# Calculate steady state charge in a silicon bar after excess holes are injected

I have to derive an equation for excess hole distribution in an silicon bar injected with a steady state hole concentration $\Delta P$.

I have been given the data $\Delta P = 10^{16}$ per cubic centimeter at $x = 0$. The diffusion length of hole $L_p = 10^{-3} cm$ and hole life time $\tau _h = 10^{-6}$ seconds.

What I need to calculate is the steady state storage charge (say $Q_s$) and hole current (say $I_h(x=0)$) at $x=0$.

I am new to this topic, so please bear to my lack of basic knowledge if there was an obvious solution.

I derived the required equation and calculated hole current by finding hole density $J_h = \frac {e D_h}{L_p} e^{-\frac{x}{L_p}}$ and multiplying with area.

I still couldn't figure out how to calculate steady state stored charge. Does it mean to calculate $p_{n0}$ (the equilibrium concentration of hole after a long time)?

• This is a common homework problem. Compare it with various other surface or bulk injection problems. – Jon Custer Jun 29 '17 at 13:28
• I didn't understand what you mean by bulk injection problems. – bikalpa Jun 29 '17 at 14:55
• I have my final exam in just two days, and this question was asked a few years before in finals. Would you guide me a way, maybe a little hint perhaps? – bikalpa Jun 29 '17 at 14:57
• Every semiconductor physics textbook I've ever read has a section on calculating carrier concentrations with either surface injection or uniform carrier injection in the bulk (often labeled as photoinjection). For example, in Sze (2nd edition) this is all in chapter 1. – Jon Custer Jun 29 '17 at 14:58
• This question was from Electrical Engineering Materials course, and my textbook provides a very basic approach. Anyway, I'm going to look into that book you suggested. Thanks :) – bikalpa Jun 29 '17 at 15:04