A question of temperature dependence of Is current of a diode

[bhl777]

Hi All, I am trying to use a diode connected circuit from https://en.wikipedia.org/wiki/Log_amplifier.

From it we can see the final equation is this


However, I have a question about Is0. From other literature, this saturation current is also a function of temperature, so the question here is:
If I want to write a equation of Ic(T), is the temperature coefficient of Is0 can be negalected? Can we treat this Iso as a constant compared with the change of e(Vbe/Vt) over a range of temperature?

For example, now I want to compare the Ic at 200K and 350K, can I say the difference of them are mainly come from e(Vbe/Vt) but not from Is0(T)?

Thank you very much!

 

[Junus2012]

Hello
although you when you work in the forward region it seem to be that the Is is not here but still it considered in the diode forward current as you showed in the diode equation. at the high temperature the value of Is will be large, so you can not neglect it or consider it constant.

 

[bhl777]

Hi Junus,

Could you tell me roughly range of temperature that I can neglect temperature coefficient for Is? And what about low temperature performance of Is?(like -100C to 0C).

Thank you very much!

Hello
although you when you work in the forward region it seem to be that the Is is not here but still it considered in the diode forward current as you showed in the diode equation. at the high temperature the value of Is will be large, so you can not neglect it or consider it constant.

 

[Junus2012]

Hello

I have just read in wiki that the Is can vary from µA at low temperature to µAs at elivated temperature. if you can cancel Is at the small T it is ok but at high T the result is not accurate to do

 

[erikl]

... I want to compare the Ic at 200K and 350K, can I say the difference of them are mainly come from e(Vbe/Vt) but not from Is0(T)?

Hi bhl,
the saturation current Is0 is a fix parameter for a diode, depends only on technology, structure and area of the diode, not on temperature.
The (exponential) temperature dependency of Ic (in first approximation) depends only on the temperature dependency of the thermal voltage Vt = kT/q .

 

[Junus2012]

Hello Erikel
these are articles regarding the Is dependency with temperature

- - - Updated - - -

Also the one here

- - - Updated - - -

and because Is is a part of the forward current equation then it will effect the forward current specially at high T

 

[timof]

The saturation current of a p-n junction (or a diode) is temperature dependent.
If SPICE model does not include this temperature dependence - that's a problem of the SPICE model.

According to Sze's book (Physics of Semiconductor devices):

Js ~ T^(3+gamma/2) * exp(-Eg/kT)

Here T is the temperature, gamma is some parameter (D/tau ~ T^gamma), and Eg is the bandgap of a semiconductor.

The dominant factor here is exponential temperature dependence.
It is determined by the fact that Js is proportional to ni^2, where ni is intrinsic concentration that is strongly temperature dependent: ni ~ exp(-Eg/2kT).

In reality, another effect is important - reverse current is not actually saturated with reverse voltage, it is increasing due to the expansion of the depletion region volume where the charges are thermally generated and extracted by the electric field in the depletion region.

Max
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[bhl777]

Hi timof, you said Js ~ T^(3+gamma/2) * exp(-Eg/kT)
Do you really want to say Jc ~ T^(3+gamma/2) * exp(-Eg/kT)? And Js ~T^(3+gamma/2) ?

Could you give me an idea what this gamma roughly is. Then I can see the change of Js(T) will take effect on Jc(T).

Thank you!

The saturation current of a p-n junction (or a diode) is temperature dependent.
If SPICE model does not include this temperature dependence - that's a problem of the SPICE model.

According to Sze's book (Physics of Semiconductor devices):

Js ~ T^(3+gamma/2) * exp(-Eg/kT)

Here T is the temperature, gamma is some parameter (D/tau ~ T^gamma), and Eg is the bandgap of a semiconductor.

The dominant factor here is exponential temperature dependence.
It is determined by the fact that Js is proportional to ni^2, where ni is intrinsic concentration that is strongly temperature dependent: ni ~ exp(-Eg/2kT).

In reality, another effect is important - reverse current is not actually saturated with reverse voltage, it is increasing due to the expansion of the depletion region volume where the charges are thermally generated and extracted by the electric field in the depletion region.

Max
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[timof]

Hi timof, you said Js ~ T^(3+gamma/2) * exp(-Eg/kT)
Do you really want to say Jc ~ T^(3+gamma/2) * exp(-Eg/kT)? And Js ~T^(3+gamma/2) ?

Could you give me an idea what this gamma roughly is. Then I can see the change of Js(T) will take effect on Jc(T).

Thank you!

In equation I copied from Sze's book, Js is saturation current density (same as Iso in your equation).

Please refer to S.Sze book, 2nd edition, page 88 (section 2.4.1 Ideal Case Shockley equation), or to any book on semiconductor device physics.

 

[erikl]

IMHO it's a question of the method of approach where you put the forward current's temperature dependence (I_{f_Tc}) : Some authors put it (perhaps only partly) into the saturation current Is itself, for SPICE models Is is a fixed parameter, the temperature dependence is calculated via a more or less complex equation depending on the model no. For a first (and already very good) approximation, you can calculate I_{f_Tc} as

If = Is * e^q|Vf|/nkT , where Is is a fixed parameter, q/kT = 1/Vt , n≈1.5 for silicon between 200..600K, s. e.g. Grove, Physics and Technology of Semiconductor Devices, 6th edition, pp. 188-189, or this clipping from the Sze book: .

 

[timof]

Erikl -

I am pretty sure that SPICE calculates the temperature dependence of Js according to the formulas given above.

You are talking about a SPICE model parameter Is0, that is "fixed", i.e. temperature-independent, while we are talking about the real life temperature behavior of diode's reverse current.

https://users.ece.gatech.edu/mleach/ece3040/notes/chap02.pdf

 

[timof]

Attached picture shows SPICE (LTSPICE) calculated I-V curves of some commercial diode - clearly, the saturation current (current at large reverse bias) depends strongly on temperature...

 

[erikl]

Erikl -

I am pretty sure that SPICE calculates the temperature dependence of Js according to the formulas given above.

You are talking about a SPICE model parameter Is0, that is "fixed", i.e. temperature-independent, while we are talking about the real life temperature behavior of diode's reverse current.

Hello Max,

thank you for the course chapter! Of course I know that the saturation current is strongly temperature dependent, so I thought I could have mixed up Is (or Js) with Is0 (or Js0), however there's no such parameter (Is0 or Js0) in any of my SPICE model files (level 1..54). The temperature dependent diode, BJT & MOS diode saturation and forward currents all are calculated from the fixed Is (or Js) parameter, also additionally considering the temperature dependence of the band gap Eg as well as that one of the intrinsic carrier concentration ni in the higher level models.

It's all a question of nomenclature, isn't it?
erikl

 

[FvM]

You are talking about a SPICE model parameter Is0, that is "fixed", i.e. temperature-independent, while we are talking about the real life temperature behavior of diode's reverse current.

The original post (about log-amplifier application of diodes) and all related contributions have been talking about diode forward current.

 

[erikl]

The original post (about log-amplifier application of diodes) and all related contributions have been talking about diode forward current.

... which also needs the saturation current Is for the calculation of its temperature dependent behavior, see e.g. the following clipping from the diode.pdf mentioned above:

Would you think these are different saturation currents with unfortunately the same abbreviation?

 

[FvM]

Would you think these are different saturation currents with unfortunately the same abbreviation?

I wanted primarly to clarify, that reverse bias current isn't the original topic of this thread.

I know, that in the shockley equation Is corresponds to an effectively voltage independent reverse bias current. Apart from the point, that the real reverse bias current is mostly ruled by additional parameters, as your literature also mentions, Shockley's Is is surely temperature dependent. In so far I agree with Max.

In SPICE the parameter IS is the saturation current at TNOM (default 300K), supplemented by an temperature exponent XTI (defaulting to 3.0). This means, IS in SPICE is somehow a different parameter with the same name. Reverse bias currents are modelled in SPICE by different parameters, not depending on IS.

P.S.: I forgot an important point about Is temperature dependency. With temperature indpendent Is, the forward current at constant Vd would have a negative temperature coefficient according to the Shockley equation. As everyone knows, the T.C. is positive, correponding to a Vd T.C. of about -2mV/K at constant Id. This means, Is must be stronger temperature dependent than the negative T.C. of exp(Vd/Vt).

 

[erikl]

P.S.: I forgot an important point about Is temperature dependency. With temperature indpendent Is, the forward current at constant Vd would have a negative temperature coefficient according to the Shockley equation. As everyone knows, the T.C. is positive, correponding to a Vd T.C. of about -2mV/K at constant Id. This means, Is must be stronger temperature dependent than the negative T.C. of exp(Vd/Vt).

This is really a telling argument, as the temperature dependence of the forward current without the saturation current's temperature dependence would not only be positive, but also terribly large, as an evaluation of the above equation for constant saturation current shows: about 15..18%/K relative If change for forward voltages between 0.6..0.7V @ 300K, s. the foll. image:

Thanks a lot, Frank!

 

[timof]

It's good that we all agree that both reverse and forward current of a diode are strongly temperature dependent - and the higher the temperature, the higher the current.

"as everyone knows" is a good argument to check the consistency of the analysis or of the results, to make sure they do not contradict the common wisdom or basic physics.

In order to get e better feeling of the problem, though, and to relate it to basic physics, we should think in terms of these arguments:
in a p-n junction (diode) in equilibrium (zero applied voltage), there is a potential barrier for electrons to go from n- to p-type doped semiconductor.
This barrier is roughly equal to Eg - bandgap (it is easy to derive the exact formula for this barrier, or to look up in textbooks).
Some high-energy electrons are still injected to p-type semiconductor, and this injection current is compensated by the electron current flowing in the opposite direction, due to the extraction of miunority carriers (electrons) from p-type region by the built-in electric field in the depletion region.

When forward voltage V is applied, the barrier for the electrons becomes smaller than Eg: Vb=Eg-V.
Since electrons in the conduction band are distributed (in energy) according to Boltzmann distribution (conc. ~ exp(-E/kT)), the electron current is equal to: I= a*[exp((V-Eg/e)/kT) -exp(-Eg/ekT)] = a*exp(-Eg/ekT)*[exp(V/kT) -1].
"minus 1" is "needed" to have zero current at V=0. "a" is some constant.
Thus, the reverse saturation current equals a*exp(-Eg/ekT), and thus increases strongly with temperature.
Forward current also increases with temperature for negative values of (V-Eg/ekT) ( almost always the case - it's hard to apply a forward voltage larger than Eg/e to a diode), but with a slower rate than the reverse current - because exponential factor (V-Eg/ekT) is smaller than (-Eg/ekT by absolute value.

One can see from the plots of SPICE simulation (see above in this thread) that the relative change of forward current is smaller than relative change of reverse current, and the higher the forward applied voltage - the lower the (relative) temperature dependence of the current.

Thus, the underlying root cause for the temperature dependence of the diode current (both forward and reverse) is - energy barriers, and Boltzmann.

Max
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