If I kown the doping concentration in one semiconductor, whether there are some methods to estimate the moblity?
Let’s assume for clarity that the semiconductor is n-type Si doped with a shallow donor impurity P in concentration Nd = 10^14 – 10^16 cm^-3. At room temperature and above, all the shallow donor impurity atoms will be ionized providing free electron carriers concentration in n-type Si n = 10^14 – 10^16 cm^-3. The relationship between conductivity and free carriers mobility is well known in the theory of semiconductors, and in our case it is:
= x x
That is
σ = enµ,
where σ = ρ^-1 (ρ is Resistivity).
Hence measuring ρ or σ and knowing n, one can find µ.
Semiconductor theory considers two major mechanisms for free carriers’ mobility dependency of crystal temperature.
One is for “high” temperatures where phonon and electron momentums become comparable, so that a free electron can change its initial direction in just one collision with a phonon. Also, the phonon concentration is growing with the temperature. It is shown that mobility depends of temperature as µ ~ T^-3/2 in the “high” temperature region (typically well above room temperature). Hence, in the “high” temperature region, scattering of free carriers on phonons with growing temperature lead to the carriers’ mobility reduction.
Another one is a “low” temperature region (typically well below room temperature) where shallow donors are not completely ionized and the concentration of free electrons changes according to the Fermi level temperature dependence – the lower the temperature, the less free electrons concentration, that is n becomes a function of T. It is shown that the dominating scattering mechanism is scattering of free carriers on ionized impurity centers where µ ~ T^3/2. Free carriers’ mobility is growing with the temperature increase in this region.
There is an intermediate region of temperatures between “low” and “high” regions where a mixture of both scattering mechanisms can co-exist.
In summary, knowing type and concentration of doping impurities and their energy level in the forbidden band and measuring a semiconductor’s conductivity, one can determine mobility of free electrons or holes.
Let’s assume for clarity that the semiconductor is n-type Si doped with a shallow donor impurity P in concentration Nd = 10^14 – 10^16 cm^-3. At room temperature and above, all the shallow donor impurity atoms will be ionized providing free electron carriers concentration in n-type Si n = 10^14 – 10^16 cm^-3. The relationship between conductivity and free carriers mobility is well known in the theory of semiconductors, and in our case it is:
= x x
That is
σ = enµ,
where σ = ρ^-1 (ρ is Resistivity).
Hence measuring ρ or σ and knowing n, one can find µ.
Semiconductor theory considers two major mechanisms for free carriers’ mobility dependency of crystal temperature.
One is for “high” temperatures where phonon and electron momentums become comparable, so that a free electron can change its initial direction in just one collision with a phonon. Also, the phonon concentration is growing with the temperature. It is shown that mobility depends of temperature as µ ~ T^-3/2 in the “high” temperature region (typically well above room temperature). Hence, in the “high” temperature region, scattering of free carriers on phonons with growing temperature lead to the carriers’ mobility reduction.
Another one is a “low” temperature region (typically well below room temperature) where shallow donors are not completely ionized and the concentration of free electrons changes according to the Fermi level temperature dependence – the lower the temperature, the less free electrons concentration, that is n becomes a function of T. It is shown that the dominating scattering mechanism is scattering of free carriers on ionized impurity centers where µ ~ T^3/2. Free carriers’ mobility is growing with the temperature increase in this region.
There is an intermediate region of temperatures between “low” and “high” regions where a mixture of both scattering mechanisms can co-exist.
In summary, knowing type and concentration of doping impurities and their energy level in the forbidden band and measuring a semiconductor’s conductivity, one can determine mobility of free electrons or holes.
Hi
The exact solution is montecarlo
by this method you can have best result and simulation
ref Tamisawa book
Hi Len Leonid Mizrah,
Thanks for your answer. Form the conductivity or Resistivity, I can get the mobility of majority carriers, but how can I know the mobility of minority carrier?
For a heavy doped Si, there are formulae to calculate electron and hole mobilities if one knows concentrations of donors and acceptors:
https://en.wikipedia.org/wiki/Electron_mobility
In this link above see the section titled 'Doping concentration dependence in heavily-doped silicon'.
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