I think so. If it was not the case then the number of mobile electrons or the number of mobile holes would be increasing and the other would be decreasing. It is just a statement that on average the rate of generation of mobile carriers is equal to the rate of recombination.does np=ni^2 holds even the space charge region of a pn junction diode?
Also remember the the relationship is about a statistical average at thermal equilibrium with no external bias or energy source (sunlight for example). In the space charge region the electric field prevents mobile carriers from entering or crossing the region in the classical sense. We are dealing with quantum mechanics here so tunneling must be a possibility. The space charge region is very narrow and its existence does not alter the statistical averages for the semiconductor as a whole. The average concentration of mobile carriers does not change when it comes into being, because even in a solid there is a great deal of empty space for all the wee bits to knock about.Yes. Which shows that the space charge region isn't really completely empty of electrons or holes. It's just that ni is a relatively small number compared to the number of electrons or holes in a typical current flow.
But if the junction is biased the np product goes up or down, depending on polarity of the external bias.
Maybe it would be more correct to say that the space charge region inhibits mobile carriers from entering or crossing. Quantum tunneling is still possible. The lack of mobile carriers in the space charge region has a negligible effect on the average concentration of mobile carriers in the semiconductor at thermal equilibrium with no external bias or energy transfer."In the space charge region the electric field prevents mobile carriers from entering or crossing the region in the classical sense."
That's why I suggest it is not so good an idea to discuss this in the classical sense.
Diffusion (tries to ) push carriers from one side to the other but the electric field opposes this rather than prevents.
There are fluxes of currents trying to flow and form a dynamic equlibrium. A reverse bias on a diode might be considered as suppressing the current flux as the np product becomes smaller, as the number of carriers available reduces.
External biases just favour one over the other, depending on which way the bias is applied.
I think that is the correct way to look at it.tunnelling might be possible but isn't usual in most junctions except perhaps for the very small ones in 7nm IC technology. Or tunnel diodes where the junction is extremely abrupt. I suppose an analogy might be plonking a boat onto a canal. The water level rise caused by the displacement is negligible. The space charge region is similarly a small fraction of the volume of the diode material.
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