METHOD FOR DETERMINING THE TEMPERATURE CHARACTERISTIC OF THE DRAIN-SOURCE ON-STATE RESISTANCE OF A MOSFET

Abstract

A method for determining the temperature characteristic of the drain-source on-state resistance of a MOSFET of a first type. The method includes: determining temperature-specific linearization coefficients of a difference between a first value of the drain-source on-state resistance at a first temperature and a second value of the drain-source on-state resistance at a reference temperature established for the MOSFET-type characterization based on a difference between a first value of the drain-source on-state resistance at the same reference temperature and the average of the drain-source on-state resistance at the same reference temperature from measurements during production for MOSFET samples of the first type; determining the temperature dependency of the determined temperature-specific linearization coefficients to determine a specific TDDR for the characterized MOSFET samples of the first type; and using the MOSFET-type-specific TDDR to reconstruct the temperature dependency of the drain-source on-state resistance of an individual MOSFET of the first type.

Claims

1-10. (canceled)

11. A method for determining a temperature characteristic of a drain-source on-state resistance of a MOSFET of a first type, comprising the following steps: determining temperature-specific linearization coefficients of a difference between a first value of the drain-source on-state resistance at a first temperature and a second value of the drain-source on-state resistance at a reference temperature established for a MOSFET-type characterization based on a difference between a first value of the drain-source on-state resistance at the same reference temperature and an average of the drain-source on-state resistance at the same reference temperature from measurements during production for a number of MOSFET samples of the first type; determining a temperature dependency of the determined temperature-specific linearization coefficients to determine a temperature-dependent delta resistance (TDDR) specific to the characterized number of MOSFET samples of the first type; and using the MOSFET-type-specific TDDR for a reconstruction of the temperature dependency of the drain-source on-state resistance of at least one individual MOSFET of the first type.

12. The method according to claim 11, wherein the MOSFET-type-specific TDDR is applied in a circuit of a plurality of MOSFETs of the first type.

13. The method according to claim 11, wherein the MOSFET-type-specific TDDR is used to take into account the temperature characteristic of the drain-source on-state resistance of a MOSFET for representation of a current measurement function.

14. The method according to claim 11, wherein a temperature dependency of the temperature-specific linearization coefficients is determined.

15. The method according to claim 11, wherein the MOSFET-type-specific TDDR is a one-dimensional TDDR.

16. The method according to claim 11, wherein the MOSFET-type-specific TDDR is a two-dimensional TDDR.

17. The method according to claim 11, wherein the reference temperature is equal to a specification temperature of a typical drain-source on-state resistance of a MOSFET in production, or the reference temperature is equal to a calibration temperature of the drain-source on-state resistance of a MOSFET to be used as a current sensor or of a MOSFET group in control device production.

18. The method according to claim 11, wherein the method is used in conjunction with a safety-critical application.

19. An arrangement for determining a temperature characteristic of a drain-source on-state resistance of a MOSFET, the arrangement being configured to: determine temperature-specific linearization coefficients of a difference between a first value of the drain-source on-state resistance at a first temperature and a second value of the drain-source on-state resistance at a reference temperature established for a MOSFET-type characterization based on a difference between a first value of the drain-source on-state resistance at the same reference temperature and an average of the drain-source on-state resistance at the same reference temperature from measurements during production for a number of MOSFET samples of the first type; determine a temperature dependency of the determined temperature-specific linearization coefficients to determine a temperature-dependent delta resistance (TDDR) specific to the characterized number of MOSFET samples of the first type; and use the MOSFET-type-specific TDDR for a reconstruction of the temperature dependency of the drain-source on-state resistance of at least one individual MOSFET of the first type.

20. The arrangement according to claim 19, wherein the arrangement is integrated in a measuring arrangement for characterization of the MOSFET in MOSFET production or is configured to be included in the measuring arrangement.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0016] FIG. 1 shows, in a graph, the most frequently encountered specification type of a normalized typical temperature dependency of the drain-source on-state resistance.

[0017] FIGS. 2 to 19 show, in graphs, curves of different variables in relation to the one-dimensional or two-dimensional TDDR.

[0018] FIG. 20 shows, in highly simplified, purely schematic form, an example arrangement for carrying out the method of the present invention.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

[0019] The present invention is represented schematically in the figures on the basis of embodiments and is described in detail below with reference to the figures.

[0020] FIG. 1 shows the temperature dependency of the drain-source on-state resistance in a graph 10, on the abscissa 12 of which the temperature T.sub.J [? C.] is plotted, and on the ordinate 14 of which the normalized drain-source on-state resistance R.sub.DS(on), norm=R.sub.DS(on)/R.sub.DS(on) @25? C. is plotted. The following applies:

R.sub.DS(on),norm=f(T.sub.j);I.sub.D=100 A;V.sub.GS=10 V

TABLE-US-00001 Drain-source R.sub.DS(on) V.sub.GS = 10 V, 0.86 1.06 m? on-state I.sub.D = 100 A resistance V.sub.GS = 10 V, 1.52 1.88 I.sub.D = 100 A, T.sub.j = 175? C..sup.1) T.sub.j denotes the junction temperature.

[0021] As has already been stated, a precise specification of the temperature behavior of the drain-source on-state resistance of each individual MOSFET, which would allow the latter to be used as a current sensor for a precise current measurement, has not been available so far.

[0022] The so-called temperature-dependent delta resistance (TDDR) is discussed below. In the process, the presented method is explained in more detail.

[0023] The TDDR denotes a temperature-dependent component of the drain-source on-state resistance independent of the proportional MOSFET-individual drain-source on-state resistance value at the reference temperature R(?.sub.Ref). The sum of the two produces the resulting temperature dependency of the drain-source on-state resistance for each individual MOSFET of the same type, which was characterized by means of this method on the basis of a representative number of samples, in conjunction with its individual drain-source on-state resistance at the reference temperature R(?.sub.Ref). This means that for a complete description of the temperature dependency of the drain-source on-state resistance of each individual MOSFET of the characterized MOSFET type, only its individual drain-source on-state resistance at the reference temperature R(?.sub.Ref), for example RDS(on) @25, and the specific TDDR determined for this MOSFET type are needed. The boundary conditions relating to the gate-source control voltage during operation must be identical to those during the characterization, e.g. Vgs=10 V.

[0024] Step 1: Determining the temperature-specific linearization coefficients of the difference R(?)?R(?.sub.Ref) as a function of the difference R(?.sub.Ref)?R.sub.Ref for the representative number of MOSFET samples of the same type.

[00001]$\begin{array}{cc}A=\left[\begin{array}{cc}{R}_1\left({?}_{Ref}\right)-{\stackrel{\_}{R}}_{Ref}& 1\\ .Math.& .Math.\\ R_{k-1}\left({?}_{Ref}\right)-{\stackrel{?}{R}}_{Ref}& 1\\ R_k\left({?}_{Ref}\right)-{\stackrel{?}{R}}_{Ref}& 1\end{array}\right],& \left(1\right)\end{array}$${\stackrel{?}{R}}_{Ref}=\underset{n.fwdarw.?}{\lim }\frac{1}{n}*{.Math.}_1^n{R}_i\left({?}_{Ref}\right)?\mathrm{mean}\left[R\left({?}_{Ref}\right)\right]$$\begin{array}{cc}Y\left({?}_i\right)=\left[\begin{array}{c}{R}_1\left({?}_i\right)-R_1\left({?}_{Ref}\right)\\ .Math.\\ R_{k-1}\left({?}_i\right)-R_{k-1}\left({?}_{Ref}\right)\\ R_k\left({?}_i\right)-R_k\left({?}_{Ref}\right)\end{array}\right]& \left(2\right)\end{array}$$\left[\begin{array}{c}{?}_{TDDR}\left({?}_i\right)\\ {?}_{TDDR}\left({?}_i\right)\end{array}\right]=\left(Y\left({?}_i\right)*A^T\right)*{\left(A*A^T\right)}^{-1}$ [0025] ?.sub.Refreference temperature, typically 25? C. [0026] R.sub.Refaverage of the resistance at ?.sub.Ref, typically at 25? C., in mass production [0027] ?.sub.iith characterization temperature [0028] R.sub.k(?.sub.i.sub.)characterization resistance of the kth sample at the ith characterization temperature

[00002]$\left[\begin{array}{c}?\left({?}_i\right)\\ ?\left({?}_i\right)\end{array}\right]$

linearization coefficients for ith characterization temperature

[0029] Step 2: Determining the higher-order, in particular second-order, temperature dependency of the linearization coefficients over the temperature range of interest and determining the MOSFET-type-specific temperature dependency of the delta resistance (TDDR).

[00003]$\begin{array}{cc}A=\left[\begin{array}{ccc}{?}_1^2& {?}_1& 1\\ .Math.& .Math.& .Math.\\ {?}_{i-1}^2& {?}_{i-1}& 1\\ {?}_i^2& {?}_i& 1\end{array}\right]& \left(3\right)\end{array}$$\begin{array}{cc}?=\left[\begin{array}{c}?\left({?}_1\right)\\ .Math.\\ ?\left({?}_{i-1}\right)\\ ?\left({?}_i\right)\end{array}\right]& \left(4\right)\end{array}$$\begin{array}{cc}?=\left[\begin{array}{c}?\left({?}_1\right)\\ .Math.\\ ?\left({?}_{i-1}\right)\\ ?\left({?}_i\right)\end{array}\right]& \left(5\right)\end{array}$$\begin{array}{cc}\left[\begin{array}{c}{p}_{2,?}\\ p_{1,?}\\ p_{0,?}\end{array}\right]={\left(A^T*A\right)}^{-1}*\left(A^T*?\right)& \left(6\right)\end{array}$$\begin{array}{cc}\left[\begin{array}{c}{p}_{2,?}\\ p_{1,?}\\ p_{0,?}\end{array}\right]={\left(A^T*A\right)}^{-1}*\left(A^T*?\right)& \left(7\right)\end{array}$

two-dimensional TDDR

[00004]$\begin{array}{cc}TDD{R}_{2D}\left(?,R\left({?}_{Ref}\right)-{\stackrel{?}{R}}_{Ref}\right)={\left[\begin{array}{c}{p}_{2,?}\\ p_{1,?}\\ p_{0,?}\end{array}\right]}^T*\left[\begin{array}{c}{?}^2\\ ?\\ 1\end{array}\right]*\left[R\left({?}_{Ref}\right)-{\stackrel{?}{R}}_{Ref}\right]+{\left[\begin{array}{c}{p}_{2,?}\\ p_{1,?}\\ p_{0,?}\end{array}\right]}^T*\left[\begin{array}{c}{?}^2\\ ?\\ 1\end{array}\right]& \left(8\right)\end{array}$

one-dimensional TDDR

[00005]$\begin{array}{cc}TDD{R}_{1D}\left(?\right)={\left[\begin{array}{c}{p}_{2,?}\\ p_{1,?}\\ p_{0,?}\end{array}\right]}^T*\left[\begin{array}{c}{?}^2\\ ?\\ 1\end{array}\right]=p_{2,?}*{?}^2+p_{1,?}*?+p_{0,?}& \left(9\right)\end{array}$

[0030] Step 3: Using the TDDR for the reconstruction of the temperature dependency of the drain-source on-state resistance of a specific MOSFET of the same MOSFET type as characterized or used for determining the MOSFET-type-specific temperature-dependent delta resistance (TDDR) on the basis of the value of the drain-source on-state resistance R(?.sub.Ref) measured at the reference temperature ??.sub.Ref, usually at 25? C., and the average of the typical resistance R.sub.Ref, at the same reference temperature, obtained using the measurements in mass production.

R(?)=R(?.sub.Ref)+TDDR.sub.2D(?,R(?.sub.Ref)?R.sub.Ref)?R(?.sub.Ref)+TDDR.sub.1D(?)(10)

[0031] FIG. 2 shows the temperature dependency of the TDDR for a MOSFET type 1 for different junction characterization temperatures in a parameter representation, wherein the junction characterization temperature is used as the parameter, in a graph 30, on the abscissa 32 of which R(25? C.)?R25 [R?10.sup.?6] is plotted, and on the ordinate 34 of which R(T)?R(25? C.) [R?10.sup.?3] is plotted.

[0032] FIG. 3 shows the temperature dependency of the TDDR for a MOSFET type 2 for different junction characterization temperatures in a parameter representation, wherein the junction characterization temperature is used as the parameter, in a graph 70, on the abscissa 72 of which R(25? C.)?R25 [R?10.sup.?6] is plotted, and on the ordinate 74 of which R(T)?R(25? C.) [R?10.sup.?3] is plotted.

[0033] FIG. 4 shows the curve of the one-dimensional TDDR for the MOSFET type 1 in a graph 100, on the abscissa 102 of which T [? C.] is plotted, and on the ordinate 104 of which R(T)?R(25? C.) [R?10.sup.?3] is plotted.

[0034] FIG. 5 shows the curve of the one-dimensional TDDR for the MOSFET type 2 in a graph 130, on the abscissa 132 of which T [?] is plotted, and on the ordinate 134 of which R(T)?R(25? C.) [R?10.sup.?3] is plotted.

[0035] FIG. 6 shows the two-dimensional TDDR for the MOSFET type 1 in a graph 150, on the abscissa 152 of which T [? C.] is plotted, and on the ordinate 154 of which R(T)?R(25? C.) [R?10.sup.?3] is plotted.

[0036] FIG. 7 shows the two-dimensional TDDR for the MOSFET type 2 in a graph 180, on the abscissa 182 of which T [? C.] is plotted, and on the ordinate 184 of which R(T)?R(25? C.) [R?10.sup.?3] is plotted.

[0037] FIG. 8 shows the exemplary application of the one-dimensional TDDR to the MOSFET type 1 for different MOSFETs of this type in a graph 200, on the abscissa 202 of which T [? C.] is plotted, and on the ordinate 204 of which R(T) [R?10.sup.?3] is plotted.

[0038] FIG. 9 shows the exemplary application of the one-dimensional TDDR to the MOSFET type 2 for different MOSFETs of this type in a graph 230, on the abscissa 232 of which T [? C.] is plotted, and on the ordinate 234 of which R(T) [R?10.sup.?3] is plotted.

[0039] FIG. 10 shows the exemplary application of the two-dimensional TDDR to the MOSFET type 1 for different MOSFETs of this type in a graph 250, on the abscissa 252 of which T [? C.] is plotted, and on the ordinate 254 of which R(T) [R?10.sup.?3] is plotted.

[0040] FIG. 11 shows the exemplary application of the two-dimensional TDDR to the MOSFET type 2 for different MOSFETs of this type in a graph 280, on the abscissa 282 of which T [? C.] is plotted, and on the ordinate 284 of which R(T) [R?10.sup.?3] is plotted.

[0041] FIG. 12 shows the absolute error of the Rds(?) for the MOSFET type 1 using the one-dimensional TDDR in a graph 300, on the abscissa 302 of which T [? C.] is plotted, and on the ordinate 304 of which ?R(T) [R?10.sup.?6] is plotted.

[0042] FIG. 13 shows the absolute error of the Rds(?) for the MOSFET type 2 using the one-dimensional TDDR in a graph 330, on the abscissa 332 of which T [? C.] is plotted, and on the ordinate 334 of which ?R(T) [R?10.sup.?6] is plotted.

[0043] FIG. 14 shows the relative error of the Rds(?) for the MOSFET type 1 using the one-dimensional TDDR in a graph 350, on the abscissa 352 of which T [? C.] is plotted, and on the ordinate 354 of which ?R(T)/R(T) [%] is plotted.

[0044] FIG. 15 shows the relative error of the Rds(?) for the MOSFET type 2 using the one-dimensional TDDR in a graph 380, on the abscissa 382 of which T [? C.] is plotted, and on the ordinate 384 of which ?R(T)/R(T) [%] is plotted.

[0045] FIG. 16 shows the absolute error of the Rds(?) for the MOSFET type 1 using the two-dimensional TDDR in a graph 400, on the abscissa 402 of which T [? C.] is plotted, and on the ordinate 404 of which ?R(T) [R?10.sup.?6] is plotted.

[0046] FIG. 17 shows the absolute error of the Rds(?) for the MOSFET type 2 using the two-dimensional TDDR in a graph 430, on the abscissa 432 of which T [? C.] is plotted, and on the ordinate 434 of which ?R(T) [R?10.sup.?6] is plotted.

[0047] FIG. 18 shows the relative error of the Rds(?) for the MOSFET type 1 using the two-dimensional TDDR in a graph 450, on the abscissa 452 of which T [? C.] is plotted, and on the ordinate 454 of which ?R(T)/R(T) [%] is plotted.

[0048] FIG. 19 shows the relative error of the Rds(?) for the MOSFET type 2 using the two-dimensional TDDR in a graph 480, on the abscissa 482 of which T [? C.] is plotted, and on the ordinate 484 of which ?R(T)/R(T) [%] is plotted.

[0049] FIG. 20 shows, purely schematically and highly simplified, an arrangement for carrying out the described method, which is denoted overall by the reference numeral 500. This arrangement 500 can be integrated in a measuring arrangement for the characterization of the MOSFET in MOSFET production or be designed as such. The arrangement 500 can be used to examine a MOSFET 502 or any number of MOSFETs of different types. This MOSFET 502 comprises a gate terminal 504, a drain terminal 506 and a source terminal 508. The temperature characteristic of a drain-source on-state resistance 510 of the MOSFET 502 is determined.