The diffusion coefficient of electrons in silicon is De=36cm2s−1 . In a silicon layer, the electron density drops linearly from n=2.7∗1016cm−3 down to n=1015cm−3 over a distance of 2μm . What is the electron diffusion current density Jdiff,e (in A/cm2 ) induced by such a density gradient?
749.1
Why did the electron cross the silicon layer? Because it was attracted to the density gradient!
To calculate the electron diffusion current density, we can use the formula Jdiff,e = -q * De * dn/dx, where q is the charge of an electron, -1.6 x 10^-19 C.
Now let's plug in the values. We have De = 36 cm^2/s, dn = (2.7 x 10^16 - 10^15) cm^-3, and dx = 2 μm = 2 x 10^-4 cm.
Using the formula, we get:
Jdiff,e = -1.6 x 10^-19 C * 36 cm^2/s * [(2.7 x 10^16 - 10^15) cm^-3 / (2 x 10^-4 cm)]
Calculating this, we get the electron diffusion current density to be approximately -1.152 A/cm^2.
But hey, don't be negative about it! Just remember to consider the direction of the current when interpreting the negative sign.
To calculate the electron diffusion current density (Jdiff,e), we can use Fick's first law of diffusion:
Jdiff,e = -De * (∂n/∂x)
where Jdiff,e is the electron diffusion current density, De is the diffusion coefficient of electrons, n is the electron density, and x is the distance.
Given:
De = 36 cm^2/s
∂n/∂x = (n2 - n1)/(x2 - x1) = (1.6 * 10^15 cm^(-3))/(2 * 10^(-4) cm)
Substituting the values into the formula:
Jdiff,e = -De * (∂n/∂x)
= -36 cm^2/s * (1.6 * 10^15 cm^(-3))/(2 * 10^(-4) cm)
= -36 cm^2/s * 8 * 10^15 cm^(-3) / 2 * 10^(-4) cm
= -36 * 8 * 10^15 cm^(-2) / 2
= -144 * 10^15 cm^(-2) A/cm^2
The electron diffusion current density (Jdiff,e) induced by the density gradient is approximately -144 * 10^15 A/cm^2.
To calculate the electron diffusion current density, we can use Ohm's law for electron current, which states that the current density (Jdiff,e) is equal to the product of the charge carrier density gradient (Δn/Δx) and the diffusion coefficient of electrons in silicon (De).
First, let's calculate the charge carrier density gradient (Δn/Δx):
The change in electron density (Δn) is given by:
Δn = n2 - n1
= (1015 cm^(-3)) - (2.7 * 10^16 cm^(-3))
= -(2.69 * 10^16 cm^(-3))
The change in distance (Δx) is given by:
Δx = x2 - x1
= (2 μm) - (0 μm)
= 2 μm
Now, we can calculate the charge carrier density gradient (Δn/Δx):
(Δn/Δx) = (-(2.69 * 10^16 cm^(-3))) / (2 μm)
= (-2.69 * 10^16 cm^(-3)) / (2 * 10^(-4) cm)
= -1.345 * 10^20 cm^(-3)/cm
Next, we can calculate the electron diffusion current density (Jdiff,e) using Ohm's law:
Jdiff,e = (Δn/Δx) * De
= (-1.345 * 10^20 cm^(-3)/cm) * (36 cm^2/s)
≈ -4.84 * 10^21 A/cm^2
Note that the negative sign indicates that the electron diffusion current is opposite to the direction of the density gradient.
Therefore, the electron diffusion current density induced by the given density gradient is approximately -4.84 * 10^21 A/cm^2.