Abstract
The present invention relates to a method of establishing specific electrode positions by providing a multi-point probe and a test sample. The method comprises the measuring or determining of a distance between two of the electrodes of the multi-point probe and establishing a resistance model representative of the test sample. The method further comprises the performing of at least three different sheet resistance measurements and establishing for each of the different sheet resistance measurement a corresponding predicted sheet resistance based on the resistance model. Thereafter the method comprises the establishment of a set of differences constituting the difference between each of the predicted sheet resistance and its corresponding measured sheet resistance, and deriving the specific electrode positions of the multi-point probe on the surface of the test sample by using the distance and performing a data fit by minimizing an error function constituting the sum of the set of differences.
Claims
1. A method of establishing specific electrode positions, on a surface of a test sample, of a multi-point probe that includes more than four parallel probe arms extending from a probe body, each of the probe arms including an electrode, wherein the method comprises the steps of: (a) positioning the multi-point probe such that each of the electrodes is in contact with the surface of the test sample; (b) selecting two of the electrodes of the multi-point probe; (c) determining a distance between the selected two of the electrodes; (d) establishing a resistance model representative of the test sample, the resistance model defining specific electrode positions of the multi-point probe relative to the surface of the test sample included as unknown parameters, the resistance model representing the test sample as at least one of a finite sheet and a multi-layered sheet; (e) performing a plurality of different resistance measurements on the test sample with the multi-point probe, each of the resistance measurements including: (i) selecting four different electrodes of the multi-point probe; (ii) dividing the four different electrodes into a first pair of electrodes and a second pair of electrodes; (iii) applying a current propagating through the test sample between the first pair of electrodes; (iv) detecting a voltage induced between the second pair of electrodes; and (v) establishing a measured resistance based on a ratio of the voltage and the current; (f) establishing for each of the different resistance measurements a corresponding predicted resistance based on the resistance model; (g) establishing a set of differences constituting the difference between each of the predicted resistances and its corresponding measured resistance; and (h) deriving the specific electrode positions of the multi-point probe on the surface of the test sample by using the distance between the selected two of the electrodes, and performing a data fit by minimizing an error function constituting the sum of the set of differences.
2. The method of claim 1, wherein the multi-point probe includes two outermost electrodes, and wherein the step of selecting two of the electrodes of the multi-point probe includes selecting the two outermost electrodes of the multi-point probe.
3. The method of claim 1, wherein the test sample is a multi-layered sheet comprising a top layer and a bottom layer, and constituting a magnetic tunnel junction, and wherein the resistance model represents a magnetic tunnel junction.
4. The method of claim 3, wherein the resistance model is defined by the equation: where R.sub.T is the top-layer resistance, R.sub.B is the bottom-layer resistance and λ is the transition length, K.sub.0 is the modified Bessel function of the second kind, 0'th order, the values x.sup.i, y.sup.i, z.sup.i and w.sup.i are the distances between probe arms in a given configuration, and λ is given by where RA is the product of resistance and rest sample surface area.
5. The method of claim 1, wherein the electrodes are placed adjacent a boundary of the surface of the test sample, and wherein the resistance model represents a micro-Hall effect measurement.
6. The method of claim 5, wherein the surface of the test sample extends in any direction less than twice the distance between two outermost electrodes of the multi-point probe.
7. The method of claim 5, wherein at least one of the electrodes is located closer to the boundary than twice the distance between two outermost electrodes of the multi-point probe.
8. The method of claim 5, wherein the resistance model is defined by the equation: where R.sub.0 is the sheet resistance of the test sample, R.sub.H is the Hall effect sheet resistance of the test sample, x.sup.i, y.sup.i, z.sup.i, and w.sup.i are the distances between probe arms in a given configuration, and 1 is the distance between a collinear probe arm and a parallel insulating test sample boundary.
9. The method of claim 1, wherein the test sample is of a semiconductor material.
10. The method of claim 1, wherein the error function is: e=Σ.sub.n=1.sup.m(ƒ(α, β.sub.n)−R.sub.n(β.sub.n)).sup.2, in which α constitutes the electrical test sample parameters, and β.sub.n represents the specific electrode positions.
11. The method of claim 1, further comprising the additional step of measuring at least one electrical parameter of the test sample selected from the group consisting of current, voltage, and resistance.
12. The method of claim 1, further comprising the additional step of determining a sheet resistance of the test sample.
13. A computer-based system for establishing specific electrode positions, on a surface of a test sample, of a multi-point probe, the system comprising: a multi-point probe having a probe body and more than four parallel probe arms extending from the probe body, each of the probe arms including an electrode, the multi-point probe being positionable such that each of the electrodes is in contact with a surface of a test sample, wherein, when the multi-point probe is so positioned, a distance is defined between two outermost electrodes of the multi-point probe, the system further including a resistance model representative of the test sample, the resistance model having the specific electrode positions of the multi-point probe relative to the surface of the test sample included as unknown parameters, the resistance model representing the test sample as at least one of a finite sheet and a multilayered sheet, the system further comprising: first means for performing a plurality of different resistance measurements, each of the resistance measurements including: (i) selecting four different electrodes of the multi-point probe; (ii) dividing the four different electrodes into a first pair of electrodes and a second pair of electrodes; (iii) applying a current propagating through the test sample between the first pair of electrodes; (iv) detecting a voltage induced between the second pair of electrodes; and (v) establishing a measured resistance based on a ratio of the voltage and the current; second means for establishing, for each of the different resistance measurements, a corresponding predicted resistance based on the resistance model; third means for establishing a set of differences constituting the difference between each of the predicted resistances and its corresponding measured resistance; and fourth means for deriving the specific electrode positions of the multi-point probe on the surface of the test sample by using the distance between the two outermost electrodes and performing a data fit by minimizing an error function constituting the sum of the set of differences.
14. The system of claim 13, wherein the test sample is a multi-layered sheet comprising a top layer and a bottom layer, and constituting a magnetic tunnel junction, and wherein the resistance model represents a magnetic tunnel junction.
15. The system of claim 13, wherein the multi-point probe is positionable such that the electrodes are placed adjacent a boundary of the surface of the test sample, and wherein the resistance model represents a micro-Hall effect measurement.
16. The system of claim 15, wherein the multi-point probe is positionable such that at least one of the electrodes is located closer to the boundary than twice the distance between two outermost electrodes of the multi-point probe.
17. The system of claim 15, wherein the resistance model is defined by the equation: where R.sub.O is the sheet resistance of the test sample, R.sub.H is the Hall effect sheet resistance of the test sample, x.sup.i, y.sup.i, z.sup.i and w.sup.i are the distances between probe arms in a given configuration, and 1 is the distance between a collinear probe arm and a parallel insulating test sample boundary.
18. The system of claim 13, wherein the error function is: e=Σ.sub.n=1.sup.m(ƒ(α, β.sub.n)−R.sub.n(β.sub.n)).sup.2 in which α constitutes the electrical sample parameters, and β.sub.n represents the specific electrode positions.
19. The system of claim 13, further comprising fifth means for measuring at least one electrical parameter of the test sample selected from the group consisting of current, voltage, and resistance.
20. The system of claim 13, further comprising fifth means for determining a sheet resistance of the test sample.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
(1) FIG. 1 is a schematic perspective view of a computer-based system according to the present invention.
(2) FIG. 2A is a schematic view of a first embodiment of a multi probe measurement setup performing a Hall effect measurement adjacent the boundary.
(3) FIG. 2B is a schematic view of a second embodiment of a multi probe measurement setup performing a current in plane tunnelling (CIPT) measurement.
(4) FIG. 2C is a schematic view of a third embodiment of a multi probe measurement setup 12′″ in accordance with the present invention. In the present setup 12′″, a Hall effect measurement is made on a small test sample 24′″.
(5) FIG. 2D is a schematic view of the ideal electrode positions versus the real electrode positions for an occasional probe landing.
(6) FIG. 3A is a flow chart showing the steps of performing a current in place tunnelling measurement for magnetic tunnel junctions.
(7) FIG. 3B is a flow chart showing the steps of performing a micro Hall effect measurement for semiconductors.
(8) FIG. 4A is a schematic view of a twelve point probe according to the present invention.
(9) FIG. 4B is a schematic view of first measurement with the above probe in which four probe arms are selected.
(10) FIG. 4C is a schematic view of second measurement with the above probe in which four probe arms are selected.
(11) FIG. 4D is a schematic view of third measurement with the above probe in which four probe arms are selected.
(12) FIG. 4E is a schematic view of fourth measurement with the above probe in which four probe arms are selected.
(13) FIG. 4F is a schematic view of fifth measurement with the above probe in which four probe arms are selected.
(14) FIG. 4G is a schematic view of sixth measurement with the above probe in which four probe arms are selected.
(15) FIG. 4H is a schematic view of seventh measurement with the above probe in which four probe arms are selected.
(16) FIG. 4I is a schematic view of eighth measurement with the above probe in which four probe arms are selected.
(17) FIG. 5A are B are graphs showing on the ordinate axis, the simulated relative error in percent and on the abscissa, the pin spacing index.
(18) FIG. 6A is a bar diagram showing on the ordinate axis, the relative standard deviation of the estimated magnetoresistance (MR) and resistance area product (RA) and on the abscissa, different characteristic length scales of the test sample.
(19) FIG. 6B is a bar diagram showing on the ordinate axis, the mean value of the estimated magnetoresistance (MR) and resistance area product (RA) and on the abscissa, different characteristic length scales of the test sample.
(20) FIG. 7A is a graph showing on the ordinate axis, the resistance area product (RA) and on the abscissa, the number of the probe landing for MTJ sample.
(21) FIG. 7B is a graph showing on the ordinate axis, the magnetoresistance (MR) and on the abscissa, the number of the probe landing for MTJ sample.
(22) FIG. 7C is a graph showing on the ordinate axis, the resistance area product (RA) and on the abscissa, the number of the probe landing for MTJ sample.
(23) FIG. 7D is a graph showing on the ordinate axis, the magnetoresistance (MR) and on the abscissa, the number of the probe landing for MTJ sample.
DETAILED DESCRIPTION OF THE DRAWINGS
(24) FIG. 1 shows a schematic perspective view of a computer-based system 10 according to the present invention, illustrating schematically the multi probe measurement setup 12 used for performing a multi-probe resistance measurement. The computer-based system 10 comprises the multi-probe measurement setup 12 connected to a stationary computer 14 for controlling the measurements. The stationary computer 14 may be located in a separate cabinet as illustrated here or alternatively be integrated as a part of the multi probe measurement setup 12. The stationary computer 14 may be connected to a laptop computer 16 for providing an easy user interface for illustrating and controlling the measurements, however, the laptop computer 16 may evidently be replaced by a monitor and a keyboard, or other suitable interfaces.
(25) The multi probe measurement setup 12 is located in a controlled clean environment and includes a probe body 18. The probe body 18 in turn includes a plurality of probe arms, in the present case five probe arms 20a-e. Each of the probe arms 20a-e includes an electrode 22a-e constituting the tip of the respective probe arm 20a-e. The electrodes 22a-e contact the surface of a test sample 24.
(26) FIG. 2A shows a first embodiment of a multi probe measurement setup 12′ in accordance with the present invention. In the present setup 12′, a micro-Hall effect measurement is made adjacent to a boundary of the test sample 24′ meaning that the electrodes 22a-e are contacting the surface of the test sample 24′ adjacent an outer edge of the test sample 24′ or alternatively adjacent an insulating barrier of the test sample 24′. The test sample 24′ is a single semi-infinite layer test sheet.
(27) FIG. 2B shows a second embodiment of a multi probe measurement setup 12″ in accordance with the present invention. In the present setup 12″, a current in plane tunnelling (CIPT) measurement is made on the test sample 24″. The test sample 24 comprises multiple layers constituting a top conductive layer 24a, a bottom conductive layer 24b and an insulating layer 24c in-between the top layer 24a and the bottom layer 24b. This constitutes a magnetic tunnel junction. The electrodes are contacting the surface of the top layer 24a of the test sample 24′. Additional layers are possible.
(28) FIG. 2C shows a third embodiment of a multi probe measurement setup 12′″ in accordance with the present invention. In the present setup 12′″, a Hall effect measurement is made on a small test sample 24′″ meaning that the test sample has approximately the same size as the distance between the outermost probe arms 20a and 20e, or slightly larger. The test sample 24′″ is a single layer test sheet.
(29) FIG. 2D shows the ideal electrode positions as a + and one example of real electrode positions for an occasional probe landing. The difference between the ideal and real electrode positions is designated δ.sub.x and δ.sub.y.
(30) FIG. 3A shows the steps of performing a current in place tunnelling measurement for magnetic tunnel junctions. The steps are described below:
(31) 1: The sample is provided and a model is established corresponding to the sample and the measurement.
(32) 2: Resistance measurements are performed using the multi probe measurement setup.
(33) 3: The industry is moving towards smaller characteristic length scales of the test samples in order to be able to design compact devices.
(34) 4: The obvious solution to perform accurate measurement would be to use a smaller electode distance, increase the measurement current or fabricate probes with more pins in order to keep a high accuracy of the measurement.
(35) 5: In the prior art, electrode position corrections were made according to van der Pauw or Rymaszewski, which assume an infinite single layer test sample.
(36) 6: The sample parameters derived for multi-layered test samples (MTJ) or micro-Hall measurements near the boundary will be incorrect.
(37) 7: Instead, it is suggested that the exact geometry is used for the position correction, i.e. the test sample, probe position is taken into account for establishing a better model used in the measurement setup.
(38) 8: Better results are achieved by better position correction.
(39) FIG. 3B shows the steps of performing a micro Hall effect measurement for semiconductors. The steps are described below:
(40) 1: The sample is provided and a model is established corresponding to the sample and the measurement.
(41) 2: Resistance measurements are performed using the multi probe measurement setup.
(42) 3: The industry is moving towards smaller characteristic length scales of the test samples in order to be able to design compact devices.
(43) 4: The obvious solution to perform accurate measurement would be to use a smaller electrode distance, increase the measurement current or fabricate probes with more pins in order to keep a high accuracy of the measurement.
(44) 5: A correction free Hall effect approximation is made.
(45) 6: In the prior art, electrode position corrections were made according to van der Pauw or Rymaszewski, which assume an infinite single layer test sample.
(46) 7: The sample parameters derived for multi-layered test samples (CIPT) or Hall measurements near the boundary will be incorrect.
(47) 8: Instead, it is suggested that the exact geometry is used for the position correction, i.e. the test sample, probe position is taken into account for establishing a better model used in the measurement setup.
(48) 9: Better results are achieved by better position correction, allows fully automatic tools, higher quality control, better precision, MTJ stack with one or multiple tunnelling barrier, smaller test samples and thicker electrodes.
(49) FIG. 4A shows a twelve point probe according to the present invention. The twelve-point probe has twelve probe arms 20a-l, each having an electrode 22a-l.
(50) FIG. 4B shows a first measurement with the above probe, in which four of the twelve probe arms 20a-l and corresponding electrodes 22a-l are selected, and of which two will constitute current electrodes between which a current is injected, and the other two will contribute voltage electrodes between which a voltage is measured. The selected electrodes are a, d, i, and l.
(51) FIG. 4C shows a second measurement with the above probe, in which four of the twelve probe arms 20a-l and corresponding electrodes 22a-l are selected. The selected electrodes are a, c, h, and k.
(52) FIG. 4D shows a second measurement with the above probe, in which four of the twelve probe arms 20a-l and corresponding electrodes 22a-l are selected. The selected electrodes are c, g, j, and l.
(53) FIG. 4E shows a second measurement with the above probe, in which four of the twelve probe arms 20a-l and corresponding electrodes 22a-l are selected. The selected electrodes are a, b, d, and g.
(54) FIG. 4F shows a second measurement with the above probe, in which four of the twelve probe arms 20a-l and corresponding electrodes 22a-l are selected. The selected electrodes are b, d, g, and i.
(55) FIG. 4G shows a second measurement with the above probe, in which four of the twelve probe arms 20a-l and corresponding electrodes 22a-l are selected. The selected electrodes are b, c, e, and g.
(56) FIG. 4H shows a second measurement with the above probe, in which four of the twelve probe arms 20a-l and corresponding electrodes 22a-l are selected. The selected electrodes are h, i, j, and k.
(57) FIG. 4I shows a second measurement with the above probe, in which four of the twelve probe arms 20a-l and corresponding electrodes 22a-l are selected. The selected electrodes are c, d, e, and f.
(58) FIGS. 5A and B are two graphs, representing two proof of concept experiments, each showing on the ordinate axis the position error (in micrometers) of the electrode positions for two simulated CIPT measurements and on the abscissa an index that identifies each electrode. The dash-dotted line represents the simulated real position error of each electrode for two specific simulated CIPT measurements, the dashed and solid lines represent the position error estimations done by the position correction method according to the present invention. As can be seen the estimated position errors follow remarkably well the real position errors.
(59) FIG. 6A is a bar diagram showing on the ordinate axis the relative standard deviations of the estimated magnetoresistance (MR) and resistance area product (RA) and on the abscissa different characteristic length scales in μm for the corresponding four test samples under test. As proof of concept of the benefit of the invention for CIPT measurements, the experiment was conducted by measuring on four different MTJ samples 100 data points and the repeatability (defined as the relative standard deviation) has been calculated. The filled bar designates RA derived according to the prior art technique, the coarsely hatched bar designates MR derived according to the prior art technique, the finely hatched bar designates RA derived according to the technique claimed according to present invention and the non-filled bar designates MR derived according to the technique claimed according to present invention. For each of the four samples there is a drastic reduction in the relative standard deviations both on the MR and RA parameter implies a much improved repeatability of the CIPT measurement. The improvement for the sample with lambda 0.46 μm is about 80% on the repeatability of MR.
(60) FIG. 6B is a bar diagram showing on the ordinate axis the mean values of the estimated magnetoresistance (MR) and resistance area product (RA) and on the abscissa different characteristic length scales in μm for the corresponding four test samples under test. As proof of concept of the benefit of the invention for CIPT measurements, the experiment was conducted by measuring on four different MTJ samples 100 data points and the mean values have been calculated. The filled bar designates RA derived according to the prior art technique, the coarsely hatched bar designates MR derived according to the prior art technique, the finely hatched bar designates RA derived according to the technique claimed according to present invention and the non-filled bar designates MR derived according to the technique claimed according to present invention. As can be seen, the mean values calculated using the prior art methods for position correction are the same as the mean values estimated using the invention to compensate for position errors. Clearly the mean values should be dependent only on the sample and not from the error position correction method used.
(61) FIG. 7A is a graph showing on the ordinate axis, the resistance area product (RA) in Ωμm.sup.2 and on the abscissa, the number of the probe landing. 100 probe landings are made in total in this proof of concept experiment using a test sample having a lambda of 0.46 μm. The filled squares designate RA derived according to the prior art technique, whereas the line designates RA derived according to the technique claimed according to the present invention.
(62) FIG. 7B is a graph showing on the ordinate axis, the magnetoresistance (MR) in % and on the abscissa, the number of the probe landing. 100 probe landings are made in total in this proof of concept experiment using a test sample having a lambda of 0.46 μm. The filled squares designate MA derived according to the prior art technique, whereas the line designates MA derived according to the technique claimed according to the present invention.
(63) FIG. 7C is a graph showing on the ordinate axis, the resistance area product (RA) in Ωμm.sup.2 and on the abscissa, the number of the probe landing. 100 probe landings are made in total in this proof of concept experiment using a test sample having a lambda of 0.8 μm. The filled squares designate RA derived according to the prior art technique, whereas the line designates RA derived according to the technique claimed according to the present invention.
(64) FIG. 7D is a graph showing on the ordinate axis, the magnetoresistance (MR) in % and on the abscissa, the number of the probe landing. 100 probe landings are made in total in this proof of concept experiment using a test sample having a lambda of 0.8 μm. The filled squares designate MA derived according to the prior art technique, whereas the line designates MA derived according to the technique claimed according to present invention.
(65) The above graphs illustrate the drastically improved precision, in particular the repeatability, of the technique claimed according to present invention.
(66) The above-described embodiments describe specific realizations according to the present invention showing specific features, however, it is apparent to the skillful individual that the above-described embodiments may be modified, combined or aggregated to form numerous further embodiments.
REFERENCE NUMERALS
(67) 10. Computer-based measurement system 12. Multi probe measurement setup 14. Stationary computer 16. Laptop computer 18. Probe body 20. Probe arms 22. Electrodes 24. Test sample
