- Email: [email protected]
An investigation into the termination resistance of thin film resistors
Mlcroelectron. Reliab., Vol. 27, No. 3, pp. 423-428, 1987. Printed in Great Britain.
0026-2714/8753.00 + .00 © 1987 Pergamon Journals Ltd.
AN INVESTIGATION INTO THE TERMINATION RESISTANCE OF THIN FILM RESISTORS A. G. VA~ NIE Philips Research Laboratories, 5600 JA Eindhoven, The Netherlands (Receivedfor publication 1 September 1986) Abstraet--A mathematical analysis of the termination resistance of thin-filmresistors is given and a method of measuring this type of resistance is discussed. As examples, the termination resistances of sputtered and evaporated thin-film resistors have been measured. Relevant parameters of the termination to be specified are discussed. l. I N T R O D U C T I O N
The termination resistance of a thin-film resistor is the result of the interfacial resistance which occurs between the materials of the resistor and the interconnection, respectively. In general, the T C R (temperature coefficient of the resistance) of the termination resistance differs from the T C R of the "bulk" material of the thin-film resistor. Consequently, the T C R of a thin-film resistor depends on its length. The termination resistance has already been widely investigated. Fisher et al, have given a relation between the termination resistance, the specific throughconductance of the interfacial layer and the sheet resistivities of the resistor and conductor [1]. However, the derivation of that relation was not given. We have found another relationship, which is equivalent to Fisher's equation for the case that the sheet resistance of the conductor is zero. Fisher et al. probably ignored the forward current in the conductor at the termination. Although Galla et al. took this forward current into account, their calculations are rather complicated and sometimes not very clear [2]. In our calculations, we have used transmission line theory in which "distributed" network elements occur. This theory enables us to derive the relevant relations in a straightforward manner. We have also derived rules of thumb for cases where the conductor resistivity is negligibly small. We determined relevant parameters of the termination resistance by using a special test circuit. Mostly, the termination resistance is small compared to the total resistance of the resistor, so that accurate measuring methods must be used. The test circuits have to be made by reliable processing methods, because the physical dimensions must also be determined with high precision. We investigated the termination resistance of thinfilm resistors with evaporated NiCr or sputtered NiCrbased layers which have sheet resistivities of about 200QI-q -1. AI20 3 substrates and Au conductors were used.
consists of the sandwich: resistive layer/interracial layer/conductor layer. The current flow is sketched in Fig. lb. The current flows gradually from the conductor through the interface into the resistor. The network of the "distributed" elements shown in Fig. lc will be used for a first order calculation of the current flow. As already remarked, the termination resistance is in our cases relatively small, so that this first approximation of the current flow gives a sufficient accuracy for calculation of the termination parameters. Figure 2a shows the termination in greater detail. In fact, the resistor layer extends beneath the entire conductor, however, we assume in our calculation that there only exists a resistance overlap of length d. Doing so, the minimum allowable overlap can be calculated and the minimum length of the connecting pad can be so obtained. The termination width is w. Figure 2b shows a section with length dx of the distributed network, where Rr = Rs,/w (Q m - 1),
(la)
~'~ onductor inet:irftac~e
VW/W a
Fig. la. A sketch of a cross-section of the thin-film resistor and its terminations.
Fig. lb. The current flow at the terminations. ]i
Ii .
= 2. M A T H E M A T I C A L
ANALYSIS
A sketch of the cross-section of the thin-film resistor termination is shown in Fig. la. The termination
C
|i
Fig. lc. Modelling of the termination by 'distributed' network elements. 423
424
A.G. VAN Nm
P -I
Q
ooo
~
The integration constants A and B can be found from the boundary conditions. The terms with A are related to a current flowing in the positive x direction and the terms with B to a current flowing in the opposite direction. At x = 0, the current I = Ii. F r o m equation (5) it can then be shown that
' 'o ' o " "
in'terfaeial
o
x
Rr + Rc I~ = (A - B ) - R,
d
Fig. 2a. The termination in greater detail.
_,
dV c [i
At x = d, the current I = 0, so that from equations (5) and (8) it follows that Rr e - ~d+ Rc B = A R , e+~a+R c.
+
.
i, .
A+B Ri = R° (A - B)(1 + Re~R,)"
Fig. 2b. A part of the termination with 'distributed' network elements. Rc = R~dw ( Q m - 1),
(lb)
Y = Y~.w (I)-x m - l ) ,
(lc)
in which R,,(f~) is the sheet resistance of the resistor material, R~ (f~) is the sheet resistance of the conductor material, y~(f~-1 m-2) is the specific through-conductance of the interfacial material. The current I~ enters the termination at x = 0 and the same current leaves the termination at x = d. At any point x the sum of the currents flowing in the x direction must be equal to I~. We will assume that the current in the conductor is a combination of the current I~ and the transfer current I, as shown in Fig. 2b. The transfer current I is calculated by means of transmission line. Application of Kirchoff's law yields the following simultaneous equations dV = - I . ( R , + R~)+ I,. R~, dx
(2)
dI -dx
(3)
-
=
(9)
The constant B--, 0, if the overlap d is taken infinitely long (yd---, oo). The ratio B/A is analogous to the reflection coefficient in transmission lines. In infinitely long lines the reflection coefficient is zero. The input resistance Ri at x = 0 can be obtained from equations (4), (5) and (8),
b
-
(8)
- V.Y.
After integrating equations (2) and (3) we arrive at V = Ro(Ae-~*+Be+~),
Re
(10)
In the case that 7d >> 1, where B--,0, we arrive at the limit Rr Ri---~ / y ( R , + R c ) .
(11)
Apart from the voltage drop due to R i, a drop occurs between the points P and Q (see Fig. 2a). F r o m Fig. 2b it can be seen that d V~ = (I - li)Rc. dx
(12)
At x = 0, the voltage V~(0)= 0, so that integrating equation (12) yields V ~ ( x ) = _ _Rc _ l[A e - ~ + B e
+~,x+I i 1{ - R, -
\n,+&
7x - - -Rl li .' ~
Roll (13)
At x = d we get, if yd >> 1 and R, >> R~, V~(d)---, - - I , . Re. d.
(14)
The voltage drop V~(d) can he added to the other voltage drops across the conductor. Usually, the voltage drop over the total conductor is taken from the boundary of the resistor to the end. When this is done, the voltage drop V~(d)is taken into account.
(4)
(5)
3. R U L E S O F T H U M B : R, = 0
y= ~ ) Y ,
(6)
In the cases where the conductor resistivity is negligibly small, the input resistance becomes [see equations (6), (7), (9) and (10)]
Ro
(7)
1 -~-e-2~'d Ri = R° 1 - e -2rd'
I = Ae-~X-Be+rX+IiR
, -t- R~
where
=
q~ R
c
(15)
Thin-film resistors
425
Rs,
(fl- 1 m - 2).
Y, = R2" w 2
Ri/Ro
(20)
The specific termination resistance R,e,~ is defined as
T ,°8
Rte,m =
/Rs, = w" R o = w" Ri
(f~" m). (21)
6 The input resistance Ri can be interpreted as an apparent change ltermin the resistor length
Ri
Rterrn
lie,= = - - w = Rs, R~, 0
(m).
(22)
The condition for the overlap d can be found from equations (19), (20) and (22),
1 Vd
d >> lt~,m Fig. 3. The ratio Ri/R o plotted as a function of Td.
(m).
(23)
Let us take as an example Rs,=200f21"q -1, R~ = 1 f~, w = 1 mm. Then we arrive at Ys = 2 0 0 f l - l m m - 2 ,
in which = ~
Y,
Rte,, = 1 f~" mm,
(16)
1,~,= = 5 rtm, Ro = R/_~.
(17)
In Fig. 3 the ratio R~/R o is plotted as a function of ?d. F o r ?d--+ oo the input resistance R~--+R o. We see that for 7d = 5 the minimum value of R i is already nearly reached. Let us assume that the input resistance Ri, the sheet resistance R~,, the width w and the overlap d of the termination are known. If the overlap zd >> 1 then the resistance go= gi
(~).
(18)
d >> 51am. 4. EXPERIMENTAL We investigated the termination resistances of two kinds of thin-film resistor made by P M A (Phillips & M B L E Associated, Brussels). The (nominal) manufacturing data were: technology resistor material sheet resistance termination
evaporated NiCr 200 f~ [] - 1 NiCr/Ni/Au-Ni-Au
conductor conductor thickness substrate coating
Au-Ni-Au 2 I~m AI203 no
F r o m equations (1) and (16) it can be found that = , , / / ~ , • Y~
(m-l).
(19)
The specific conductance of the interfacial layer can be found from equations (1), (17) and (18),
19 I/ 23 mm ~
resistive area
Fig. 4. The circuit for measuring the parameters of the resistor termination. The measuring current is supplied between pins 1 and 10. The voltages of the several sections have been measured (see Table 1). The nominal length of l~ = 100gm for i = 3..... 11.
sputtered NiCr-base 200 f~ [] - 1 NiCr-base/Ni/Nibase-Au-Ni-Au Au-Ni-Au 2 lain A120 a no
426
A.G. VANNtE
Table 1. The voltages and connecting pins of the several sections (R,c is the sheet resistance of the conductor material, R,, is the sheet resistance of the resistor material and Rt,,,, is the termination resistance) Section
Voltage
The physical lengths of the sections were measured with methods described in Section 5. The termination resistance (Rte,,,) i of the ith section (i = 3, 4 . . . . . 11) was calculated using the equation
Properties to be determined
Pins
(Rterm)i : 0.5 ~/ V- mi " w -(Rsr)i
"li),
(24)
/
1
1,'1
2
v2
3 4 5
V3 V4 V5
6 7 8
V6 V-1 Vs
9
17 18 15 16 3 4 5
R~
Rs,
2 3 4
Rter.,
14 5 13 14 6 13
Rte,,.
Rterra
Rterm Rterm
Rt~,,. Rterm
V9
7
6
10
V10
8
7
Rt,,, .
11
Vx x
9
8
Rt~,~
12
1/12
11
12
Rs,
The parameters of the resistor termination are determined with the test circuit shown in Fig. 4. The measuring current (10 mA) was supplied between pins 1 and 10 and we measured the voltages between the pins noted in Table 1. The measuring current was delivered by Keithley's current source 225, which has a stability of less than 0.05%. In order to prevent interference with the measuring current the voltages must be measured with a high ohmic voltmeter whoe input floats with respect to ground. A Datron 1071 with an accuracy better than 5 P P M was used for these voltage measurements. The voltages were measured at 30"C and 80°C in order to obtain the T C R of the termination resistances.
in which V~ is the voltage drop across the ith section, I,, is the measuring current, (R~r)i is the sheet resistance of the resistor of the ith section, li is the physical length of the ith section, w is the width of the sections. The sheet resistance (Rs,)~ was determined by linear interpolation (Section 5). As the properties of the terminations are probably dependent on the direction of the resistor on the substrate, we test resistors which are "horizontally" and "vertically" situated on the same substrate. The resistors are indicated by H and V, respectively. 5. MEASURING THE PHYSICAL LENGTH OF THE SEVERAL SECTIONS The physical dimensions of the sections were measured with the aid of a Zeiss U M M 5 0 0 apparatus which has a measuring accuracy of about 2 p,m. The edges of sections were detected by means of a microscope and/or a "Talysurf". The measuring accuracy is also dependent on the quality of the conductor edges at the sections. These edges must be steep and without
Fig. 5. A SEM photograph of a conductor edge at the resistor termination. The indicated line segments have a length of 10 txm.
Thin-film resistors Table 3. The sheet resistivities measured at sections 2 and 12
Table 2. The measured lengths of sections of one test circuit (the nominal lengths were 100 ~tm) Microscope (Ftm)
Talysurf 0tin)
3 4 5 6 7 8 9 10
97.8 98.6 98.0 96.0 98.4 98.6 102.2 96.0 96.0
100.2 99.6 97.2 97.0 97.6 98.2 101.0 98.2 101.4
Mean value Standard deviation
97.96
98.69
4.5
1.9
Section
427
Number
Section 2 (f~ [] - 1)
Section 12 (f2 [] - 2)
Difference (%)
SH1 SH3 SV4 SV5 EH2 EH4 EV3 EV6
201.1 206.8 200.0 203.2 179.5 173.7 182.6 197.8
201.2 207.4 201.5 205.4 178.5 175.3 177.9 181.0
+0.05 + 0.03 +0.75 + 1.08 -0.56 + 0.92 -2.61 + 1.78
S H
The lengths were measured with a Zeiss UMM 500 apparatus and the edges of the sections were detected using a microscope or a Talysurf. ripples and the conductor thickness must be homogeneous. A SEM photograph of an edge is shown in Fig. 5; the conductor thickness is about 2 lam. The lengths of the sections 3-12 of a test circuit were determined with the use of a microscope and a "Talysurf" (see Table 2). The sets of measuring results do not show Gaussian distributions and therefore we applied a "robust" statistical method for calculating the mean values and standard deviations. In this method, discussed by Rey [3], the function "fair" was used with the constants K 1 = 5.68107 and K 2 = 2.30976, so that the efficiency is about 80%. The mean values differ by 0.73 p.m, which is much smaller than the standard deviations. The "Talysurf" method showed the lowest scatter. The nominal value of the termination region length is 100 p.m. The deviations between the measured and nominal values are smaller than 1 p.m at each edge. These discrepancies are probably caused by the "mushroom" form of the edge (see Fig. 5). We therefore take the nominal length of the termination region in the calculations. 6. MEASURING RESULTS AND EVALUATION
The sheet resistances Rs, 2 and R~,12 of Sections 2 and 12, respectively, were determined and the results
sputtered, horizontal,
E evaporated, V vertical.
are listed in Table 3. The differences in resistance of these sections a m o u n t to only a few per cent for all the test circuits. Sputtered samples show a somewhat lower spread than the evaporated ones. The sheet resistances of sections 3 - I 1 were found by using linear interpolation with respect to the position of the section between Sections 2 and 12. The termination resistances were calculated with equation (24). Table 4 gives the mean values and standard deviations of the measurement results for several test samples. These estimators were calculated with the robust statistical method mentioned before. The apparent length changes ((Ite,,,,)i), also given in Table 4, were derived from the ((Rte,,,)i) using equation (22). The apparent length change l,~,m is important for the design rules concerning m i n i m u m length of the connecting pad and the length of the resistors. In our cases the requirement of equation (23) is satisfied, because the connecting tracks have widths of /> 400 ~tm. The apparent length change ((l,er,,,)i) can be determined within an accuracy of less than 1 p.m. This accuracy is satisfactory having regard to the geometrical accuracy with which the resistors can be made. The termination resistance is nearly dependent on the position of the resistor on the substrate, but the termination resistance of sputtered resistors is much higher than the termination resistance of evaporated resistors. The measuring accuracy is too poor for determining
Table 4. The termination resistances Rte,,, and termination lengths lie,,. of two kinds of thin-film resistor f2 [] - x Technology
Situation
Number
R,e,,.(f~•ram)
(1,e,,,) (~m)
Sputtered NiCr-base
Horizontal
SH1 SH3 SV4 SV5 EH2 EH4
2.73 _+0.14 2.654-0.15 2.42+0.15 2.394-0.07 1.154-0.12 1.134-0.08 0.90 _+0.07 0.98+0.22
144-0.7 134-0.7 12_+_+0.6 12+0.3 6_+0.6 6_+0.4 5 ___0.4 5_+0.5
Vertical Evaporated NiCr
Horizontal Vertical
E V3 EV6
428
A. G. VANN~E Table 5. The sheet resistances R~ and their TCR's and TCR's of resistors with a length of 100 ~tm for the two technologies Technology Sputtered NiCr-base
Situation
Number
~ [] - ~
PPM/K sheet resistance
PPM/K (Ira,, = 100 lain)
Horizontal
SH 1 SH3 SV4 SV5 EH2 EH2 EV3 EV6
201 207 201 204 179 174 180 179
- 23 - 22 - 22 - 21 + 80 + 54 + 105 + 108
- 20 - 22 - 22 - 19 + 84 + 63 + 111 + 110
Vertical Evaporated NiCr
Horizontal Vertical
Table 6. Relevant parameters of thin-film resistors and their terminations Sheet resistance of the resistor material Sheet resistance of the conductor material Temperature coefficient of the resistor material Temperature coefficient of the conductor material Temperature coefficient of the shortest permitted resistor Termination resistance Specific through conductance Apparent increase in resistor length Length of the connecting pad
the T C R of the t e r m i n a t i o n resistance, however the T C R of the shortest permitted resistor, say 100 Ixm long, can be measured a n d this T C R should be specified. The TCR~ of a resistor with a uniform length 1 can then be f o u n d from
TCRt =
R, c Rs, TCRs, TCR,c TCRI.~. R,er,, Y~e,~, l,e,,, d
f~ [] - x fl [] - 1 PPM/K PPM/K PPM/K ~ . mm f~- 1 m m - 2 lam lain
widely discussed in the literature, b u t the stability, a n d also the reliability, of the t e r m i n a t i o n resistances should be investigated. The described test circuit is p r o b a b l y suitable for such investigations.
[TCRs, .(1 - lmi,) + TCRt.,." (lmi n + 2./,~,,,)]
7. CONCLUSIONS
(1 + 2 . lie,,, )
1. The t e r m i n a t i o n resistance of thin film resistors can be determined within a sufficient accuracy. 2. T h e t e r m i n a t i o n resistance can be interpreted as a n a p p a r e n t change l,e,,, in the resistor length. 3. T h e r e q u i r e m e n t " c o n n e c t i n g p a d length d >> lter,," should be satisfied.
(25) in which lmi.
is the length of the shortest permitted resistor and TCRt,,, is the T C R of the shortest permitted resistor.
Table 5 shows the TCR's of the sheet resistances a n d those of the resistors with a length of 100 Ixm. W e see t h a t TCR's of the resistors have been s o m e w h a t shifted to higher values with respect to the TCR's of the sheet resistances, the TCR's of sputtered resistors being less negative a n d the TCR's of e v a p o r a t e d resistors more positive. Relevant parameters of the thin-film resistors a n d their terminations are listed in Table 6. It should be n o t e d t h a t the T C R of (small) resistors can be deteriorated by the T C R of the conductor. Beside these parameters, the (long) term stability of resistors is also often important. This stability has already been
Acknowledgment--We wish to thank F. M. Heesterbeek for his assistance in carrying out the electrical measurements. Further, we are indebted to W. Mesman's department for measuring the physical dimensions of the test resistors. REFERENCES
1. J. S. Fisher and P. M. Hall, Termination materials for thin film resistors, Proc. IEEE 59, 1418-1424 (1971). 2. R. T. Galla, H. M. Greenhouse and W. C. Vergara, Evaluation of the interfacial resistance of thin film interconnexions, Microelectron. Reliab. 7, 185-212 (1968). 3. W. J. J. Rey, Introduction to Robust and Quasi-Robust Statistical Methods, pp. 110-116, Springer-Verlag, Berlin (1983).
0026-2714/8753.00 + .00 © 1987 Pergamon Journals Ltd.
AN INVESTIGATION INTO THE TERMINATION RESISTANCE OF THIN FILM RESISTORS A. G. VA~ NIE Philips Research Laboratories, 5600 JA Eindhoven, The Netherlands (Receivedfor publication 1 September 1986) Abstraet--A mathematical analysis of the termination resistance of thin-filmresistors is given and a method of measuring this type of resistance is discussed. As examples, the termination resistances of sputtered and evaporated thin-film resistors have been measured. Relevant parameters of the termination to be specified are discussed. l. I N T R O D U C T I O N
The termination resistance of a thin-film resistor is the result of the interfacial resistance which occurs between the materials of the resistor and the interconnection, respectively. In general, the T C R (temperature coefficient of the resistance) of the termination resistance differs from the T C R of the "bulk" material of the thin-film resistor. Consequently, the T C R of a thin-film resistor depends on its length. The termination resistance has already been widely investigated. Fisher et al, have given a relation between the termination resistance, the specific throughconductance of the interfacial layer and the sheet resistivities of the resistor and conductor [1]. However, the derivation of that relation was not given. We have found another relationship, which is equivalent to Fisher's equation for the case that the sheet resistance of the conductor is zero. Fisher et al. probably ignored the forward current in the conductor at the termination. Although Galla et al. took this forward current into account, their calculations are rather complicated and sometimes not very clear [2]. In our calculations, we have used transmission line theory in which "distributed" network elements occur. This theory enables us to derive the relevant relations in a straightforward manner. We have also derived rules of thumb for cases where the conductor resistivity is negligibly small. We determined relevant parameters of the termination resistance by using a special test circuit. Mostly, the termination resistance is small compared to the total resistance of the resistor, so that accurate measuring methods must be used. The test circuits have to be made by reliable processing methods, because the physical dimensions must also be determined with high precision. We investigated the termination resistance of thinfilm resistors with evaporated NiCr or sputtered NiCrbased layers which have sheet resistivities of about 200QI-q -1. AI20 3 substrates and Au conductors were used.
consists of the sandwich: resistive layer/interracial layer/conductor layer. The current flow is sketched in Fig. lb. The current flows gradually from the conductor through the interface into the resistor. The network of the "distributed" elements shown in Fig. lc will be used for a first order calculation of the current flow. As already remarked, the termination resistance is in our cases relatively small, so that this first approximation of the current flow gives a sufficient accuracy for calculation of the termination parameters. Figure 2a shows the termination in greater detail. In fact, the resistor layer extends beneath the entire conductor, however, we assume in our calculation that there only exists a resistance overlap of length d. Doing so, the minimum allowable overlap can be calculated and the minimum length of the connecting pad can be so obtained. The termination width is w. Figure 2b shows a section with length dx of the distributed network, where Rr = Rs,/w (Q m - 1),
(la)
~'~ onductor inet:irftac~e
VW/W a
Fig. la. A sketch of a cross-section of the thin-film resistor and its terminations.
Fig. lb. The current flow at the terminations. ]i
Ii .
= 2. M A T H E M A T I C A L
ANALYSIS
A sketch of the cross-section of the thin-film resistor termination is shown in Fig. la. The termination
C
|i
Fig. lc. Modelling of the termination by 'distributed' network elements. 423
424
A.G. VAN Nm
P -I
Q
ooo
~
The integration constants A and B can be found from the boundary conditions. The terms with A are related to a current flowing in the positive x direction and the terms with B to a current flowing in the opposite direction. At x = 0, the current I = Ii. F r o m equation (5) it can then be shown that
' 'o ' o " "
in'terfaeial
o
x
Rr + Rc I~ = (A - B ) - R,
d
Fig. 2a. The termination in greater detail.
_,
dV c [i
At x = d, the current I = 0, so that from equations (5) and (8) it follows that Rr e - ~d+ Rc B = A R , e+~a+R c.
+
.
i, .
A+B Ri = R° (A - B)(1 + Re~R,)"
Fig. 2b. A part of the termination with 'distributed' network elements. Rc = R~dw ( Q m - 1),
(lb)
Y = Y~.w (I)-x m - l ) ,
(lc)
in which R,,(f~) is the sheet resistance of the resistor material, R~ (f~) is the sheet resistance of the conductor material, y~(f~-1 m-2) is the specific through-conductance of the interfacial material. The current I~ enters the termination at x = 0 and the same current leaves the termination at x = d. At any point x the sum of the currents flowing in the x direction must be equal to I~. We will assume that the current in the conductor is a combination of the current I~ and the transfer current I, as shown in Fig. 2b. The transfer current I is calculated by means of transmission line. Application of Kirchoff's law yields the following simultaneous equations dV = - I . ( R , + R~)+ I,. R~, dx
(2)
dI -dx
(3)
-
=
(9)
The constant B--, 0, if the overlap d is taken infinitely long (yd---, oo). The ratio B/A is analogous to the reflection coefficient in transmission lines. In infinitely long lines the reflection coefficient is zero. The input resistance Ri at x = 0 can be obtained from equations (4), (5) and (8),
b
-
(8)
- V.Y.
After integrating equations (2) and (3) we arrive at V = Ro(Ae-~*+Be+~),
Re
(10)
In the case that 7d >> 1, where B--,0, we arrive at the limit Rr Ri---~ / y ( R , + R c ) .
(11)
Apart from the voltage drop due to R i, a drop occurs between the points P and Q (see Fig. 2a). F r o m Fig. 2b it can be seen that d V~ = (I - li)Rc. dx
(12)
At x = 0, the voltage V~(0)= 0, so that integrating equation (12) yields V ~ ( x ) = _ _Rc _ l[A e - ~ + B e
+~,x+I i 1{ - R, -
\n,+&
7x - - -Rl li .' ~
Roll (13)
At x = d we get, if yd >> 1 and R, >> R~, V~(d)---, - - I , . Re. d.
(14)
The voltage drop V~(d) can he added to the other voltage drops across the conductor. Usually, the voltage drop over the total conductor is taken from the boundary of the resistor to the end. When this is done, the voltage drop V~(d)is taken into account.
(4)
(5)
3. R U L E S O F T H U M B : R, = 0
y= ~ ) Y ,
(6)
In the cases where the conductor resistivity is negligibly small, the input resistance becomes [see equations (6), (7), (9) and (10)]
Ro
(7)
1 -~-e-2~'d Ri = R° 1 - e -2rd'
I = Ae-~X-Be+rX+IiR
, -t- R~
where
=
q~ R
c
(15)
Thin-film resistors
425
Rs,
(fl- 1 m - 2).
Y, = R2" w 2
Ri/Ro
(20)
The specific termination resistance R,e,~ is defined as
T ,°8
Rte,m =
/Rs, = w" R o = w" Ri
(f~" m). (21)
6 The input resistance Ri can be interpreted as an apparent change ltermin the resistor length
Ri
Rterrn
lie,= = - - w = Rs, R~, 0
(m).
(22)
The condition for the overlap d can be found from equations (19), (20) and (22),
1 Vd
d >> lt~,m Fig. 3. The ratio Ri/R o plotted as a function of Td.
(m).
(23)
Let us take as an example Rs,=200f21"q -1, R~ = 1 f~, w = 1 mm. Then we arrive at Ys = 2 0 0 f l - l m m - 2 ,
in which = ~
Y,
Rte,, = 1 f~" mm,
(16)
1,~,= = 5 rtm, Ro = R/_~.
(17)
In Fig. 3 the ratio R~/R o is plotted as a function of ?d. F o r ?d--+ oo the input resistance R~--+R o. We see that for 7d = 5 the minimum value of R i is already nearly reached. Let us assume that the input resistance Ri, the sheet resistance R~,, the width w and the overlap d of the termination are known. If the overlap zd >> 1 then the resistance go= gi
(~).
(18)
d >> 51am. 4. EXPERIMENTAL We investigated the termination resistances of two kinds of thin-film resistor made by P M A (Phillips & M B L E Associated, Brussels). The (nominal) manufacturing data were: technology resistor material sheet resistance termination
evaporated NiCr 200 f~ [] - 1 NiCr/Ni/Au-Ni-Au
conductor conductor thickness substrate coating
Au-Ni-Au 2 I~m AI203 no
F r o m equations (1) and (16) it can be found that = , , / / ~ , • Y~
(m-l).
(19)
The specific conductance of the interfacial layer can be found from equations (1), (17) and (18),
19 I/ 23 mm ~
resistive area
Fig. 4. The circuit for measuring the parameters of the resistor termination. The measuring current is supplied between pins 1 and 10. The voltages of the several sections have been measured (see Table 1). The nominal length of l~ = 100gm for i = 3..... 11.
sputtered NiCr-base 200 f~ [] - 1 NiCr-base/Ni/Nibase-Au-Ni-Au Au-Ni-Au 2 lain A120 a no
426
A.G. VANNtE
Table 1. The voltages and connecting pins of the several sections (R,c is the sheet resistance of the conductor material, R,, is the sheet resistance of the resistor material and Rt,,,, is the termination resistance) Section
Voltage
The physical lengths of the sections were measured with methods described in Section 5. The termination resistance (Rte,,,) i of the ith section (i = 3, 4 . . . . . 11) was calculated using the equation
Properties to be determined
Pins
(Rterm)i : 0.5 ~/ V- mi " w -(Rsr)i
"li),
(24)
/
1
1,'1
2
v2
3 4 5
V3 V4 V5
6 7 8
V6 V-1 Vs
9
17 18 15 16 3 4 5
R~
Rs,
2 3 4
Rter.,
14 5 13 14 6 13
Rte,,.
Rterra
Rterm Rterm
Rt~,,. Rterm
V9
7
6
10
V10
8
7
Rt,,, .
11
Vx x
9
8
Rt~,~
12
1/12
11
12
Rs,
The parameters of the resistor termination are determined with the test circuit shown in Fig. 4. The measuring current (10 mA) was supplied between pins 1 and 10 and we measured the voltages between the pins noted in Table 1. The measuring current was delivered by Keithley's current source 225, which has a stability of less than 0.05%. In order to prevent interference with the measuring current the voltages must be measured with a high ohmic voltmeter whoe input floats with respect to ground. A Datron 1071 with an accuracy better than 5 P P M was used for these voltage measurements. The voltages were measured at 30"C and 80°C in order to obtain the T C R of the termination resistances.
in which V~ is the voltage drop across the ith section, I,, is the measuring current, (R~r)i is the sheet resistance of the resistor of the ith section, li is the physical length of the ith section, w is the width of the sections. The sheet resistance (Rs,)~ was determined by linear interpolation (Section 5). As the properties of the terminations are probably dependent on the direction of the resistor on the substrate, we test resistors which are "horizontally" and "vertically" situated on the same substrate. The resistors are indicated by H and V, respectively. 5. MEASURING THE PHYSICAL LENGTH OF THE SEVERAL SECTIONS The physical dimensions of the sections were measured with the aid of a Zeiss U M M 5 0 0 apparatus which has a measuring accuracy of about 2 p,m. The edges of sections were detected by means of a microscope and/or a "Talysurf". The measuring accuracy is also dependent on the quality of the conductor edges at the sections. These edges must be steep and without
Fig. 5. A SEM photograph of a conductor edge at the resistor termination. The indicated line segments have a length of 10 txm.
Thin-film resistors Table 3. The sheet resistivities measured at sections 2 and 12
Table 2. The measured lengths of sections of one test circuit (the nominal lengths were 100 ~tm) Microscope (Ftm)
Talysurf 0tin)
3 4 5 6 7 8 9 10
97.8 98.6 98.0 96.0 98.4 98.6 102.2 96.0 96.0
100.2 99.6 97.2 97.0 97.6 98.2 101.0 98.2 101.4
Mean value Standard deviation
97.96
98.69
4.5
1.9
Section
427
Number
Section 2 (f~ [] - 1)
Section 12 (f2 [] - 2)
Difference (%)
SH1 SH3 SV4 SV5 EH2 EH4 EV3 EV6
201.1 206.8 200.0 203.2 179.5 173.7 182.6 197.8
201.2 207.4 201.5 205.4 178.5 175.3 177.9 181.0
+0.05 + 0.03 +0.75 + 1.08 -0.56 + 0.92 -2.61 + 1.78
S H
The lengths were measured with a Zeiss UMM 500 apparatus and the edges of the sections were detected using a microscope or a Talysurf. ripples and the conductor thickness must be homogeneous. A SEM photograph of an edge is shown in Fig. 5; the conductor thickness is about 2 lam. The lengths of the sections 3-12 of a test circuit were determined with the use of a microscope and a "Talysurf" (see Table 2). The sets of measuring results do not show Gaussian distributions and therefore we applied a "robust" statistical method for calculating the mean values and standard deviations. In this method, discussed by Rey [3], the function "fair" was used with the constants K 1 = 5.68107 and K 2 = 2.30976, so that the efficiency is about 80%. The mean values differ by 0.73 p.m, which is much smaller than the standard deviations. The "Talysurf" method showed the lowest scatter. The nominal value of the termination region length is 100 p.m. The deviations between the measured and nominal values are smaller than 1 p.m at each edge. These discrepancies are probably caused by the "mushroom" form of the edge (see Fig. 5). We therefore take the nominal length of the termination region in the calculations. 6. MEASURING RESULTS AND EVALUATION
The sheet resistances Rs, 2 and R~,12 of Sections 2 and 12, respectively, were determined and the results
sputtered, horizontal,
E evaporated, V vertical.
are listed in Table 3. The differences in resistance of these sections a m o u n t to only a few per cent for all the test circuits. Sputtered samples show a somewhat lower spread than the evaporated ones. The sheet resistances of sections 3 - I 1 were found by using linear interpolation with respect to the position of the section between Sections 2 and 12. The termination resistances were calculated with equation (24). Table 4 gives the mean values and standard deviations of the measurement results for several test samples. These estimators were calculated with the robust statistical method mentioned before. The apparent length changes ((Ite,,,,)i), also given in Table 4, were derived from the ((Rte,,,)i) using equation (22). The apparent length change l,~,m is important for the design rules concerning m i n i m u m length of the connecting pad and the length of the resistors. In our cases the requirement of equation (23) is satisfied, because the connecting tracks have widths of /> 400 ~tm. The apparent length change ((l,er,,,)i) can be determined within an accuracy of less than 1 p.m. This accuracy is satisfactory having regard to the geometrical accuracy with which the resistors can be made. The termination resistance is nearly dependent on the position of the resistor on the substrate, but the termination resistance of sputtered resistors is much higher than the termination resistance of evaporated resistors. The measuring accuracy is too poor for determining
Table 4. The termination resistances Rte,,, and termination lengths lie,,. of two kinds of thin-film resistor f2 [] - x Technology
Situation
Number
R,e,,.(f~•ram)
(1,e,,,) (~m)
Sputtered NiCr-base
Horizontal
SH1 SH3 SV4 SV5 EH2 EH4
2.73 _+0.14 2.654-0.15 2.42+0.15 2.394-0.07 1.154-0.12 1.134-0.08 0.90 _+0.07 0.98+0.22
144-0.7 134-0.7 12_+_+0.6 12+0.3 6_+0.6 6_+0.4 5 ___0.4 5_+0.5
Vertical Evaporated NiCr
Horizontal Vertical
E V3 EV6
428
A. G. VANN~E Table 5. The sheet resistances R~ and their TCR's and TCR's of resistors with a length of 100 ~tm for the two technologies Technology Sputtered NiCr-base
Situation
Number
~ [] - ~
PPM/K sheet resistance
PPM/K (Ira,, = 100 lain)
Horizontal
SH 1 SH3 SV4 SV5 EH2 EH2 EV3 EV6
201 207 201 204 179 174 180 179
- 23 - 22 - 22 - 21 + 80 + 54 + 105 + 108
- 20 - 22 - 22 - 19 + 84 + 63 + 111 + 110
Vertical Evaporated NiCr
Horizontal Vertical
Table 6. Relevant parameters of thin-film resistors and their terminations Sheet resistance of the resistor material Sheet resistance of the conductor material Temperature coefficient of the resistor material Temperature coefficient of the conductor material Temperature coefficient of the shortest permitted resistor Termination resistance Specific through conductance Apparent increase in resistor length Length of the connecting pad
the T C R of the t e r m i n a t i o n resistance, however the T C R of the shortest permitted resistor, say 100 Ixm long, can be measured a n d this T C R should be specified. The TCR~ of a resistor with a uniform length 1 can then be f o u n d from
TCRt =
R, c Rs, TCRs, TCR,c TCRI.~. R,er,, Y~e,~, l,e,,, d
f~ [] - x fl [] - 1 PPM/K PPM/K PPM/K ~ . mm f~- 1 m m - 2 lam lain
widely discussed in the literature, b u t the stability, a n d also the reliability, of the t e r m i n a t i o n resistances should be investigated. The described test circuit is p r o b a b l y suitable for such investigations.
[TCRs, .(1 - lmi,) + TCRt.,." (lmi n + 2./,~,,,)]
7. CONCLUSIONS
(1 + 2 . lie,,, )
1. The t e r m i n a t i o n resistance of thin film resistors can be determined within a sufficient accuracy. 2. T h e t e r m i n a t i o n resistance can be interpreted as a n a p p a r e n t change l,e,,, in the resistor length. 3. T h e r e q u i r e m e n t " c o n n e c t i n g p a d length d >> lter,," should be satisfied.
(25) in which lmi.
is the length of the shortest permitted resistor and TCRt,,, is the T C R of the shortest permitted resistor.
Table 5 shows the TCR's of the sheet resistances a n d those of the resistors with a length of 100 Ixm. W e see t h a t TCR's of the resistors have been s o m e w h a t shifted to higher values with respect to the TCR's of the sheet resistances, the TCR's of sputtered resistors being less negative a n d the TCR's of e v a p o r a t e d resistors more positive. Relevant parameters of the thin-film resistors a n d their terminations are listed in Table 6. It should be n o t e d t h a t the T C R of (small) resistors can be deteriorated by the T C R of the conductor. Beside these parameters, the (long) term stability of resistors is also often important. This stability has already been
Acknowledgment--We wish to thank F. M. Heesterbeek for his assistance in carrying out the electrical measurements. Further, we are indebted to W. Mesman's department for measuring the physical dimensions of the test resistors. REFERENCES
1. J. S. Fisher and P. M. Hall, Termination materials for thin film resistors, Proc. IEEE 59, 1418-1424 (1971). 2. R. T. Galla, H. M. Greenhouse and W. C. Vergara, Evaluation of the interfacial resistance of thin film interconnexions, Microelectron. Reliab. 7, 185-212 (1968). 3. W. J. J. Rey, Introduction to Robust and Quasi-Robust Statistical Methods, pp. 110-116, Springer-Verlag, Berlin (1983).