# Thermal generation of electron-hole couples and reverse biasing

I'm studying the PN junction and I have some problems figuring out thermal generation of couples electron-hole in reverse biasing. The analysis is the standard one (for example, one can find it in the Sedra-Smith book, PN junction chapter) and it assumes the two-region approximation with an abrupt change, as in the following figure (from Wikipedia):

Intuitively, how the following relation is explained (always in a condition of thermodynamical equilibrium)?

$$p_n(x_n)=p_{n_0}e^{\frac{V}{V_T}}$$

Notation: $$\p_n(x_n)\$$ holes in n-zone at the edge between depletion region and neutral region, $$\p_{n_0}\$$ thermally generated holes in the n-zone at equilibrium without biasing, $$\V\$$ voltage applied between p and n terminals, $$\V_T\$$ thermal voltage.

What bothers me is the fact that for heavy reverse polarization ($$\V\$$ very negative) the thermally generated holes at that edge are practically 0, which for me is very strange, because this is a thermal phenomenon that in principle, I think, has not to be influentiated from the presence of an electric field.

Thank you.

• Is $x_n$ a constant position, not a function of $V$? – Matt Apr 1 '19 at 15:30
• The width of the depletion region depends on V. – Nameless Apr 1 '19 at 17:25
• Before I bother with anything on this, please read/skim this and tell me if any of it helps here. And if I do bother, I'll probably need some clarification from you. Your question isn't entirely clear to me (though I could guess.) – jonk Apr 1 '19 at 17:51
• @Nameless Correct. I'm asking is $x_n$ the depletion region width as a function of $V$? Or is it the depletion region width at $V=0$? – Matt Apr 1 '19 at 17:55
• @ Matt $x_n$ is how much the depletion region extends in the n-zone. The width of the depletion region is $x_n+x_p$, where analogously $x_p$ is how much the depletion region extends in the p-zone. Both $x_p$ and $x_n$ are function of V. @jonk thanks for the link, but it doesn't help me. Tell me what you want to clarify, please, and I'll try to explain better myself. – Nameless Apr 2 '19 at 7:41

I'm no expert in solid state physics, but if $$\p_n\$$ is a concentration then wouldn't one expect it to be altered by holes getting pulled away by the electric field? The same number of holes are still generated there, they just don't stay there as long as the field accelerates them away.
• But we are using the "two-zone" approximation. In $x=x_n$ we already are in the neutral region, the field exists only in the depletion region. – Nameless Apr 1 '19 at 17:26