TWI803916B - Method to measure chip internal resistance by a chip test equipment - Google Patents

Method to measure chip internal resistance by a chip test equipment Download PDF

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TWI803916B
TWI803916B TW110127207A TW110127207A TWI803916B TW I803916 B TWI803916 B TW I803916B TW 110127207 A TW110127207 A TW 110127207A TW 110127207 A TW110127207 A TW 110127207A TW I803916 B TWI803916 B TW I803916B
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curve
point
value
chip
internal resistance
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TW202227842A (en
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津 魏
經祥 張
蔣子凡
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大陸商勝達克半導體科技（上海）有限公司
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    • 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
    • G01R31/28—Testing of electronic circuits, e.g. by signal tracer
    • 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

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Abstract

A method to measure a chip internal resistance used in a chip test equipment is provided. (S1) Voltage data and current data are retrieved when the chip test equipment performs measurement on a chip and a distributed points diagram is illustrated accordingly. (S2) An X-axis value and a Y-axis value of each of the distributed points are introduced to a curve-fitting formula to calculate at least one parameter thereof. (S3) The value of the parameter is introduce to the curve-fitting formula to obtain a voltage-to-current curve formula. (S4) A curve fitting is performed to obtain a fitting curve. (S5) Voltage values and current values corresponding to the fitting curve are retrieved to calculate the chip internal resistance to input the chip internal resistance to the chip test equipment to finish measuring. Comparing to a current technology, the voltage-to-current curve obtain after the fitting process is more close to the actual voltage-to-current variation curve such that a measuring error is decreased, a measuring accuracy is increased, a sampled data amount is less and an operation efficiency is increased.

Description

一種晶片測試機測量晶片內阻的方法Method for measuring chip internal resistance by a chip testing machine

本發明是關於半導體技術領域，具體地說是一種晶片測試機測量晶片內阻的方法。The invention relates to the technical field of semiconductors, in particular to a method for measuring wafer internal resistance by a wafer testing machine.

在晶片測試機中，需要測試晶片的真實內阻。在實際測量情況中，晶片內阻會隨著電壓的升高而導致電路功耗的增加，功耗增加會導致溫度升高，溫度升高會影響測出的阻值，即電壓對電流曲線會在曲線的首末兩端表現出明顯的非線性。In the wafer testing machine, it is necessary to test the real internal resistance of the wafer. In the actual measurement situation, the internal resistance of the chip will increase the power consumption of the circuit with the increase of the voltage. Significant nonlinearity is shown at the first and last ends of the curve.

目前，根據晶片測試機得到電壓變化資料與電流變化資料，再採用y=kx+b的直線擬合公式來得到電壓對電流函數關係式，最後根據公式得到電壓對電流變化圖線，但是直線擬合方式得到的電壓對電流變化圖線與實際資料偏差較大。申請號為202011217240.9的中國專利公開了一種用於晶片測試機的自動校準方法及其應用，採用斜率標準差法選取分段點，得出校準資料的擬合曲線，但是需要採集較多點的資料來確定擬合公式中的參數，採集工作量較大 。At present, the voltage change data and current change data are obtained according to the wafer testing machine, and then the linear fitting formula of y=kx+b is used to obtain the voltage-current function relational expression, and finally the voltage-current change graph is obtained according to the formula, but the straight line fits The voltage-to-current change graph obtained by the combined method deviates greatly from the actual data. The Chinese patent with the application number 202011217240.9 discloses an automatic calibration method for wafer testing machines and its application. The slope standard deviation method is used to select segment points to obtain the fitting curve of the calibration data, but more data points need to be collected To determine the parameters in the fitting formula, the acquisition workload is relatively large.

因此，設計一種晶片測試機測量晶片內阻的方法，擬合後的電壓對電流曲線更貼近實際的電壓對電流變化圖線，減小測量誤差，提高測量精確度，並且採集資料量較小，提高了工作效率。Therefore, a method for measuring the internal resistance of the wafer by a wafer testing machine is designed. The voltage-current curve after fitting is closer to the actual voltage-current change graph, which reduces measurement errors, improves measurement accuracy, and the amount of data collected is small. Improve work efficiency.

本發明為克服現有技術的不足，提供一種晶片測試機測量晶片內阻的方法，擬合後的電壓對電流曲線更貼近實際的電壓對電流變化圖線，減小測量誤差，提高測量精確度，並且採集資料量較小，提高了工作效率。In order to overcome the deficiencies in the prior art, the present invention provides a method for measuring the internal resistance of a wafer by a wafer testing machine. The fitted voltage-to-current curve is closer to the actual voltage-to-current change graph, which reduces measurement errors and improves measurement accuracy. And the amount of collected data is small, which improves work efficiency.

為實現上述目的，設計一種晶片測試機測量晶片內阻的方法，其特徵在於包括如下步驟：In order to achieve the above object, a method for measuring wafer internal resistance by a wafer tester of design is characterized in that it comprises the steps:

（S1）獲取晶片測試機測量晶片時的電壓資料以及電流資料，並根據電壓資料以及電流資料繪製散點圖；(S1) Obtain the voltage data and current data when the wafer testing machine measures the wafer, and draw a scatter diagram according to the voltage data and current data;

（S2）將散點圖中各複數散點的橫座標以及縱座標代入曲線擬合公式中計算曲線擬合公式中的至少一參數；(S2) Substituting the abscissa and ordinate of each complex scatter point in the scatter diagram into the curve fitting formula to calculate at least one parameter in the curve fitting formula;

（S3）將參數之數值代入曲線擬合公式中得到電壓對電流曲線公式；(S3) Substituting the value of the parameter into the curve fitting formula to obtain the voltage versus current curve formula;

（S4）根據電壓對電流曲線公式進行曲線擬合得到擬合曲線；(S4) performing curve fitting according to the voltage versus current curve formula to obtain a fitting curve;

（S5）提取步驟（S4）獲取的擬合曲線對應的電壓數值以及電流數值計算晶片內阻，並將晶片內阻輸入晶片測試機即完成晶片測試機對晶片內阻的測量。(S5) The voltage value and current value corresponding to the fitting curve obtained in the extraction step (S4) calculate the internal resistance of the chip, and input the internal resistance of the chip into the chip tester to complete the measurement of the chip internal resistance by the chip tester.

步驟（S2）中的曲線擬合公式為

Figure 02_image001
。 The curve fitting formula in step (S2) is
Figure 02_image001
.

步驟（S2）具體包括如下步驟：Step (S2) specifically includes the following steps:

（S21）確定曲線擬合公式中a的數值：取散點圖中橫座標X最大的N個散點，計算各N個點縱座標的平均值，並選擇縱座標最接近平均值的其中之一散點為第一點，第一點的縱座標即為a的數值，其中N為3~5；(S21) Determine the value of a in the curve fitting formula: take the N scatter points with the largest abscissa X in the scatter diagram, calculate the average value of the ordinates of each N points, and select one of the ordinates closest to the average value A scattered point is the first point, and the ordinate of the first point is the value of a, where N is 3~5;

（S22）確定曲線擬合公式中Xc的數值：取散點圖中的散點中，縱座標Y=a/2的第二點，第二點的橫座標即為Xc的數值；(S22) Determine the value of Xc in the curve fitting formula: take the second point of the scatter point in the scatter diagram, the ordinate Y=a/2, and the abscissa of the second point is the value of Xc;

（S23）確定曲線擬合公式中k的數值：取散點圖中的散點中，橫座標X=Xc+b的第三點，獲取第三點的縱座標，將第三點的橫座標和縱座標代入曲線擬合公式計算得出k的數值。(S23) Determine the value of k in the curve fitting formula: take the third point of the scatter point in the scatter diagram with the abscissa X=Xc+b, obtain the ordinate of the third point, and set the abscissa of the third point and ordinate are substituted into the curve fitting formula to calculate the value of k.

步驟（S22）中，當散點圖中的散點在縱座標Y=a/2沒有對應的點時，取縱座標距a/2值最接近的一點為第二點。In step (S22), when the scatter point in the scatter diagram has no corresponding point on the ordinate Y=a/2, take the point closest to the value of a/2 on the ordinate as the second point.

步驟（S23）中b的取值為1~5的正整數。The value of b in the step (S23) is a positive integer ranging from 1 to 5.

本發明同現有技術相比，擬合後的電壓對電流曲線更貼近實際的電壓對電流變化圖線，減小測量誤差，提高測量精確度，並且採集資料量較小，提高了工作效率。Compared with the prior art, the voltage-to-current curve after fitting is closer to the actual voltage-to-current change graph, reduces measurement errors, improves measurement accuracy, and has a small amount of collected data, thereby improving work efficiency.

有關本案的特徵、實作與功效，茲配合圖式作較佳實施例詳細說明如下。About the feature, implementation and effect of this case, hereby cooperate with drawing as preferred embodiment and describe in detail as follows.

下面根據附圖對本發明做進一步的說明。The present invention will be further described below according to the accompanying drawings.

實施例1：Example 1:

請參照圖1A。圖1A為本發明一實施例中，一種晶片測試機測量晶片內阻的方法100的流程圖。方法100包括如下步驟：Please refer to Figure 1A. FIG. 1A is a flow chart of a method 100 for measuring internal resistance of a wafer by a wafer tester according to an embodiment of the present invention. Method 100 includes the steps of:

（S1）獲取晶片測試機測量晶片時的電壓資料以及電流資料，並根據電壓資料以及電流資料繪製散點圖；(S1) Obtain the voltage data and current data when the wafer testing machine measures the wafer, and draw a scatter diagram according to the voltage data and current data;

（S2）將散點圖中各複數散點的橫座標以及縱座標代入曲線擬合公式中計算曲線擬合公式中的至少一參數；(S2) Substituting the abscissa and ordinate of each complex scatter point in the scatter diagram into the curve fitting formula to calculate at least one parameter in the curve fitting formula;

（S3）將參數之數值代入曲線擬合公式中得到電壓對電流曲線公式；(S3) Substituting the value of the parameter into the curve fitting formula to obtain the voltage versus current curve formula;

（S4）根據電壓對電流曲線公式進行曲線擬合得到擬合曲線；(S4) performing curve fitting according to the voltage versus current curve formula to obtain a fitting curve;

（S5）提取步驟（S4）獲取的擬合曲線對應的電壓數值以及電流數值計算晶片內阻，並將晶片內阻輸入晶片測試機即完成晶片測試機對晶片內阻的測量。(S5) The voltage value and current value corresponding to the fitting curve obtained in the extraction step (S4) calculate the internal resistance of the chip, and input the internal resistance of the chip into the chip tester to complete the measurement of the chip internal resistance by the chip tester.

步驟（S2）中的曲線擬合公式為

Figure 02_image001
。 The curve fitting formula in step (S2) is
Figure 02_image001
.

步驟（S2）具體包括如下步驟：Step (S2) specifically includes the following steps:

（S21）確定曲線擬合公式中a的數值：取散點圖中橫座標X最大的N個散點，計算各N個散點縱座標的平均值，並選擇縱座標最接近平均值的其中之一散點為第一點，第一點的縱座標即為a的數值，其中N為3~5；(S21) Determine the value of a in the curve fitting formula: take the N scatter points with the largest abscissa X in the scatter diagram, calculate the average value of the ordinates of each N scatter points, and select the one whose ordinate is closest to the average value One of the scattered points is the first point, and the ordinate of the first point is the value of a, where N is 3~5;

（S22）確定曲線擬合公式中Xc的數值：取散點圖中的散點中，縱座標Y=a/2的第二點，第二點的橫座標即為Xc的數值；(S22) Determine the value of Xc in the curve fitting formula: take the second point of the scatter point in the scatter diagram, the ordinate Y=a/2, and the abscissa of the second point is the value of Xc;

（S23）確定曲線擬合公式中k的數值：取散點圖中的散點中，橫座標X=Xc+b的第三點，獲取第三點的縱座標，將第三點的橫座標和縱座標代入曲線擬合公式計算得出k的數值。(S23) Determine the value of k in the curve fitting formula: take the third point of the scatter point in the scatter diagram with the abscissa X=Xc+b, obtain the ordinate of the third point, and set the abscissa of the third point and ordinate are substituted into the curve fitting formula to calculate the value of k.

步驟（S22）中，當散點圖中的散點在縱座標Y=a/2沒有對應的點時，取縱座標距a/2值最接近的一點為第二點。In step (S22), when the scatter point in the scatter diagram has no corresponding point on the ordinate Y=a/2, take the point closest to the value of a/2 on the ordinate as the second point.

步驟（S23）中b的取值為1~5的正整數。The value of b in the step (S23) is a positive integer ranging from 1 to 5.

下表範例性地示出晶片測試機的電壓與電流資料的範例數值。The table below exemplarily shows the sample values of the voltage and current data of the wafer tester.

表1 X（v） Y（I） 0 0.23 1 0.35 2 0.52 3 0.73 4 1.42 5 2.16 6 3 7 3.67 8 4.38 9 5.04 10 5.75 11 6.44 12 7.07 13 7.79 14 8.47 15 9.16 16 9.84 17 10.53 18 10.78 19 11 20 11.2 21 11.36 22 11.49 23 11.57 24 11.69 25 11.81 26 11.91 27 12 28 12.1 29 12.16 Table 1 X(v) Y (I) 0 0.23 1 0.35 2 0.52 3 0.73 4 1.42 5 2.16 6 3 7 3.67 8 4.38 9 5.04 10 5.75 11 6.44 12 7.07 13 7.79 14 8.47 15 9.16 16 9.84 17 10.53 18 10.78 19 11 20 11.2 twenty one 11.36 twenty two 11.49 twenty three 11.57 twenty four 11.69 25 11.81 26 11.91 27 12 28 12.1 29 12.16

根據上表中電壓與電流資料的範例數值，在步驟（S21）中，取散點圖中橫座標X最大的4個散點，計算這4個散點的縱座標的平均值為12.04，並選擇縱座標最接近該平均值的散點為第一點，則選取的第一點為X1=27，Y1=12。由函數定義域Y∈(0，a)可得Y＜a，即擬合曲線的漸近線為y=a，根據曲線最大值即可確定a的值。因此本實施例取橫座標最大的散點為第一點，第一點的縱座標即為a因此a=12。According to the sample values of the voltage and current data in the above table, in step (S21), take the 4 scattered points with the largest abscissa X in the scatter diagram, calculate the average value of the ordinates of these 4 scattered points as 12.04, and Select the scatter point whose ordinate is closest to the average value as the first point, then the selected first point is X1=27, Y1=12. From the function domain Y ∈ (0, a), it can be obtained that Y<a, that is, the asymptote of the fitting curve is y=a, and the value of a can be determined according to the maximum value of the curve. Therefore, in this embodiment, the scatter point with the largest abscissa is taken as the first point, and the ordinate of the first point is a, so a=12.

步驟（S22）中，當Y=a/2=6沒有對應的點，取縱座標與6最接近的一散點為第二點。則選取的第二點為X2=10，Y2=5.75。當X=Xc時，Y=a/2，因此計算得出Xc=10。In step (S22), when there is no corresponding point for Y=a/2=6, take a scatter point whose ordinate is closest to 6 as the second point. Then the selected second point is X2=10, Y2=5.75. When X=Xc, Y=a/2, so Xc=10 is calculated.

步驟（S23）中，取散點圖中的散點中，橫座標X=Xc+1的第三點，則選取的第三點為X3=11，Y3=6.44。當y=a/2時，曲線線性度良好，因此在第二點右側取點確定的曲線更加貼合實際資料，減小誤差。因此將第三點的橫座標X3、縱座標Y3代入曲線擬合公式

Figure 02_image001
中，計算得出k=0.29。 In step (S23), the third point of the abscissa X=Xc+1 is taken among the scatter points in the scatter diagram, and the selected third point is X3=11, Y3=6.44. When y=a/2, the linearity of the curve is good, so the curve determined by taking points on the right side of the second point fits the actual data more closely and reduces the error. Therefore, the abscissa X3 and ordinate Y3 of the third point are substituted into the curve fitting formula
Figure 02_image001
In , it is calculated that k=0.29.

得到本實施例的曲線擬合公式為

Figure 02_image001
。 Obtain the curve fitting formula of this embodiment as
Figure 02_image001
.

步驟（S3）中，將a、Xc、k的數值分別代入曲線擬合公式中，得到本實施例的具體曲線擬合公式，根據曲線擬合公式得到的擬合曲線如圖2所示。In step (S3), the numerical values of a, Xc, and k are respectively substituted into the curve fitting formula to obtain the specific curve fitting formula of this embodiment, and the fitting curve obtained according to the curve fitting formula is shown in FIG. 2 .

採用y=kx+b的直線擬合公式所得的擬合曲線如圖1所示。The fitting curve obtained by using the straight line fitting formula of y=kx+b is shown in Figure 1.

針對圖1和圖2各點計算與測試資料各個點的和方差與均方根，其結果如圖3和圖4所示。和方差與均方根的值越大越說明擬合圖線與實際資料偏離越大。Calculate and test the sum, variance and root mean square of each point in Figure 1 and Figure 2, and the results are shown in Figure 3 and Figure 4. The larger the value of the sum variance and the root mean square, the greater the deviation between the fitted graph and the actual data.

如圖1B至圖4所示，本發明曲線擬合的平均誤差遠小於直線擬合，即本發明與真實資料的偏離程度都小於直線擬合，更接近真實測量值。As shown in Figure 1B to Figure 4, the average error of the curve fitting of the present invention is much smaller than that of the straight line fitting, that is, the degree of deviation between the present invention and the real data is smaller than that of the straight line fitting, and is closer to the real measured value.

本發明擬合後的電壓對電流曲線更貼近實際的電壓對電流變化圖線，減小測量誤差，提高測量精確度，並且採集資料量較小，提高了工作效率。The fitted voltage versus current curve of the present invention is closer to the actual voltage versus current change graph, reduces measurement errors, improves measurement accuracy, and has a small amount of collected data, thereby improving work efficiency.

雖然以上描述了本發明的具體實施方式，但是本領域的技術人員應該理解，這些僅是舉例說明，在不違背本發明的原理和實質的前提下，可以對這些實施方式做出多種變更或修改。Although the specific implementations of the present invention have been described above, those skilled in the art should understand that these are only examples, and various changes or modifications can be made to these implementations without departing from the principle and essence of the present invention. .

100:方法 S1~S5:步驟 S21~S23:步驟 100: method S1~S5: steps S21~S23: Steps

［圖1A］為本發明一實施例中，一種晶片測試機測量晶片內阻的方法的流程圖； ［圖1B］直線擬合所得的擬合圖線的示意圖； ［圖2］為本發明一實施例中，曲線擬合所得的擬合圖線的示意圖； ［圖3］為直線擬合與曲線擬合和方差的對比示意圖；以及 ［圖4］為直線擬合與曲線擬合均方根的對比示意圖。 [Fig. 1A] is a flow chart of a method for measuring the internal resistance of a wafer by a wafer testing machine in an embodiment of the present invention; [Fig. 1B] Schematic diagram of the fitting graph obtained by straight line fitting; [Fig. 2] is a schematic diagram of a fitting graph obtained by curve fitting in an embodiment of the present invention; [Figure 3] is a schematic diagram of comparison between straight line fitting and curve fitting and variance; and [Figure 4] is a schematic diagram of the comparison between straight line fitting and curve fitting root mean square.

100:方法 100: method

S1~S5:步驟 S1~S5: steps

S21~S23:步驟 S21~S23: Steps

Claims (3)

一種晶片測試機上利用曲線擬合方式測量晶片內阻的方法，包括如下步驟：(S1)獲取一晶片測試機測量晶片時的一電壓資料以及一電流資料，並根據該電壓資料以及該電流資料繪製一散點圖；(S2)將該散點圖中各複數散點的一橫座標以及一縱座標代入一曲線擬合公式中計算該曲線擬合公式中的至少一參數；(S3)將該參數之一數值代入該曲線擬合公式中得到一電壓對電流曲線公式；(S4)根據該電壓對電流曲線公式進行曲線擬合得到一擬合曲線；(S5)提取步驟(S4)獲取的該擬合曲線對應的一電壓數值以及一電流數值計算一晶片內阻，並將該晶片內阻輸入該晶片測試機即完成該晶片測試機對該晶片內阻的測量；其中，步驟(S2)中的曲線擬合公式為Y=a/(1+e -K(X-Xc))；其中，步驟(S2)具體包括如下步驟：(S21)確定該曲線擬合公式中a的數值：取該散點圖中該橫座標X最大的N個該等散點，計算各該N個該等散點之一縱座標的一平均值，並選擇該縱座標最接近該平均值的其中之一該等散點為一第一點，該第一點的該縱座標即為a的數值，其中N為3~5；(S22)確定該曲線擬合公式中Xc的數值：取該散點圖中的該等散點中，該縱座標Y=a/2的一第二點，該第二點的該橫座標即為Xc的數值； (S23)確定該曲線擬合公式中k的數值：取該散點圖中的該等散點中，該橫座標X=Xc+b的一第三點，獲取該第三點的該縱座標，將該第三點的該橫座標和該縱座標代入該曲線擬合公式計算得出k的數值。 A method for measuring chip internal resistance on a chip testing machine using a curve fitting method, comprising the following steps: (S1) obtaining a voltage data and a current data when a chip testing machine measures a chip, and according to the voltage data and the current data Draw a scatter diagram; (S2) substitute an abscissa and an ordinate of each complex scatter point in the scatter diagram into a curve fitting formula to calculate at least one parameter in the curve fitting formula; (S3) One of the numerical values of the parameters is substituted into the curve fitting formula to obtain a voltage-to-current curve formula; (S4) performing curve fitting according to the voltage-to-current curve formula to obtain a fitted curve; (S5) extracting step (S4) obtained A voltage value corresponding to the fitting curve and a current value calculate a chip internal resistance, and input the chip internal resistance into the chip tester to complete the measurement of the chip internal resistance by the chip tester; wherein, step (S2) The curve fitting formula in is Y= a /(1+ e - K ( X - Xc ) ); wherein, step (S2) specifically includes the following steps: (S21) determine the value of a in the curve fitting formula: take In the scatter diagram, for the N scatter points with the largest abscissa X, calculate an average value of the ordinate of one of the N scatter points, and select one of the ordinates closest to the average value The scatter points are a first point, and the ordinate of the first point is the value of a, wherein N is 3 to 5; (S22) determine the value of Xc in the curve fitting formula: take the scatter diagram Among these scatter points in, the second point of the ordinate Y=a/2, the abscissa of the second point is the numerical value of Xc; (S23) determine the numerical value of k in the curve fitting formula: Take a third point of the abscissa X=Xc+b among the scatter points in the scatter diagram, obtain the ordinate of the third point, and obtain the abscissa and the ordinate of the third point Substituting the curve fitting formula to calculate the value of k. 如請求項1所述的一種晶片測試機上利用曲線擬合方式測量晶片內阻的方法，更包含：步驟(S22)中，當該散點圖中的該等散點在縱座標Y=a/2沒有對應的點時，取該縱座標距a/2值最接近的一點為該第二點。 A method for measuring wafer internal resistance on a wafer testing machine as described in claim 1, further comprising: in step (S22), when the scatter points in the scatter diagram are on the ordinate Y=a When there is no corresponding point for /2, take the point closest to the value of the ordinate distance a/2 as the second point. 如請求項1所述的一種晶片測試機上利用曲線擬合方式測量晶片內阻的方法，更包含：步驟(S23)中b的取值為1~5的正整數。 A method for measuring the internal resistance of a wafer by curve fitting on a wafer testing machine as described in claim 1, further comprising: the value of b in step (S23) is a positive integer ranging from 1 to 5.
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