Method for determining a mathematical model of the electric behavior of a PN junction diode, and corresponding device

1. A method for determining a mathematical model of the electric behavior of a reverse-biased PN junction diode, comprising:

measuring the value of voltage V present across the diode and the value of the corresponding current I running through this diode, said diode being reverse-biased and said voltage V varying within a range of values including the value of breakdown voltage V BK of said diode;

establishing a representation of function

ln

⁡

(

I

-

I

s

)

according to voltage V, from said measured values of current I and of voltage V, I S being the saturation current of said diode;

determining a first linear function representative of an approximately linear portion of said function

ln

⁡

(

I

-

I

s

)

,

said linear portion being characterized by voltages V greater than breakdown voltage V BK in terms of absolute value;

calculating an avalanche multiplication factor defined by:

MM

=

1

+

ⅇ

(

-

slbv

·

V

+

bv

bv

)

,

 wherein:

the values of parameters slbv and bv being extracted from said linear function,

slbv being equal to the ordinate at the origin of said linear function, and

slbv/bv being equal to the slope of said linear function.

2. The method according to claim 1 , wherein it further comprises the step of extracting the value of the saturation current Is of said diode by determining the current I when the voltage V across the diode is equal to zero, from a current-vs-voltage characteristic of said diode in forward-bias operation, and for a given temperature.

3. The method of claim 1 , wherein the step of determining said first linear function comprises:

based on the measured values of voltage V and current I, determining the value of a inflection voltage V LIN for which second numerical derivative d 2 I/dV 2 is maximum; and

determining the equation of the tangent of said function

ln

⁡

(

I

-

I

s

)

at an inflection point, said inflection point having said inflection voltage V LIN as an abscissa.

4. The method according to claim 3 , wherein parameters slbv and bv are extracting from said tangent, slbv being equal to the ordinate at the origin of said tangent and slbv/bv being equal to the slope of said tangent.

5. The method of claim 1 , wherein it further comprises:

establishing a representation of function

ln

(

I

-

I

s

·

ⅇ

(

-

slbv

·

V

+

bv

bv

)

-

I

s

)

according to voltage V, from said measured values of current I and of voltage V, and from said extracted values of slbv and bv;

determining a second linear function representative of an approximately linear portion of said function

ln

(

I

-

I

s

·

ⅇ

(

-

slbv

·

V

+

bv

bv

)

-

I

s

)

,

said portion being characterized by voltages V smaller than breakdown voltage V BK in terms of absolute value;

calculating the avalanche multiplication factor defined by:

MM

=

1

+

ⅇ

(

-

slbv

·

V

+

bv

bv

)

+

ⅇ

-

smbv

⁡

(

V

+

bv

+

off

)

,

 wherein:

the values of parameters smbv and off being extracted from said second linear portion;

smbv being the slope of said second linear function; and

smbv (bv+off) being the ordinate at the origin of said second linear function.

6. The method of claim 5 , wherein the step of determining said second linear function is performed for values of reverse voltage V ranging between a first voltage and bv, said first voltage being smaller than the value of bv in term of absolute value.

7. The method of claim 5 , wherein the step of determining said second linear function is performed for values of reverse voltage V ranging between a second voltage and by, said second voltage being greater than the value of bv in term of absolute value.

8. A method, comprising:

measuring the voltage versus current characteristics of a reverse biased PN junction diode over a range of voltages including a breakdown voltage;

identifying a functional relationship according to voltage between measured values of current and saturation current of the PN junction diode;

determining a linear function that represents an approximately linear portion of the identified functional relationship for voltages in excess of the breakdown voltage; and

calculating an avalanche multiplication factor for the PN junction diode as a function of an ordinate value at an origin of the determined linear function and a slope value of the determined linear function.

9. The method of claim 8 , further comprising determining the saturation current from the measured voltage versus current characteristic when voltage is equal to zero.

10. The method of claim 8 , wherein determining the linear function comprises identifying an inflection point corresponding to an inflection voltage of the voltage versus current characteristic, and wherein determining the linear function comprises identifying a tangent line of the functional relationship at the identified inflection point.

11. The method of claim 8 , further comprising:

identifying an additional functional relationship according to voltage between measured values of current and saturation current of the PN junction diode;

determining an additional linear function that represents an approximately linear portion of the identified additional functional relationship for voltages less than the breakdown voltage; and

calculating an additional component of the avalanche multiplication factor for the PN junction diode as a function of an ordinate value at an origin of the determined additional linear function and a slope value of the determined additional linear function.