Determine the position of the intrinsic fermi energy level

Question

Question 1: For a given semiconductor E_g = 1.5 eV, m_p* = 10 m_n*, T = 300 Kelvin, and n_i = 1× 10⁵ cm^-3.

(i). Determine the position of the intrinsic Fermi energy level with respect to the center of the bandgap. Then sketch the relative position of the fermi energy level with respect to the center of the bandgap (using Ec, Ev, Efi to show where Ef is)

(ii). Impurity atoms are added so that the Fermi energy level is 0.45 eV below the center of the bandgap. Are acceptor or donor atoms added?

(iii). What is the concentration of impurity atoms added?

Question 2: A silicon device is doped with donor impurity atoms at a concentration of 1× 10¹⁵ cm^-3. For the device to operate properly, the intrinsic carriers must contribute no more than 10% to the total electron concentration.

(i) What is the maximum temperature that the device may operate?

(ii) Is the Fermi level closer or further from the intrinsic value at the higher temperature?

Question 3: The total current density in a silicon semiconductor is constant and equal to J = -10 A/cm². The total current is composed of a hole drift current and electron diffusion current.

Assume that the electron concentration is given by n(x) = 2 × 10¹⁵ × e^-x/L cm^-3 where L = 15 μm. The electron diffusion coefficient is Dn = 27 cm²/s and the hole mobility is μ_p = 420 cm²/V-s at T = 300 Kelvin.

(i). Plot n(x) over x=[0, 60]μm. Pay attention to scale, legend, notations, etc.

(ii). calculate the electron diffusion current density for x > 0;

(iii). the hole drift current density for x > 0; (d). the required electric field for x > 0.

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