[ 0040 ] fig1 shows a top view of an initial setup 100 according to the present invention to measure a capacitance per unit area , for use in determining narrow line - widths of fingers of the gate of a semiconductor device , such as a mosfet , using capacitive measurements of the fingered gate , shown as reference number 210 in fig4 . as shown in fig1 a substrate 105 has a gate oxide layer 110 formed thereon . an undoped or intrinsic polysilicon layer 120 is formed over the gate oxide layer 110 . the polysilicon layer 120 , which may be undoped or lightly doped , is later patterned and doped to form the gate of the semiconductor device . a capacitor meter 130 is connected between the substrate 105 and the intrinsic polysilicon layer 120 . illustratively , the positive or high terminal 132 of the capacitor meter 130 is connected to the intrinsic polysilicon layer 120 , while the negative or low terminal 134 is connected to the substrate 105 . fig2 is a cross sectional view of fig1 along the line 2 - 2 ′. [ 0042 ] fig3 is an equivalent circuit of fig1 where the substrate 105 and the intrinsic polysilicon layer 120 represent plates of a capacitor 140 , and the gate oxide layer 120 represents the dielectric material located between the plates of the capacitor 140 . the polysilicon layer 120 has minimal electrical conductivity since it is not doped or lightly doped . instead of doping the polysilicon layer 120 , which is conventionally done after patterning the polysilicon layer 120 to obtain the proper gate dimensions , an external energy source is used to provide or enhance electrical characteristics of the polysilicon layer 120 . the energy source enhances electrical characteristics by generating carriers in the polysilicon layer 120 . illustratively , the external energy source is an optical light , such as a low power laser and / or heat , where the setup 100 is heated up to approximately 200 ° c . for approximately one minute , for example . fig2 shows the energy source as an optical light source 150 . the area of the polysilicon layer 120 is large , with physical dimensions that are large enough to render negligible tolerances of the dimensions . illustratively , the polysilicon layer 120 is 100 μm long and 100 μm wide . after generating carriers in the polysilicon layer 120 , capacitance per unit area c ox of the thin gate oxide layer portion , which is located between the polysilicon layer 120 and the substrate 105 , is measured with the capacitor meter 130 . as will be explained , the capacitance per unit area c ox is used to determine width of fingers formed from patterning and etching the polysilicon layer 120 , or patterning polysilicon layers of other devices having a gate oxide and polysilicon layers which are of a similar size as those of the structure 100 shown in fig1 . [ 0046 ] fig4 shows a top view of a structure 200 having a similar size as the structure 100 shown in fig1 . in fig4 an intrinsic polysilicon layer is patterned and etched to form a fingered gate 210 , having fingers 220 . each finger portion located over the gate oxide layer 110 has a length l and a width w . the finger width w is the minimum critical dimension and the finger length l is large enough so that the tolerance in finger dimensions is negligible . the capacitance meter 130 is used to measure the capacitance c m of the fingered polysilicon layer 210 . this measured capacitance c m is given by equation ( 1 ): c ox is the capacitance per unit area of the thin oxide layer 110 , as measured by the capacitance meter 130 using the setup 100 shown in fig1 ; w is the physical line width of the finger 220 shown in fig4 ; c of is the finger outer fringe capacitance per unit length , or the capacitance per unit length of the fingers 220 due to edge effects , and is obtained through computer simulation of the structure 200 ; and p is the perimeter of the fingered intrinsic poly 210 located over the thin gate oxide 120 . the polysilicon line is formed to have a length which is larger than a critical dimension or feature size . accordingly , the polysilicon line length is known by design , and is used to approximate the perimeter p thereof . equation ( 1 ) is solved for the finger width w to yield equation ( 2 ): w =[ c m /(( p / 2 )× c ox )]− c of / c ox ( 2 ) thus , using equation ( 2 ), the finger width w of the fingered gate 210 is determined from capacitive measurements of the rectangular gate 120 shown in fig1 and of the fingered gate 210 shown in fig4 knowing the length l and the number n of the fingers 220 . the finger width measurement is performed without the need to dope the intrinsic gate polysilicon , thus providing rapid feedback of the poly gate etch that forms the gated fingers . accordingly , the finger widths and electrical characterization of the semiconductor device having the fingered gate are quickly determined , without having to wait till after forming the source and drain regions , and without the need to dope the gate polysilicon . the gate polysilicon has a high resistance , since it is not doped and , thus , has a low carrier concentration . to reduce the resistance of the gate poly , and form a low contact resistance to the intrinsic gate poly , a two point probe is used . the capacitance measurement is performed in accordance to another embodiment of the present invention shown in fig5 . similar to that shown in fig2 in fig5 the capacitance meter 130 is connected between the gate poly electrode 210 and the substrate 105 . however , instead of connecting one terminal the capacitance meter 130 , e . g ., the high terminal 132 , to a single probe contacting the gate poly electrode 210 , two probes 250 , 255 are electrically connected to the gate poly electrode 210 , one via a capacitor . to reduce the resistance of the intrinsic gate poly electrode 210 , carriers therein are generated by an external energy source , such as heat or light , using for example the light source 150 shown in fig2 . to further reduce the resistance of the surface contact , such as the resistance of the intrinsic ( or lightly doped ) gate poly 210 under optical or thermal excitation , a direct current ( dc ) bias is applied through the two probes 250 , 255 . illustratively , the dc bias is provided by a current source 260 connected between the two probes 250 , 255 . contact to semiconductors with low carrier concentrations is highly non - ohmic , and gives rise to current - voltage characteristics 270 shown in fig6 . for very low voltages and currents , such as at an operating point a shown in fig6 the small - signal impedance dv / di is very high , as shown by the nearly horizontal tangent 275 to the current - voltage characteristics 270 at the low voltage and current operating point a . by applying the dc bias across the two probes 250 , 255 shown in fig5 a large current in induced in the gate poly 210 . this changes the operating point from a to b , as shown in fig6 . at the high voltage and current operating point b , the small - signal impedance dv / di is greatly reduced . in particular , the slope of the tangent 275 at operating point a , where the slope di / dv is the inverse of the small - signal impedance dv / di , is larger than the slope of the tangent 280 at operating point b . thus , the small - signal impedance dv / di at operating point b is smaller than the small - signal impedance at operating point a . reducing the small - signal impedance dv / di , allows accurate differential capacitance measurements on semiconductors with relatively low carrier concentration , such as the intrinsic gate poly 210 under optical or thermal excitation . to provide the proper dc current 260 flowing through the intrinsic gate poly electrode 210 , between the two probes 250 , 255 , bias resistors and capacitors are used . illustratively , a 1 mω resistor has a first terminal connected to one terminal of the current source 260 and a second terminal connected to the first probes 250 ; and another 1 mω resistor has its first terminal connected to the other terminal of the current source 260 and its second terminal connected to the second probes 255 . in addition , a 1 . 5 nf capacitor is connected between the two second terminals of the two 1 mω resistors , for example , which two terminals are also connected to the two probes 250 , 255 , respectively . capacitance measurements are performed using the capacitance meter 130 , which has one terminal , e . g ., the high terminal 132 , connected to one of the probes contacting the gate poly 210 , such as the first probe 250 . the other terminal , e . g ., the low terminal 134 , of the capacitance meter 130 is connected to the substrate 105 . furthermore a d . c . bias voltage is provided ( e . g . by the capacitance meter 130 ) to either invert or accumulate the substrate silicon at the oxide interface . as shown in fig5 to assure both good dc and high frequency contact to the substrate wafer 105 , the substrate 105 is placed on a conductor , referred to as a chuck 300 , and the low terminal 134 of the capacitance meter 130 is connected to the chuck 300 . thus , the low capacitance meter terminal 134 is connected to both a substrate probe 310 that electrically contacts the substrate 105 , and a chuck probe 320 that electrically contacts the chuck 300 . [ 0065 ] fig7 shows in greater detail the two probes 310 , 320 contacting the substrate 105 and chuck 300 , respectively . the substrate probe 310 electrically contacts a region of the substrate 105 which is not covered by the gate oxide 110 and gate poly 210 . illustratively , the substrate 105 is lightly doped silicon with p - type material . due to the small contact area and low doping of the substrate 105 , the substrate contact or probe 310 provides a dc contact of very high impedance . while this is adequate to maintain a proper dc bias , it is not adequately sufficient for the high frequency current that the capacitance meter 130 requires for accurate capacitance measurements . to improve capacitance measurement , the second contact or chuck probe 320 is provided to electrically contact the chuck 300 located on the back side of the wafer or substrate 105 , which back side is opposite the front substrate side having the gate 210 formed thereon . illustratively , the back side of the substrate 105 is coated with various insulating films 330 which block direct current ( dc ) and separate the chuck 300 from the substrate 105 . the wafer chuck 300 provides a high capacitance to the entire back side of the wafer 105 . [ 0067 ] fig8 shows an equivalent circuit of the wafer and chuck probes 310 , 320 , where the chuck capacitance is shown as a capacitor 340 connected in parallel to a resistor 350 , which is the equivalent of the high impedance wafer front side contact 310 ( fig7 ). thus , the wafer and chuck probes 310 , 320 , shown in fig7 provide a good dc contact at the wafer probe 310 , in parallel with a good high frequency probe or contact at the chuck probe 320 . this allows capacitive line - width measurements , as described in connection with fig1 - 4 , to be performed without special processing for contacting the wafer 105 . while the invention has been particularly shown and described with respect to illustrative and preferred embodiments thereof , it will be understood by those skilled in the art that the foregoing and other changes in form and details may be made therein without departing from the spirit and scope of the invention which should be limited only by the scope of the appended claims .