Reduction of positional errors in a four point probe resistance measurement

• US 20040183554A1
• Filed: 03/18/2003
• Published: 09/23/2004
• Est. Priority Date: 03/18/2003
• Status: Active Grant

• Current Assignee: International Business Machines Corporation
• Original Assignee: International Business Machines Corporation
• Inventors: Worledge, Daniel
• Granted Patent: US 6,943,571 B2
• Time in Patent Office: Days
• US Class Current: 324/719
• CPC Class Codes: G01R 27/14 Measuring resistance by measuring current or voltage obtained from a reference source G01R27/16, G01R27/20, G01R27/22 take precedence
• CPC Class Codes: G01R 31/2648 Characterising semiconductor materials testing of materials or semi-finished products G01R31/2831; testing during manufacture H01L22/00

Abstract

A system and method for measuring a resistance or a resistance per square, R_sq, of a material having a surface using a multi-point probe comprising four or more collinear contact points placed in the interior of the sample, the method comprising: making a first measurement using a first set of probe electrodes for inducing a current and a second set of probe electrodes for measuring the voltage difference when the current is induced; making a second measurement using a set of probe electrodes different from the first set for inducing a current and a set of probe electrodes different from the second set for measuring the voltage difference when the current is induced; and using a known relationship among the currents induced, the voltages measured, the nominal probe positions and the resistance per square to determine the resistance per square such that measurement errors resulting from positioning of the probes are reduced.

Claims

1. A method for measuring a resistance, R, of a material having a surface using a multi-point probe comprising four or more substantially collinear contact points, the method comprising:

making a first measurement using a first set of probe electrodes for inducing a current and a second set of probe electrodes for measuring a first voltage difference when the current is induced;

making a second measurement using a set of probe electrodes different from the first set for inducing a current and a set of probe electrodes different from the second set for measuring a second voltage difference when the current is induced; and

using a known relationship among the currents induced, the voltages measured, the nominal probe positions and the resistance per square to determine the resistance per square such that measurement errors resulting from positioning of the probes are reduced.

2. The method of claim 1 wherein the multi-point probe comprises contact points a, b, c, and d;

wherein the points located along a horizontal axis on the surface at locations (0,0), (x,0), (y,0) and (z,0) respectively, such that x is greater than 0, y is greater than x, and z is greater than y;

the resistance measured is resistance per square, and wherein the method comprises;

inducing a current between points a and d;

measuring a voltage difference between point b and point c;

reporting a resistance measurement A;

inducing a current between points a and c;

measuring a voltage difference between point b and point d;

reporting a resistance measurement B; and

determining the resistance per square, R_sq, according to the following relationship, where α

is a number such that α

=z(y−

x)/y(z−

x);

$R_{\mathrm{•<br><br>}}=2<br><br>\mathrm{\pi <br><br>}<br><br>\frac{A-\mathrm{\alpha <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>B}{\ln <br><br>\left[\frac{y<br><br>\left(z-x\right)}{x<br><br>\left(z-y\right)}\right]-\mathrm{\alpha <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>\ln <br><br>\left[\frac{z<br><br>\left(y-x\right)}{x<br><br>\left(z-y\right)}\right]}.$

3. The method of claim 1 wherein the measurement is made with the probes in the interior of the material being measured.

4. The method of claim 1 wherein the multi-point probe comprises contact points a, b, c, and d;

wherein the points located along a horizontal axis on the surface at locations (0,0), (x,0), (y,0) and (z,0) respectively, such that x is greater than 0, y is greater than x, and z is greater than y;

the resistance measured is resistance per square, and wherein the method comprises;

inducing a current between points a and d;

measuring a voltage difference between point b and point c;

reporting a resistance measurement A;

inducing a current between points a and b;

measuring a voltage difference between points c and d;

reporting a resistance measurement G; and

determining the resistance per square, R_sq, according to the following relationship, where α

is a number such that α

=z(y−

x)/y(z−

x);

$R_{\mathrm{•<br><br>}}=2<br><br>\mathrm{\pi <br><br>}<br><br>\frac{A-\mathrm{\alpha <br><br>}<br><br>\left(A+G\right)}{\ln <br><br>\left[\frac{y<br><br>\left(z-x\right)}{x<br><br>\left(z-y\right)}\right]-\mathrm{\alpha <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>\ln <br><br>\left[\frac{z<br><br>\left(y-x\right)}{x<br><br>\left(z-y\right)}\right]}.$

5. The method of claim 1 wherein the multi-point probe comprises contact points a, b, c, and d;

wherein the points located along a horizontal axis on the surface at locations (0,0), (x,0), (y,0) and (z,0) respectively, such that x is greater than 0, y is greater than x, and z is greater than y;

the resistance measured is resistance per square, and wherein the method comprises;

inducing a current between points a and c;

measuring a voltage difference between point b and point d;

reporting a resistance measurement B;

inducing a current between points a and b;

measuring a voltage difference between points c and point d;

reporting a resistance measurement G; and

determining the resistance per square, R_sq, according to the following relationship, where α

is a number such that α

=z(y−

x)/y(z−

x);

$R_{\mathrm{•<br><br>}}=2<br><br>\mathrm{\pi <br><br>}<br><br>\frac{\left(B-G\right)-\mathrm{\alpha <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>B}{\ln <br><br>\left[\frac{y<br><br>\left(z-x\right)}{x<br><br>\left(z-y\right)}\right]-\mathrm{\alpha <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>\ln <br><br>\left[\frac{z<br><br>\left(y-x\right)}{x<br><br>\left(z-y\right)}\right]}.$

6. A method for measuring a resistance per square, R_sq, of a material having a surface using a four-point probe comprising contact points a, b, c, and d, wherein the points are substantially collinear, equally-spaced and are located along a horizontal axis on the surface at locations (0,0), (x,0), (2x,0) and (3x,0) respectively, the method comprising:

inducing a current between points a and d;

measuring a voltage difference between point b and point c;

reporting a resistance measurement A;

inducing a current between points a and c;

measuring a voltage difference between point b and point d;

reporting a resistance measurement B; and

determining the resistance, R_sq, according to the following relationship, where;

$R_{\mathrm{•<br><br>}}=2<br><br>\mathrm{\pi <br><br>}<br><br>\frac{A-\frac{3}{4}<br><br>B}{\ln <br><br>\text{\hspace{1em}<br><br>}<br><br>\left(4\right)-\frac{3}{4}<br><br>\text{\hspace{1em}<br><br>}<br><br>\ln <br><br>\left(3\right)}.$

7. A system for measuring resistance per square on a surface of a material, the system comprising:

a probe comprising first, second, third and fourth electrodes, wherein the electrodes are configured for contacting a surface to be probed at substantially collinear points;

a current source for inducing a current from a selected electrode to a second selected electrode;

a voltage meter for measuring a voltage difference between a pair of selected electrodes;

a multiplexer comprising a plurality of output lines connected to the probe and a plurality of input connections, at least two of which are connected to the current source and at least another two of which are connected to the voltage meter; and

a controller coupled to the multiplexer, the controller comprising logic for;

making a first measurement using a first set of probe electrodes for inducing a current and a second set of probe electrodes for measuring the voltage difference when the current is induced;

making a second measurement using the second set of probe electrodes different from the first set for inducing a current and a set of probe electrodes different from the second set for measuring the voltage difference when the current is induced; and

using a known relationship among the currents induced, the voltages measured, the nominal probe positions and the resistance per square to determine the resistance per square such that measurement errors resulting from positioning of the probes are reduced.

8. A computer-readable medium comprising program instructions for:

making a first measurement using a first set of probe electrodes for inducing a current and a second set of probe electrodes for measuring the voltage difference when the current is induced, wherein the electrodes are configured for contacting a surface to be probed at substantially collinear points;

making a second measurement using a second set of probe electrodes different from the first set for inducing a current and a set of probe electrodes different from the second set for measuring the voltage difference when the current is induced; and

using a known relationship among the currents induced, the voltages measured, the nominal probe positions and the resistance per square to determine the resistance per square such that measurement errors resulting from positioning of the probes are reduced.

9. The computer-readable medium of claim 8 further comprising instructions for:

inducing a current between points a and d;

measuring a voltage difference between point b and point c;

reporting a resistance measurement A;

inducing a current between points a and c;

measuring a voltage difference between point b and point d;

reporting a resistance measurement B; and

determining the resistance, R_sq, according to the following relationship, where α

is a number such that α

=z(y−

x)/y(z−

x);

$\mathrm{Rsq}=2<br><br>\mathrm{\pi <br><br>}<br><br>\frac{A-\mathrm{\alpha <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>B}{\ln <br><br>\left[\frac{y<br><br>\left(z-x\right)}{x<br><br>\left(z-y\right)}\right]-\mathrm{\alpha <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>\ln <br><br>\left[\frac{z<br><br>\left(y-x\right)}{x<br><br>\left(z-y\right)}\right]}.$