A vacuum condition with lower than 50Pa is required. Plus, what are the conditions people consider whether ECV or Hall is chosen for carrier mobility/concentration measurement
Thermal stability is very important in the measurement of carrier concentration. Basically, we measure the hall voltage to calculate the hall resistance, which is further used to estimate the carrier concentration of the sample using the formula obtain from the single parabolic band model or quantum theory of charge transportation. The fundamental protocol in the hall voltage measurement is the measurement of voltage drop perpendicular to the current flow direction and externally applied magnetic field. Under high vacuum conditions, we minimise the number of gas molecules present in the surrounding sample, which make collisions randomly at a different rate depending upon the sample temperature. If the vacuum is not good, then the gas molecules will exchange the heat energy with the sample. Now, the more exchange of gas molecules will create the temperature gradient or thermal instability i.e. non-uniform temperature across the sample. This may cause the extra voltage drop (thermoelectric voltage), or thermal fluctuation. This thermal fluctuation act as driven force for the charge carriers moving through the sample in a random way. If we look at the samples which have the carrier concentrations in the range of heavily doped semiconductors or metals, the actual drop of hall voltage is very small. If the noise or extra voltage is more than the actual hall voltage from the sample, one might get the wrong estimation of the carrier concentration of the material or noisy data. Of course, we can increase the magnitude of hall voltage, being measured by increasing the applied field and current, but it has limitations either in case of the constraint of the measurement setup, or Joule heating occurs due to high applied current to the sample. So, the best way to get the accurate signal coming from the sample could be in a condition with the best thermal stability. This can be achieved with very good vacuum conditions. Last but not least, a good vacuum also protects any reaction or sample degradation or chemical composition change due to interaction of gas molecules and sample, which might get occur when the temperature-dependent measurement is carried out, especially at high-temperature range measurement chemical stability and thermal stability is very crucial. I hope it will help you plan your measurement. Good luck.
Dear Saurabh Singh,
I have some query on your answer.
You say that the vacuum is needed to reduce the collision of surrounding gas particles with the sample and thus reduces the thermal fluctuations.
But, how can you reduce the temperature change due to Joul heating and heat radiation?
I think, about 10 to 20 amp current is needed to flow through the conductors for producing Hall voltage of few micro volts.
( depends on Magnetic field).
This causes change in temperature, if the experiment is carried out for a comparatively longer time.
Thanks
N Das
Nityananda Das Dear Sir, I appreciate the fundamental questions pointed out. It is correct that the radiation effect can not be minimized by vacuum as the radiation propagates through the vacuum. To prevent heat radiation, the best way is to use the heat shield, which is typically done by making metallic baffle (mostly copper as it has high thermal conductivity, is cheap and is easy to machine in the desired shape). Using a heat shield we can make more thermal stable conditions around the sample.
Now, come to the second point about the amount of current. With my understanding and experience, I have never come across the use of high current (in ampere range) use in hall measurement. Mathematically, it is correct that a large current will provide the largely driven force for the charge carriers and thus the large voltage drop (or quick achievement of equilibrium condition). typically the current use in hall measurement is a few milliamperes (Quantum design PPMS system having very precise and sensitive voltmeter). The Joule heating effect is more prominent when we measure the intrinsic semiconductor or insulator system having large resistance as compared to the metal. As the semiconductor and insulator materials have a large Seebeck coefficient, thus any small temperature difference caused by Joule heating will add the thermoelectric voltage. here, it is important to note that, hall voltage is measured perpendicular to the current flow direction. Thus, the thermoelectric voltage which is perpendicular to the hall voltage might not have an effect on the magnitude of measured voltage (ideal condition when both hall voltages measured probe have contact exactly perpendicular), but this will affect the stability condition as induced thermoelectric voltage have thermo emf and affect the trajectory of charge carriers from the magnetic field and current flow. The optimized current condition can be checked during the experiment. Which is quite tricky. The best way to deal with the metallic sample is to prepare the sample with a very small thickness (~0.1 mm) which help to increase the resistance, thus with a small applied current also, one can get a sufficient voltage signal. This is my understanding. Some experts working in the field of hall measurement can add more detailed information about your query. I will be thankful to them.
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