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# Cont act resistance to a thin semiconductor layer The contact between a metal contact and a thin conducting layer of semiconductor can be described with the resistive network shown in Figure PDF document - DocSlides

cheryl-pisano | 2014-12-13 | General

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3.5.4. Cont act resistance to a thin semiconductor layer The contact between a metal contact and a thin conducting layer of semiconductor can be described with the resistive network shown in Figure 3.5 , which is obtained by slicing the structure into small sections with length , so that the contact resistance, , and the semiconductor resistance, , are given by: 3.5 and 3.5 is the contact resistance of the metal to semiconductor interface per unit area with units of cm , is the sheet resistance of the semiconductor layer with units of and is the width of the contact. x + Figure 3.5 Distributed resistance model of a contact to a thin semiconductor layer. Using Kirchoff's laws one obtains the following relations between the voltages and currents at and + 3.5 3.5 By letting approach zero one finds the following differential equations for the current, ), and voltage, ): dx dV 3.5

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dx dI 3.5 Which can be combined into: dx with 3.5 The parameter is the characteristic distance over which the current occurs under the metal contact and is also referred to as the penetration length. The general solution for ) and ) are: sinh sinh 3.5 sinh cosh 3.5 Both are plotted in Figure 3.5 0.00E+00 5.00E-05 1.00E-04 1.50E-04 2.00E-04 2.50E-04 3.00E-04 3.50E-04 4.00E-04 Distance (micron) Voltage (V) 0.00E+00 2.00E-04 4.00E-04 6.00E-04 8.00E-04 1.00E-03 1.20E-03 Current (A) Figure 3.5 Lateral current a nd voltage underneath a 5 m long and 1 mm wide metal contact with a contact resistivity of 10 cm on a thin semiconductor layer with a sheet resistance of 100 The total resistance of the contact is:

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coth coth 3.5 10 In the limit for an infinitely long contact (or >> ) the contact resistance is given by: , for >> 3.5 11 A measurement of the resistance between a set of contacts with a variab le distance between the contacts (also referred to as a transmission line structure) can therefore be fitted to the following straight line: 3.5 12 so that the resistance per square, , can be obtained from the slope, while the contact resistivity, , can be obtained from the intersection with the axis. The penetration depth, , can be obtained from the intersection with the x axis. This is illustrated with Figure 3.5 . Figure 3.5 Resistance versus contact spacing, , of a transmission line structure. In the limit for a short contact (or << ) the contact resistance can be approximated by expanding the hyperbolic cotangent Wd ...) , for << 3.5 13 ... 45 coth for << 1

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The total resistance of a short contact therefore equals the resistance between the contact metal and the semiconductor layer (i.e. the parallel connection of all the res istors, , in Figure 3.5 ), plus one third of the end to end resistance of the conducting layer underneath the contact metal (i.e the series connection of all resistors, , in Figure 3.5 ).

54 Cont act resistance to a thin semiconductor layer The contact between a metal contact and a thin conducting layer of semiconductor can be described with the resistive network shown in Figure 35 which is obtain ID: 23173

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Page 1

3.5.4. Cont act resistance to a thin semiconductor layer The contact between a metal contact and a thin conducting layer of semiconductor can be described with the resistive network shown in Figure 3.5 , which is obtained by slicing the structure into small sections with length , so that the contact resistance, , and the semiconductor resistance, , are given by: 3.5 and 3.5 is the contact resistance of the metal to semiconductor interface per unit area with units of cm , is the sheet resistance of the semiconductor layer with units of and is the width of the contact. x + Figure 3.5 Distributed resistance model of a contact to a thin semiconductor layer. Using Kirchoff's laws one obtains the following relations between the voltages and currents at and + 3.5 3.5 By letting approach zero one finds the following differential equations for the current, ), and voltage, ): dx dV 3.5

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dx dI 3.5 Which can be combined into: dx with 3.5 The parameter is the characteristic distance over which the current occurs under the metal contact and is also referred to as the penetration length. The general solution for ) and ) are: sinh sinh 3.5 sinh cosh 3.5 Both are plotted in Figure 3.5 0.00E+00 5.00E-05 1.00E-04 1.50E-04 2.00E-04 2.50E-04 3.00E-04 3.50E-04 4.00E-04 Distance (micron) Voltage (V) 0.00E+00 2.00E-04 4.00E-04 6.00E-04 8.00E-04 1.00E-03 1.20E-03 Current (A) Figure 3.5 Lateral current a nd voltage underneath a 5 m long and 1 mm wide metal contact with a contact resistivity of 10 cm on a thin semiconductor layer with a sheet resistance of 100 The total resistance of the contact is:

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coth coth 3.5 10 In the limit for an infinitely long contact (or >> ) the contact resistance is given by: , for >> 3.5 11 A measurement of the resistance between a set of contacts with a variab le distance between the contacts (also referred to as a transmission line structure) can therefore be fitted to the following straight line: 3.5 12 so that the resistance per square, , can be obtained from the slope, while the contact resistivity, , can be obtained from the intersection with the axis. The penetration depth, , can be obtained from the intersection with the x axis. This is illustrated with Figure 3.5 . Figure 3.5 Resistance versus contact spacing, , of a transmission line structure. In the limit for a short contact (or << ) the contact resistance can be approximated by expanding the hyperbolic cotangent Wd ...) , for << 3.5 13 ... 45 coth for << 1

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The total resistance of a short contact therefore equals the resistance between the contact metal and the semiconductor layer (i.e. the parallel connection of all the res istors, , in Figure 3.5 ), plus one third of the end to end resistance of the conducting layer underneath the contact metal (i.e the series connection of all resistors, , in Figure 3.5 ).

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