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Absolute measurement of transient carrier concentration and temperature gradients in power semiconductor devices by internal IR-laser deflection
MICROF,HC~I'ROIHIC ENo, nlEEI~INO
ELSEVIER
MicroelectronicEngineering31 (1996)299-307
Absolute measurement of transient carrier concentration and temperature gradients in power semiconductor devices by internal IR-laser deflection G. Deboya, G. S61knera, E. Wolfgang" and W. Claeysb aSiemens AG, Corporate Research and Development, Otto-Hahn-Ring 6, D-81739 MOnchen bUniversit6 de Bordeaux I, CPMOH, 351, Cours de la Lib6ration, F-33405 Talence 1. ~TRODUCTION High frequency applications in power electronics require a thorough investigation of the dynamic current distribution and heat dissipation. With recent trends to higher blocking voltage and enhanced current transport capability heat dissipation becomes a critical problem. Besides electrothermal simulation experimental measurements are a necessity for a continuous improvement of the device performance. A new contactless probing technique for the absolute evaluation of carrier density and temperature gradients in the bulk of power semiconductor devices has therefore been developed. This article will focus on methodological aspects and experimental results. 2. MEASUREMENT PRINCIPLE Due to its dependence on free carrier concentration and temperature, the silicon refractive index will vary temporally and spatially during transient switching conditions of the device. The gradient of the refractive index is probed by the deflection of an infrared laser beam within the bulk of the device. The principle is outlined in Fig. 1. The beam is focused through optically polished side faces. A long distance objective transforms its ~Gate Emitter/ . Parallel- internal deflection shift into a parallel shift, which is detected by ~al~~r" a quadrant photo diode within two directions normal to Collector~ the optical axis. The probing technique yields an integral Figure 1: Measurement principle value of the gra-
T
0167-9317/96/$15.00e 1996- ElsevierScienceB.V. All rights reserved. 0167-9317(95)00352-5
SSDI
300
G. Deboy et al. / Microelectronic Engineering 31 (1996) 299-307
dients of temperature and carder concentration along the optical beam path. The distribution along the optical axis can be measured by turning the device by 90 ° and scanning along the horizontal axis. Using a 1300 nm-laser source we can neglect optical carrier generation. The optical power losses due to free cartier absorption are more than six orders of magnitude below the electrically dissipated power. In fact we have never observed any changes in the electrical performance of the device due to laser irradiation.
3. C A L I B R A T I O N Absolute measurements require the exact knowledge of the derivative of the refractive index on carrier concentration and temperature. The cartier dependence can be derived from Drudes theory or via Kramers-Kronig-calculations from absorption spectra l':. Unfortunately, the data differs by more than a magnitude. Thus it is not clear whether electrons or holes affect the refractive index more efficiently. As power semiconductor devices are driven under strong injection conditions we are interested in a more generalized value dn/dC = dn/dC, + dn/dCv, where Cn, Cp represents the electron or hole concentration, respectively. Here the uncertainty of literature data amounts to a factor 5. We therefore decided to calibrate this dependence experimentally by means of absorption measurements. The plasma free cartier absorption at our laser wavelength (%=1300 nm) is discussed with good agreement in literature. Theory z as well as experiments u yield identical results within an error bar of 25%. The dependence of the absorption coefficient on carder concentration is linear or can at least be linearized within the range of interest for our application. As our setup allows the simultaneous measurement of deflection signals and absorption, we can determine both the real and the imaginary part of the refractive index. Carrier and temperature contributions to the deflection signal are separated by means of time resolution. Fig. 2 shows typical measurement results for a power diode. Both signals are electrically amplified and normalized to the total intensity of the laser beam.
18 •-" b
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v I
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,
I
.......... Absorption t
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60 80 100 120 Time [ ~ ]
,
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140 160
,
I.
7
86
.o
Figure 2: Temporally resolved deflection and absorption signals measured at a 1600 V buffer diode during a 70 ~ts current pulse (oscillations on the absorption signal arise from electronic amplification).
G. Deboy et al. / Microelectronic Engineering 31 (1996) 299-307
301
The injection of carriers into the bulk of the device is detected by free carrier absorption as well as by beam deflection on a time scale of around 1 las. Both signals show the same temporal behaviour. During the pulse width of 70 ~ts heat is dissipated leading to an additional temperature contribution to the deflection signal. Thus a comparison of the pure carrier contribution with the carrier density profile measured by absorption yields the required calibration of dn/dC. Fig. 3 shows the experimental results of a 1600V-power diode being forward biased by a current load of 250 A/cm 2. The active region of the device has a width of 160 ~tm; the adjacent buffer layer is more than 500 ~tm thick. The absorption results have 3 been transformed into absolute carrier concentrations with 2 the linear absorption O 200 ' ~ " law proposed by Huang et al. 2. His o O approach takes the 100 ~ nonparabolicity of 0 "~ o the silicon bands into e" account. The expe• o Absorption signal 8 rimental values are .~'" Fit curve fitted by a polynom • Deflection signal for better numerical ............ Gradient of fit curve -200 treatment. The gra20 40 60 80 100 120 140 dient of this Vertical position [larn] curve is fitted to experimental deflection signals through Figure 3: Calibration of dn/dC by means of absorption measurements. a calibration factor:
I0
_ 007
d n / d C = - 4.58.10 -21 cm 3 + 16%.
(1)
The experimental uncertainty arises mainly from the measurement of optical parameters as the numerical aperture of the laser beam and the detector response function. Our value differs from the result of Huang et al.2, but is in reasonable agreement with the value of Sorer and Bennett 1.
The dependence of the refractive index on temperature has been calibrated by means of dilatation measurements with a highly sensitive Michelson interferometer4 and, independently, by the calculation of the dissipated heat on the basis of electrically measured voltage and current curves. We used the 1600 V-buffer diode described above at identical current conditions. Fig. 4 shows the profile of the temperature contribution to the deflection signal at the end of a 70 ~s long current pulse.
(7. Deboy et al. / Microelectronic Engineering 31 (1996) 299-307
302
Assuming a homogenous distribution o Deflection signal 1.5 of the gradient of 1 . . . . . . . Fit curve the refractive index Temperature rise 1.2 "~ "¢ \ '0 .......... Dllatatl0n ¢~ along the beam path ~.0.8 120 ~', 0.9 ~ within an interaction length given by the '.el geometrical device o 80-, 0.6 ~ 0.4 diameter, the measured deflection 0.2 40 , '""i ~ 0.3 [.--, (open circles) can be transformed directly into the local tempe00 0 100 200 300 400 500 600 700 rature gradient. It Vertical position [gin] reaches its maximum value at the Figure 4: Temperature and dilatation profile in the bulk of a minimal carrier con1600 V-buffer diode (250 A/cm2). centration (see Fig. 3); due to the low conductivity the dissipation of Joule heat is locally enhanced. Towards the surface and the back side of the device (position 0 and 700 lam, respectively) the temperature gradient decreases to The spatial integral of the local temperature gradient yields the absolute temperature distribution along the vertical axis of the device. With this information the total heat stored in the device can be calculated and compared to the electrical energy, which is the integral of the product of forward voltage drop and current. On the other hand the knowledge of the temperature profile allows the calculation of the infinitesimal dilatation at every position and the integral surface displacement. This result is also shown in Fig. 4. 1.2
,_200 ~%-o ~_~ ~ < # qg, ~"o160 +- % , o"
x
\
.
.
°,?
o.6
o Dilatation
0
1.6
.,.q
~
0.8 0.4 O.~ ,
-500
~..~0 I
-300
,
I
,
I
-100 100 Position [gm]
r
I
300
O0 0 O0 ,
500
Figure 5: Absolute surface displacement measured by Michelson interferometry.
G. Deboy et al. / Microelectronic Engineering 31 0996) 299-307
303
By Michelson interferometry the dilatation profile of the diode along a horizontal surface line has been measured. A maximum displacement in the center of the device of 0.98 nm has been found. Fig. 5 shows the result. The interaction length of the laser beam with the temperature gradient increases with rising vertical position due to heat flow into the silicon embedding the cylindrical diode. The measurement signal is proportional to the product of temperature gradient and interaction length, the dilatation, however, is linear related to the local temperature alone. On the other hand, the stored heat is correlated with the product of temperature and the square of the interaction length. The comparison of both calibration methods allows therefore to overcome the systematic error introduced by the broadening of the temperature profile. Calculating the geometrical mean value of both methods we find dn/dT = 4.05-10-4K -1 + 16%.
(2)
This value is approximately a factor 2 bigger than literature values 5'6'7. We believe that this difference is due to the strong injection conditions, which are typical for power semiconductor applications. The product of cartier concentration is more than 12 orders of magnitude beyond the value of thermal equilibrium. As the temperature dependence of the silicon refractive index is affected by the change of the occupation probability in both the conduction and the valence band it must make a difference whether both bands are occupied or only one. The experiments in references 5-7, however, were performed under thermal equilibrium.
4. RESOLUTION AND SENSITIVITY
The spatial resolution of the system is limited by diffraction of the laser beam. The numerical aperture is adapted to the length of the device to be investigated. With a typical dimension of 4 mm (1200 V/10 A-IGBT), we achieve a focus diameter of 8 ~tm and a beam waist at both side faces of maximum 25 lam. The time resolution is at present 300 ns. The limitation is due to the capacitive load of the detector, which has to be counterbalanced by reducing the bandwidth of the first transimpedance amplifier. The internal m-laser deflection technique allows the detection of gradients of the refractive index down to 5.10s ~tm"1 referred to a device length of 1 mm. The sensitivity increases linear with the interaction length. Thus the detection limit for gradients of the carrier concentration is approximately 1-1013cm3~tmq and for temperature gradients around 0.1 mK/~tm. Fig. 6 shows an experimental example measured near the backside of a 1600 V-buffer diode (vertical position 600 ~tm, see Fig. 4) with 0.5 mm diameter.
304
G. Deboy et al. / Microelectronic Engineering 31 (1996) 299-307
The minimum of the deflection signal at the end of the current pulse (70 ;is) bv--.4 amounts to a tem-5 perature gradient of 0.5 mK lim1, whereas the signal at 600 ~ts indicates a gradient of 0.25mK "~ -15 ~tm1. Due to the difference of the - Peltier cooling -20 coefficients of thermoelectric power s between silicon and --2 00 0 200 400 600 800 aluminium (0.26 Time [;is] eV), the current flow across the interface Figure 6: High sensitivity seperation of different heat sources at a leads to a net cooling rate (Peltier n÷/metal interface (temperature gradient 0.25 mK/~m). cooling) of 6.5.10 -7 W/ttm 2. At the end of the current pulse the system returns to thermal equilibrium. After several 100 ~ts the temperature gradient rises again due to the slow dispersion of Joule heat, which has been dissipated within the active region of the diode (around 500 ~tm distant). As the direction of the temperature gradient is the same, it produces also a deflection of negative sign. The time resolution of our probing technique allows therefore to separate different contributions to the thermal load of the device.
5. E X P E R I M E N T A L RESULTS E
G
?
?
•
. s j
n-
p\
The main interest of our study is the understanding of the internal behaviour of the Insulated Gate Bipolar Transistor (1200 V/10 A-IGBT). Fig. 7 shows a cross section through one of several thousand parallel cells, which form the entire device. An electron current is 220 ~tm driven through a MOS-n-channel formed by a typical gate voltage of 15 V. Holes are injected from a shallow p-layer on the rear side. The IGBT combines thus bipolar and MOS features, leading to facile driving control, low forward voltage drop and high rigidity.
C
We scan with our laser probe the active n-substrate along its thickness of 220 ~tm. The device was switched with an ohmic load versus a relative low battery voltage of 28 V for a time intervall of 70 ~ts, thus ensuring both fast current rise and
Figure 7: Cross section of an IGBT.
G. Deboy et al. I Microelectronic Engineering 31 (1996) 299-307
305
low dynamic losses. Fig. 8 represents 40 ~rn L"' characteristic .......... 110 [am f ~ 150 measurements at sites 40 ~tm from top and rear side, 100 respectively, and at r,¢] the center of the g 50 device. The main con0 tribution near the \\ 1I top side is Joule heat dissipation -5O4o 0 40 80 120 160 within the channel Time ~s] region. As the lateral position of the laser beam is very Figure 8: Internal deflection measurements inside the active substrate of a 1200 V/10 A-IGBT (current pulse 100 A/cm 2, 70 gs). near to the heat source, carrier and temperature contributions have the same rise time and cannot longer be separated by means of time resolution. During turn-off, a steep carrier gradient rises with the build=up of the depletion layer, which spreads from the p-well/n-junction. At the center position and more pronounced near backside steep cartier gradients are observed during turn-on. They arise from the injection of holes from the back side, which tend to decrease towards steady-state. During turn-off the carriers gather within the bulk of the device; the direction of the carrier gradient therefore changes its sign, as can clearly be seen by comparing the two curves at position 40 lam and 180 ~tm, respectively. The temperature contribution at the rear side shows two competing effects. The joule contribution is quite weak due to both low power dissipation in the bulk and a big distance to the channel heat source. The second contribution, which causes a negative temperature gradient, is Peltier heat at the rear pn-junction. The pn-junction acts as a heat sink, whereas the p/metal-junction is a heat source. The net effect is Peltier heat amounting to 2 W for the entire device. This rate is relatively small compared to the Joule heat, which amounts to approximately 35 W, but sufficient to build up a locally inverse temperature gradient. For current pulses longer than 300 ~ts the Peltier contribution disappears within the stronger temperature gradient caused by Joule heating. Besides thermoelectric effects, which are not taken into account, the qualitative features are well described by electrothermal simulation9. The absolute temperature at every position and different time steps can be calculated from a set of deflection curves, if the extremely dynamic carrier contributions are omitted. The steadystate gradient of the carrier concentration is almost constant across the device, as can be seen from the carrier density profile in Fig. 9. 200
306
G. Deboy et al. / Microelectronic Engineering 31 (1996) 299-307
'~ 0.8 O o
0.6
~0.4
The deflection signal therefore includes a constant carrier contribution, which can easily be subtracted. The according temperature rise is shown in Fig. 10.
O O
0
0
The temperature rise on the back side cannot be measured with our technique. 0 ~ ~ I ~ I ~ I ~ I ~ I However, we as0 40 80 120 160 200 Vertical position [gm] sume again, that the device can be deFigure 9: Carrier concentration profile in the active region scribed by adiabatic of the IGBT measured by free carrier absorption boundary conditions during the current pulse. As the Peltier 0.8 contribution does . . . . . . . . . , 160 laS heat and not cool (as ", 110 gs e.g. shown at metal/ ~ ' 0.6 "-~,, . . . . . . . . 70 n÷-semiconductor ini-.--i o ~--" ""-. ............ 40 ItS terfaces) the tem"1:2 , \ - ' - . -. 20 N perature minimum should show a positive rise with time. The absolute temperature has been E--, 0.2 measured at position 110 gm by a multiple Fabry-Perotinterference. The 00 , i , I , I , I , t 40 80 120 160 200 value assigned in Vertical position [grn] Fig. 10 has been met within 0.1 K. After Figure 10: Absolute temperature profile in the active region of turn-off the heat is the IGBT calculated by experimental deflection curves (time steps transferred to the are relative to the start of a 70 gs-current pulse). rear contact. The temperature gradients within the device are substantially lower. The temperature offset of the rear side for the time steps 110 ps and 160 ps has been adjusted in order to meet a cooling of the surface, which is physically reasonable. •~ 0.2
0
Cartier concentration Linear fit curve
G. Deboy et al. / Microelectronic Engineering 31 (1996) 299-307
307
ACKNOWLEDGEMENT
The fruitful discussions with H. Brunner and R. Thalhammer are gratefully acknowledged. A part of this work is supported by a NATO grant (CGR.931091).
REFERENCES
R. Soref and B. Bennett, "Electrooptical effects in silicon", IEEE J.Qu.Elec. QE-23(1), 123 (1987). 2 H. Huang, S. Yee and M. Soma, "Quantum calculations of the change of refractive index due to free carriers in silicon with nonparabolic band structure", J.Appl.Phys. 67(4), 2033 (1990). 3 C. Horwitz and R. Swanson, "The optical (free-carrier) absorption of a hole-electron plasma in silicon", Sol.St.Elec. 23, 1191 (1980). 4 W. Claeys, S. Dilhalre and V. Quintard, "Laser probing of thermal behaviour of electronic components and its application in quality and reliability testing", Microelectronic Engineering 24, 411 (1994). s M. Bertolotti, V. Bogdanov, A. Ferrari, A. Jascow, N. Nazorova, A. Pikhtin and L. Sehirone, "Temperature dependence of the refractive index in semiconductors", J.Opt.Soc.Am.B 7(6), 918 (1990). 6 A.N. Magunov, "Temperature dependence of the refractive index of silicon single-crystal in the 300-700-K range", Opt.Spectrosc. 73(2), 205 (1992). 7 G.E. Jellison and H.H. Burke, "The temperature dependence of the refractive index of silicon at elevated temperatures at several wavelengths", J.Appl.Phys. 60(2), 841 (1986). s T.H. Geballe and G.W. Hull, "Seebeck effect in silicon", Phys.Rev. 98(4), 940 (1955). 9 G. Deboy, H. Brunner, G. S61kner, W. Claeys, S.Dilhaire, V. Quintard and F. Koch, "A contactless analysis scenario for the investigation of the dynamic behaviour of power semiconductors: Internal and external laser probing in comparison with computer simulation", Proc. ESREF, 189, Glasgow 1994.
ELSEVIER
MicroelectronicEngineering31 (1996)299-307
Absolute measurement of transient carrier concentration and temperature gradients in power semiconductor devices by internal IR-laser deflection G. Deboya, G. S61knera, E. Wolfgang" and W. Claeysb aSiemens AG, Corporate Research and Development, Otto-Hahn-Ring 6, D-81739 MOnchen bUniversit6 de Bordeaux I, CPMOH, 351, Cours de la Lib6ration, F-33405 Talence 1. ~TRODUCTION High frequency applications in power electronics require a thorough investigation of the dynamic current distribution and heat dissipation. With recent trends to higher blocking voltage and enhanced current transport capability heat dissipation becomes a critical problem. Besides electrothermal simulation experimental measurements are a necessity for a continuous improvement of the device performance. A new contactless probing technique for the absolute evaluation of carrier density and temperature gradients in the bulk of power semiconductor devices has therefore been developed. This article will focus on methodological aspects and experimental results. 2. MEASUREMENT PRINCIPLE Due to its dependence on free carrier concentration and temperature, the silicon refractive index will vary temporally and spatially during transient switching conditions of the device. The gradient of the refractive index is probed by the deflection of an infrared laser beam within the bulk of the device. The principle is outlined in Fig. 1. The beam is focused through optically polished side faces. A long distance objective transforms its ~Gate Emitter/ . Parallel- internal deflection shift into a parallel shift, which is detected by ~al~~r" a quadrant photo diode within two directions normal to Collector~ the optical axis. The probing technique yields an integral Figure 1: Measurement principle value of the gra-
T
0167-9317/96/$15.00e 1996- ElsevierScienceB.V. All rights reserved. 0167-9317(95)00352-5
SSDI
300
G. Deboy et al. / Microelectronic Engineering 31 (1996) 299-307
dients of temperature and carder concentration along the optical beam path. The distribution along the optical axis can be measured by turning the device by 90 ° and scanning along the horizontal axis. Using a 1300 nm-laser source we can neglect optical carrier generation. The optical power losses due to free cartier absorption are more than six orders of magnitude below the electrically dissipated power. In fact we have never observed any changes in the electrical performance of the device due to laser irradiation.
3. C A L I B R A T I O N Absolute measurements require the exact knowledge of the derivative of the refractive index on carrier concentration and temperature. The cartier dependence can be derived from Drudes theory or via Kramers-Kronig-calculations from absorption spectra l':. Unfortunately, the data differs by more than a magnitude. Thus it is not clear whether electrons or holes affect the refractive index more efficiently. As power semiconductor devices are driven under strong injection conditions we are interested in a more generalized value dn/dC = dn/dC, + dn/dCv, where Cn, Cp represents the electron or hole concentration, respectively. Here the uncertainty of literature data amounts to a factor 5. We therefore decided to calibrate this dependence experimentally by means of absorption measurements. The plasma free cartier absorption at our laser wavelength (%=1300 nm) is discussed with good agreement in literature. Theory z as well as experiments u yield identical results within an error bar of 25%. The dependence of the absorption coefficient on carder concentration is linear or can at least be linearized within the range of interest for our application. As our setup allows the simultaneous measurement of deflection signals and absorption, we can determine both the real and the imaginary part of the refractive index. Carrier and temperature contributions to the deflection signal are separated by means of time resolution. Fig. 2 shows typical measurement results for a power diode. Both signals are electrically amplified and normalized to the total intensity of the laser beam.
18 •-" b
1 0
12
% -2
~
-3
0
-4
-5 ~ -12
v I
-1820 ' 0
,
I
20
,
I
40
,
I
.......... Absorption t
,
I
,
I
60 80 100 120 Time [ ~ ]
,
I
,
-6 I
140 160
,
I.
7
86
.o
Figure 2: Temporally resolved deflection and absorption signals measured at a 1600 V buffer diode during a 70 ~ts current pulse (oscillations on the absorption signal arise from electronic amplification).
G. Deboy et al. / Microelectronic Engineering 31 (1996) 299-307
301
The injection of carriers into the bulk of the device is detected by free carrier absorption as well as by beam deflection on a time scale of around 1 las. Both signals show the same temporal behaviour. During the pulse width of 70 ~ts heat is dissipated leading to an additional temperature contribution to the deflection signal. Thus a comparison of the pure carrier contribution with the carrier density profile measured by absorption yields the required calibration of dn/dC. Fig. 3 shows the experimental results of a 1600V-power diode being forward biased by a current load of 250 A/cm 2. The active region of the device has a width of 160 ~tm; the adjacent buffer layer is more than 500 ~tm thick. The absorption results have 3 been transformed into absolute carrier concentrations with 2 the linear absorption O 200 ' ~ " law proposed by Huang et al. 2. His o O approach takes the 100 ~ nonparabolicity of 0 "~ o the silicon bands into e" account. The expe• o Absorption signal 8 rimental values are .~'" Fit curve fitted by a polynom • Deflection signal for better numerical ............ Gradient of fit curve -200 treatment. The gra20 40 60 80 100 120 140 dient of this Vertical position [larn] curve is fitted to experimental deflection signals through Figure 3: Calibration of dn/dC by means of absorption measurements. a calibration factor:
I0
_ 007
d n / d C = - 4.58.10 -21 cm 3 + 16%.
(1)
The experimental uncertainty arises mainly from the measurement of optical parameters as the numerical aperture of the laser beam and the detector response function. Our value differs from the result of Huang et al.2, but is in reasonable agreement with the value of Sorer and Bennett 1.
The dependence of the refractive index on temperature has been calibrated by means of dilatation measurements with a highly sensitive Michelson interferometer4 and, independently, by the calculation of the dissipated heat on the basis of electrically measured voltage and current curves. We used the 1600 V-buffer diode described above at identical current conditions. Fig. 4 shows the profile of the temperature contribution to the deflection signal at the end of a 70 ~s long current pulse.
(7. Deboy et al. / Microelectronic Engineering 31 (1996) 299-307
302
Assuming a homogenous distribution o Deflection signal 1.5 of the gradient of 1 . . . . . . . Fit curve the refractive index Temperature rise 1.2 "~ "¢ \ '0 .......... Dllatatl0n ¢~ along the beam path ~.0.8 120 ~', 0.9 ~ within an interaction length given by the '.el geometrical device o 80-, 0.6 ~ 0.4 diameter, the measured deflection 0.2 40 , '""i ~ 0.3 [.--, (open circles) can be transformed directly into the local tempe00 0 100 200 300 400 500 600 700 rature gradient. It Vertical position [gin] reaches its maximum value at the Figure 4: Temperature and dilatation profile in the bulk of a minimal carrier con1600 V-buffer diode (250 A/cm2). centration (see Fig. 3); due to the low conductivity the dissipation of Joule heat is locally enhanced. Towards the surface and the back side of the device (position 0 and 700 lam, respectively) the temperature gradient decreases to The spatial integral of the local temperature gradient yields the absolute temperature distribution along the vertical axis of the device. With this information the total heat stored in the device can be calculated and compared to the electrical energy, which is the integral of the product of forward voltage drop and current. On the other hand the knowledge of the temperature profile allows the calculation of the infinitesimal dilatation at every position and the integral surface displacement. This result is also shown in Fig. 4. 1.2
,_200 ~%-o ~_~ ~ < # qg, ~"o160 +- % , o"
x
\
.
.
°,?
o.6
o Dilatation
0
1.6
.,.q
~
0.8 0.4 O.~ ,
-500
~..~0 I
-300
,
I
,
I
-100 100 Position [gm]
r
I
300
O0 0 O0 ,
500
Figure 5: Absolute surface displacement measured by Michelson interferometry.
G. Deboy et al. / Microelectronic Engineering 31 0996) 299-307
303
By Michelson interferometry the dilatation profile of the diode along a horizontal surface line has been measured. A maximum displacement in the center of the device of 0.98 nm has been found. Fig. 5 shows the result. The interaction length of the laser beam with the temperature gradient increases with rising vertical position due to heat flow into the silicon embedding the cylindrical diode. The measurement signal is proportional to the product of temperature gradient and interaction length, the dilatation, however, is linear related to the local temperature alone. On the other hand, the stored heat is correlated with the product of temperature and the square of the interaction length. The comparison of both calibration methods allows therefore to overcome the systematic error introduced by the broadening of the temperature profile. Calculating the geometrical mean value of both methods we find dn/dT = 4.05-10-4K -1 + 16%.
(2)
This value is approximately a factor 2 bigger than literature values 5'6'7. We believe that this difference is due to the strong injection conditions, which are typical for power semiconductor applications. The product of cartier concentration is more than 12 orders of magnitude beyond the value of thermal equilibrium. As the temperature dependence of the silicon refractive index is affected by the change of the occupation probability in both the conduction and the valence band it must make a difference whether both bands are occupied or only one. The experiments in references 5-7, however, were performed under thermal equilibrium.
4. RESOLUTION AND SENSITIVITY
The spatial resolution of the system is limited by diffraction of the laser beam. The numerical aperture is adapted to the length of the device to be investigated. With a typical dimension of 4 mm (1200 V/10 A-IGBT), we achieve a focus diameter of 8 ~tm and a beam waist at both side faces of maximum 25 lam. The time resolution is at present 300 ns. The limitation is due to the capacitive load of the detector, which has to be counterbalanced by reducing the bandwidth of the first transimpedance amplifier. The internal m-laser deflection technique allows the detection of gradients of the refractive index down to 5.10s ~tm"1 referred to a device length of 1 mm. The sensitivity increases linear with the interaction length. Thus the detection limit for gradients of the carrier concentration is approximately 1-1013cm3~tmq and for temperature gradients around 0.1 mK/~tm. Fig. 6 shows an experimental example measured near the backside of a 1600 V-buffer diode (vertical position 600 ~tm, see Fig. 4) with 0.5 mm diameter.
304
G. Deboy et al. / Microelectronic Engineering 31 (1996) 299-307
The minimum of the deflection signal at the end of the current pulse (70 ;is) bv--.4 amounts to a tem-5 perature gradient of 0.5 mK lim1, whereas the signal at 600 ~ts indicates a gradient of 0.25mK "~ -15 ~tm1. Due to the difference of the - Peltier cooling -20 coefficients of thermoelectric power s between silicon and --2 00 0 200 400 600 800 aluminium (0.26 Time [;is] eV), the current flow across the interface Figure 6: High sensitivity seperation of different heat sources at a leads to a net cooling rate (Peltier n÷/metal interface (temperature gradient 0.25 mK/~m). cooling) of 6.5.10 -7 W/ttm 2. At the end of the current pulse the system returns to thermal equilibrium. After several 100 ~ts the temperature gradient rises again due to the slow dispersion of Joule heat, which has been dissipated within the active region of the diode (around 500 ~tm distant). As the direction of the temperature gradient is the same, it produces also a deflection of negative sign. The time resolution of our probing technique allows therefore to separate different contributions to the thermal load of the device.
5. E X P E R I M E N T A L RESULTS E
G
?
?
•
. s j
n-
p\
The main interest of our study is the understanding of the internal behaviour of the Insulated Gate Bipolar Transistor (1200 V/10 A-IGBT). Fig. 7 shows a cross section through one of several thousand parallel cells, which form the entire device. An electron current is 220 ~tm driven through a MOS-n-channel formed by a typical gate voltage of 15 V. Holes are injected from a shallow p-layer on the rear side. The IGBT combines thus bipolar and MOS features, leading to facile driving control, low forward voltage drop and high rigidity.
C
We scan with our laser probe the active n-substrate along its thickness of 220 ~tm. The device was switched with an ohmic load versus a relative low battery voltage of 28 V for a time intervall of 70 ~ts, thus ensuring both fast current rise and
Figure 7: Cross section of an IGBT.
G. Deboy et al. I Microelectronic Engineering 31 (1996) 299-307
305
low dynamic losses. Fig. 8 represents 40 ~rn L"' characteristic .......... 110 [am f ~ 150 measurements at sites 40 ~tm from top and rear side, 100 respectively, and at r,¢] the center of the g 50 device. The main con0 tribution near the \\ 1I top side is Joule heat dissipation -5O4o 0 40 80 120 160 within the channel Time ~s] region. As the lateral position of the laser beam is very Figure 8: Internal deflection measurements inside the active substrate of a 1200 V/10 A-IGBT (current pulse 100 A/cm 2, 70 gs). near to the heat source, carrier and temperature contributions have the same rise time and cannot longer be separated by means of time resolution. During turn-off, a steep carrier gradient rises with the build=up of the depletion layer, which spreads from the p-well/n-junction. At the center position and more pronounced near backside steep cartier gradients are observed during turn-on. They arise from the injection of holes from the back side, which tend to decrease towards steady-state. During turn-off the carriers gather within the bulk of the device; the direction of the carrier gradient therefore changes its sign, as can clearly be seen by comparing the two curves at position 40 lam and 180 ~tm, respectively. The temperature contribution at the rear side shows two competing effects. The joule contribution is quite weak due to both low power dissipation in the bulk and a big distance to the channel heat source. The second contribution, which causes a negative temperature gradient, is Peltier heat at the rear pn-junction. The pn-junction acts as a heat sink, whereas the p/metal-junction is a heat source. The net effect is Peltier heat amounting to 2 W for the entire device. This rate is relatively small compared to the Joule heat, which amounts to approximately 35 W, but sufficient to build up a locally inverse temperature gradient. For current pulses longer than 300 ~ts the Peltier contribution disappears within the stronger temperature gradient caused by Joule heating. Besides thermoelectric effects, which are not taken into account, the qualitative features are well described by electrothermal simulation9. The absolute temperature at every position and different time steps can be calculated from a set of deflection curves, if the extremely dynamic carrier contributions are omitted. The steadystate gradient of the carrier concentration is almost constant across the device, as can be seen from the carrier density profile in Fig. 9. 200
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G. Deboy et al. / Microelectronic Engineering 31 (1996) 299-307
'~ 0.8 O o
0.6
~0.4
The deflection signal therefore includes a constant carrier contribution, which can easily be subtracted. The according temperature rise is shown in Fig. 10.
O O
0
0
The temperature rise on the back side cannot be measured with our technique. 0 ~ ~ I ~ I ~ I ~ I ~ I However, we as0 40 80 120 160 200 Vertical position [gm] sume again, that the device can be deFigure 9: Carrier concentration profile in the active region scribed by adiabatic of the IGBT measured by free carrier absorption boundary conditions during the current pulse. As the Peltier 0.8 contribution does . . . . . . . . . , 160 laS heat and not cool (as ", 110 gs e.g. shown at metal/ ~ ' 0.6 "-~,, . . . . . . . . 70 n÷-semiconductor ini-.--i o ~--" ""-. ............ 40 ItS terfaces) the tem"1:2 , \ - ' - . -. 20 N perature minimum should show a positive rise with time. The absolute temperature has been E--, 0.2 measured at position 110 gm by a multiple Fabry-Perotinterference. The 00 , i , I , I , I , t 40 80 120 160 200 value assigned in Vertical position [grn] Fig. 10 has been met within 0.1 K. After Figure 10: Absolute temperature profile in the active region of turn-off the heat is the IGBT calculated by experimental deflection curves (time steps transferred to the are relative to the start of a 70 gs-current pulse). rear contact. The temperature gradients within the device are substantially lower. The temperature offset of the rear side for the time steps 110 ps and 160 ps has been adjusted in order to meet a cooling of the surface, which is physically reasonable. •~ 0.2
0
Cartier concentration Linear fit curve
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ACKNOWLEDGEMENT
The fruitful discussions with H. Brunner and R. Thalhammer are gratefully acknowledged. A part of this work is supported by a NATO grant (CGR.931091).
REFERENCES
R. Soref and B. Bennett, "Electrooptical effects in silicon", IEEE J.Qu.Elec. QE-23(1), 123 (1987). 2 H. Huang, S. Yee and M. Soma, "Quantum calculations of the change of refractive index due to free carriers in silicon with nonparabolic band structure", J.Appl.Phys. 67(4), 2033 (1990). 3 C. Horwitz and R. Swanson, "The optical (free-carrier) absorption of a hole-electron plasma in silicon", Sol.St.Elec. 23, 1191 (1980). 4 W. Claeys, S. Dilhalre and V. Quintard, "Laser probing of thermal behaviour of electronic components and its application in quality and reliability testing", Microelectronic Engineering 24, 411 (1994). s M. Bertolotti, V. Bogdanov, A. Ferrari, A. Jascow, N. Nazorova, A. Pikhtin and L. Sehirone, "Temperature dependence of the refractive index in semiconductors", J.Opt.Soc.Am.B 7(6), 918 (1990). 6 A.N. Magunov, "Temperature dependence of the refractive index of silicon single-crystal in the 300-700-K range", Opt.Spectrosc. 73(2), 205 (1992). 7 G.E. Jellison and H.H. Burke, "The temperature dependence of the refractive index of silicon at elevated temperatures at several wavelengths", J.Appl.Phys. 60(2), 841 (1986). s T.H. Geballe and G.W. Hull, "Seebeck effect in silicon", Phys.Rev. 98(4), 940 (1955). 9 G. Deboy, H. Brunner, G. S61kner, W. Claeys, S.Dilhaire, V. Quintard and F. Koch, "A contactless analysis scenario for the investigation of the dynamic behaviour of power semiconductors: Internal and external laser probing in comparison with computer simulation", Proc. ESREF, 189, Glasgow 1994.