# Q. on Diode Equation

Discussion in 'Electronic Basics' started by Blake, May 26, 2005.

1. ### BlakeGuest

Recently I was looking into the use of a diode as a temperature sensor. I

Id=Is*(exp(qVd/NKT)-1)

This equation predicts that an increase in temperature T will result in an
increase in diode voltage Vd, assuming constant current. But I know from
experience that the opposite is true. Diode voltage drops as temperature
increases.

What gives? Is saturation current (Is) a function of temperature, strong
enough to reverse the upward dVd/dT predicted by the diode equation? Or do I
completely misunderstand the basics here?

2. ### Jonathan KirwanGuest

Yes, that's why. If you are interested, I'll post that equation, as
well.

Jon

3. ### BanGuest

Yes you misunderstand, look at the equation. The temperature T is appearing
in the denominator making the *current* increase with constant Vd, or in
other words you need less voltage for the same current. The relationship
dVd/dT (partial d) is roughly -2mV/K.

4. ### SpajkyGuest

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converter for diode to thermistor read-outs:
how to make a gadget that can do that for Cpu onDie diode for a PC
MoBo that is natively not supporting that feature:
my project is on my site under electronics ...
may be of use for some other purpose for someone ...

5. ### Jonathan KirwanGuest

I think you may be wrong in your rationalizing, here. An increase in
T would cause a _decrease_ in Id, not an increase. Thus, it would
require an increase in Vd in order to keep Id unchanged.

In this case, one needs to solve for Vd before taking the derivative
with respect to T. Thus:

Vd(T) = (kT/q) * ln( 1+Ic/Is )

The derivative (assuming 'Is' is constant relative to T) is then
trivially:

d Vd(T) = (k/q) * ln( 1+Ic/Is ) dT

and thus positive-going with respect to T.

I believe the OP was not mixed up about the question. See my other

Jon

6. ### Jonathan KirwanGuest

Ignoring the emission coefficient (taken as 1, for now), the equation
is:

Id(T) = Is(T) * (e^(q*Vd/(k*T))-1)

which becomes:

Vd(T) = (kT/q) * ln( 1 + Ic/Is(T) )

The derivative is trivially:

d Vd(T) = (k/q) * ln( 1 + Ic/Is(T) ) dT

which is a positive trend, very nearly +2mV/K for modest Ic... but
positive.

However:

Is(T) = Is(Tnom) * (T/Tnom)^3 * e^(-(q*Eg/k)*(1/T-1/Tnom))

which complicates things.

The new derivative is a bit large.

Assume:
X = T^3 * Isat * e^(q*Eg/(k*Tnom))
Y = Tnom^3 * Ic * e^(q*Eg/(k*T))

Then the derivative, I think, is:

X+Y
k*Tnom*T*( (X+Y) * ln( -------- ) - 3*Y ) - q*Eg*( X*T+Y*T+Y*Tnom )
Isat*T^3

---------------------------------------------------------------------

q * Tnom * T * (X+Y)

Tnom is the nominal temperature (Kelvin, of course) at which the
device data is taken and Eg is the effective energy gap in electron
volts for the semiconductor material. Of course, 'k' is Boltzmann's
constant and T is the temperature of interest.

Eg defaults to 1.11 eV in spice, I think. For an Ic=10uA and a stock
Isat of about 1E-15, the figure comes out to about -2.07mV/K in the
vicinity of 20 Celsius ambient.

Jon

7. ### Bob MastaGuest

<snip>
Check it out. Use an standard DMM on the 2 kOhm range to put
a constant current through the diode, while reading the voltage
across it. Now try warming and cooling the diode and you will
see that the voltage is directly proportional to temperature.
In fact, it is *so* proportional that this is one of the most linear
temperature sensors you will find, from near absolute zero until
the junction melts.

Best regards,

Bob Masta

D A Q A R T A
Data AcQuisition And Real-Time Analysis
www.daqarta.com
Home of DaqGen, the FREEWARE signal generator

8. ### Larry BrasfieldGuest

Then read Mr. Kirwan's contribution to see why you
are seriously mistaken with your assertion.
I expect the leads will melt first. And long
before that happens, the approximations
underlying the diode equation will fail to
be useful predictors of the junction voltage.

9. ### BanGuest

I throw in the formula for Is(T) = Isk * e(-Eg/mkT)
Eg = 1.11eV bandgap of silicon; m=q=1.1; Isk= 1E6A; k=1.38E-23Ws/K
Boltzmann

for 300K we get Is = 11.2pA; for 310K Is= 39.3pA
We put that into your formula and we get for 1mA current @300K 520.7mV and
@310K 501.0mV
-19.7mV/10K. The influence of Is is much bigger than the small change in
Vt= from 25.9mV to 26,7mV.
THX for the correction, Jon

10. ### Jonathan KirwanGuest

No problem. I'm just a hobbyist in electronics, so I rarely get to
say all that much about it. But I'm okay in math, so I can work a
model once in a while, here and there. It's nice when I can say
something but it doesn't mean I know a darned thing about the reality,
since my experience is so very limited.

Jon

11. ### Bob MastaGuest

OOPS! My face is red now! (And not from
high temperatures!)

OK, to set the record straight, my point
about the linearity still holds... I just got
the direction backwards: The voltage
goes *down* as the temperature goes
up. (I've never actually pushed it to see
what melts first, just assumed it was
the junction. I seem to recall that linearity
is typically good to well over 100C, though.)

Hey, nobody's purfekt! ;-)

Best regards,

Bob Masta