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A magnetic sensor array for two-dimensional pattern-shift measurements
137
Sensors and Actuators A, 25-27 (1991) 737-740
A Magnetic Sensor Array for Two-dimensional Pattern-shift Measurements A. BOSSCHE, H. C. J. M. VAN GESTEL and JEFF R. MOLLINGER Derfi University of Technology, Department of Electrical Engineering, P.O. Box 5031, 2628 GA De,ft (The Nether/an&)
AbStR3Ct
The large mismatch in thermal expansion coefficients of silicon and the plastic encapsulants available today introduces severe stresses at the chip surface that might lead to stress-induced displacements of metalhzation paths. The sensor array discussed here has been designed to measure such displacements. All rows and columns of the array are separated by metal conductors at the chip surface, while each ceil contains a Hall device. When a local magnetic field is introduced at the surface by leading a well-known current through one of the metal conductors, two neighbouring Hall elements positioned symmetrically along this conductor can be used to measure the magnetic field. The difference in output voltage of both Hall elements is a measure for the displacement of the current’s centre and so of the metal conductor itself.
quantification of the properties of these encapsulants requires stress and displacement measurements at the chip surface. This paper introduces a magnetic sensor array for twodimensional package-related pattern-shift measurements. The array configuration makes possible a large number of measuring points per unit area.
Notation aw d
r s SW
Introduction Plastic encapsulation of semiconductor devices is economically attractive because of the low cost. However, the large mismatch in thermal expansion coefficients of silicon and the available encapsulants introduces severe stresses acting at the chip surface that might lead to stress-induced failures [ 11. Since these stresses increase with the distance from the chip centre [2], the problems grow with larger chip sizes and, therefore, might obstruct further integration. Recently, efforts have been made to reduce plastic-induced failures through development of new low-stress encapsulation materials. However, a good 0924-4247/91/$3.50
sd Ill
metal width of central conductor (8 pm) vertical position in semiconductor measured from the centre of the central conductor (1 pm) lateral position measured from the axis of symmetry. lateral shift of the central conductor. sensor width (80 pm) sensor distance (30 pm) current through Hall element (0.5 mA) current through metal conductor (lOOmA) magnetic field vector vertical component of B Hall constant Hall voltage across right sensor Hall voltage across left sensor relative differential output signal.
Sensor Design The principal sensor design is given in Fig. 1. At the chip surface a local magnetic field is 0 Elsevier Sequoia/Printed
in The Netherlands
738
Fig. 1. The principal sensor design.
introduced by leading a well-known current through the central conductor. Two Hall elements integrated symmetrically along this conductor are used to measure the magnetic field. The difference in output voltage of both Hall elements is a measure for the displacement of the current’s centre and so of the central conductor itself. The Hall elements are realized as symmetrical normally off MOS devices with four contacts each. When the gate of such a transistor is activated, the inversion layer can be used as a Hall element. When the Hall elements are placed in an array configuration, see Fig. 2, the elements can be used for displacement measurements in both lateral directions and a high density of measuring points can be achieved.
Sensor Sensitivity The vertical component of the magnetic field introduced by the central conductor
Fig. 3. Cross section of sensor.
causes horizontal electric fields in the Hall elements and, therefore, is responsible for the Hall voltages. For the dimensions given in Fig. 3 this vertical magnetic field can be calculated as +aw/2 x+-r--s Mr,
s, 4
= PO & s -w/2
+
r -
s)’
+
d2 dx
ln(r-s+yr+d2
I
=
(x
PO& (r-s--y)2+d2
(1) Figure 4 shows the magnetic field’s vertical component in the inversion layer as a function of the distance to the centre. In the next calculations we will assume the current density to be homogeneous throughout the inversion layer, although the presence of the low-ohmic Hall contacts will undoubtedly affect the current distribution to some extent. Then, in a first-order approximation we can calculate the Hall voltage by integrating the
1
-\______
0 0
Fig. 2. Array configuration. Horizontal and vertical displacements can be measured using the same sensor array.
5
IO
15
20 25 30 distance r (pm)
35
40
45
50
Fig. 4. Vertical component of the magnetic field in the inversion layer as function of the distance to the centre.
739
-
contributions over the sensor’s cross-sectional area from
actwl
- -
simulated
sd/Z + SW
~I&, 4
s
$ R,,B,(r,
=
s,
d) dr
(2)
sd/2
for the right sensor, while the expression for the left sensor can be found as Vi,,& sd) = V,,( -s, sd). However, these Hall voltages are also functions of the Hall constant Rh,which may vary with different positions on the Si wafer and with temperature. In order to reduce these sensitivity variations, it is better to calculate the differential output voltage relative to the absolute Hall voltages as
Figure 5 shows the simulated curves for three different sensor distances. As can be seen, I/d& sd) varies quite linearly with the displacement s as long as the metal conductor does not overlap with one of the Hall elements. Therefore, the sensor distance should be chosen large enough to, ensure a sufficiently linear curve for practical displacements ( z 5 pm), but not too large since the Hall voltages decrease with sd. In this case a sensor distance of 30 ,um was chosen. Since the Hall constant R,,appears in a similar manner in the numerator and the denominator of eqn. (3), Vd(s, sd) is (within certain limits) temperature independent.
-
sd= 2Ojtm
-
sd-
--
sd-30Nm
40 urn
displacement
[wn)
Fig. 6. The theoretical output curves for displacements simulated with two conductors (x = 6 pm) and for actual displacements of a single conductor (sensor distance 30 pm).
Test measurements for determination of the sensor sensitivity might be difficult since the central conductor cannot be moved freely. Therefore an extra test sensor has been developed of which the central conductor is replaced by two conductors in parallel positioned at --x pm and +x pm respectively from the centre. Then, a non-proportional distribution of the modulating current between the two conductors introduces a change in the magnetic field which could simulate an actual displacement of a single central conductor. An appropriate distribution factor as a function of displacement s was found to be x-s
a(4 = 7
resulting in currents cr(s)Z, through the left conductor and (1 - +))I,,, through the right conductor. Figure 6 compares the theoretical output curves for displacements simulated with two conductors (x = 6 pm) and for actual displacements of a single conductor. Since the curves are nearly identical for displacements up to 6-7 pm, the test sensor can be very well used to determine the sensor sensitivity.
offset and Noise Reduction Fig. 5. Theoretical curves for three different sensor distances.
Up to now we have considered the desired signals only. However, due to internal
-8
-6
-4
-2
0
2
6
6
10
Fig. 7. Measurement results from a previous design with displacements simulated by current distributions among two conductors.
stresses silicon integrated Hall elements show relatively large offsets while additional stress (and so offset) may be introduced by die-bonding and encapsulation. Furthermore, the offset is not constant but varies with temperature. Therefore, the modulating current through the central conductor is reversed periodically with a frequency of z 10 Hz to allow a sufficient reduction of offset and low-frequency offset changes when measurements are made in subsequent positive and negative periods. The Hall-elements’ output voltages are relatively small ( ~0.5 mV for the values given) and, therefore, might be sensitive to noise. Noise reduction can be achieved by averaging measurements over a number of periods [3]. Calibration of the sensor is done in the following manner: (i) in order to account for alignment errors, the zero-shift output is measured in the premoulded situation. (ii) in order to compensate for ~nsiti~~ differences between the Hall elements, these sensitivities are measured with an external magnetic field.
Measurements Unfortunately the sensor chip was not ready at the deadline for this paper. However, we did
some measurem~ts on the previous design in which the Hall elements were realized as diffused layers instead of inversion layers 131. Figure 7 shows the output of a typical sensor as a function of the displacement. The sensitivity f x5%/km) and linearity are in accordance with the theory. The offset (at zero displacement) is due to different sensitivities for the left and right Hall devices.
c0ne1usiotts The integrated metal-shift sensor introduced in this paper allows on-chip measurements to be made of stress-induced displacements of metallization paths in plastic-moulded semiconductor devices. Since the measurement method is a non-destructive one, it is possible to observe the displacement at multiple stages of an environmental test procedure. As a result of the magnetic approach, the sensor measures the central conductor’s buik displa~ment and, hence, will be less sensitive to defo~ation of the conductor’s crosssectional area than a capacitive sensor would be. The sensor shows a good linearity for moderate displacements ( 6 10 pm). A larger linear range can be achieved by enlarging the sensor distance sd.
References 1 R. E. Thomas, S~e~indu~ d~o~ation on &IIminium metal&&on in plastic molded semiconductor devices, L!?EE Trans. Congmmts, Hybrids Mar&. Technol., CHMT-8 (1985) 427-434. 2 K. Miyake, H. Suzuki and S. Yamamoto, Heat transfer and thermal stress analysis of plastic-encapsulated KS, IEEE Trans. Reliab., R-34 (1985) 402-409. 3 A. Bossche, On-chip measurement of package-related metal shift using an integrated silicon sensor, Inf. Reliability Physics Symp. (IRPS) ‘89, Phoenix, AZ, U.S.A., Apr. 11-14, 1989, pp. 127-130.
Sensors and Actuators A, 25-27 (1991) 737-740
A Magnetic Sensor Array for Two-dimensional Pattern-shift Measurements A. BOSSCHE, H. C. J. M. VAN GESTEL and JEFF R. MOLLINGER Derfi University of Technology, Department of Electrical Engineering, P.O. Box 5031, 2628 GA De,ft (The Nether/an&)
AbStR3Ct
The large mismatch in thermal expansion coefficients of silicon and the plastic encapsulants available today introduces severe stresses at the chip surface that might lead to stress-induced displacements of metalhzation paths. The sensor array discussed here has been designed to measure such displacements. All rows and columns of the array are separated by metal conductors at the chip surface, while each ceil contains a Hall device. When a local magnetic field is introduced at the surface by leading a well-known current through one of the metal conductors, two neighbouring Hall elements positioned symmetrically along this conductor can be used to measure the magnetic field. The difference in output voltage of both Hall elements is a measure for the displacement of the current’s centre and so of the metal conductor itself.
quantification of the properties of these encapsulants requires stress and displacement measurements at the chip surface. This paper introduces a magnetic sensor array for twodimensional package-related pattern-shift measurements. The array configuration makes possible a large number of measuring points per unit area.
Notation aw d
r s SW
Introduction Plastic encapsulation of semiconductor devices is economically attractive because of the low cost. However, the large mismatch in thermal expansion coefficients of silicon and the available encapsulants introduces severe stresses acting at the chip surface that might lead to stress-induced failures [ 11. Since these stresses increase with the distance from the chip centre [2], the problems grow with larger chip sizes and, therefore, might obstruct further integration. Recently, efforts have been made to reduce plastic-induced failures through development of new low-stress encapsulation materials. However, a good 0924-4247/91/$3.50
sd Ill
metal width of central conductor (8 pm) vertical position in semiconductor measured from the centre of the central conductor (1 pm) lateral position measured from the axis of symmetry. lateral shift of the central conductor. sensor width (80 pm) sensor distance (30 pm) current through Hall element (0.5 mA) current through metal conductor (lOOmA) magnetic field vector vertical component of B Hall constant Hall voltage across right sensor Hall voltage across left sensor relative differential output signal.
Sensor Design The principal sensor design is given in Fig. 1. At the chip surface a local magnetic field is 0 Elsevier Sequoia/Printed
in The Netherlands
738
Fig. 1. The principal sensor design.
introduced by leading a well-known current through the central conductor. Two Hall elements integrated symmetrically along this conductor are used to measure the magnetic field. The difference in output voltage of both Hall elements is a measure for the displacement of the current’s centre and so of the central conductor itself. The Hall elements are realized as symmetrical normally off MOS devices with four contacts each. When the gate of such a transistor is activated, the inversion layer can be used as a Hall element. When the Hall elements are placed in an array configuration, see Fig. 2, the elements can be used for displacement measurements in both lateral directions and a high density of measuring points can be achieved.
Sensor Sensitivity The vertical component of the magnetic field introduced by the central conductor
Fig. 3. Cross section of sensor.
causes horizontal electric fields in the Hall elements and, therefore, is responsible for the Hall voltages. For the dimensions given in Fig. 3 this vertical magnetic field can be calculated as +aw/2 x+-r--s Mr,
s, 4
= PO & s -w/2
+
r -
s)’
+
d2 dx
ln(r-s+yr+d2
I
=
(x
PO& (r-s--y)2+d2
(1) Figure 4 shows the magnetic field’s vertical component in the inversion layer as a function of the distance to the centre. In the next calculations we will assume the current density to be homogeneous throughout the inversion layer, although the presence of the low-ohmic Hall contacts will undoubtedly affect the current distribution to some extent. Then, in a first-order approximation we can calculate the Hall voltage by integrating the
1
-\______
0 0
Fig. 2. Array configuration. Horizontal and vertical displacements can be measured using the same sensor array.
5
IO
15
20 25 30 distance r (pm)
35
40
45
50
Fig. 4. Vertical component of the magnetic field in the inversion layer as function of the distance to the centre.
739
-
contributions over the sensor’s cross-sectional area from
actwl
- -
simulated
sd/Z + SW
~I&, 4
s
$ R,,B,(r,
=
s,
d) dr
(2)
sd/2
for the right sensor, while the expression for the left sensor can be found as Vi,,& sd) = V,,( -s, sd). However, these Hall voltages are also functions of the Hall constant Rh,which may vary with different positions on the Si wafer and with temperature. In order to reduce these sensitivity variations, it is better to calculate the differential output voltage relative to the absolute Hall voltages as
Figure 5 shows the simulated curves for three different sensor distances. As can be seen, I/d& sd) varies quite linearly with the displacement s as long as the metal conductor does not overlap with one of the Hall elements. Therefore, the sensor distance should be chosen large enough to, ensure a sufficiently linear curve for practical displacements ( z 5 pm), but not too large since the Hall voltages decrease with sd. In this case a sensor distance of 30 ,um was chosen. Since the Hall constant R,,appears in a similar manner in the numerator and the denominator of eqn. (3), Vd(s, sd) is (within certain limits) temperature independent.
-
sd= 2Ojtm
-
sd-
--
sd-30Nm
40 urn
displacement
[wn)
Fig. 6. The theoretical output curves for displacements simulated with two conductors (x = 6 pm) and for actual displacements of a single conductor (sensor distance 30 pm).
Test measurements for determination of the sensor sensitivity might be difficult since the central conductor cannot be moved freely. Therefore an extra test sensor has been developed of which the central conductor is replaced by two conductors in parallel positioned at --x pm and +x pm respectively from the centre. Then, a non-proportional distribution of the modulating current between the two conductors introduces a change in the magnetic field which could simulate an actual displacement of a single central conductor. An appropriate distribution factor as a function of displacement s was found to be x-s
a(4 = 7
resulting in currents cr(s)Z, through the left conductor and (1 - +))I,,, through the right conductor. Figure 6 compares the theoretical output curves for displacements simulated with two conductors (x = 6 pm) and for actual displacements of a single conductor. Since the curves are nearly identical for displacements up to 6-7 pm, the test sensor can be very well used to determine the sensor sensitivity.
offset and Noise Reduction Fig. 5. Theoretical curves for three different sensor distances.
Up to now we have considered the desired signals only. However, due to internal
-8
-6
-4
-2
0
2
6
6
10
Fig. 7. Measurement results from a previous design with displacements simulated by current distributions among two conductors.
stresses silicon integrated Hall elements show relatively large offsets while additional stress (and so offset) may be introduced by die-bonding and encapsulation. Furthermore, the offset is not constant but varies with temperature. Therefore, the modulating current through the central conductor is reversed periodically with a frequency of z 10 Hz to allow a sufficient reduction of offset and low-frequency offset changes when measurements are made in subsequent positive and negative periods. The Hall-elements’ output voltages are relatively small ( ~0.5 mV for the values given) and, therefore, might be sensitive to noise. Noise reduction can be achieved by averaging measurements over a number of periods [3]. Calibration of the sensor is done in the following manner: (i) in order to account for alignment errors, the zero-shift output is measured in the premoulded situation. (ii) in order to compensate for ~nsiti~~ differences between the Hall elements, these sensitivities are measured with an external magnetic field.
Measurements Unfortunately the sensor chip was not ready at the deadline for this paper. However, we did
some measurem~ts on the previous design in which the Hall elements were realized as diffused layers instead of inversion layers 131. Figure 7 shows the output of a typical sensor as a function of the displacement. The sensitivity f x5%/km) and linearity are in accordance with the theory. The offset (at zero displacement) is due to different sensitivities for the left and right Hall devices.
c0ne1usiotts The integrated metal-shift sensor introduced in this paper allows on-chip measurements to be made of stress-induced displacements of metallization paths in plastic-moulded semiconductor devices. Since the measurement method is a non-destructive one, it is possible to observe the displacement at multiple stages of an environmental test procedure. As a result of the magnetic approach, the sensor measures the central conductor’s buik displa~ment and, hence, will be less sensitive to defo~ation of the conductor’s crosssectional area than a capacitive sensor would be. The sensor shows a good linearity for moderate displacements ( 6 10 pm). A larger linear range can be achieved by enlarging the sensor distance sd.
References 1 R. E. Thomas, S~e~indu~ d~o~ation on &IIminium metal&&on in plastic molded semiconductor devices, L!?EE Trans. Congmmts, Hybrids Mar&. Technol., CHMT-8 (1985) 427-434. 2 K. Miyake, H. Suzuki and S. Yamamoto, Heat transfer and thermal stress analysis of plastic-encapsulated KS, IEEE Trans. Reliab., R-34 (1985) 402-409. 3 A. Bossche, On-chip measurement of package-related metal shift using an integrated silicon sensor, Inf. Reliability Physics Symp. (IRPS) ‘89, Phoenix, AZ, U.S.A., Apr. 11-14, 1989, pp. 127-130.