109年 - 108 國立中山大學_碩士班招生考試_電機系(甲組)：半導體概論#124080

(a) Calculate the electron and hole concentrations at x = 0, 5, and 10 μm.

(b) Plot the electric field (with units) vs x for 0 ≤ x ≤ 10 μm.

(c) Calculate the electron drift current density at x = 5 μm.

(d) Calculate the electron diffusion current density at x = 5 μm.

(a) What is the built-in potential for this structure?

(b) What is the thickness of each depletion region?

(c) Sketch the electrostatic potential in equilibrium from one metal contact to the other.
Label your sketch. Indicate important potential values.

(d) Sketch the electric field in equilibrium from one metal contact to the other. Label your sketch.

(a) Given that the excess electron concentration in the p-side during forward bias V_F is:
Δn(x) = n_po[exp(V_F/V_T) – 1] exp[(x_p-x)/L_n]
Derive an expression for the electron current in the p quasi-neutral region in terms of the appropriate parameters including the doping concentration.

(b) Without doing any more derivations, but by symmetry arguments only, provide an expression for the minority carrier current in the n quasi-neutral region.

(c) If there is no recombination or generation in the depletion region, mathematically show that the electron and hole currents must be constant in this region, and obtain these constant values.

(d) Derive the expression for the total current using your results from above.

(a) Calculate the drift velocity of electrons in Si at T = 90 K for a field of 10² V/cm.

(b) Calculate the transit time of the carrier if we applied voltage of 3 V at 550 K.