- Email: [email protected]
Heat-flux sensor to support transient thermal characterisation of IC packages
Sensors and Actuators A 116 (2004) 284–292
Heat-flux sensor to support transient thermal characterisation of IC packages M. Rencz a,b,∗ , E. Kollár a , V. Székely a b
a Budapest University of Technology, Hungary MicReD Ltd., Research, Gulyas u 27, H1112 Budapest, Hungary
Received 4 December 2003; received in revised form 23 April 2004; accepted 3 May 2004 Available online 10 June 2004
Abstract In this paper the idea and the analysis of a microelectronic heat-flux sensor, designed for fast transient measurements in package characterisation is presented. The sensor was fabricated in a prototype version, and the measured results prove the validity of the design concepts. The sensitivity, temperature dependence and resolution values are calculated and evaluated. The questions of calibration are discussed. Three application examples are presented. In the first two it is demonstrated, how the sensor may support compact model generation of packages by measuring the time dependence of the heat flux leaving the package on a certain surface, and by enabling the direct measurement of the thermal transfer admittance parameters of packages. In the third example the sensor is realised in array form, providing the possibility to obtain the coarse heat flux map of a package surface. © 2004 Elsevier B.V. All rights reserved. Keywords: Heat-flux sensor; Sensor array; Packaging qualification; Heat-flow sensor
1. Introduction In the package thermal verification and model generation practice it is frequently needed to know the exact value of the time dependence of the heat flux crossing a certain surface. For these purposes such a heat-flow sensor is needed that is representing a sufficiently small thermal resistance and thermal capacitance, not to disturb considerably the heat flow in the usual microelectronic structures. In the normal practice of the transient thermal measurement of microelectronic packages power is applied to the chip inside the package and the temperature is measured in various locations, e.g. on the chip itself, on the top or bottom surface of the package, etc. Such measurements may serve for various testing purposes, and/or the measured data may provide the base of dynamic compact model generation. For the thermal characterisation it is advantageous to know not only the temperature values, but the heat fluxes (the thermal “currents”) as well. This may be especially useful in case of model generation, since the more independent data are provided, the more accurate thermal model may be
∗ Corresponding author. Tel.: +36-1-463-2727; fax: +36-1-463-2973. E-mail addresses: [email protected], [email protected] (M. Rencz).
0924-4247/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2004.05.002
generated. In case of simple Rth measurements knowing the heat fluxes is equally advantageous: it can be measured what proportion of the dissipated power is leaving via the top surface, what proportion is flowing through the bottom surface, etc. Heat-flow sensors are represented broadly in the scientific literature, a good summary and survey of the various types of heat-flow sensors can be found in [1]. A variety of techniques for measuring convective, conductive and radiative heat transfer are described there, but the targeted applications, consequently the sensor parameters, are different from what we need for package surface, in situ transient measurements. The sensor described recently in [2] is designated to measure the heat transfer of the far surface of a wall by measuring the temperature on an accessible boundary. It is using active heater and passive sensor elements that are mounted close to each other. The heater is controlled to have the same temperature as the passive sensor that is cooled through convection. From the energy balance the heat flow can be calculated if the temperatures and the heat transfer coefficients are known. This is not the case in package characterisation. The heat-flow sensor of Leclercq and Thery [3] measures the heat flux by determining the temperature gradient over a tangent plane to the heat flux surface. Physical asymmetries are used to deflect the heat flux lines and generate a
M. Rencz et al. / Sensors and Actuators A 116 (2004) 284–292
Nomenclature A cv Cth f g I, i k L P P, p q rms Re Rth S S0 T U, u Ug yij
area, surface (m2 ) volumetric heat capacity (W s/K m3 ) thermal capacitance (W s/K) frequency, bandwidth (1/s) conductance (1/) current (A) the Boltzmann constant (V A s/K) length (m) power (W) heat current, heat rate (W) heat flux (W/m2 ) root mean square the electrical resistance () thermal resistance (K/W) the Seebeck coefficient (V/K) Seebeck coefficient at T0 reference temperature (V/K) temperature (K, ◦ C) voltage (V) electromotive force (V) admittance parameters, thermal admittance parameters (1/)(W/K)
Greek letters αS temperature coefficient of the Seebeck coefficient (1/◦ C, 1/K) αγ temperature coefficient of the sensitivity (1/◦ C, 1/K) temperature coefficient of the thermal αλ conductivity (1/◦ C, 1/K) γ sensitivity (V/W) γ0 sensitivity at T0 reference temperature (V/W) λ thermal conductivity (W/m K) λ0 thermal conductivity at T0 reference temperature (W/m K) σ electrical conductivity (1/)
temperature gradient over a planar thermopile. The structure is very complex and represents a considerable thermal resistance. There are numerous heat-flow sensors in the market that can be used for package thermal measurements [4–6] are only some of them. A common feature of these is, that they were designed to support static measurements, so their Rth values are relatively low, but the Cth values that they represent are either even not provided, or prohibitively high. This means that we can not use them in fast thermal transient measurements without considerably altering the transient behaviour of the thermal system where they are used. For these reasons we have decided to construct a heat-flow sensor that is targeted for measuring in situ conductive heat transfer via package surfaces, representing sufficiently small
285
thermal resistance and thermal capacitance values, not disturbing significantly the transient behaviour of the heat-flow path. Below we present the idea of the new heat-flow sensor, discuss some design issues, such as material selection, etc., and calculate the most important sensor parameters. To check the feasibility of the sensor we have fabricated some pre-prototype versions of the sensor in the laboratories of the Department of Electron Devices of the Budapest University of Technology and Economics, and verified with measurements sensor operation and the most important parameters. At the end of the paper we present some typical application examples.
2. The proposed structure For the heat-flux sensor we have designed a temperature gradient based sensor [1], where the heat flux is measured by the temperature difference along the way of the heat streaming. The structure we propose is shown in Fig. 1. The sensor consists of a thin silicon layer with homogeneous doping concentration metalised on both surfaces. The heat current flows through this sandwich structure, resulting in a very small temperature drop between the upper and the lower surfaces. Since both sides of the silicon die are covered by metal, these form two thermocouples with the silicon, connected in anti-series. The output voltage of the two thermocouples is proportional to the temperature difference between the two sides, that is proportional to the heat flux [6]. In order to assure a well-defined surface area, where the heat flux is measured, insulating SiO2 between the metal and the silicon limits the sensor area. Where the oxide separates and insulates the metal from the silicon the structure does not act as a heat-flux sensor any further. This part may be used for contacting the two metal surfaces. The left hand side output wire in Fig. 1 is contacting the upper metal, while the right hand side contact wire is contacting the bottom metal through the short circuit of the thin (less than 0.5 mm) silicon layer, since outside the sensing area there is no voltage difference between the two metals. This solution was needed to provide a flat bottom surface to enable good contact with the underlying, e.g. cold-plate surface.
Fig. 1. The proposed structure of the heat-flux sensor. The figure is not to scale.
286
M. Rencz et al. / Sensors and Actuators A 116 (2004) 284–292
Let us suppose first, that the heat flux, that is power, is crossing the chip exactly on this area, with uniform lateral distribution. The thermal resistance inserted into the heat-flow path is given by Fig. 2. Cross-sectional view of a targeted application. The figure is not to scale.
A suggested application is shown in Fig. 2. The heat-flux sensor is electrically isolated but thermally contacted via the applied heat conductive ceramics, while measuring the heat flow through the package bottom surface towards the heat sinking cold plate. As it is shown in Fig. 2 the flat bottom surface of the heat-flux sensor enables good and well reproducible contact with the cold plate.
3. Design concepts and calculation of the main sensor parameters In the design of the heat-flux sensor the selection of the materials is critical for the performance of the device. This strongly influences the two main parameters of the sensor: the sensitivity and the maximal operating speed, that is, the cut-off frequency of the operation. Two main issues have to be kept in mind in the selection of the materials as follows [7]: (i) The material of the die has to be a good thermal conductor, in order to reduce the temperature drop across it. (ii) The Seebeck coefficient of the contacts has to be as high as possible, assuring appropriate sensitivity. Silicon is a good candidate because of its high thermal conductivity and the good (∼1 mV/K) Seebeck emf of the Si–Al contacts. Since the Seebeck emf is increasing with decreasing doping level of the silicon, medium or low doping material has to be used [8]. The Si–Al contacts should be of non-rectifying nature—this is why p-doped silicon was selected as the base material [9]. 3.1. Calculation of the sensitivity To construct a good heat-flow sensor the main design principle must be to maximise the sensitivity of the sensor. In our case the sensitivity is maximal if the output voltage is maximal for the unit heat flux. Let us calculate the value of the sensitivity. The principal geometric sizes of the structure are shown in Fig. 3. The active area A is the area of the contact window on the oxide.
Rth =
1L λA
(1)
where λ is the thermal conductivity of the silicon and L the thickness of the structure. If P power is flowing across the silicon the temperature difference between the two sides is PRth and the output voltage is Uout = SPRth = P
SL λA
(2)
where S is the Seebeck coefficient. This means that the sensitivity (output voltage for unity power flow) is γ=
SL λA
(3)
In case of L = 0.5 mm, A = 1 cm2 , λ = 100 W/m K, S = 1 mV/K this sensitivity value is 0.05 mV/W which is a well measurable value. The insertion resistance of the probe is only about 0.05 K/W, this is in most of the cases negligible. In real circumstances the heat flow is generally not uniform. Inserting the heat-flow sensor between the bottom area of a package and the heat sink we have to expect uneven distribution of heat flux crossing the sensor. It is not straightforward to answer the question, of what is measured in this case, and how to interpret the output voltage of the sensor? The answer is however simple and pleasant: the output voltage is proportional to the total heat-flow crossing the contacted A area of the die, and independent of the lateral distribution of the heat-flow. This can be proven as follows. Let us suppose p(x, y) uneven heat-flux distribution on the sensor surface and examine how this effects the output voltage of the sensor. The considered structure is shown in Fig. 4a. The sensor material parameters, the λ thermal conductivity, σ electrical conductivity and the S Seebeck coefficient are considered to be constant along the A active sensor area. The metal contacts to both sizes of the sensor are considered to behave as ideal conductors in the lateral direction. The sensor plate is thin enough to allow neglecting any lateral heat-flow. An elementary section of the structure with dA area, perpendicular to the heat flow is considered. Caused by the p(x, y) dA heat rate, a temperature difference develops between the two sides of the elementary column of the silicon as follows: T = p(x, y) dA
L L = p(x, y) λ dA λ
(4)
As a result of the Seebeck effect, this temperature difference generates an Ug electromotive force: Fig. 3. The structure of the sensor.
Ug = Sp(x, y)
L λ
(5)
M. Rencz et al. / Sensors and Actuators A 116 (2004) 284–292
287
3.2. Calculation of the cut-off frequency of the sensor operation Considering that in the targeted application the heat-flow sensor is inserted between the investigated package and a (quasi ideal) heat sink, the cut-off frequency is calculated for this case. To calculate the cut-off frequency we consider the heat sensor as an uniform, distributed thermal RC line, short-circuited by the heat sink at the far end. For such cases according to [11] the first pole of the impedance, giving the cut-off frequency of the device is at the frequency of f =
π 1 8 Rth Cth
(11)
where Rth is the insertion thermal resistance calculated by (1) and Cth the thermal capacitance given by Cth = cv AL Fig. 4. The considered sensor structure with the electrical model of the parallel connected sections.
The electrical conductance of the dA section is dA g=σ L
(6)
This means that the electrical model of the dA section is a voltage source, with finite serial inner resistance (Thévenin model) as it is shown in Fig. 4a. As the whole structure consists of many dA sections, many such model networks are to be connected in parallel in order to describe the complete sensor. The calculations, however, will be easier if we substitute this Thévenin model by its Norton equivalent. According to the textbook transformation of the electrical network theory [10] the current value of this current source is σ L dA Ig = Ug g = Sp(x, y) σ = S p(x, y) dA (7) λ L λ while the inner conductance is the same as for the Thévenin model. Finally, we connect in parallel the elementary Norton models, see Fig. 4b. The resulting network is a Norton model as well, see Fig. 4c, with the current of σ Ires = Ig = S p(x, y) dA (8) λ A A and with the inner conductance of σ σ g= dA = A. gres = L L A A The open-circuit voltage of this resulting network is Ires SL SL = p(x, y) dA = P Uout = gres λA λA A
(9)
(10)
This means that Eq. (2) holds independently from the heat-flow distribution in the window of A.
(12)
Using the geometrical data introduced above and cv = 1.67 × 106 W s/m3 K for the volumetric heat capacitance of silicon the following results can be obtained: Cth = 0.083 W s/K and f = 95 Hz. This means that the sensor is capable to follow time variations up to some 10 Hz. 3.3. Calculation of the sensor resolution The minimum of the perceptible heat-flux value is limited by the noise. The sources of noise are the Johnson or thermal noise of the sensor itself and the noise of the sensor amplifier. The rms noise voltage of the sensing may be written as: unoise = usensnoise + uampnoise
(13)
where uampnoise is the rms noise generated by the amplifier. usensnoise is the rms value of the Johnson noise of the sensor, given by usensnoise = 4kTRe fm , where k = 1.38 × 10−23 V A s/K is the Boltzmann constant, T the absolute temperature, Re the electrical resistance of the sensor and f the bandwidth of the measurement system. The magnitude of this noise may be calculated as follows. The resistivity of the considered material is 5 cm, the geometrical sizes are the same as above. The calculated electrical resistance is Re = 0.25 . Considering an f = 25 Hz bandwidth, the RMS noise voltage is 0.325×10−3 V. Since this is really negligible, it can be concluded that the noise of the sensor amplifier will certainly dominate the own noise of the sensor. Using a low-noise amplifier with an equiva√ lent input noise of 1 nV/ Hz the input noise is u RMS = 5 × 10−3 V. Calculating with the 50 V/W sensitivity of the device, this corresponds to 0.1 mW heat-flow rate. This is the (approximate) ultimate limit of the resolution of the sensor.
288
M. Rencz et al. / Sensors and Actuators A 116 (2004) 284–292
4. Calculation of the temperature dependence of the sensitivity As long as the parameters in Eq. (3) may be considered constant, the γ sensitivity value is constant. This means that the sensor characteristic is linear and independent from the temperature. In Eq. (3) however all the constants do have a certain temperature dependence. Since the coefficient of the thermal expansion for silicon is three orders of magnitude smaller that the coefficients of the temperature dependence of the Seebeck coefficient and the thermal conductivity, only this latter two are to be considered in the calculation of the temperature dependence of the sensitivity value. The temperature dependence of the sensitivity may be obtained by calculating the derivative of Eq. (3) versus temperature. Let us approximate the temperature dependence of the material parameters with the following equations: λ = λ0 (1 − αλ (T − T0 ))
(14)
and S = S0 (1 − αS (T − T0 ))
(15)
where λo and S0 are the thermal conductivity and the Seebeck coefficient values at the T0 reference temperature, and αλ and αS the coefficients of their temperature dependence. In this case the temperature dependence of the sensitivity is obtained in a form very similar to Eqs. (14) and (15): γ = γ0 (1 − αγ (T − T0 ))
5. Calibration and experimental results In order to prove the feasibility of such a heat-flow sensor a prototype version was produced to facilitate experimental investigations. The applied substrate was lightly doped p-type, homogeneous, single-crystal silicon, with about 5 cm electrical resistance. The thickness of the die was 340 m. The area of the contact window was A = 1 cm × 1 cm. The Seebeck coefficient is S = 1.25 mV/K for the given doping level (see 7). The expected sensitivity, calculated with Eq. (3) is about 40 V/W. In the first step of investigations the sensor was calibrated. Fig. 5 shows the schematic measurement arrangement. The heat-flow in the structure is maintained by a transistor, placed on the top of the structure. The dissipation of the transistor is known from the known transistor current and voltage values. The heat-flow sensor is mounted between the two copper jaws. In this structure the heat flows entirely in the copper jaws from the transistor towards the cold plate, through the heat-flow sensor. This was verified by 3D thermal simulation, with the help of the SUNRED thermal solver [12]. The simulated results are shown in Fig. 6, demonstrating that with the selected materials, the entire well-determined amount of heat, generated by the transistor, flows across the sensor, if the transistor is isolated upwards.
(16)
where γ 0 is the sensitivity value of the sensor at the T0 reference temperature and αγ the coefficient of the temperature dependence of the sensitivity value. After substituting all the temperature derivatives αγ = αλ − αS .
(17)
may be obtained. All the values in Eq. (17) are slightly temperature dependent. In a limited range however, e.g. in the range between 10 and 70 ◦ C we may calculate with the following average values for silicon:
Fig. 5. Experimental arrangement to determine the sensitivity of the heat-flux sensor. The structure is not to scale.
αλ = 0.004 αS = 0.002 that according to Eq. (17) gives αγ = 0.002. This is a conveniently small value, showing half as much temperature dependence than that of the thermal conductivity is the silicon material. This is indicating that the heat-flow sensor operation is fairly independent from the temperature. Since during the measurements where the cold side of the sensor is always on a heat sink surface, the temperature of the sensor is known. Thus we can carry out the necessary correction in the sensitivity with the αγ value, eliminating the effects of the nonlinearities of the thermal parameters.
Fig. 6. Simulated heat flow in the (to scale) structure of Fig. 5. The simulation shows practically no heat loss towards the surrounding air and a negligible heat loss upwards.
M. Rencz et al. / Sensors and Actuators A 116 (2004) 284–292
289
devices fabricated in the same party, we may assume that it is enough to calibrate one sensor only for a given party of fabrication. The calibrated sensor has to be exactly of the size of the calibrating device faces, and the sensitivity of any-size device may be calculated from the calibrated device by a simple multiplication with the geometrical ratios as Ssensor = Scalibrated
Fig. 7. The measured heat-flux versus sensor voltage diagram.
In the calibration and sensitivity measurement the power of the transistor was increased stepwise and the steady state output voltage of the sensor was measured. The results are plotted in Fig. 7. The measured sensitivity is 41–42.5 V/W, in good agreement with the calculated value. The linearity of the sensor in the investigated range is very good. The two curves correspond to measurements on the same sample but the arrangement was dismounted/mounted between the two measurements. The difference indicates that the measurement is sensitive to the perfection of the mounting. The presented way of sensor calibration is accurate only if the faces of the copper are not larger than the sensing area of the sensor. Considering however that our sensor is fabricated with silicon micro-technology, and the material parameter values in the silicon technology are fairly constant for the
sensor
Acalibrated sensor Asensor
(18)
In the second experiment heat-flow transients were recorded with the help of the investigated sensor. The T3Ster [13] thermal tester was used to record simultaneously the transient temperature of the transistor and the transient heat-flow on the sensor. The experimental arrangement is the same as in the steady state case. Since the output voltage of the sensor is relatively low, a preamplifier was used, with Av = 100 V gain. The noise was suppressed with a filter of 8 Hz cut-off frequency. The results are plotted in Fig. 8. It is visible on the figure that the internal temperature of the transistor begins to rise at about 0.1 ms but the heat streaming reaches the sensor with a delay of about 0.2 s.
6. Application perspectives This new thin heat-flux sensor offers a broad range of possible applications. The targeted field of use was package characterisation, especially in order to determine the model parameter values of the dynamic compact models. Three proposed fields of application are outlined below. However all the three presented applications are in connection with package thermal characterisation, we think that
Fig. 8. Step-function responses (transistor temperature and sensor output voltage).
290
M. Rencz et al. / Sensors and Actuators A 116 (2004) 284–292
where yij are the admittance parameters, p the heat current and t the temperature. The short circuit at the heat sink side is equivalent with t2 = 0. p1 is the excitation and t1 is the chip temperature. The out-streaming flux p2 can be measured by using the heat-flux sensor. With Eq. (19) the y11 and y21 admittance values may be determined directly: p1 p2 p2 (20) and y21 = = y11 y11 = t1 t1 p1
Fig. 9. Measurement of partial heat-fluxes.
the utility of the presented sensor is much broader. Especially broad applicability is expected for the sensor matrix arrangement realisation that enables even heat flux mapping.
This way the direct measurement of a transfer thermal admittance value became possible. 6.3. Heat flux mapping
6.1. Measurement of heat-flux partitioning To measure what ratio of the heat is leaving the package via the cooling mount and what ratio is moving towards the board this new thin heat-flow sensor may be used advantageously. Let us examine as an example the arrangement of Fig. 9. An IC is soldered into the printed wiring board. The top surface of the package is equipped with a cooling mount. We wish to measure what percentage of the dissipated power leaves the package via the cooling mount and what is the percentage that passes through the PWB. Inserting the heat-flux sensor into the indicated interface the power leaving upwards can be easily measured. It is supposed that the rest of the power is leaving via the PWB. 6.2. Measurement of transfer thermal admittance values The usual dynamic measurement methods drive the chip in the package with a certain power and measure the temperature response of the same chip. This method provides only the one-port thermal impedance or admittance of the package, see Fig. 10. If we intended to measure transfer parameters the heat-flux or temperature at the heat-sink side of the package has to be measured. To express more precisely: either the heat-flux on the thermally short-circuited heat-sink side or the temperature on the thermally open or floating heat-sink side has to be measured. Obviously the first case is closer to the real operating conditions. This first condition can be realised with the help of the heat-flow sensor, which is suitable to be inserted between the package and the “thermal short circuit” cold plate. The two-port equations of the model can be written as follows: p1 = y11 t1 + y12 t2 ,
p2 = y21 t1 + y22 t2
Fig. 10. The two-port model of a package on a cold plate.
A main advantage of this sensor technology is that with independent sensor patches on the surface the distribution of the heat flux on a certain surface may be also very easily measured. The applied silicon technology enables the realisation of a fine structure of the metal layers on the silicon surface. If we realise a matrix of uniform sensors on the surface, from the distribution of the output signals of the sensors the heat-flow map of the examined surface is obtained. Already a two sensors arrangement may be useful which is capable to measure separately the heat-flux at the “top centre” and “top periphery” since these data can be applied directly to the identification of model parameters for multi-port dc thermal package models. To verify the feasibility of the idea a 3 × 3 sensor array has been realised in our laboratories. An array of 6 × 7 sensors has been fabricated recently as well. Results with this enhanced resolution variant will be presented in a separate paper. The complexity of the structure and the line widths were determined by our very limited in-house masking capabilities. In Fig. 11 the layout of the 3 × 3 sensor matrix array is presented. The sensors are the larger rectangles in the upper three lines of the chip. The smaller rectangles in the bottom lines are the contact pads. These are outside the sensor area,
(19)
Fig. 11. Heat-flux sensor matrix to measure flux distribution through a surface.
M. Rencz et al. / Sensors and Actuators A 116 (2004) 284–292
Fig. 12. Measuring the heat flux distribution through a package surface.
291
The temperature rise of the junction together with some of the measured transient heat flux curves as a result of applying a 10 W dissipation step on the chip are presented in Fig. 14. Note, that it is the output signal of the S22 sensor that follows first the heating curve of the transistor junction, and the absolute value of the heat-flow through this sensor is considerably higher than the heat flow perceived by the farther sensors. This experiment proves the idea that with the help of such array-sensors the distribution of the heat flow across a certain area may be conveniently measured. It also demonstrates that the sensors are fast enough to detect rapid changes in the heat flow, as expected from the calculations. 7. Conclusions
Fig. 13. The numbering of the sensors under the measured BD245 transistor. The chip in the package is outlined with dashed line.
not disturbing the measurements. If the connecting wires in the sensing surface are thin enough the flux perceived by them can be negligible. The prototype version of this sensor matrix was used to measure the heat flux through a transistor package surface in the arrangement presented in Fig. 12 [14]. Fig. 13 shows the numbering of the different sensors in the matrix arrangement of Fig. 12. The dissipating area is the chip in the package, the approximate location is outlined with dashed line in the figure.
Encouraging experiments have been accomplished in order to produce a heat-flow sensor, suitable for the experimental thermal investigation of IC packages or other microelectronic structures, both in steady state and transient case. The measured results show the appropriateness of the presented design concept, and prove the feasibility of the idea. The sensors have linear characteristics in a broad temperature range. A possible way for the calibration is presented, the calibration is fast and simple. When the sensors are fabricated in a large number with standard silicon technology it is expected that most of the devices will not even need individual calibration. The presented micro-sensors are applicable to determine experimentally the partitioning of the heat-flow between several heat streaming paths, or for the verification of the distribution of the heat flow on larger surfaces. The sensor can be used also for the direct measurement of thermal transfer admittance values for package thermal characterisation. By realising an array of such sensors with the same technological steps we can easily measure the heat flux map of any flat surface, providing a further broad field of applicability of the presented heat-flux sensors. The demonstrated features candidate the sensor an invaluable verification tool in the compact thermal model generation of packages or other microelectronic subsystems. Acknowledgements The authors are indebted to A. Poppe and G. Farkas for the helpful discussions, to J. Mizsei, S. Török, M. Ádám and G. Végh for the technical assistance. This work was partially supported by the PROFIT IST-1999-12529 project of the EU, and by the 2/018/NKFP2001 INFOTERM projects of the Hungarian Government.
References Fig. 14. Heating curves measured on the different sensors. The numbering refers to Fig. 13.
[1] K. Azar (Ed.), Thermal Measurements in Electronic Cooling, CRC Press, Boca Raton, 1997.
292
M. Rencz et al. / Sensors and Actuators A 116 (2004) 284–292
[2] A. Saidi, J. Kim, Heat-flux sensor with minimal impact on boundary conditions, in: Proceedings of the ASME National Heat Transfer Conference, Las Vegas, NV, July 21–23, 2003, p. 40567. [3] D. Leclercq, P. Thery, Apparatus for simultaneous temperature and heat flux measurements under transient conditions, Rev. Sci. Instrum. 54 (1983) 374–380. [4] http://www.arborsci.com/Products Pages/Dataloggers/Sensors/HeatFlow.asp. [5] http://www.kenda.net/QUALIheatflow.htm. [6] http://www.wuntronic.de/heat flux/heat-flo.htm. [7] V. Székely, M. Rencz, E. Kollár, J. Mizsei, Heat–flux sensor for the thermal measurement of IC packages, in: Proceedings of the Eighth Therminic Workshop, Madrid, October 1–4, 2002, pp. 83–89. [8] T.H. Geballe, G.W. Hull, Seebeck effect in silicon, Phys. Rev. 98 (4) (1955) 940–947. [9] S.M. Sze, Physics of Semiconductor Devices, Wiley, New York, 1981. [10] A. Sedra, K. Smith, Microelectronic Circuits, Oxford University Press, New York, Oxford, 1998. [11] V. Székely, Thermodel: a tool for compact dynamic thermal model generation, Microelectron. J. 29 (1998) 257–267. [12] V. Székely, M. Rencz, Fast field solvers for thermal and electrostatic analysis, in: DATE Proceedings, Paris, February 23–26, 1998, pp. 519–523. [13] http://www.micred.com/index1.html. [14] E. Kollár, 3 × 3 heat-flux sensor array for the thermal measurement of IC packages, in: Proceedings of the 26th International Spring Seminar on Electronics Technology, Stará Lesná, Slovak Republic, May 8–11, 2003, pp. 133–136.
Biographies M. Rencz received the Electrical Engineering degree in 1973, and the PhD degree in 1980, from the Technical University of Budapest, Hungary. Her first research area was the simulation of semiconductor devices. Her latest research interests include the thermal investigation of ICs and MEMS,
thermal sensors, thermal testing, thermal simulation, electro-thermal simulation, SOI modelling, heat transfer simulation in SOI structures. She is Co-Founder and CEO of MicReD Ltd.. She is a Member of IEEE and IMAPS. She is Organising Committee and Program Committee Member of several international conferences and workshops. She has published her theoretical and practical results in more than 200 technical papers. For her research results is thermal modelling she has received in 2001 the Harvey Rosten Award of Excellence from the Electronics Thermal Management Community. E. Kollár received his BSc degree in Electrical Engineering and Teaching of Electrical Engineering at Kálmán Kandó Technical College in 1995. He obtained his MSc degree in Electrical Engineering in 2001 from Budapest University of Technology and Economics, Faculty of Electrical Engineering. He works as a PhD student at Department of Electron Devices. His research fields are heat-flux measuring on electron devices, dynamic thermal multi-port modelling of IC packages and heat sinks, and local board thermal conductivity measurements. V. Székely received the Electrical Engineering degree from the Technical University of Budapest, Hungary, in 1964. He joined the Department of Electron Devices of the Technical University of Budapest in 1964. Currently he is a Full Time Professor and the Head of Department of Electron Devices. His earlier research interests were mainly in the area of computer aided design of integrated circuits, with particular emphasis on circuit simulation, thermal simulation and device modelling. He conducted the development of several CAD programs in the field of integrated circuit design and simulation. Other areas of his technical interest are the theory of distributed networks and the problems of computer-graphics and image processing. He has been engaged in the investigation of thermal properties of semiconductor devices and integrated circuits for the last 25 years. This resulted in the development of novel thermal based IC elements and thermal IC simulator programs. Dr. Székely has published his theoretical and practical results in more than 300 technical papers and 15 books or book-chapters.
Heat-flux sensor to support transient thermal characterisation of IC packages M. Rencz a,b,∗ , E. Kollár a , V. Székely a b
a Budapest University of Technology, Hungary MicReD Ltd., Research, Gulyas u 27, H1112 Budapest, Hungary
Received 4 December 2003; received in revised form 23 April 2004; accepted 3 May 2004 Available online 10 June 2004
Abstract In this paper the idea and the analysis of a microelectronic heat-flux sensor, designed for fast transient measurements in package characterisation is presented. The sensor was fabricated in a prototype version, and the measured results prove the validity of the design concepts. The sensitivity, temperature dependence and resolution values are calculated and evaluated. The questions of calibration are discussed. Three application examples are presented. In the first two it is demonstrated, how the sensor may support compact model generation of packages by measuring the time dependence of the heat flux leaving the package on a certain surface, and by enabling the direct measurement of the thermal transfer admittance parameters of packages. In the third example the sensor is realised in array form, providing the possibility to obtain the coarse heat flux map of a package surface. © 2004 Elsevier B.V. All rights reserved. Keywords: Heat-flux sensor; Sensor array; Packaging qualification; Heat-flow sensor
1. Introduction In the package thermal verification and model generation practice it is frequently needed to know the exact value of the time dependence of the heat flux crossing a certain surface. For these purposes such a heat-flow sensor is needed that is representing a sufficiently small thermal resistance and thermal capacitance, not to disturb considerably the heat flow in the usual microelectronic structures. In the normal practice of the transient thermal measurement of microelectronic packages power is applied to the chip inside the package and the temperature is measured in various locations, e.g. on the chip itself, on the top or bottom surface of the package, etc. Such measurements may serve for various testing purposes, and/or the measured data may provide the base of dynamic compact model generation. For the thermal characterisation it is advantageous to know not only the temperature values, but the heat fluxes (the thermal “currents”) as well. This may be especially useful in case of model generation, since the more independent data are provided, the more accurate thermal model may be
∗ Corresponding author. Tel.: +36-1-463-2727; fax: +36-1-463-2973. E-mail addresses: [email protected], [email protected] (M. Rencz).
0924-4247/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2004.05.002
generated. In case of simple Rth measurements knowing the heat fluxes is equally advantageous: it can be measured what proportion of the dissipated power is leaving via the top surface, what proportion is flowing through the bottom surface, etc. Heat-flow sensors are represented broadly in the scientific literature, a good summary and survey of the various types of heat-flow sensors can be found in [1]. A variety of techniques for measuring convective, conductive and radiative heat transfer are described there, but the targeted applications, consequently the sensor parameters, are different from what we need for package surface, in situ transient measurements. The sensor described recently in [2] is designated to measure the heat transfer of the far surface of a wall by measuring the temperature on an accessible boundary. It is using active heater and passive sensor elements that are mounted close to each other. The heater is controlled to have the same temperature as the passive sensor that is cooled through convection. From the energy balance the heat flow can be calculated if the temperatures and the heat transfer coefficients are known. This is not the case in package characterisation. The heat-flow sensor of Leclercq and Thery [3] measures the heat flux by determining the temperature gradient over a tangent plane to the heat flux surface. Physical asymmetries are used to deflect the heat flux lines and generate a
M. Rencz et al. / Sensors and Actuators A 116 (2004) 284–292
Nomenclature A cv Cth f g I, i k L P P, p q rms Re Rth S S0 T U, u Ug yij
area, surface (m2 ) volumetric heat capacity (W s/K m3 ) thermal capacitance (W s/K) frequency, bandwidth (1/s) conductance (1/) current (A) the Boltzmann constant (V A s/K) length (m) power (W) heat current, heat rate (W) heat flux (W/m2 ) root mean square the electrical resistance () thermal resistance (K/W) the Seebeck coefficient (V/K) Seebeck coefficient at T0 reference temperature (V/K) temperature (K, ◦ C) voltage (V) electromotive force (V) admittance parameters, thermal admittance parameters (1/)(W/K)
Greek letters αS temperature coefficient of the Seebeck coefficient (1/◦ C, 1/K) αγ temperature coefficient of the sensitivity (1/◦ C, 1/K) temperature coefficient of the thermal αλ conductivity (1/◦ C, 1/K) γ sensitivity (V/W) γ0 sensitivity at T0 reference temperature (V/W) λ thermal conductivity (W/m K) λ0 thermal conductivity at T0 reference temperature (W/m K) σ electrical conductivity (1/)
temperature gradient over a planar thermopile. The structure is very complex and represents a considerable thermal resistance. There are numerous heat-flow sensors in the market that can be used for package thermal measurements [4–6] are only some of them. A common feature of these is, that they were designed to support static measurements, so their Rth values are relatively low, but the Cth values that they represent are either even not provided, or prohibitively high. This means that we can not use them in fast thermal transient measurements without considerably altering the transient behaviour of the thermal system where they are used. For these reasons we have decided to construct a heat-flow sensor that is targeted for measuring in situ conductive heat transfer via package surfaces, representing sufficiently small
285
thermal resistance and thermal capacitance values, not disturbing significantly the transient behaviour of the heat-flow path. Below we present the idea of the new heat-flow sensor, discuss some design issues, such as material selection, etc., and calculate the most important sensor parameters. To check the feasibility of the sensor we have fabricated some pre-prototype versions of the sensor in the laboratories of the Department of Electron Devices of the Budapest University of Technology and Economics, and verified with measurements sensor operation and the most important parameters. At the end of the paper we present some typical application examples.
2. The proposed structure For the heat-flux sensor we have designed a temperature gradient based sensor [1], where the heat flux is measured by the temperature difference along the way of the heat streaming. The structure we propose is shown in Fig. 1. The sensor consists of a thin silicon layer with homogeneous doping concentration metalised on both surfaces. The heat current flows through this sandwich structure, resulting in a very small temperature drop between the upper and the lower surfaces. Since both sides of the silicon die are covered by metal, these form two thermocouples with the silicon, connected in anti-series. The output voltage of the two thermocouples is proportional to the temperature difference between the two sides, that is proportional to the heat flux [6]. In order to assure a well-defined surface area, where the heat flux is measured, insulating SiO2 between the metal and the silicon limits the sensor area. Where the oxide separates and insulates the metal from the silicon the structure does not act as a heat-flux sensor any further. This part may be used for contacting the two metal surfaces. The left hand side output wire in Fig. 1 is contacting the upper metal, while the right hand side contact wire is contacting the bottom metal through the short circuit of the thin (less than 0.5 mm) silicon layer, since outside the sensing area there is no voltage difference between the two metals. This solution was needed to provide a flat bottom surface to enable good contact with the underlying, e.g. cold-plate surface.
Fig. 1. The proposed structure of the heat-flux sensor. The figure is not to scale.
286
M. Rencz et al. / Sensors and Actuators A 116 (2004) 284–292
Let us suppose first, that the heat flux, that is power, is crossing the chip exactly on this area, with uniform lateral distribution. The thermal resistance inserted into the heat-flow path is given by Fig. 2. Cross-sectional view of a targeted application. The figure is not to scale.
A suggested application is shown in Fig. 2. The heat-flux sensor is electrically isolated but thermally contacted via the applied heat conductive ceramics, while measuring the heat flow through the package bottom surface towards the heat sinking cold plate. As it is shown in Fig. 2 the flat bottom surface of the heat-flux sensor enables good and well reproducible contact with the cold plate.
3. Design concepts and calculation of the main sensor parameters In the design of the heat-flux sensor the selection of the materials is critical for the performance of the device. This strongly influences the two main parameters of the sensor: the sensitivity and the maximal operating speed, that is, the cut-off frequency of the operation. Two main issues have to be kept in mind in the selection of the materials as follows [7]: (i) The material of the die has to be a good thermal conductor, in order to reduce the temperature drop across it. (ii) The Seebeck coefficient of the contacts has to be as high as possible, assuring appropriate sensitivity. Silicon is a good candidate because of its high thermal conductivity and the good (∼1 mV/K) Seebeck emf of the Si–Al contacts. Since the Seebeck emf is increasing with decreasing doping level of the silicon, medium or low doping material has to be used [8]. The Si–Al contacts should be of non-rectifying nature—this is why p-doped silicon was selected as the base material [9]. 3.1. Calculation of the sensitivity To construct a good heat-flow sensor the main design principle must be to maximise the sensitivity of the sensor. In our case the sensitivity is maximal if the output voltage is maximal for the unit heat flux. Let us calculate the value of the sensitivity. The principal geometric sizes of the structure are shown in Fig. 3. The active area A is the area of the contact window on the oxide.
Rth =
1L λA
(1)
where λ is the thermal conductivity of the silicon and L the thickness of the structure. If P power is flowing across the silicon the temperature difference between the two sides is PRth and the output voltage is Uout = SPRth = P
SL λA
(2)
where S is the Seebeck coefficient. This means that the sensitivity (output voltage for unity power flow) is γ=
SL λA
(3)
In case of L = 0.5 mm, A = 1 cm2 , λ = 100 W/m K, S = 1 mV/K this sensitivity value is 0.05 mV/W which is a well measurable value. The insertion resistance of the probe is only about 0.05 K/W, this is in most of the cases negligible. In real circumstances the heat flow is generally not uniform. Inserting the heat-flow sensor between the bottom area of a package and the heat sink we have to expect uneven distribution of heat flux crossing the sensor. It is not straightforward to answer the question, of what is measured in this case, and how to interpret the output voltage of the sensor? The answer is however simple and pleasant: the output voltage is proportional to the total heat-flow crossing the contacted A area of the die, and independent of the lateral distribution of the heat-flow. This can be proven as follows. Let us suppose p(x, y) uneven heat-flux distribution on the sensor surface and examine how this effects the output voltage of the sensor. The considered structure is shown in Fig. 4a. The sensor material parameters, the λ thermal conductivity, σ electrical conductivity and the S Seebeck coefficient are considered to be constant along the A active sensor area. The metal contacts to both sizes of the sensor are considered to behave as ideal conductors in the lateral direction. The sensor plate is thin enough to allow neglecting any lateral heat-flow. An elementary section of the structure with dA area, perpendicular to the heat flow is considered. Caused by the p(x, y) dA heat rate, a temperature difference develops between the two sides of the elementary column of the silicon as follows: T = p(x, y) dA
L L = p(x, y) λ dA λ
(4)
As a result of the Seebeck effect, this temperature difference generates an Ug electromotive force: Fig. 3. The structure of the sensor.
Ug = Sp(x, y)
L λ
(5)
M. Rencz et al. / Sensors and Actuators A 116 (2004) 284–292
287
3.2. Calculation of the cut-off frequency of the sensor operation Considering that in the targeted application the heat-flow sensor is inserted between the investigated package and a (quasi ideal) heat sink, the cut-off frequency is calculated for this case. To calculate the cut-off frequency we consider the heat sensor as an uniform, distributed thermal RC line, short-circuited by the heat sink at the far end. For such cases according to [11] the first pole of the impedance, giving the cut-off frequency of the device is at the frequency of f =
π 1 8 Rth Cth
(11)
where Rth is the insertion thermal resistance calculated by (1) and Cth the thermal capacitance given by Cth = cv AL Fig. 4. The considered sensor structure with the electrical model of the parallel connected sections.
The electrical conductance of the dA section is dA g=σ L
(6)
This means that the electrical model of the dA section is a voltage source, with finite serial inner resistance (Thévenin model) as it is shown in Fig. 4a. As the whole structure consists of many dA sections, many such model networks are to be connected in parallel in order to describe the complete sensor. The calculations, however, will be easier if we substitute this Thévenin model by its Norton equivalent. According to the textbook transformation of the electrical network theory [10] the current value of this current source is σ L dA Ig = Ug g = Sp(x, y) σ = S p(x, y) dA (7) λ L λ while the inner conductance is the same as for the Thévenin model. Finally, we connect in parallel the elementary Norton models, see Fig. 4b. The resulting network is a Norton model as well, see Fig. 4c, with the current of σ Ires = Ig = S p(x, y) dA (8) λ A A and with the inner conductance of σ σ g= dA = A. gres = L L A A The open-circuit voltage of this resulting network is Ires SL SL = p(x, y) dA = P Uout = gres λA λA A
(9)
(10)
This means that Eq. (2) holds independently from the heat-flow distribution in the window of A.
(12)
Using the geometrical data introduced above and cv = 1.67 × 106 W s/m3 K for the volumetric heat capacitance of silicon the following results can be obtained: Cth = 0.083 W s/K and f = 95 Hz. This means that the sensor is capable to follow time variations up to some 10 Hz. 3.3. Calculation of the sensor resolution The minimum of the perceptible heat-flux value is limited by the noise. The sources of noise are the Johnson or thermal noise of the sensor itself and the noise of the sensor amplifier. The rms noise voltage of the sensing may be written as: unoise = usensnoise + uampnoise
(13)
where uampnoise is the rms noise generated by the amplifier. usensnoise is the rms value of the Johnson noise of the sensor, given by usensnoise = 4kTRe fm , where k = 1.38 × 10−23 V A s/K is the Boltzmann constant, T the absolute temperature, Re the electrical resistance of the sensor and f the bandwidth of the measurement system. The magnitude of this noise may be calculated as follows. The resistivity of the considered material is 5 cm, the geometrical sizes are the same as above. The calculated electrical resistance is Re = 0.25 . Considering an f = 25 Hz bandwidth, the RMS noise voltage is 0.325×10−3 V. Since this is really negligible, it can be concluded that the noise of the sensor amplifier will certainly dominate the own noise of the sensor. Using a low-noise amplifier with an equiva√ lent input noise of 1 nV/ Hz the input noise is u RMS = 5 × 10−3 V. Calculating with the 50 V/W sensitivity of the device, this corresponds to 0.1 mW heat-flow rate. This is the (approximate) ultimate limit of the resolution of the sensor.
288
M. Rencz et al. / Sensors and Actuators A 116 (2004) 284–292
4. Calculation of the temperature dependence of the sensitivity As long as the parameters in Eq. (3) may be considered constant, the γ sensitivity value is constant. This means that the sensor characteristic is linear and independent from the temperature. In Eq. (3) however all the constants do have a certain temperature dependence. Since the coefficient of the thermal expansion for silicon is three orders of magnitude smaller that the coefficients of the temperature dependence of the Seebeck coefficient and the thermal conductivity, only this latter two are to be considered in the calculation of the temperature dependence of the sensitivity value. The temperature dependence of the sensitivity may be obtained by calculating the derivative of Eq. (3) versus temperature. Let us approximate the temperature dependence of the material parameters with the following equations: λ = λ0 (1 − αλ (T − T0 ))
(14)
and S = S0 (1 − αS (T − T0 ))
(15)
where λo and S0 are the thermal conductivity and the Seebeck coefficient values at the T0 reference temperature, and αλ and αS the coefficients of their temperature dependence. In this case the temperature dependence of the sensitivity is obtained in a form very similar to Eqs. (14) and (15): γ = γ0 (1 − αγ (T − T0 ))
5. Calibration and experimental results In order to prove the feasibility of such a heat-flow sensor a prototype version was produced to facilitate experimental investigations. The applied substrate was lightly doped p-type, homogeneous, single-crystal silicon, with about 5 cm electrical resistance. The thickness of the die was 340 m. The area of the contact window was A = 1 cm × 1 cm. The Seebeck coefficient is S = 1.25 mV/K for the given doping level (see 7). The expected sensitivity, calculated with Eq. (3) is about 40 V/W. In the first step of investigations the sensor was calibrated. Fig. 5 shows the schematic measurement arrangement. The heat-flow in the structure is maintained by a transistor, placed on the top of the structure. The dissipation of the transistor is known from the known transistor current and voltage values. The heat-flow sensor is mounted between the two copper jaws. In this structure the heat flows entirely in the copper jaws from the transistor towards the cold plate, through the heat-flow sensor. This was verified by 3D thermal simulation, with the help of the SUNRED thermal solver [12]. The simulated results are shown in Fig. 6, demonstrating that with the selected materials, the entire well-determined amount of heat, generated by the transistor, flows across the sensor, if the transistor is isolated upwards.
(16)
where γ 0 is the sensitivity value of the sensor at the T0 reference temperature and αγ the coefficient of the temperature dependence of the sensitivity value. After substituting all the temperature derivatives αγ = αλ − αS .
(17)
may be obtained. All the values in Eq. (17) are slightly temperature dependent. In a limited range however, e.g. in the range between 10 and 70 ◦ C we may calculate with the following average values for silicon:
Fig. 5. Experimental arrangement to determine the sensitivity of the heat-flux sensor. The structure is not to scale.
αλ = 0.004 αS = 0.002 that according to Eq. (17) gives αγ = 0.002. This is a conveniently small value, showing half as much temperature dependence than that of the thermal conductivity is the silicon material. This is indicating that the heat-flow sensor operation is fairly independent from the temperature. Since during the measurements where the cold side of the sensor is always on a heat sink surface, the temperature of the sensor is known. Thus we can carry out the necessary correction in the sensitivity with the αγ value, eliminating the effects of the nonlinearities of the thermal parameters.
Fig. 6. Simulated heat flow in the (to scale) structure of Fig. 5. The simulation shows practically no heat loss towards the surrounding air and a negligible heat loss upwards.
M. Rencz et al. / Sensors and Actuators A 116 (2004) 284–292
289
devices fabricated in the same party, we may assume that it is enough to calibrate one sensor only for a given party of fabrication. The calibrated sensor has to be exactly of the size of the calibrating device faces, and the sensitivity of any-size device may be calculated from the calibrated device by a simple multiplication with the geometrical ratios as Ssensor = Scalibrated
Fig. 7. The measured heat-flux versus sensor voltage diagram.
In the calibration and sensitivity measurement the power of the transistor was increased stepwise and the steady state output voltage of the sensor was measured. The results are plotted in Fig. 7. The measured sensitivity is 41–42.5 V/W, in good agreement with the calculated value. The linearity of the sensor in the investigated range is very good. The two curves correspond to measurements on the same sample but the arrangement was dismounted/mounted between the two measurements. The difference indicates that the measurement is sensitive to the perfection of the mounting. The presented way of sensor calibration is accurate only if the faces of the copper are not larger than the sensing area of the sensor. Considering however that our sensor is fabricated with silicon micro-technology, and the material parameter values in the silicon technology are fairly constant for the
sensor
Acalibrated sensor Asensor
(18)
In the second experiment heat-flow transients were recorded with the help of the investigated sensor. The T3Ster [13] thermal tester was used to record simultaneously the transient temperature of the transistor and the transient heat-flow on the sensor. The experimental arrangement is the same as in the steady state case. Since the output voltage of the sensor is relatively low, a preamplifier was used, with Av = 100 V gain. The noise was suppressed with a filter of 8 Hz cut-off frequency. The results are plotted in Fig. 8. It is visible on the figure that the internal temperature of the transistor begins to rise at about 0.1 ms but the heat streaming reaches the sensor with a delay of about 0.2 s.
6. Application perspectives This new thin heat-flux sensor offers a broad range of possible applications. The targeted field of use was package characterisation, especially in order to determine the model parameter values of the dynamic compact models. Three proposed fields of application are outlined below. However all the three presented applications are in connection with package thermal characterisation, we think that
Fig. 8. Step-function responses (transistor temperature and sensor output voltage).
290
M. Rencz et al. / Sensors and Actuators A 116 (2004) 284–292
where yij are the admittance parameters, p the heat current and t the temperature. The short circuit at the heat sink side is equivalent with t2 = 0. p1 is the excitation and t1 is the chip temperature. The out-streaming flux p2 can be measured by using the heat-flux sensor. With Eq. (19) the y11 and y21 admittance values may be determined directly: p1 p2 p2 (20) and y21 = = y11 y11 = t1 t1 p1
Fig. 9. Measurement of partial heat-fluxes.
the utility of the presented sensor is much broader. Especially broad applicability is expected for the sensor matrix arrangement realisation that enables even heat flux mapping.
This way the direct measurement of a transfer thermal admittance value became possible. 6.3. Heat flux mapping
6.1. Measurement of heat-flux partitioning To measure what ratio of the heat is leaving the package via the cooling mount and what ratio is moving towards the board this new thin heat-flow sensor may be used advantageously. Let us examine as an example the arrangement of Fig. 9. An IC is soldered into the printed wiring board. The top surface of the package is equipped with a cooling mount. We wish to measure what percentage of the dissipated power leaves the package via the cooling mount and what is the percentage that passes through the PWB. Inserting the heat-flux sensor into the indicated interface the power leaving upwards can be easily measured. It is supposed that the rest of the power is leaving via the PWB. 6.2. Measurement of transfer thermal admittance values The usual dynamic measurement methods drive the chip in the package with a certain power and measure the temperature response of the same chip. This method provides only the one-port thermal impedance or admittance of the package, see Fig. 10. If we intended to measure transfer parameters the heat-flux or temperature at the heat-sink side of the package has to be measured. To express more precisely: either the heat-flux on the thermally short-circuited heat-sink side or the temperature on the thermally open or floating heat-sink side has to be measured. Obviously the first case is closer to the real operating conditions. This first condition can be realised with the help of the heat-flow sensor, which is suitable to be inserted between the package and the “thermal short circuit” cold plate. The two-port equations of the model can be written as follows: p1 = y11 t1 + y12 t2 ,
p2 = y21 t1 + y22 t2
Fig. 10. The two-port model of a package on a cold plate.
A main advantage of this sensor technology is that with independent sensor patches on the surface the distribution of the heat flux on a certain surface may be also very easily measured. The applied silicon technology enables the realisation of a fine structure of the metal layers on the silicon surface. If we realise a matrix of uniform sensors on the surface, from the distribution of the output signals of the sensors the heat-flow map of the examined surface is obtained. Already a two sensors arrangement may be useful which is capable to measure separately the heat-flux at the “top centre” and “top periphery” since these data can be applied directly to the identification of model parameters for multi-port dc thermal package models. To verify the feasibility of the idea a 3 × 3 sensor array has been realised in our laboratories. An array of 6 × 7 sensors has been fabricated recently as well. Results with this enhanced resolution variant will be presented in a separate paper. The complexity of the structure and the line widths were determined by our very limited in-house masking capabilities. In Fig. 11 the layout of the 3 × 3 sensor matrix array is presented. The sensors are the larger rectangles in the upper three lines of the chip. The smaller rectangles in the bottom lines are the contact pads. These are outside the sensor area,
(19)
Fig. 11. Heat-flux sensor matrix to measure flux distribution through a surface.
M. Rencz et al. / Sensors and Actuators A 116 (2004) 284–292
Fig. 12. Measuring the heat flux distribution through a package surface.
291
The temperature rise of the junction together with some of the measured transient heat flux curves as a result of applying a 10 W dissipation step on the chip are presented in Fig. 14. Note, that it is the output signal of the S22 sensor that follows first the heating curve of the transistor junction, and the absolute value of the heat-flow through this sensor is considerably higher than the heat flow perceived by the farther sensors. This experiment proves the idea that with the help of such array-sensors the distribution of the heat flow across a certain area may be conveniently measured. It also demonstrates that the sensors are fast enough to detect rapid changes in the heat flow, as expected from the calculations. 7. Conclusions
Fig. 13. The numbering of the sensors under the measured BD245 transistor. The chip in the package is outlined with dashed line.
not disturbing the measurements. If the connecting wires in the sensing surface are thin enough the flux perceived by them can be negligible. The prototype version of this sensor matrix was used to measure the heat flux through a transistor package surface in the arrangement presented in Fig. 12 [14]. Fig. 13 shows the numbering of the different sensors in the matrix arrangement of Fig. 12. The dissipating area is the chip in the package, the approximate location is outlined with dashed line in the figure.
Encouraging experiments have been accomplished in order to produce a heat-flow sensor, suitable for the experimental thermal investigation of IC packages or other microelectronic structures, both in steady state and transient case. The measured results show the appropriateness of the presented design concept, and prove the feasibility of the idea. The sensors have linear characteristics in a broad temperature range. A possible way for the calibration is presented, the calibration is fast and simple. When the sensors are fabricated in a large number with standard silicon technology it is expected that most of the devices will not even need individual calibration. The presented micro-sensors are applicable to determine experimentally the partitioning of the heat-flow between several heat streaming paths, or for the verification of the distribution of the heat flow on larger surfaces. The sensor can be used also for the direct measurement of thermal transfer admittance values for package thermal characterisation. By realising an array of such sensors with the same technological steps we can easily measure the heat flux map of any flat surface, providing a further broad field of applicability of the presented heat-flux sensors. The demonstrated features candidate the sensor an invaluable verification tool in the compact thermal model generation of packages or other microelectronic subsystems. Acknowledgements The authors are indebted to A. Poppe and G. Farkas for the helpful discussions, to J. Mizsei, S. Török, M. Ádám and G. Végh for the technical assistance. This work was partially supported by the PROFIT IST-1999-12529 project of the EU, and by the 2/018/NKFP2001 INFOTERM projects of the Hungarian Government.
References Fig. 14. Heating curves measured on the different sensors. The numbering refers to Fig. 13.
[1] K. Azar (Ed.), Thermal Measurements in Electronic Cooling, CRC Press, Boca Raton, 1997.
292
M. Rencz et al. / Sensors and Actuators A 116 (2004) 284–292
[2] A. Saidi, J. Kim, Heat-flux sensor with minimal impact on boundary conditions, in: Proceedings of the ASME National Heat Transfer Conference, Las Vegas, NV, July 21–23, 2003, p. 40567. [3] D. Leclercq, P. Thery, Apparatus for simultaneous temperature and heat flux measurements under transient conditions, Rev. Sci. Instrum. 54 (1983) 374–380. [4] http://www.arborsci.com/Products Pages/Dataloggers/Sensors/HeatFlow.asp. [5] http://www.kenda.net/QUALIheatflow.htm. [6] http://www.wuntronic.de/heat flux/heat-flo.htm. [7] V. Székely, M. Rencz, E. Kollár, J. Mizsei, Heat–flux sensor for the thermal measurement of IC packages, in: Proceedings of the Eighth Therminic Workshop, Madrid, October 1–4, 2002, pp. 83–89. [8] T.H. Geballe, G.W. Hull, Seebeck effect in silicon, Phys. Rev. 98 (4) (1955) 940–947. [9] S.M. Sze, Physics of Semiconductor Devices, Wiley, New York, 1981. [10] A. Sedra, K. Smith, Microelectronic Circuits, Oxford University Press, New York, Oxford, 1998. [11] V. Székely, Thermodel: a tool for compact dynamic thermal model generation, Microelectron. J. 29 (1998) 257–267. [12] V. Székely, M. Rencz, Fast field solvers for thermal and electrostatic analysis, in: DATE Proceedings, Paris, February 23–26, 1998, pp. 519–523. [13] http://www.micred.com/index1.html. [14] E. Kollár, 3 × 3 heat-flux sensor array for the thermal measurement of IC packages, in: Proceedings of the 26th International Spring Seminar on Electronics Technology, Stará Lesná, Slovak Republic, May 8–11, 2003, pp. 133–136.
Biographies M. Rencz received the Electrical Engineering degree in 1973, and the PhD degree in 1980, from the Technical University of Budapest, Hungary. Her first research area was the simulation of semiconductor devices. Her latest research interests include the thermal investigation of ICs and MEMS,
thermal sensors, thermal testing, thermal simulation, electro-thermal simulation, SOI modelling, heat transfer simulation in SOI structures. She is Co-Founder and CEO of MicReD Ltd.. She is a Member of IEEE and IMAPS. She is Organising Committee and Program Committee Member of several international conferences and workshops. She has published her theoretical and practical results in more than 200 technical papers. For her research results is thermal modelling she has received in 2001 the Harvey Rosten Award of Excellence from the Electronics Thermal Management Community. E. Kollár received his BSc degree in Electrical Engineering and Teaching of Electrical Engineering at Kálmán Kandó Technical College in 1995. He obtained his MSc degree in Electrical Engineering in 2001 from Budapest University of Technology and Economics, Faculty of Electrical Engineering. He works as a PhD student at Department of Electron Devices. His research fields are heat-flux measuring on electron devices, dynamic thermal multi-port modelling of IC packages and heat sinks, and local board thermal conductivity measurements. V. Székely received the Electrical Engineering degree from the Technical University of Budapest, Hungary, in 1964. He joined the Department of Electron Devices of the Technical University of Budapest in 1964. Currently he is a Full Time Professor and the Head of Department of Electron Devices. His earlier research interests were mainly in the area of computer aided design of integrated circuits, with particular emphasis on circuit simulation, thermal simulation and device modelling. He conducted the development of several CAD programs in the field of integrated circuit design and simulation. Other areas of his technical interest are the theory of distributed networks and the problems of computer-graphics and image processing. He has been engaged in the investigation of thermal properties of semiconductor devices and integrated circuits for the last 25 years. This resulted in the development of novel thermal based IC elements and thermal IC simulator programs. Dr. Székely has published his theoretical and practical results in more than 300 technical papers and 15 books or book-chapters.