hi
have thermal velocities electron and hole in semiconductors constant?
What are they calculated?
thanks
Hello Ahmed,
the thermal velocity v can be estimated by
v = SQRT(3kT/m)
with k the Boltzmann constant and m the effective mass. Using this formulae, the velocity is proportional to the squareroot of the temperature. It is an approximation of classical statistical mechanics and valid only for nondegenerated semiconductors. You have a velocity distribution like in classical gases. The most particals (here electrons or holes) have a velocity near the average velocity.
Generally, the Fermi distribution must be considered. Furthermore, crystal properties like the mass anisotropy must be taken into account. But in many cases the upper expression gives a good estimation for the mean velocity.
Yours
R. Mitdank
Greetings.
See graphs of some dependencies for impurities in Fig. 1 and Fig. 2. For other SC materials there may be variations in values, but the trends of changes are approximately preserved.
The thermal velocities vn and vp are given by:
vn=(An*TL*TL)/(q*NC) and
vp=(Ap*TL*TL)/(q*NV)
where TL is the lattice temperature, NC is the conduction band density of states, NV is the valence band density of states, and An and Ap are the electron and hole Richardson constants.
For Richardson constants the following expressions will be used:
An=(4*pi*q*k2*mn)/(h3) and
Ap=(4*pi*q*k2*mp)/(h3)
where mn and mp are the electron and hole effective masses
Dear Mohsen,
Thermal velocity for thermal velocities of electron and hole in semiconductors is constant. In between two successive collisions electrons (or holes) move with an average velocity which is called the thermal velocity. It is represented by Vth. Generally it is taken 107 cm /sec.
Calculation of Vth :
Mean distance traveled between collisions=. tc
Mean distance traveled between collisions is called the mean free path λ= Vth. tc
In pure Silicon, tc = 0.1. 10-12 s= 0.1 ps(approx)
Vth= 107 cm/sec (approx)
Mean distance traveled between collisions is called the mean free path λ= Vth. tc= 107 cm/sec X 0.1. 10-12 s= 0.01µm (approx)
(**You have not asked me reason so I am skip the reason answer.)
Ashish
Dear Mohsen,
Thermal velocity for thermal velocities of electron and hole in semiconductors is constant. In between two successive collisions electrons (or holes) move with an average velocity which is called the thermal velocity. It is represented by Vth. Generally it is taken 107 cm /sec.
Calculation of Vth :
Mean distance traveled between collisions=. tc
Mean distance traveled between collisions is called the mean free path λ= Vth. tc
In pure Silicon, tc = 0.1. 10-12 s= 0.1 ps(approx)
Vth= 107 cm/sec (approx)
Mean distance traveled between collisions is called the mean free path λ= Vth. tc= 107 cm/sec X 0.1. 10-12 s= 0.01µm (approx)
(**You have not asked me reason so I am skip the reason answer.)
Ashish
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