JP2006352035A - Method and structure for evaluating contact resistance - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To correctly obtain contact resistance, while evaluating sheet resistance of a region where a semiconductor substrate under an ohmic electrode has deteriorated. <P>SOLUTION: A sheet resistance evaluation region 100 and a contact resistance evaluation region 200 are prepared in contact resistance evaluation structures 10, with respectively multiple electrical resistance evaluators 110. Furthermore in the structure, a primary electrode length d<SB>A</SB>and an electrode width W of an ohmic electrode are mutually equal, and paired first intervals L<SB>A</SB>are mutually different. The ohmic electrode, belonging to respective electrical resistance evaluators prepared in the sheet resistance evaluation region, and a pair of ohmic electrodes and their paired widths W. Paired second intervals L<SB>B</SB>ohmic electrodes and their widths W are mutually equal, and lengths d<SB>B</SB>of second electrodes are mutually different, belonging to respective electrical resistance evaluators 210 prepared in the contact resistance evaluation region. By means of the structures 10, contact resistance is evaluated between the ohmic electrode and a semiconductor substrate 20, based on the evaluated electrical resistance between a pair of ohmic electrodes formed on the semiconductor substrate. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a contact resistance evaluation method for evaluating contact resistance between a semiconductor substrate and an ohmic electrode, and a contact resistance evaluation structure used in this method.

  Reducing the contact resistance between the ohmic electrode formed on the semiconductor substrate and the semiconductor substrate is an important examination item for achieving low power and high speed of the semiconductor element.

  Conventionally, a TLM (Transmission Line Model) method is used for evaluation of contact resistance. In the TLM method, first, electrode pairs of a plurality of ohmic electrodes having different electrode intervals are formed on a semiconductor substrate, and the electrical resistance of each electrode pair is measured. Thereafter, the measured electric resistance is plotted on the coordinates with the electrode interval as the horizontal axis and the electric resistance as the vertical axis, and the slope of the approximate linear straight line obtained from the plotted points, and The contact resistance and the sheet resistance of the semiconductor substrate are obtained from the intercept (see, for example, Non-Patent Document 1).

  In the method described in Non-Patent Document 1 described above, it is assumed that the sheet resistance of the semiconductor substrate is equal between the region under the ohmic electrode and the region between the ohmic electrodes not covered with the ohmic electrode. However, the sheet resistance in the region under the electrode does not necessarily match the sheet resistance in the other region. This is because there is a possibility that an altered layer is formed at the interface of the semiconductor substrate with the metal by the heat treatment called sintering, which is necessary to form an ohmic electrode well, and this altered layer is a normal semiconductor layer. This is because they have different sheet resistances. Therefore, the contact resistance cannot be accurately obtained by the method disclosed in Non-Patent Document 1, which assumes that the sheet resistance of the region where the semiconductor substrate under the electrode is altered is equal to the other region.

Therefore, a contact resistance evaluation method has been proposed in consideration of the case where the sheet resistance in the region under the electrode is different from the sheet resistance in the other region (see, for example, Non-Patent Document 2).
Gregory S. Marlow and Mukunda B.M. Das “The effects of contact size and non-zero metal resilience on the determination of specific contact resistance”, Solid-State Electron. 198 25, no. 2, pp. 91-94 M.M. Ahmad and B.M. M.M. Aurora, “Investigation of AuGeNi contacts using rectangular and circular transmission Line model”, Solid-State Electronics (Great Britain), 1992, Vol. 35, no. 10, pp. 1441-1445 (Formula 4)

  In the method described in Non-Patent Document 2 described above, it is necessary to measure the sheet resistance of the metal electrode. However, when the inventors of the present invention have made extensive studies, the sheet resistance of the metal electrode cannot be measured because it is very small. Therefore, the method described in Non-Patent Document 2 cannot accurately evaluate the contact resistance. I understand that.

  The present invention has been made in view of the above-mentioned problems, and an object of the present invention is to evaluate a contact resistance accurately by determining a sheet resistance in a region where a semiconductor substrate under an ohmic electrode has been altered. It is providing the structure for a contact resistance used for the method and the said contact resistance evaluation method.

  In order to achieve the above-described object, the contact resistance evaluation method of the present invention uses a contact resistance evaluation structure described below to measure the measured electrical resistance between a pair of ohmic electrodes formed on a semiconductor substrate. From this, the contact resistance between the ohmic electrode and the semiconductor substrate is evaluated.

  The structure for contact resistance evaluation is provided with a sheet resistance evaluation region and a contact resistance evaluation region each including a plurality of electrical resistance measurement units, and the electrical resistance measurement unit is separated from the common semiconductor substrate and the semiconductor substrate. The surface of the semiconductor substrate between the pair of ohmic electrodes provided in the same size and shape, the under-electrode alteration layer formed in the surface region of the semiconductor substrate immediately below the ohmic electrode, and the pair of ohmic electrodes A non-altered layer of the region.

  The two ohmic electrodes belonging to the same electrical resistance measurement unit have a rectangular planar shape, the same size and shape, and the sides in the width direction of the pair of opposing ohmic electrodes are parallel to each other, The lengthwise sides of the ohmic electrode are parallel to a straight line connecting the electrode centers.

Among the plurality of electrical resistance measurement units, each electrical resistance measurement unit provided in the sheet resistance evaluation region is defined as a first electrical resistance measurement unit, and the first electrode length d of the pair of ohmic electrodes belonging to the first electrical resistance measurement unit. _a and the electrode width W is equal to each other and a first distance L _a between the pair of ohmic electrodes are different from each other. On the other hand, among the plurality of electrical resistance measurement units, each electrical resistance measurement unit provided in the contact resistance evaluation region is defined as a second electrical resistance measurement unit, and the second interval between the pair of ohmic electrodes belonging to the second electrical resistance measurement unit. L _B and the electrode width W is equal to each other and the second electrode length d _B are different from each other.

  The contact resistance evaluation method of the present invention includes the following steps.

First, the first electrical resistance _RA between the pair of ohmic electrodes is measured for each of the plurality of first electrical resistance measurement units.

Next, the horizontal axis a first distance L _A, and, approximately obtained when the first electrical resistor R _A measured and the vertical axis, the intercept of the slope A and the horizontal axis is -B From the primary straight line, the first interval L _A , the first electric resistance R _A , the sheet resistance Rs of the non-altered layer, the sheet resistance Rs ′ of the altered layer under the electrode, the electrode width W, and the following formula (1) are defined. The following formulas (3) and (4) are derived using the following formula (2) that is satisfied by the transition length Lt, and the sheet resistance Rs of the non-altered layer is obtained from the formula (3).

Lt = (ρc / Rs ′) ^1/2 (1)
R _A = 2 × Rs ′ × Lt / W + Rs × L _A / W (2)
A = Rs / W (3)
B = 2 × Rs ′ × Lt / Rs (4)

Next, each of the second plurality of electrical resistance measuring section, measuring a second electric resistance R _B between the pair of ohmic electrodes.

Next, a second electrode length _{d B} is (1) formula, _d B << against Rs' = temporary transition length obtained when the ^{Rs Lt' (= (ρc / Rs} ) 1/2) have a relationship of Lt', from the second electrical resistance R _B that is measured by the second electrical resistance measuring unit, the second electrode length d _B, the second electrical resistance R _B, the contact resistance rho] c, the non-altered layer sheet resistance Rs , obtaining the contact resistance ρc using a second distance L _B and the electrode width W satisfies the following formula (5).

R _B = 2 × ρc / (W × d) + Rs × L _B / W (5)

  Next, using the following equation (6) derived from the equations (3) and (4) and the following equation (7) derived from the above equation (1), the inclination A and the horizontal axis The sheet resistance Rs ′ of the altered layer under the electrode is obtained from the section -B and the electrode width W.

Lt = A × B × W / (2 × Rs ′) (6)
Rs ′ = A ² × B ² × W ² / (4 × ρc) (7)

  Next, the transition length Lt is obtained from the contact resistance ρc and the sheet resistance Rs ′ of the altered layer under the electrode using the equation (1).

In implementing this invention, the second electrode length _{d B} of the ohmic electrodes belonging to the second electrical resistance measuring section, the transition length Lt defined in (1) above, _exp (d B / Lt) = It is preferable that the length satisfies the approximation of 1 + d _B / Lt.

  According to the contact resistance evaluation method and the contact resistance evaluation structure of the present invention, the electrical resistance is measured for a plurality of electrode pairs with different electrode intervals L, and the equations (1) to (4) are used for the results. Then, the sheet resistance of the non-altered layer, which is the region between the electrodes of the semiconductor substrate, is obtained, and the electrical resistance is measured for a plurality of electrode pairs having different electrode lengths. Since the resistance is obtained, the contact resistance can be accurately evaluated even when the sheet resistance of the semiconductor substrate is different between the under-electrode deteriorated layer under the electrode and the other non-modified layer. Further, the sheet resistance of the under-electrode deteriorated layer can also be obtained using the equations (6) and (7) with respect to the sheet resistance and contact resistance of the non-modified layer.

  Therefore, the contact resistance can be accurately evaluated even when the region under the electrode of the semiconductor substrate is altered by the heat treatment performed when the ohmic electrode is formed, and the sheet resistance of the altered layer under the electrode is altered. Can also be evaluated accurately.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. However, the shapes, sizes, and arrangement relationships of the constituent elements are merely schematically shown to the extent that the present invention can be understood. In the following, a preferred configuration example of the present invention will be described. However, the composition (material) and numerical conditions of each component are merely preferred examples. Therefore, the present invention is not limited to the embodiments described below.

  A contact resistance evaluation structure used for evaluation of contact resistance according to the present invention will be described with reference to FIGS. FIG. 1 is a schematic plan view for explaining a contact resistance evaluation structure. 2A and 2B are schematic diagrams for explaining the configuration of the electrical resistance measurement unit. FIG. 2A is a plan view seen from the upper surface of the electrical resistance measurement unit, and FIG. 2 (A) shows a cut surface obtained by cutting along an electrode center straight line C described later.

  The contact resistance evaluation structure 10 includes a sheet resistance evaluation region 100 and a contact resistance evaluation region 200 on the first main surface 22 of the semiconductor substrate 20. The sheet resistance evaluation region 100 includes first, second, and third sheet resistance measurement units 110a to 110c as a plurality of electrical resistance measurement units. The contact resistance evaluation region 200 includes first, second, and third contact resistance measurement units 210a to 210c as a plurality of electrical resistance measurement units. In the following description, the first, second, and third sheet resistance measurement units 110a to 110c are collectively referred to as the first electrical resistance measurement unit 110, and the first, second, and third contact resistance measurement units 210a. To 210c may be collectively referred to as the second electrical resistance measurement unit 210.

  Since the configurations of the first electrical resistance measurement unit 110 and the second electrical resistance measurement unit 210 are the same, here, the first electrical resistance measurement unit 110 is referred to with reference to FIGS. 2 (A) and 2 (B). Let's take an example. 2A and 2B, the pair of ohmic electrodes provided in the plurality of first electric resistance measurement units are collectively indicated by reference numerals 122 and 124, respectively.

  The first electrical resistance measurement unit 110 is provided in a mesa structure 130 formed by etching the first main surface 22 of the semiconductor substrate 20 by a known method. Here, the semiconductor substrate 20 is, for example, a GaN substrate.

  The first electrical resistance measurement unit 110 is provided as a common semiconductor substrate, and is separated from the mesa-like structure 130 portion of the semiconductor substrate 20 and the upper surface 131 of the mesa-like structure 130 and has a size and shape. A pair of ohmic electrodes 122 and 124 that are identical to each other, an ohmic electrode pair 120 that is directly below the ohmic electrodes 122 and 124, a sub-electrode alteration layer 132 and 134 that are formed in the surface region of the mesa structure 130, and a pair of It has a non-altered layer 136 in the surface region of the mesa structure 130 between the ohmic electrodes 122 and 124.

  Further, the mesa structure 130 in which the first electric resistance measurement unit 110 is formed electrically insulates the mesa structure 130 from the surrounding semiconductor substrate 20 and is only between the pair of ohmic electrodes 122 and 124. This is to better guarantee that a current flows. The protruding height of the mesa structure 130 may be a height that allows the mesa structure 130 to be electrically insulated from the surrounding semiconductor substrate 20. When a GaN substrate is used as the semiconductor substrate 20, the height of the protrusion is high. Is about 100 nm.

  The ohmic electrodes 122 and 124 are formed by performing high-temperature heat treatment called sintering after forming a metal film in an island shape on the upper surface 131 of the mesa structure 130. The metal film formed as the ohmic electrode is preferably a laminated film of a Ti film and an Al film. In this case, for example, a Ti film is formed on the surface 131 of the mesa structure 130 with a thickness of about 50 nm, and an Al film is formed on the Ti film with a thickness of about 200 nm. The sintering is performed for about 1 minute under a nitrogen atmosphere at about 550 ° C.

  Simultaneously with the formation of the ohmic electrodes 122 and 124, under-electrode alteration layers 132 and 134 are formed in the surface region of the mesa-like structure 130 immediately below the ohmic electrodes 122 and 124, and the materials and mesa constituting the ohmic electrodes 122 and 124 are formed. It is formed as a solid solution with the material of the semiconductor substrate 20 constituting the shaped structure 130.

  The shape (planar shape) in the plane parallel to the upper surface 131 of the mesa structure 130 of the ohmic electrodes 122 and 124 is a rectangle, and the size and the shape are the same. The rectangle means a right-angled quadrilateral and includes a rectangle and a square.

  The ohmic electrodes 122 and 124 are juxtaposed in parallel with each other. The electrode centers 142a and 144a of the ohmic electrodes 122 and 124 are defined as intersections of two rectangular diagonal lines (shown by imaginary lines). A straight line virtually drawn between the electrode centers 142a and 144a of the two ohmic electrodes 122 and 124 is defined as an electrode center straight line C.

  The ohmic electrodes 122 and 124 are arranged in parallel with the electrode center straight line C as lengthwise sides 142b and 144b and perpendicular to the electrode center straight line C as widthwise sides 142c and 144c. That is, the sides 142c and 144c are parallel to each other. Here, the length of the sides 142b and 144b, that is, the electrode length is d, and the length of the sides 142c and 144c, that is, the electrode width is W.

  Further, between the ohmic electrodes 122 and 124, the length of the non-altered layer 136 in the direction along the electrode center straight line C, that is, the interval between the ohmic electrodes 122 and 124 (hereinafter also referred to as electrode interval) L. And

  Here, the electrode width W is set to a value equal to the width in the direction perpendicular to the electrode center straight line C of the mesa structure 130. That is, the lengthwise sides 142b and 144b of the ohmic electrodes 122 and 124 coincide with the edges of the mesa structure 130 in the direction parallel to the electrode center straight line C. This is for better ensuring that all of the current flowing between the ohmic electrodes 122 and 124 flows only between the pair of ohmic electrodes 122 and 124.

In the sheet resistance evaluation region 100, as described above, the plurality of first electrical resistance measurement units 110, that is, the first, second, and third sheet resistance measurement units 110a, 110b, and 110c are respectively the first and second. 2 and a third ohmic electrode pair 120a, 120b and 120c. Here, the first, second, and third ohmic electrode pairs 120a, 120b, and 120c are collectively referred to as the ohmic electrode pair 120. The first electrode length d _A and the electrode width W, which are the electrode lengths of the ohmic electrodes 122a to 122c and 124a to 124c belonging to the different first, second and third electric resistance measuring units 110a, 110b and 110c, are the same, , second and third electric resistance measuring unit 110a, for each 110b and 110c, the first distance _{L a} is the electrode spacing is provided as a different intervals L1, L2 and L3.

  When a GaN substrate is used as the semiconductor substrate 20, the first electrical resistance measurement unit 110 (first, second and third sheet resistance measurement units 110a, 110b and 110c) and the second electrical resistance measurement unit 210 (first Instead of forming the second and third contact resistance measurement units 210a, 210b, and 210c) in the mesa-like structure 130, the periphery of each of the first electrical resistance measurement unit 110 and the second electrical resistance measurement unit 210 is increased. An insulating film may be formed by performing ion implantation at a concentration so that no current flows in a region other than the electric resistance measurement units 110 and 210.

Here, the electrode length d of the ohmic electrode in the sheet resistance evaluation region 100 may be long enough to use a conventionally known TLM (Transmission Line Model) method. In that case, the sheet resistance of the semiconductor substrate itself, that is, the sheet resistance of the non-altered layer (hereinafter also referred to as the first sheet resistance) is Rs (Ω / □), and the sheet resistance of the altered layer under the electrode (hereinafter, the first resistance) 2 is sometimes referred to as sheet resistance), and Rs ′ (Ω / □) and the contact resistance between the ohmic electrode and the semiconductor substrate as ρc (Ωcm ² ), the transition defined by the following equation (1) It is preferable to set the length to Lt so that d / Lt ′ = ∞.

Lt = (ρc / Rs ′) ^1/2 (1)

  The exact value of the transition length Lt is not determined before the contact resistance ρc and the second sheet resistance Rs ′ are measured. Therefore, as disclosed in Non-Patent Document 1, here, provisional transition is obtained by the expression (1a) obtained by assuming that the second sheet resistance Rs ′ and the first sheet resistance Rs are equal to the expression (1). A length Lt ′ is defined.

Lt ′ = (ρc / Rs) ^1/2 (1a)

For example, when a GaN substrate is used as the semiconductor substrate, it is known by measurement that the temporary transition length Lt ′ is about 0.5 to 1 μm. Therefore, the first electrode length d _A is the temporary transition length Lt ′. It is preferable that the value is 10 μm or more as a value of 10 times or more.

Using the contact resistance evaluation structure 10 described with reference to FIG. 1, a first electrical resistance measurement unit 110 (first, second, and third sheet resistance measurement units 110 a, provided in the sheet resistance evaluation region 100, For 110b and 110c), the first electrical resistance _RA between the electrodes is measured.

With reference to FIG. 3, the measurement result about the sheet | seat resistance evaluation area | region 100 is demonstrated. Figure 3 is a graph showing the measurement results of the sheet resistance evaluation region 100 indicates the horizontal axis of the first distance L _A, and, a first electrical resistor R _A as the vertical axis. For the first, second, and third sheet resistance measurement units 110a, 110b, and 110c in the sheet resistance evaluation region 100, the measurement results of the electrical resistance, the first interval L _A (L1, L2, and L3) as the horizontal axis, and , The first electric resistance R _A (R1, R2 and R3) is plotted on the orthogonal coordinate plane with the vertical axis.

When the first electric resistance _RA obtained with respect to the electrode interval L is evaluated by the conventionally known TLM method disclosed in Non-Patent Document 1, the electrodes in the sheet resistance evaluation region 100 shown in FIG. The measurement result of the first electric resistance _RA with respect to the distance L can be approximated by a linear line represented by the following formula (2).

R _A = 2 × Rs ′ × Lt / W + Rs × L _A / W (2)

  In view of this, a linear straight line (hereinafter also referred to as an approximate straight line) is approximately obtained from the measured values plotted on the coordinate plane by any suitable method such as the least square method, and the obtained approximate straight line (FIG. 3 (indicated by reference numeral I in FIG. 3) and the intercept -B between the horizontal axis (L axis) and the following equations (3) and (4) are derived.

A = Rs / W (3)
B = 2 × Rs ′ × Lt / Rs (4)

  When the slope A and the electrode width W of the approximate line are substituted into the equation (3), the first sheet resistance Rs (= A × W) of the non-altered layer, which is a region between the electrodes of the semiconductor substrate, is obtained.

On the other hand, in the contact resistance evaluation region 200, the plurality of second electrical resistance measurement units 210, that is, the first, second, and third contact resistance measurement units 210a, 210b, and 210c are respectively the first, second, and third ohmics. Electrode pairs 220a, 220b, and 220c (collectively referred to as ohmic electrode pairs 220) are provided. Ohmic electrodes 222a to 222c (hereinafter referred to generically as 222) and 224a to 224c (hereinafter referred to as ohmic electrodes) belonging to different first, second and third contact resistance measuring units 210a, 210b and 210c. collectively indicated by reference numeral 224.) Although equal second distance _{L B} is an electrode width W and the electrode spacing of the first, second and third contact resistance measuring unit 210a, for each 210b and 210c, the electrode length is the second electrode length _{d B} are provided as different lengths d1, d2 and d3.

Next, for the plurality of second electrical resistance measurement units 210 (first, second, and third contact resistance measurement units 210a, 210b, and 210c) included in the contact resistance evaluation region 200, the second electrical resistance R _B between the electrodes, respectively. (R4, R5 and R6) are measured. Figure 4 is a graph showing the measurement results of the contact resistance evaluation region 200 indicates the horizontal axis a second electrode length d _B, and the second electrical resistance R _B as the vertical axis. The measurement result of the electric resistance R in the contact resistance evaluation region 200 is expressed by using the second electrode length d _B (d1, d2, and d3) as the horizontal axis and the second electric resistance R _B (R4, R5, and R6) as the vertical axis. Plot on the Cartesian coordinate plane.

With reference to FIG. 1, FIG. 2 (A), FIG. 2 (B) and FIG. 5, the second sheet resistance Rs ′ (Ω / □) which is the sheet resistance in the under-electrode deteriorated layers 232 and 234 of the semiconductor substrate 20 A method for obtaining the contact resistance ρc (Ωcm ² ) of the ohmic electrodes 222 and 224 to the semiconductor substrate 20 will be described. FIG. 5 is a schematic diagram for explaining the distributed constant circuit model, and illustrates the second electrical resistance measurement unit 210 in the contact resistance evaluation region 200 as an example. In FIG. 5, the x-axis is taken in the direction parallel to the electrode center straight line C (see FIG. 2A), that is, the length direction of the ohmic electrode, and the x-coordinates at both ends in the length direction of the ohmic electrode 222 are respectively shown. 0 and d. In addition, the x coordinate of the part which hits the boundary of the non-altered layer 236 and the under-electrode degraded layer 232 in both ends of the ohmic electrode 222 is set to 0.

A second electrode length d _B of the ohmic electrode 222, and, if the electrode width is W, per minute length [Delta] x, the contact resistance (hereinafter, also referred to as minute contact resistance.) Ra and electrodes under The sheet resistance (hereinafter also referred to as “micro sheet resistance”) Rb in the altered layer 232 is Ra = ρc / (W × Δx) and Rb = Rs ′ × Δx / W, respectively. In the distributed constant circuit model shown in FIG. 5, the minute sheet resistance Rb and the minute contact resistance Ra are evenly distributed in the x-axis direction, the minute sheet resistance Rb is connected to each other in series, and the minute contact resistance Ra is an ohmic electrode. This model is connected in parallel between 222 and the minute sheet resistance Rb.

  Using Kirchhoff's law, the voltage drop between the point x on the x-axis and the point x + Δx on the x-axis separated by a minute length Δx and the magnitude of the change in current can be expressed as (5a ) And (5b) are obtained.

V (x + Δx) −V (x) = − Rb × I (x)
= − (Rs ′ × Δx / W) × I (x) (5a)
I (x + Δx) −I (x) = − V (x) / Ra
= − (W × Δx / ρc) × V (x) (5b)

  Considering the limit where Δx is 0 for each of these equations (5a) and (5b), the following equations (5c) and (5d), which are differential equations, are obtained.

dV / dx = −Rs / W × I (x) (5c)
dI / dx = −W / ρc × V (x) (5d)

  The equations (5c) and (5d) obtained here are further differentiated by x, and when the equations (5c) and (5d) are substituted into the equations obtained as a result of the differentiation, the following equations (5e) and ( 5f) Equation is obtained.

d ² V / dx ² = −Rs ′ / W × dI (x) / dx
= (Rs ′ / ρc) × V (x) (5e)
d ² I / dx ² = −W / ρc × dV (x) / dx
= (Rs ′ / ρc) × I (x) (5f)

  Here, when the transition length Lt defined by the above equation (1) is used, the equation (5h) is obtained as a general solution of the equation (5f) which is a differential equation.

       I (x) = a * exp (x / Lt) + b * exp (-x / Lt) (5h)

  Here, a and b are constants.

If the current flowing from the region between the electrodes of the semiconductor substrate into the region below the electrode is I ₀ , I (0) = I ₀ . Further, in the region of x> d _B , no current flows because the sub-electrode alteration layer 232 and the electrode 222 are not present, and therefore I (d _B ) = 0. Substituting I (0) = I ₀ and I (d _B ) = 0 into the equation (5h), the following equations (5i) and (5j) are obtained.

a + b = I ₀ (5i)
0 = a × exp (d _B / Lt) + b × exp (−d _B / Lt) (5j)

  When the constants a and b are obtained from the equations (5i) and (5j) and substituted into the equation (5h), the following equation (5k) is obtained.

I (x) = I ₀ / {exp (d _B / Lt) −exp (−d _B / Lt)}
_{× [exp {(d B -x} ) / Lt} -exp {- (d B -x) / Lt}]
= I ₀ × sinh {(d _B −x) / Lt} / {sinh (d _B / Lt)}
(5k)

  Further, when the formula (5k) is substituted into the formula (5d), the following formula (5m) is obtained.

V (x) = − (ρc / W) × dI (x) / dx
= (Ρc × I ₀ ) / (W × Lt) × cosh {(d _B −x) / Lt}
/ Sinh (d _B / Lt)} (5 m)

Here, when exp (d _B / Lt) is expanded in series, the following equation (8a) is obtained.

exp (d _B / Lt)
_{= 1 + (d B / Lt} ) + (d B / Lt) 2/2! ^{_{+ (D B / Lt) 3}} /3!
+ ... + (d _B / Lt) ^k / k! + ... (8a)

  For an integer k of 1 or more, k! Is represented by the following equation (8b).

       k! = K * (k-1) * ... * 2 * 1 (8b)

Here, for _example, in the case of d B / Lt = 1/3 , the difference between the true value, and _{1 +} d B / Lt is an approximation of exp _(d B / Lt) of exp _(d B / Lt) is is about _5%, in the case of d B / Lt = 1/10 , and exp true value of _{(d B / Lt) ((} 8c) left side of equation) in approximation of exp _(d B / Lt) The difference from a certain 1 + d _B / Lt (the right side of the equation (8c)) is 1% or less. Accordingly, when d _B << Lt, that is, the second-order or higher term of (d _B / Lt) can be ignored according to the required measurement accuracy, the following approximation of equation (8c) holds. .

exp (d _B / Lt) = 1 + d _B / Lt (8c)

  When the approximation shown in the equation (8c) is performed on the equation (5m), the following equation (5n) can be obtained.

V (0)
= (Ρc × I ₀ ) / (W × Lt) × {(1 + d _B / Lt) + (1−d _B / Lt)}
/ {(1 + d _B / Lt)-(1-d _B / Lt)}
= (Ρc × I ₀ ) / (W × d _B ) (5n)

Here, the size per unit length of the first sheet resistance Rs (Ω / □) in the non-altered layer 236 that is a region between the electrodes of the semiconductor substrate is Rs / W. Therefore, if the voltage drop at x = 0 is V ₀ , the potential difference ΔV between the electrodes is the voltage drop due to the voltage drop (2 × V ₀ ) at the ohmic electrodes 222a and 224a and the first sheet resistance between the electrodes. It is represented by the following equation (5r) as the sum of minutes (I ₀ × Rs × L _B / W).

_{ΔV = 2 × V 0 + I} 0 × Rs × L B / W (5r)

  In this case, the potential difference ΔV between the electrodes can be expressed by the following equation (5s) obtained from the equations (5n) and (5r).

ΔV = I ₀ × {2 × ρc / (W × d) + Rs × L _B / W} (5 s)

Accordingly, the second electrode length d _B is the transition length Lt, if the approximation of the above mentioned (8c) expression is a length holds, second electrical resistance R _B and a second electrode contact resistance evaluation region 200 the length _{d B} satisfy the following equation (5).

R _B = ρc / (W × d _B ) + Rs × L _B / W (5)

  From the measurement result of the contact resistance measurement region 200, the contact resistance ρc is evaluated using the above-described equation (5). Here, since the sheet resistance evaluation region 100 and the contact resistance evaluation region 200 are provided on the same semiconductor substrate 20, the first sheet resistance Rs obtained using the TLM method described with reference to FIG. One sheet resistance Rs can be used.

The second electrical resistance measurements of _{R B} of the sheet resistance evaluation region 100, the first sheet resistance Rs, the second electrode length _{d B,} electrode width W, the second distance _{L B,} and the second measured substituting electrical resistance R _B in (5), the contact resistance ρc is determined.

Here, a second electrode length d _B and the second electrical resistance R _B is, to satisfy the relationship of the above equation (5), second electrode length d _B is the transition length Lt, above The length must be such that the approximation of equation (8c) holds. However, since the second electrode length d _B (d1, d2, and d3) of the ohmic electrode formed in the contact resistance evaluation region 200 is not known with an accurate value of the transition length Lt before measurement, The approximation of equation (8c) does not hold for the electrodes. Therefore, here, the second electrode length d _B has a relationship of _{B B} << Lt ′ with respect to the temporary transition length Lt ′ obtained when Rs ′ = Rs in the expression (1). measured by the resistance measuring unit 210, a measurement result of the second electrical resistance R _B is used. When the normal TLM method is used, the size has a relationship of d >> Lt ′. In this case, the measured electric resistance R ((2) In the equation, the value of the first electric resistance R _A ) does not depend on the electrode length d (in the equation (2), the first electrode length d _A ). Therefore, as shown in FIG. 4, a graph plotting the measurement results of the electrical resistance R in the contact resistance evaluation region 200, the measured value of the electric resistance R of the area changes depending on the second electrode length d _B The measurement result (in FIG. 4, for example, the measurement result when the electrode length is d3) may be regarded as the measurement result of the region having the relationship of d _B << Lt ′ and substituted into the above-described equation (5).

In addition, when a plurality of measurement results of the second electric resistance R _B with respect to the second electrode length d _B having the relationship of d _B << Lt are obtained, any suitable method such as a least square method is obtained from these measurement results. A curve corresponding to the following equation (5t) (indicated by reference numeral II in FIG. 4) can be approximately obtained using a simple method.

R _B = C / d _B + D (5t)
Here, C and D are constants.

  Approximately obtained curve (hereinafter also referred to as approximate curve) represented by the equation (5t) and the following equation (5u) obtained from the equation (5) The contact resistance ρc may be obtained by substituting.

       C = ρc / W (5u)

  The following equation (7) is further derived from the following equation (6) derived from the equations (3) and (4) and the above equation (1).

Lt = A × B × W / (2 × Rs ′) (6)
Rs ′ = A ² × B ² × W ² / (4 × ρc) (7)

  In Equation (7), the contact resistance ρc, the electrode width W, and the slope A of the linear straight line obtained approximately from the measurement result in the sheet resistance evaluation region and the intercept −B with the horizontal axis are obtained in the above-described process. By substituting, the second sheet resistance Rs ′ is obtained.

  Furthermore, the transition length Lt can be obtained using the equation (1) from the contact resistance ρc and the second sheet resistance Rs ′ obtained in the above-described process.

Here, instead of the transition length Lt that is not determined before the measurement according to the present invention is performed, the approximation of the equation (8c) is established based on the provisional transition length Lt ′ defined by the above equation (1a). has been described as an example when assigning the second select the electrical resistance measuring section 210 (5) having a second electrode length d _B, it is not limited to this example.

  For example, in the above equation (4) obtained when obtaining the sheet resistance Rs of the unaltered layer, the value of Lt (= B / 2) obtained by assuming that Rs ′ = Rs is used as the temporary transition length Lt ″. This value may be used as a reference.

In addition, after obtaining the contact resistance ρc and the second sheet resistance Rs ′ using the equations (5) and (7) by the above-described process, the obtained transition length Lt can be used as a reference. In this case, the second electrical resistance measurement unit 210 having the electrode length d that satisfies the approximation of the equation (8c) is selected with respect to the transition length Lt as the measurement result, and the above-described contact resistance ρc is evaluated again. What is necessary is just to perform the process. As a result, the transition length Lt and even when the difference between the temporary transition length Lt' or Lt'' is large, the second electrical resistance measuring section 210 having a second electrode length d _B which holds the approximation (8c) formula Therefore, the more accurate contact resistance ρc, the second sheet resistance Rs ′ that is the sheet resistance of the altered layer under the electrode, and the transition length Lt can be obtained.

In FIG. 1, the sheet resistance evaluation region 100 and the contact resistance evaluation region 200 have been described as an example of a configuration including three first and second electrical resistance measurement units 110 and 210, but the number is limited to three. It is not something. The sheet resistance evaluation region 100 may be Sonaere the first electrical resistance measuring unit 110 of the necessary number to obtain a first distance L _A first electrical resistor R _A and satisfies (2). Therefore, two or more first electrical resistance measurement units 110 may be provided in the sheet resistance evaluation region 100.

The contact resistance evaluation region 200 may be Sonaere the second electrical resistance measuring unit 210 of the necessary number to obtain a second electrode length d _B and the second electrical resistance R _B satisfy (5). For example, the electrode width W and the second distance L _B is obtained by any suitable measurement from the shape of the second electrical resistance measuring unit 210, moreover, the first sheet resistance Rs is, since obtained by TLM method, (8c) One or more second electrical resistance measurement units 210 having ohmic electrodes that can be approximated by the equation need only be provided.

However, in order to approximate the (8c) formula with respect to the second electrode length d _B to determine whether satisfied is preferable to use two or more second electrical resistance measuring section 210, also, In order to improve the measurement accuracy, it is preferable to provide two or more second electric resistance measurement units 210 that can approximate the equation (8c).

  According to the contact resistance evaluation method and the contact resistance evaluation structure of the present invention, the electrical resistance R is measured for a plurality of electrode pairs having different electrode intervals L, and the formulas (1) to (4) are expressed for the results. The sheet resistance Rs of the non-altered layer that is the region between the electrodes of the semiconductor substrate is obtained, and the electrical resistance R is measured for a plurality of electrode pairs having different electrode lengths d. Therefore, even when the sheet resistance of the semiconductor substrate differs between the under-electrode altered layer and the other non-altered layers, the contact resistance can be accurately evaluated. Further, the sheet resistance of the under-electrode deteriorated layer can also be obtained using the equations (6) and (7) with respect to the sheet resistance and contact resistance of the non-modified layer.

  Therefore, the contact resistance can be accurately evaluated even when the region under the electrode of the semiconductor substrate is altered by the heat treatment performed when the ohmic electrode is formed, and the sheet resistance of the altered layer under the electrode is altered. Can also be evaluated accurately.

It is a schematic plan view for demonstrating the structure for contact resistance evaluation. It is the schematic for demonstrating an electrical resistance measurement part. It is a graph for demonstrating the measurement result in a sheet resistance evaluation area. It is a graph for demonstrating the measurement result in a contact resistance evaluation area | region. It is a schematic diagram for demonstrating a distributed constant circuit model.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Contact resistance evaluation structure 20 Semiconductor substrate 22 1st main surface 100 Sheet resistance evaluation area 110 1st electrical resistance measurement part 110a, 110b, 110c Sheet resistance measurement part 120, 120a, 120b, 120c Ohmic electrode pair 122, 122a , 122b, 122c Ohmic electrode 124, 124a, 124b, 124c Ohmic electrode 130 Mesa structure 131 Upper surface 132, 134, 232, 234 Under-electrode altered layer 136, 236 Non-altered layer 142a, 144a Electrode center 142b, 144b Length direction Side 142c, 144c width direction side 200 contact resistance evaluation region 210 second electric resistance measurement unit 210a, 210b, 210c contact resistance measurement unit 220, 220a, 220b, 220c ohmic electrode pair 222, 222a, 222b, 222c Ohmic electrodes 224, 224a, 224b, 224c Ohmic electrodes

Claims (3)

A sheet resistance evaluation region and a contact resistance evaluation region each having a plurality of electrical resistance measurement units are provided,
The electrical resistance measurement unit includes a common semiconductor substrate, a pair of ohmic electrodes that are spaced apart on the semiconductor substrate and have the same size and shape, and the semiconductor substrate directly below the ohmic electrode. It has an under-electrode altered layer formed in the surface region, and a non-altered layer in the surface region of the semiconductor substrate between the pair of ohmic electrodes,
Two ohmic electrodes belonging to the same electrical resistance measuring unit have a rectangular planar shape, the same size and shape, and the sides in the width direction of a pair of opposing ohmic electrodes are parallel to each other. And the lengthwise sides of the ohmic electrode are parallel to a straight line connecting the electrode centers,
Among the plurality of electrical resistance measurement units, each of the electrical resistance measurement units provided in the sheet resistance evaluation region is defined as a first electrical resistance measurement unit, and the ohmic electrodes belonging to each of the first electrical resistance measurement units the first electrode length d _a and the electrode width W is equal to each other and a first distance L _a pair of ohmic electrodes are different from each other,
Among the plurality of electrical resistance measurement units, each of the electrical resistance measurement units provided in the contact resistance evaluation region is a second electrical resistance measurement unit, and the pair of ohmics belonging to each of the second electrical resistance measurement units the second distance L _B, and the electrode width W is equal to each other of the electrodes, and, using a second electrode length d _B each other Mixed contact resistance evaluation structure, the pair of which are formed on the semiconductor substrate In evaluating the contact resistance between the ohmic electrode and the semiconductor substrate from the measured electrical resistance between the ohmic electrodes,
For each of the plurality of first electrical resistance measurement units, a process of measuring a first electrical resistance _RA between the pair of ohmic electrodes;
The horizontal axis of the first distance L _A, and, approximately obtained when the measured first electrical resistor R _A has a longitudinal axis, the intercept of the slope A and the horizontal axis is a -B 1 From the next straight line, the first distance L _A , the first electric resistance R _A , the sheet resistance Rs of the non-altered layer, the sheet resistance Rs ′ of the altered layer under the electrode, the electrode width W, and the following (1 ) The following formulas (3) and (4) are derived using the following formula (2) that is satisfied by the transition length Lt defined by the formula, and the sheet resistance Rs of the non-altered layer is calculated from the formula (3). The process of seeking
Lt = (ρc / Rs ′) ^1/2 (1)
R _A = 2 × Rs ′ × Lt / W + Rs × L _A / W (2)
A = Rs / W (3)
B = 2 × Rs ′ × Lt / Rs (4)
For each of a plurality of the second electrical resistance measuring section, and a process of measuring a second electric resistance R _B between the pair of ohmic electrodes,
The second electrode length _{d B} is the (1) _d B << having a relationship Lt', second electrical resistance measuring unit relative to the temporary transition length Lt' obtained when the Rs' = Rs in formula From the second electrical resistance R _B measured in Step 2, the second electrode length d _B , the second electrical resistance R _B , the contact resistance ρc, the sheet resistance Rs of the non-altered layer, the second spacing L _B and A process of obtaining the contact resistance ρc using the following formula (5) that the electrode width W satisfies:
R _B = 2 × ρc / (W × d) + Rs × L _B / W (5)
Using the following equation (6) derived from the equations (3) and (4) and the following equation (7) derived from the equation (1), the slope A, the intercept −B, and Obtaining the sheet resistance Rs ′ of the altered layer under the electrode from the electrode width W;
Lt = A × B × W / (2 × Rs ′) (6)
Rs ′ = A ² × B ² × W ² / (4 × ρc) (7)
A method for evaluating contact resistance, comprising: obtaining a transition length Lt from the contact resistance ρc and the sheet resistance Rs ′ of the altered layer under the electrode using the equation (1). A contact resistance evaluation structure used for evaluating contact resistance between the ohmic electrode and the semiconductor substrate from an electrical resistance between a pair of ohmic electrodes formed on the semiconductor substrate,
A sheet resistance evaluation region and a contact resistance evaluation region each having a plurality of electrical resistance measurement units are provided,
The electrical resistance measurement unit includes a common semiconductor substrate, a pair of ohmic electrodes that are spaced apart on the semiconductor substrate and have the same size and shape, and the semiconductor substrate directly below the ohmic electrode. It has an under-electrode altered layer formed in the surface region, and a non-altered layer in the surface region of the semiconductor substrate between the pair of ohmic electrodes,
Two ohmic electrodes belonging to the same electrical resistance measuring unit have a rectangular planar shape, the same size and shape, and the sides in the width direction of a pair of opposing ohmic electrodes are parallel to each other. And the lengthwise sides of the ohmic electrode are parallel to a straight line connecting the electrode centers,
Among the plurality of electrical resistance measurement units, each of the electrical resistance measurement units provided in the sheet resistance evaluation region is set as a first electrical resistance measurement unit, and the first ohmic electrode belonging to the first electrical resistance measurement unit is used. electrode length d _a and the electrode width W is equal to each other and a first distance L _a pair of ohmic electrodes are different from each other,
Of the plurality of electrical resistance measurement units, each of the electrical resistance measurement units provided in the contact resistance evaluation region is a second electrical resistance measurement unit, and the pair of ohmic electrodes belonging to the second electrical resistance measurement unit the second distance L _B, and the electrode width W is equal to each other, the contact resistance evaluation structure, wherein a second electrode length d _B are different from each other. The second electrode length d _B belonging to the second electric resistance measurement unit is approximated by exp (d _B / Lt) = 1 + d _B / Lt with respect to the transition length Lt defined by the following equation (1). The structure for contact resistance evaluation according to claim 2, wherein the structure is a length.
Lt = (ρc / Rs ′) ^1/2 (1)