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7-9 October 2009, Leuven, Belgium A Temperature-Dependent POWER MOSFET Mode1 for Switching Application H. DIA 1,2 , J.B. Sauveplane 1 , P. Tounsi 1,2 , J-M. Dorkel 1,2 1 CNRS; LAAS; 7 avenue du Colonel Roche, F-31077 Toulouse, France 2 Université de Toulouse; UPS, INSA, INP, ISAE; LAAS; F-31077 Toulouse, France dia@laas.fr Abstract- in this paper, an electrical model of a power vertical MOSFET sensitive to temperature is proposed using VHDL-AMS code. Our modeling approach is based on basic physical MOSFET effect and on its technological structure. Thermal sensitivity of MOSFET parameters is discussed and characterized. Validation of the model accuracy is presented by comparison between simulations and experimental results. Among the benefits of this technique are fast simulation, good agreement between simulations and measurements and useful insights into thermal sensitivity of MOSFET performance in switching applications. This work is the first step to electro-thermal simulation of power device by simulator coupling. studies of the device [4] addressing basic equations in the semiconductor. Each area of the MOSFET structure shown on “Fig.1.”((1) Channel, (2) access, (3) PN - junction, (4) drift and (5) substrate) is described taking into account the main characteristics of the power device: linear, saturated behavior and non linearity of the gate-drain and drain-source capacitances. Keywords-modeling, power MOSFET, power diode, VHDL-AMS. I. INTRODUCTION Continuous improvement in power devices performances involves the reduction of their sizes which increases power losses density even in a same application context. As reliability relies most of the time on maximum temperature variation of the chip, electro-thermal simulation of a power device within its environment becomes a key tool to avoid re-design of a chip. In this context electro-thermal model has already been presented in literature [1]-[2], but the major drawbacks of previous model is that power device is assumed to be “ON state” during the simulation. This assumption is valid only if power switching losses are negligible or if switching behavior is not relevant to the application. To overcome these limitations a new approach has been developed based on simulator coupling to accurately simulate the electro-thermal behavior of the power device [3]. This paper is the first step toward this modeling approach as it presents an electrical model of a power vertical MOSFET, sensitive to temperature, using VHDL-AMS code. The power device studied is a low voltage vertical power MOSFET with ultra low on state resistance. The paper is divided in two parts. First the electrical model of the power device sensitive to temperature is detailed, based on basic physical MOSFET effect and on its technological structure. Then the extraction procedure to obtain the model parameter is presented and at the end a comparison between simulations and experimental result are shown for a power device in a switching application. II. THE POWER MOSFET MODEL A. The Electrical Model The modeling approach relies on experimental and simulation Fig. 1. Cross section of power MOSFET The body diode, P (body)/ N- (epitaxial layer) junction has also been implemented in the model. This diode allows the simulation of the transistor's reverse bias behavior. The model of the body diode is based on a previous work on the power PIN diode [5]. Fig. 2. The body diode model This model “Fig.2.” takes into account the forward and reverse behavior of a diode and also the reverse recovery current phenomena caused by the charge stocked in the intrinsic region during the forward polarization. The forward phase is modeled by a resistor R on , which means that the forward polarization phase is a simple one “Fig.3.” And it’s sufficient enough to address the thermal issues, a conductance G off for the reverse phase and to model the leakage current; all this is compact in the IdealDiode model. The voltage depended current source Jc ©EDA Publishing/THERMINIC 2009 87 ISBN: 978-2-35500-010-2
is used to model the forward polarization capacitor. 7-9 October 2009, Leuven, Belgium The current source I ds is responsible of the linear and saturation state of the transistor, I I DS DS ⋅ ( Vcom − Vth ) − ⋅VI DS ) ⋅VI DS ( V −V ) 2 = Kp 1 (2) 2 = ⋅ (3) Kp 2 com th Fig. 3. The forward polarization of the body diode I J c = K. V L (1) This current “(1),” depends of the drop voltage of the inductance L and magnified by a constant K, during the transient blocking stage of the diode the inductance L energy will discharge in the resistor R L , and the current source Jc will deliver a reverse current simulating the reverse state current of this diode, an example of this reverse current simulation is shown on “Fig.4.”, in this paper we will show only a simulation of the reverse current because the body diode of our MOSFET DUT is a very fast one, it have a very low reverse current, and it doesn’t vary in a significant matter with temperature. Fig. 4.Simulation of the diode current during commutation for two given temperature, the dotted curve(blue) is at 150°C and the normal one is at 25°C By using this model as a body diode we have a complete power MOSFET electrical model “Fig.5.”. We should mention that the C ds capacitor is the reverse polarization capacitor of the diode model play the role of the drain-source capacitor and this capacitor is a non linear with voltage as mentioned above. Fig. 5. Power MOSFET electrical & thermo-sensible model for switching circuits. “(2),” describe the linear phase knowing that I DS is the drop voltage of the current source Ids and V com is the command voltage. “(3),” describe the saturation phase B. Temperature dependents parameters The expansion of the electrical model into a thermal sensible one is done by introducing the temperature as a variable into the equations of the electrical parameters in the electrical model. The first step is to identify the electrical parameters influenced by the temperature in a way that the electrical behavior of the MOSFET is changed. These parameters are (Kp, V th , R sub , R g , R s , R on , I ss , V knee ) where Kp is the transconductance parameter and V th is the threshold voltage, R epi , R sub , R g , R s are the epitaxial resistor, substrate resistor, gate resistor, source resistor of the MOSFET. Ron is the forward phase resistor, I ss is the leakage current, and V knee is the threshold voltage of the diode. We don’t need to include the capacitors as temperature dependent because it doesn’t vary much with temperature [6]. The extraction of the temperature dependent parameters has been done by electrical characterization of a power MOSFET and the body diode under different temperature imposed by the air flux of the thermo stream. III. MODEL’S PARAMETER EXTRACTION AND VALIDATION A. Parameter extraction The model parameters were carefully identified based on simulations and an automatic experimental acquisition method developed in our laboratory which is sufficiently general to be applied to Power MOSFET devices. The experimental measurements are done under different temperature using the thermo-stream (25°C, 50°C, 75°C…175°C), We faced a serious problem for temperature above 175°C; the experimental dispositive melted down cause’s short circuit, so the temperature dependent equations are valid between 25°C and 175°C. The determination of the static parameters Kp “(4),” transconductance parameter, the threshold voltage V th “(5),” and the series resistor R ON “(6),” is done by measuring the transfer characteristics and the output characteristics using the Agilent HP4142. Kp = 244 − 0.7( T − 25) (4) −3 V th = 2.6 − 3.3e ( T − 25) (5) −6 3 −4 2 −4 R on = 1.0e ( T −25) −2.0e ( T −25) + 1.9e ( T −25) + 1.97 (6) For the diode parameters, they are represented by the following equations, −3 V Knee = 0.7 − 2.0e ( T − 25) (7) V ©EDA Publishing/THERMINIC 2009 88 ISBN: 978-2-35500-010-2
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