Redefine the constants and equation for electrons:ĭ n is the electron diffusion coefficient with units cm 2/s. *this derivation can also be used for holes! In order to approximate the electron concentration as x changes, assume that x is very small. We assume l is very small, and therefore can use the slope at x o in order to determine the electron concentration (n) at x o ± We can define both n 1 and n 2 using an excerpt of the above graph. The difference in electron concentration between the two points (n 1 and n 2) needs to be written in terms that we understand. Therefore, the electron flux density from left to right = Rate of diffusion for electrons in semiconductors =Įlectron flux density = number of electrons passing x o per unit time per unit areaĬonsider small segments of width l to the left and right of x 0 and approximate the electron concentrations n 1 and n 2 in these segments as uniform. Concentration is supposed to be constant for every segment. Arbitrary part of n(x) is divided into the segments of length equal to a mean free path for the electrons. Spreading of a pulse of electrons by diffusion. With time (t1, t2, t3), an initial pulse of electrons will diffuse. N and p = electron and hole concentrations Equation of diffusion for carriers in the bulk of semiconductor J n and J p = the diffusion current densitiesĭ n and D p = diffusion coefficients for electrons and holes One-dimensional diffusion equationsįor electrons (n) and holes (p) can be written as follows: It is known from the molecular physics that the flux of diffusing particles is proportional to the concentration gradient. The holes (colored blue) have a lower diffusivity than the electrons (colored red), and so take longer to fill the full space. The holes (blue) and the electrons (red) move from areas of high concentration to low concentration w/in a semiconductor towards an even distribution. If we let random movement do it's thing, over time, the carriers will become evenly spread across the space through random motion alone. The net movement of carriers is therefore from areas of high concentration to low. The constant random motion of carriers can lead to a net movement of carriers if one particular region has a higher concentration of carriers than another region (a concentration gradient between the high carrier-concentration region and the low carrier-concentration region).
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