the magnitude of the leakage current in the substrate 15 which is a portion of the current injected into the wafer by the two electrodes 19 and 25 of the first probe head 17 . more particularly , the voltage difference δv across probes 37 and 39 is applied to preamplifier 43 which has a high input impedance on the order of 10 11 ohms and a high common mode rejection ratio of approximately 100 db or more . the amplified voltage signal from preamplifier 43 is applied to amplifier 45 and then to a computation network 47 . the relationship between the differential voltage δv and the leakage current in the substrate 15 of wafer 11 has been derived as follows : where , δv is the voltage measured between probes 37 and 39 , s is the spacing between these two probes , ρ and w are the resistivity and the thickness of substrate 15 , respectively , c is euler &# 39 ; s constant ( i . e ., 0 . 577215665 ), and i 1 is the leakage current through the substrate 15 . equation 1 can be solved for the leakage current , i 1 , and simplified as follows : ## equ1 ## network 47 includes conventional analog or digital computation circuitry for performing the computation of equation 2 to produce an output voltage indicative of the leakage current i 1 . the value of the differential voltage δv is received from amplifier 45 , and the values for the substrate resistivity ρ and thickness w are set as input voltage levels by potentiometers 48 in accordance with the particular characteristics of the substrate 15 . the other values of the parameters in equation 2 are preset in network 47 . the output voltage from computation network 47 is applied to one input of a third circuit means including a difference circuit 49 . the other input to difference circuit 49 is received on signal line 33 and represents the magnitude of the current i s injected into layer 13 of wafer 11 by the electrodes 19 and 25 from current source 27 . the output of circuit 49 is a voltage signal i d representing the magnitude of the difference in current between the injected current i s and the leakage current i 1 . the current i d determined by circuit 49 represents the portion of the injected current which is confined to layer 13 of wafer 11 . this is because the current which leaks through layer 13 into substrate 15 has been determined and subtracted from the injected source current i s . a fourth circuit means includes a divider 51 having two inputs . one input is the voltage signal v from amplifier 31 which represents the voltage difference between electrodes 21 and 23 of the first probe head 17 . the other input is the voltage signal representing the magnitude of the current i d confined to layer 13 . divider circuit 51 calculates the sheet resistivity of layer 13 , ρ s , from the inputs v and i d according to the following equation : equation 3 is basically the same as the well known equation for determining thin layer sheet resistivity by a four - point probe , except that the current signal has been compensated to account for the leakage current i 1 through the substrate 15 of wafer 11 . the output ρ s from divider 51 is applied to a display circuit 53 which produces a digital or analog representation of sheet resistivity . to assure the accuracy of the resistivity measurement , there is provided an optically opaque conductive , aluminum screen 55 which encloses the assemblage of the first and second probes 17 and 41 , the respective preamplifiers 29 and 43 , and the wafer 11 which serves as the sample . screen 55 precludes light and stray electromagnetic fields from adversely affecting the measurement process . fig2 illustrates the second probe 36 in greater detail . the platen 35 includes a perforated support plate 56 upon which is disposed a perforated teflon pad 57 . the pad 57 in turn supports the sample wafer 11 . the first probe head 17 is positioned over wafer 11 and the probe electrodes 19 , 21 , 23 , and 25 are positioned in contact with the wafer 11 . support plate 56 has an aperture therein receiving a piston 59 which may travel on an axis perpendicular to the plane of the wafer 11 . the upper portion of piston 59 forms a vacuum chamber 69 along with sidewalls 61 , and the bottom surface of support plate 56 . vertical movement of the piston 59 is limited upwardly by surfaces 63 of the chamber ; whereas , downward movement of the piston is limited by the surfaces 65 . when the vacuum chamber 69 is filled with air , the piston 59 is biased away from wafer 11 against the limit surfaces 65 by a coil spring 67 . the vacuum chamber 69 communicates through a vacuum port 71 and inlet pipe 73 to a vacuum source 74 . when chamber 69 is evacuated of air , piston 59 travels upwardly against the bias of spring 67 by action of the pressure of atmospheric air on the bottom of piston 59 . air enters the chamber portion 74 through a port 76 . disposed internally of piston 59 and along the vertical axis of movement thereof are two tubes 73 and 75 . the tubes are spaced apart and have ends which terminate a predetermined distance below the teflon pad 57 when piston 59 is positioned in its upward most position , as shown . contained within the two tubes 73 and 75 , and extending therefrom , are the two electrodes 37 and 39 which comprise the second probe . each of the two electrodes 37 and 39 are resiliently biased upward toward the bottom portion of the wafer 11 so that the substrate of the wafer is firmly contacted by the electrodes when piston 59 is moved into its upward position by operation of the vacuum source . the resilient biasing of the two electrodes 37 and 39 is achieved by a spring ( not shown ) contained within each of the tubes 73 and 75 . the electrodes 37 and 39 extend upwardly through apertures or perforations 78 and 78 &# 39 ; in the teflon pad 57 . teflon pad 57 also includes a plurality of grooves 77 inscribed on the surface thereof . these grooves 77 may be in the form of concentric circles , for example . each groove has the lower portion thereof communicating with a plurality of apertures 79 in the pad 57 . these apertures in turn communicate through ports 81 in the support plate 56 . ports 81 communicate with vacuum chamber 69 . in operation , vacuum applied to the chamber 69 by vacuum source 74 is also applied to each of the ports 81 and thence through the apertures 79 in the teflon pad to the grooves 77 , thereby to firmly hold the wafer onto pad 57 during the testing and measuring process . electrodes 37 and 39 are respectively electrically coupled by wires 83 and 85 through respective support posts 87 and 89 to the preamplifier 43 . support posts 87 and 89 are held respectively by teflon insulators 91 and 93 . the voltage difference on the substrate 15 sensed by the two electrodes 37 and 39 is applied to the preamplifier 43 and then processed by the circuitry of fig1 described above .