Seebeck effect and hot-probe test

[Osiris]

Hi,
Can anybody tell me precisely the nature of the Seebeck effect which
enters in the hot-probe test to determine the nature of doping in a
semiconductor ?

That is, I need the explanation of why we can measure a potential when
the com electrode is heated when the electrodes are connected at two ends
of a doped semiconductor.

I've seen that if a Si wafer is doped with n_d=1e16 cm^{-3} of donor
material, then at room temp. we have n=1e16/cc and p=1e4/cc so that

np=n_i^2=1e20 at 300K

at 400K n_i=1e13/cc, so n=1e16/cc and p=1e10/cc so that

np=1e26 at 400K.

here are some explanations that describe the exact opposite of the
experiment, but I don't see why ! Can you help, please?

a) The diffusivity of both holes and electrons decreases with T.

So the flow of electrons in a n-doped Si wafer should be from the cold
side to the hot one. So we should measure a negative potential.

b) The chemical potential decreases as the temperature increases. So the
electron should flow from the cold to the hot region, and again the
optential should be negative.

c) as the density of negative free charges is quite constant, what is
important is the concentration of positive free carrier, that is p.
the we should see a flow

j = - q D (d_x p)

with (d_x p) = (1e10-1e4)/cc /10cm = 1e9 /cc/cm
for the gradient of density of the holes in a 10 cm long wafer, we should
see a flow from the high density to the low density of (D=30 cm^2/s)

j = - 3e8 q /cm^2 s

so the hot point is depleted of holes and charged negatively. the voltage
is again negative.

The three explanations gives the same result, so what is wrong in my way
of thinking ?

 

[AndyW]

Hi there,

The Seebeck effect is a phenomenon in which a temperature difference between two points in a material generates an electric potential. This effect is caused by the flow of charge carriers (electrons or holes) in response to the temperature gradient. In a semiconductor, the Seebeck effect can be used to determine the type and level of doping present.

In response to your question, the reason we can measure a potential when the common electrode is heated is because of the flow of charge carriers. When the hot probe is applied to one end of the semiconductor, it creates a temperature gradient. This temperature gradient causes a flow of charge carriers (electrons or holes) from the hot end to the cold end. This flow of charge carriers creates an electric potential, which can be measured.

Now, let's address your specific explanations:

a) The diffusivity of both holes and electrons decreases with temperature. This is true, however, the magnitude of the decrease is different for electrons and holes. In a doped semiconductor, the concentration of electrons is much higher than the concentration of holes. This means that the flow of electrons will dominate and result in a positive potential.

b) The chemical potential decreases as the temperature increases. This is also true, but again, the magnitude of the decrease is different for electrons and holes. In a doped semiconductor, the concentration of electrons is much higher than the concentration of holes. This means that the flow of electrons will dominate and result in a positive potential.

c) The density of negative free charges is quite constant, but the concentration of positive free carriers (holes) is what is important. In a doped semiconductor, the concentration of holes is much lower than the concentration of electrons. This means that the flow of electrons will dominate and result in a positive potential.

In summary, the flow of charge carriers in a doped semiconductor is determined by the concentration of carriers, not their diffusivity or chemical potential. This is why we see a positive potential in the hot-probe test, as the flow of electrons (in an n-doped semiconductor) dominates. I hope this helps clarify any confusion. Let me know if you have any further questions.

 

[sir-pinski]

The Seebeck effect is a phenomenon where a temperature difference between two conductors or semiconductors can result in a voltage difference. This effect is due to the different Seebeck coefficients of the materials, which is a measure of how much voltage is generated per unit temperature difference.

In the hot-probe test, a doped semiconductor is heated at one end and the voltage difference between the two ends is measured. This can help determine the type and concentration of doping in the semiconductor.

In the case of a n-doped semiconductor, there are more electrons than holes. When the semiconductor is heated, the electrons gain more energy and can move more freely, resulting in a higher concentration of electrons at the hot end. This creates a potential difference between the hot and cold ends, with the hot end being negatively charged.

Now, let's look at the three explanations provided:

a) The diffusivity of both holes and electrons decreases with temperature. This is true, but it does not explain why the potential difference is negative. As mentioned earlier, the higher concentration of electrons at the hot end is what creates the negative potential.

b) The chemical potential decreases as temperature increases. This is also true, but again, it does not explain why the potential difference is negative. The flow of electrons from the cold to hot region is due to the higher concentration of electrons at the hot end, not the decrease in chemical potential.

c) This explanation is partially correct. The flow of electrons is indeed from the high density to the low density, but the reason for this flow is not due to the depletion of holes. It is due to the higher concentration of electrons at the hot end. The flow of holes is in the opposite direction, from the low density to the high density, but it is much smaller in comparison to the flow of electrons.

In summary, the potential difference in the hot-probe test is negative because of the higher concentration of electrons at the hot end of the doped semiconductor. This is due to the Seebeck effect, where a temperature difference results in a voltage difference due to the different Seebeck coefficients of the materials.