CN106872784B - The test method of HEMT device ohmic contact regions square resistance - Google Patents

The test method of HEMT device ohmic contact regions square resistance Download PDF

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CN106872784B
CN106872784B CN201710116018.1A CN201710116018A CN106872784B CN 106872784 B CN106872784 B CN 106872784B CN 201710116018 A CN201710116018 A CN 201710116018A CN 106872784 B CN106872784 B CN 106872784B
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electrode
group
resolution chart
resistance value
ohmic
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CN106872784A (en
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郑雪峰
董帅帅
王颖哲
李小炜
王冲
马晓华
郝跃
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Xidian University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R27/00—Arrangements for measuring resistance, reactance, impedance, or electric characteristics derived therefrom
    • G01R27/02—Measuring real or complex resistance, reactance, impedance, or other two-pole characteristics derived therefrom, e.g. time constant
    • G01R27/08—Measuring resistance by measuring both voltage and current
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/26—Testing of individual semiconductor devices
    • G01R31/2607—Circuits therefor
    • G01R31/2621—Circuits therefor for testing field effect transistors, i.e. FET's

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Abstract

The invention discloses a kind of test methods of HEMT device ohmic contact regions square resistance, its implementation is: the resolution chart that three groups of electrode widths of preparation are W, every kind of resolution chart includes three Ohmic electrodes, the first electrode size of three groups of resolution charts is identical and third electrode size is identical, the total distance of first electrode and third electrode is fixed, the second electrode length of second group of resolution chart and third group resolution chart is α times of first group of resolution chart second electrode length and β times respectively, and α ≠ β ≠ 1；Test the resistance value in three groups of resolution charts between first electrode and third electrode；It is poor to be made with the resistance value that second group of resolution chart and first group of resolution chart are surveyed, and in the resistance equation that difference equation substitution third group test chart is surveyed, obtains the square resistance of ohmic contact regions in every group of resolution chart.Resolution chart of the present invention is simply easy to manufacture, and test is easy, and result is accurate, can be used for high electron mobility heterojunction transistor fabrication evaluation and Performance Evaluation.

Description

The test method of HEMT device ohmic contact regions square resistance
Technical field
The invention belongs to the field of test technology, in particular to the test of the ohmic contact regions square resistance of a kind of HEMT device Method can be used for fabrication evaluation and Performance Evaluation to semiconductor devices.
Background technique
GaN material compares the first generation semiconductor material using Si as representative and the second generation semiconductor by representative of GaAs Material, has that forbidden bandwidth is big, breakdown electric field is high, high temperature resistant, the advantages such as anticorrosive, therefore becomes third generation semiconductor material Typical Representative.The heterojunction structure high electron mobility transistor (HEMT) especially formed with materials such as AlGaN, in heterojunction boundary There are high concentrations, the two-dimensional electron gas of high electron mobility at place, thus have many advantages, such as that operating current is big, operating rate is fast, High frequency, high-power field have big advantage and broad application prospect.In recent years, related device has become international heat Point, partially has been carried out commercial applications.
Square resistance is an important parameter for characterizing HEMT device Ohmic electrode quality.Current square resistance characterization side It is more to be measured for the square resistance of device active region, and then can not to the square resistance of ohmic contact regions in method Accurate measurement.By taking most common transmission line model TLM method as an example, by one group of device architecture of design, more complex number is carried out It learns and derives and test the numerical value that test obtains active area square resistance, and using the square resistance approximation of active area as ohmic region Square resistance.Since the square resistance of active area is mainly derived from the two-dimensional electron gas at hetero-junctions, and ohmic contact regions It is then to implement the technique of the complexity such as Metal deposition, high annealing on the active area, therefore the square resistance of the two and unequal, Even differ greatly.Obviously, this approximate method can make the characterization accuracy rate of Ohmic contact square resistance low, influence high electricity The Performance Evaluation of transport factor heterojunction transistor.
With the further development of semiconductor power device in recent years, the accurate characterization of ohmic contact regions square resistance is to device The accurate detection and the assessment of performance of part critical process influence increasing.Therefore, how accurately measure HEMT device Europe The square resistance in nurse area becomes a urgent problem to be solved.
Summary of the invention
It is an object of the invention in view of the above shortcomings of the prior art, propose a kind of test HEMT device ohmic contact regions The method of square resistance to improve the accuracy rate of measurement, and then carries out fabrication evaluation and improves the heterogeneous crystalline solid of electron mobility The performance of pipe.
To achieve the above object, technical solution of the present invention includes the following:
(1) Ohmic contact resolution chart is prepared:
Metal electrode is first deposited on semiconductor material, then prepares three groups using the method for high annealing, mesa-isolated Ohmic contact square resistance resolution chart of same size, every kind of resolution chart include three Ohmic electrodes；
If the first Ohmic electrode length L in first group of resolution chart11, the first Ohmic electrode in second group of resolution chart Length L21, the first Ohmic electrode length L in third group resolution chart31Three is equal, i.e. L11=L21=L31；
If the second Ohmic electrode length L in second group of resolution chart22It is second ohm of electricity in first group of resolution chart Pole length L12α times, i.e. L22=α L12；If second electrode length is second in first group of resolution chart in third group resolution chart β times of electrode length, i.e. L32=β L12, wherein α > 0, β > 0, and α ≠ β ≠ 1；
If the first Ohmic electrode and the second Ohmic electrode spacing are L in first group of resolution chart1a, in second group of resolution chart First Ohmic electrode and the second Ohmic electrode spacing are L2a, the first Ohmic electrode and the second Ohmic electrode in third group resolution chart Spacing is L3a；
If the second Ohmic electrode and third Ohmic electrode spacing are L in first group of resolution chart1b, in second group of resolution chart Second Ohmic electrode and third Ohmic electrode spacing are L2b, the second Ohmic electrode and third Ohmic electrode in third group resolution chart Spacing is L3b；
If the third Ohmic electrode length L in first group of resolution chart13, third Ohmic electrode in second group of resolution chart Length L23, third Ohmic electrode length L in third group resolution chart33Three is equal, i.e. L13=L23=L33；
If the total distance in three groups of resolution charts between first electrode and third electrode is L, i.e. L1a+L1b+L12=L, L2a+ L2b+L22=L, L3a+L3b+L32=L, the width of each electrode is designed to W in three groups of resolution charts, and wherein the value of L is according to institute Test sample on piece electrode pattern linear measure longimetry show that the value of W is obtained according to institute's test sample on piece electrode pattern width measurement；
(2) square resistance is measured using Ohmic contact resolution chart:
(2a) applies bias voltage V between the first electrode and third electrode of first group of resolution chart1, and in the loop Series electrical flow table reads the value I of ammeter1, the resistance between first electrode and third electrode is calculated using I-V relationship Value:
RL1=V1/I1；
(2b) applies bias voltage V between the first electrode and third electrode of second group of resolution chart2, and in the loop Series electrical flow table reads the value I of ammeter2, the resistance between first electrode and third electrode is calculated using I-V relationship Value:
RL2=V2/I2；
(2c) applies bias voltage V between the first electrode and third electrode of third group resolution chart3, and in the loop Series electrical flow table reads the value I of ammeter3, the resistance between first electrode and third electrode is calculated using I-V relationship Value:
RL3=V3/I3；
(2d) three resistance value R according to measured by (2a)-(2c)L1, RL2And RL3, construct resolution chart ohmic contact regions Square resistance calculation formula:
(2e) is by the R in step (2a)L1Measured value, the R in step (2b)L2Measured value and step (2c) in RL3 Measured value and known parameters W, L, α, β, L12Substitute into the R in step (2d)shcCalculation formula in, obtain RshcValue.
The invention has the following advantages over the prior art:
1) resolution chart production method is easy
Conventional transmission line model is when making Ohmic contact resolution chart, it is necessary to make multiple ohms by mesa etch and connect Touched electrode, complex process, present invention only requires three groups of resolution charts of preparation, and resolution chart is simple, and test method is quick and convenient.
2) square resistance test method is simple
Transmission line model solves ohmic contact regions square resistance and has to carry out linear fit, and the present invention is only needed to three groups not Same resolution chart carries out electrical measurement and can be obtained Ohmic contact using resulting resistance value by simple mathematical computations The square resistance in area.
3) square resistance test value error is small
When active area square resistance is smaller, when being measured using traditional sonde method combination multimeter, due to multimeter sheet The factors such as the performance of body will have reading shakiness and indeterminable situation with multimeter.In addition, conventional transmission line model is being surveyed When measuring ohmic contact regions square resistance, it is believed that the square resistance R of ohmic contact regionsshcWith active area square resistance RshIt is approximately equal, i.e., Pass through active area square resistance RshObtain ohmic contact regions square resistance RshcValue, therefore there is very big error in measured value. The present invention passes through the method solved equation and eliminates the R of square resistance containing active areashItem, thus solve RshcDuring do not include Source region square resistance Rsh, can direct solution go out ohmic contact regions square resistance RshcValue, improve the precision of measurement, reliability Height has great role to the performance and reliability of accurate evaluation gallium nitride device.Use test method of the invention, it is only necessary to logical The resistance value for crossing test can directly obtain the worth size of active area square resistance by mathematical computations.
Detailed description of the invention
Fig. 1 is implementation flow chart of the invention；
Fig. 2 is existing resolution chart the schematic diagram of the section structure；
Fig. 3 is the top view structural schematic diagram of the first group of resolution chart constructed in the present invention；
Fig. 4 is the top view structural schematic diagram of the second group of resolution chart constructed in the present invention；
Fig. 5 is the top view structural schematic diagram of the third group resolution chart constructed in the present invention；
Fig. 6 is the circuit diagram of test resistance value in the present invention.
Specific embodiment
With reference to the accompanying drawings and examples, specific embodiments of the present invention will be described in further detail.Embodiment For illustrating the present invention, but it is not intended to limit the scope of the invention.
Referring to Fig.1, steps are as follows for realization of the invention:
Step 1, ohmic contact regions square resistance resolution chart is prepared.
As shown in Fig. 2, the cross-section structure of existing resolution chart is followed successively by substrate layer, nitride buffer layer and aluminium from bottom to top Gallium nitrogen barrier layer, and nitride buffer layer and aluminum gallium nitride barrier layer constitute heterojunction structure, three metal electrodes are deposited on aluminium On gallium nitrogen barrier layer.
The test of the cross-section structure preparation ohmic contact regions square resistance of the existing resolution chart of this step according to Fig.2, Figure, implementation step are as follows:
1a) utilize heterogenous junction epitaxy growth method successively growing gallium nitride buffer layer and aluminum gallium nitride gesture from bottom to top on substrate Barrier layer；
1b) first deposit metal electrode in aluminum gallium nitride barrier layer, then carry out the techniques such as high annealing and mesa etch, with The Ohmic contact resolution chart that three groups of electrode widths are W is formed on gallium nitride heteroepitaxial structure, in which:
For first group of resolution chart as shown in figure 3, it includes three Ohmic electrodes, the length of each Ohmic electrode is different, Often use length range and test request by tester's reasonable set according to Ohmic electrode in metal electrode depositing technics.This example is set But being not limited to the first Ohmic electrode length in first group of resolution chart is L11=110 μm, the second Ohmic electrode length is L12= 100 μm, third Ohmic electrode length is L13=120 μm, and the distance between the first Ohmic electrode and the second Ohmic electrode L1a= 5 μm, the distance between the second Ohmic electrode and third Ohmic electrode L1b=8 μm；
Second group of resolution chart is as shown in figure 4, it includes three Ohmic electrodes, and the length of each Ohmic electrode is according to first The Ohmic electrode length of group resolution chart determines.This example sets but is not limited to take first Ohmic electrode of second group of resolution chart long Degree is L21=110 μm, the second Ohmic electrode length L22It is first group of resolution chart the first Ohmic electrode length L12α times, i.e., L22=α L12, third Ohmic electrode length is L23=120 μm；The first Ohmic electrode in second group of resolution chart and second ohm The distance between electrode is L2a=3 μm, the distance between the second Ohmic electrode and third Ohmic electrode are L2b=5 μm, wherein α > 0, and α ≠ 1；This example is in taking α=1.05；
Third group resolution chart is as shown in figure 5, it includes three Ohmic electrodes, and the length of each Ohmic electrode is according to first The Ohmic electrode length of group resolution chart determines that this example sets but is not limited to take the first Ohmic electrode of third group resolution chart long Degree is L31=110 μm, the second Ohmic electrode length L32It is first group of resolution chart the second Ohmic electrode length L12β times, i.e., L32=β L12, third Ohmic electrode length L33=120 μm, the first Ohmic electrode and second ohm of electricity in third group resolution chart The distance between pole is L3a=1 μm, the distance between the second Ohmic electrode and third Ohmic electrode are L3b=3 μm, wherein β > 0 and β ≠ α ≠ 1, this example take β=1.09.
Total distance 1c) set in three groups of resolution charts between first electrode and third electrode is L, obtains relational expression: L1a+ L1b+L12=L, L2a+L2b+L22=L, L3a+L3b+L32=L.
Step 2, the resistance value between the first electrode in three kinds of figures and third electrode is tested.
Referring to resistance test schematic diagram shown in fig. 6, first electrode and third electrode of this step to three kinds of resolution charts Between resistance value testing procedure it is as follows:
2a) apply bias voltage V between the first electrode and third electrode of first group of resolution chart1, and in the loop Series electrical flow table reads the value I of ammeter1, using Ohm's law be calculated first electrode in first group of resolution chart with Resistance value between third electrode: RL1=V1/I1；
2b) apply bias voltage V between the first electrode and third electrode of second group of resolution chart2, and in the loop Series electrical flow table reads the value I of ammeter2, using Ohm's law be calculated first electrode in second group of resolution chart with Resistance value between third electrode: RL2=V2/I2；
2c) apply bias voltage V between the first electrode and third electrode of third group resolution chart3, and in the loop Series electrical flow table reads the value I of ammeter3, using Ohm's law be calculated first electrode in third group resolution chart with Resistance value between third electrode: RL3=V3/I3；
Step 3, resolution chart ohmic contact regions square resistance is calculated.
3a) according to Fig. 3, the resistance value in first group of resolution chart between first electrode and third electrode is indicated are as follows:
RL1=RA1+RA12+RA2+RA23+RA3,
Wherein, RA1For the resistance value of first electrode in first group of resolution chart, RA12For the first electricity in first group of resolution chart The resistance value of active area, R between pole and second electrodeA2For the resistance value below second electrode in first group of resolution chart, RA23For In first group of resolution chart between second electrode and third electrode active area resistance value, RA3For third in first group of resolution chart The resistance value of electrode；
3b) the top view structure of second group of resolution chart according to Fig.4, by first electrode in second group of resolution chart and Resistance value between third electrode indicates are as follows:
RL2=RB1+RB12+RB2+RB23+RB3,
Wherein, RB1For the resistance value of first electrode in second group of resolution chart, RB12For the first electricity in second group of resolution chart The resistance value of active area, R between pole and second electrodeB2For the resistance value below second electrode in third group resolution chart, RB23For In second group of resolution chart between second electrode and third electrode active area resistance value, RB3For third in second group of resolution chart The resistance value of electrode；
3c) according to the top view structure of Fig. 5 third group resolution chart, by first electrode in third group resolution chart and third electricity Resistance value between pole indicates are as follows:
RL3=RC1+RC12+RC2+RC23+RC3,
Wherein, RC1For the resistance value of first electrode in third group resolution chart, RC12For the first electricity in third group resolution chart The resistance value of active area, R between pole and second electrodeC2For the resistance value below second electrode in second group of resolution chart, RC23For In third group resolution chart between second electrode and third electrode active area resistance value, RC3For third in third group resolution chart The resistance value of electrode；
3d) calculate the resistance value of each section in three kinds of resolution charts:
Third electrode sizes 3d1) identical according to the first electrode size in three groups of resolution charts, in three groups of resolution charts The equal relationship of the sum of resistance value between first electrodes identical, in three groups of resolution charts and third electrode obtains three kinds of surveys Attempt the corresponding resistance value relationship of shape each section:
RA1=RB1=RC1,
RA3=RB3=RC3,
RA1+RA3=RB1+RB3=RC1+RC3=RO,
Wherein, ROIt is the sum of the resistance value between the first electrode in three groups of resolution charts and third electrode；
3d2) define the resistance R in first group of resolution chart below second electrodeA2, the second electricity in second group of resolution chart Resistance R below poleB2And the resistance R in third group resolution chart below second electrodeC2Calculation formula difference it is as follows:
RA2=(RshcL12)/W,
RB2=(RshcαL12)/W,
RC2=(RshcβL12)/W,
Wherein, RshcIt is the square resistance of ohmic contact regions to be asked in resolution chart, W is the electricity in every group of resolution chart Pole width, L12For the length of second electrode in first group of resolution chart, α, β, W, L12For known constant, α > 0, β > 0 and α ≠ β ≠1；
3d3) define in three groups of resolution charts the active area resistance R between under first electrode and second electrodeA12, RB12With RC12Calculation formula difference it is as follows:
RA12=(RshL1a)/W,
RB12=(RshL2a)/W,
RC12=(RshL3a)/W,
Wherein RshIt is active area square resistance to be asked in resolution chart；
3d4) define in three groups of resolution charts the active area resistance R between under second electrode and third electrodeA23, RB23With RC23Calculation formula difference it is as follows:
RA23=(RshL1b)/W,
RB23=(RshL2b)/W,
RC23=(RshL2b)/W；
3e) by the R in step 3d2)A2, step 3d3) in RA12With the R in step 3d4)A23Substitute into step 3a) in electricity Expression formula is hindered, the all-in resistance R in first group of resolution chart between first electrode and third electrode is obtainedL1Expression formula:
RL1=RA1+(RshL1a)/W+(RshcL12)/W+(RshL1b)/W+RA3,
3f) by the R in step 3d2)B2, step 3d3) in RB12With step 3d4) RB23Substitute into step 3b) in ohmmeter Up to formula, the all-in resistance R in first group of resolution chart between first electrode and third electrode is obtainedL2Expression formula:
RL2=RB1+(RshL2a)/W+(RshcαL12)/W+(RshL2b)/W+RB3,
3g) by the R in step 3d2)C2, step 3d3) in RC12With step 3d4) RC23Substitute into step 3c) in ohmmeter Up to formula, the all-in resistance R in first group of resolution chart between first electrode and third electrode is obtainedL3Expression formula:
RL3=RC1+(RshL2a)/W+(RshcβL12)/W+(RshL2b)/W+RC3,
3h) simultaneous step 3f) and step 3e) in expression formula, calculate RL2-αRL1Difference expression formula:
RL2-αRL1=(α -1) (RO-Rsh L12/ W),
The difference expression formula is done and obtains first group, second group, first electrode in third group resolution chart after deformation arranges
With the sum of the resistance value of third electrode ROExpression formula:
It is poor 3i) to be made with the expression formula of step 3f) and step 3e), obtains RL2-RLDifference expression formula:
RL2-RL1=(Rshc-Rsh)(α-1)L12/ W,
The difference expression formula is deformed and arranges to obtain ohmic contact regions square resistance RshcWith active area square resistance Rsh's Relationship:
3j) by the R in step 3h)OExpression formula, step 3i) in RshcWith RshRelational expression substitute into step 3g) In expression formula, active area square resistance R is obtainedshExpression formula are as follows:
3k) by the R in step 3j)shExpression formula takes back step 3i) in RshcWith RshRelational expression in, obtain Europe Nurse contact zone square resistance RshcExpression formula are as follows:
3l) by the R in step 2a)L1Measured value, step 2b) in RL2Measured value and step 2c) in RL3Measurement Value and known parameters W, L, α, β, L12Substitute into step 3k) in RshcCalculation formula in, obtain RshcValue.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, it is clear that for this field Professional for, after understanding the contents of the present invention and principle, can modify within the spirit and principles in the present invention, Equivalent replacement and improvement etc., for example, resolution chart of the present invention can also be different using GaAs etc. based on GaN material Semiconductor material prepares the resolution chart in present aspect.Made modifications, equivalent substitutions and improvements should be included in the present invention Protection scope within.

Claims (2)

1. a kind of test method of HEMT device ohmic contact regions square resistance, includes the following steps:
(1) Ohmic contact resolution chart is prepared:
Metal electrode is first deposited on semiconductor material, then three groups of width are prepared using the method for high annealing, mesa-isolated Identical Ohmic contact square resistance resolution chart, every kind of resolution chart include three Ohmic electrodes；
If the first Ohmic electrode length L in first group of resolution chart11, the first Ohmic electrode length in second group of resolution chart L21, the first Ohmic electrode length L in third group resolution chart31Three is equal, i.e. L11=L21=L31；
If the second Ohmic electrode length L in second group of resolution chart22It is that the second Ohmic electrode in first group of resolution chart is long Spend L12α times, i.e. L22=α L12；If second electrode length is second electrode in first group of resolution chart in third group resolution chart β times of length, i.e. L32=β L12, wherein α > 0, β > 0, and α ≠ β ≠ 1；
If the first Ohmic electrode and the second Ohmic electrode spacing are L in first group of resolution chart1a, first in second group of resolution chart Ohmic electrode and the second Ohmic electrode spacing are L2a, the first Ohmic electrode and the second Ohmic electrode spacing in third group resolution chart For L3a；
If the second Ohmic electrode and third Ohmic electrode spacing are L in first group of resolution chart1b, second in second group of resolution chart Ohmic electrode and third Ohmic electrode spacing are L2b, the second Ohmic electrode and third Ohmic electrode spacing in third group resolution chart For L3b；
If the third Ohmic electrode length L in first group of resolution chart13, third Ohmic electrode length in second group of resolution chart L23, third Ohmic electrode length L in third group resolution chart33Three is equal, i.e. L13=L23=L33；
If the total distance in three groups of resolution charts between first electrode and third electrode is L, i.e. L1a+L1b+L12=L, L2a+L2b+ L22=L, L3a+L3b+L32=L, the width of each electrode is designed to W in three groups of resolution charts, and wherein the value of L is according to institute's test sample On piece electrode pattern linear measure longimetry show that the value of W is obtained according to institute's test sample on piece electrode pattern width measurement；
(2) square resistance is measured using Ohmic contact resolution chart:
(2a) applies bias voltage V between the first electrode and third electrode of first group of resolution chart1, and connect in the loop Ammeter reads the value I of ammeter1, the resistance value between first electrode and third electrode: R is calculated using Ohm's lawL1 =V1/I1；
(2b) applies bias voltage V between the first electrode and third electrode of second group of resolution chart2, and connect in the loop Ammeter reads the value I of ammeter2, the resistance value between first electrode and third electrode: R is calculated using Ohm's lawL2 =V2/I2；
(2c) applies bias voltage V between the first electrode and third electrode of third group resolution chart3, and connect in the loop Ammeter reads the value I of ammeter3, the resistance value between first electrode and third electrode: R is calculated using Ohm's lawL3 =V3/I3；
(2d) three resistance value R according to measured by (2a)-(2c)L1, RL2And RL3, construct the side of resolution chart ohmic contact regions Block resistance calculations formula:
(2e) is by the R in step (2a)L1Measured value, the R in step (2b)L2Measured value and step (2c) in RL3Survey Magnitude and known parameters W, L, α, β, L12Substitute into the R in step (2d)shcCalculation formula in, obtain resolution chart Central Europe Nurse contact zone square resistance RshcValue.
2. according to the method described in claim 1, wherein constructing the square resistance of resolution chart ohmic contact regions in step (2d) Calculation formula carries out as follows:
(2d1) indicates the resistance value in first group of resolution chart between first electrode and third electrode are as follows:
RL1=RA1+RA12+RA2+RA23+RA3,
Wherein, RA1For the resistance value of first electrode in first group of resolution chart, RA12For first electrode in first group of resolution chart with The resistance value of active area, R between second electrodeA2For the resistance value below second electrode in first group of resolution chart, RA23It is first Organize the resistance value of active area between second electrode and third electrode in resolution chart, RA3For third electrode in first group of resolution chart Resistance value；
(2d2) indicates the resistance value in second group of resolution chart between first electrode and third electrode are as follows:
RL2=RB1+RB12+RB2+RB23+RB3,
Wherein, RB1For the resistance value of first electrode in second group of resolution chart, RB12For first electrode in second group of resolution chart with Active area resistance value between second electrode, RB2For the resistance value below second electrode in second group of resolution chart, RB23It is second group In resolution chart between second electrode and third electrode active area resistance value, RB3For third electrode in second group of resolution chart Resistance value；
(2d3) indicates the resistance value in third group resolution chart between first electrode and third electrode are as follows:
RL3=RC1+RC12+RC2+RC23+RC3,
Wherein, RC1For the resistance value of first electrode in third group resolution chart, RC12For first electrode in third group resolution chart with The resistance value of active area, R between second electrodeC2For the resistance value below second electrode in third group resolution chart, RC23For third Organize the resistance value of active area between second electrode and third electrode in resolution chart, RC3For third electrode in third group resolution chart Resistance value；
(2d4) identical according to the first electrode size in three groups of resolution charts, the third electrode size phase in three groups of resolution charts The equal relationship of the sum of the same, first electrode in three groups of resolution charts and the resistance value between third electrode obtains three kinds of tests The corresponding resistance value relationship of figure each section:
RA1=RB1=RC1,
RA3=RB3=RC3,
RA1+RA3=RB1+RB3=RC1+RC3=RO,
Wherein, ROIt is the sum of the resistance value of the first electrode and third electrode in three groups of resolution charts；
(2d5) defines first group, second group, the resistance R in third group resolution chart below second electrodeA2, RB2And RC2Meter Formula is calculated to be respectively as follows:
RA2=(RshcL12)/W,
RB2=(RshcαL12)/W,
RC2=(RshcβL12)/W,
Wherein, RshcIt is ohmic contact regions square resistance to be asked in resolution chart, W is the electrode width in every group of resolution chart, L12For the length of second electrode in first group of resolution chart, α, β, W, L12For known constant, α > 0, β > 0, and α ≠ β ≠ 1；
(2d6) define first group, second group, in third group resolution chart under first electrode and second electrode between active area electricity Hinder RA12, RB12And RC12Calculation formula difference it is as follows:
RA12=(RshL1a)/W,
RB12=(RshL2a)/W,
RC12=(RshL3a)/W,
Wherein RshIt is active area square resistance to be asked in resolution chart；
(2d7) define first group, second group, in third group resolution chart under second electrode and third electrode between active area electricity Hinder RA23, RB23And RC23Calculation formula difference it is as follows:
RA23=(RshL1b)/W,
RB23=(RshL2b)/W,
RC23=(RshL2b)/W；
(2d8) is by the R in step (2d5)A2, R in step (2d6)A12With the R in step (2d7)A23It substitutes into step (2d1) Resistance expression formula, obtain the resistance value expression R in first group of resolution chart between first electrode and third electrodeL1:
RL1=RA1+(RshL1a)/W+(RshcL12)/W+(RshL1b)/W+RA3；
(2d9) is by the R in step (2d5)B2, R in step (2d6)B12R in (2d7)B23Substitute into the electricity in step (2d2) Expression formula is hindered, the resistance value expression R in second group of resolution chart between first electrode and third electrode is obtainedL2:
RL2=RB1+(RshL2a)/W+(RshcαL12)/W+(RshL2b)/W+RB3；
(2d10) is by the R in step (2d5)C2, R in step (2d6)C12With the R in step (2d7)C23It substitutes into step (2d3) Resistance expression formula, obtain the resistance value expression R in third group resolution chart between first electrode and third electrodeL3:
RL3=RC1+(RshL3a)/W+(RshcβL12)/W+(RshL3b)/W+RC3；
Expression formula in (2d11) simultaneous step (2d8) and step (2d9) calculates RL2-αRL1Difference: RL2-αRL1=(α -1) (RO-RshL12/ W), deformation is done to the difference expression formula and arranges the first electrode and third electrode obtained in three groups of resolution charts The sum of resistance value ROExpression formula:
It is poor that (2d12) makees the expression formula of step (2d9) and step (2d8), obtains RL2-RL1Difference expression formula: RL2-RL1= (Rshc-Rsh)(α-1)L12/ W deforms the difference expression formula and arranges to obtain ohmic contact regions square resistance RshcAnd active area Square resistance RshRelationship:
(2d13) is by the R in step (2d11)OExpression formula, R in step (2d12)shcWith RshRelational expression substitute into step In the expression formula of (2d10), active area square resistance R is obtainedshExpression formula are as follows:
(2d14) is by the R in step (2d13)shExpression formula takes back the R in step (2d12)shcWith RshRelational expression in, obtain To RshcExpression formula are as follows:
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