SaM - Sensors Based on Silicon Junctions (BJT and Integrated Circuits)

Remeber:

This kind of devices are absolute temperature sensors, and we can find integrated circuits which behave linearly, and have very good performances.
However they have a limited temperature range, which is ==the usual temperature range for integrated circuit which goes up to 150 degrees== or something like this

BjT used as a Constant Current Generator:

• Specifically here we have an npn transistor, remeber that: C is the collector, E the emitter, and B the base.
• ==There is a short-circuit between the base and the collector, therefore this device operates in the active region== (since $V_{BC}=0\text{V}$).
• The formula for a BjT in active region is:IMPORTANTE$V_{out}=V_{BE}=\frac{kT}{q}\ln \left(\frac{I_C}{I_S}\right)$
• If we use some standard values, we find:IMPORTANTE
  • For $T=T_A$ (ambience temperature), so $300\text{°K}$.
  • $V_{BE}=V_{out}=600\text{mV}$.
  • The dependency on temperature is actually non-linear, due to the dependency of $I_S$ on temperature, this has to be comensated.
  • More specifically:
    • Ideally its sensitivity would be $2\frac{\text{mV}}{\text{°K}}$.
    • Actually around $300°K$ if $I_S$ is not compensated, we have $\alpha =-4\frac{\text{mV}}{\text{°K}}$.NOT_SURE_ABOUT_THIS (It is a huge difference)

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Now we will see that there are also another class of sensors which can be conveniently placed here but finds also many other applications. And these are sensors based on silicon junctions.

This kind of devices are absolute temperature sensors and there actually are integrated circuits which behave linearly, and have very good performances. But have a limited temperature range to the usual temperature range for integrated circuit which goes up to 150 degrees or something like this. We will know see a simple example, which unfortunatly will not behave linearly.

The basic idea is this one, first we consider a BJT:

• Remember this is the collector ($C$), the emitter ($E$) and the base ($B$).
• There is a short circuit between the base and the collector, therefore this device operates in the active region.

The formula which governs the BJT is:

• $K$ is the Boltzmann constant
• $q$ is the charge of the electron.
• $I_S$ is the reverse saturation current.
• $I_C$ is the collector’s current, and it’s related to the density of the intrinsic carriers, the minority carriers.
• $N_A$ is the density of the hole in the base
• $D_n$ is the diffusion coefficient
• $A_q$ is the emitter area, and $w$ is the width of the base.

So, using the formula for the number of free electrons ($n_i$):

• $E_g$ : energy gap, can be considered approximated constant.
• I don’t know what we use the $n_i$ formula for.
• So at the end it will be that: $V_{out}=\frac{KT}{q}\ln \left(\frac{I_C}{I_S}\right)$ So for $T=T_A=300°K$ (ambience temperature) and using some standard values for the other variables, we have:
• We have a stronger influence due to the variation of this current here which makes this behavior here not linear.
  ⇒ therefore it should be compensated.
• There are some integrated circuit which exploits the dependence of the conductance in a BJT due to temperature, tho they are a little bit more complex, they encompass also a compensation strategy for the dependence of $I_S$ on temperature.

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