The image you provided shows a band diagram for a semiconductor. It indicates the conduction band, valence band, and the Fermi level ($E_f$).

To address the statements regarding the effect of temperature and effective mass on the Fermi level:

1. Fermilevel will go up:

   • The position of the Fermi level is influenced by both temperature and the effective masses of electrons and holes. If the temperature is halved, the intrinsic carrier concentration decreases, which could potentially raise the Fermi level closer to the conduction band in an intrinsic or lightly doped semiconductor. The doubling of the effective mass of holes means that the hole contribution to the density of states decreases, which might also cause the Fermi level to shift upwards.

2. Fermilevel will go down:

   • A decrease in temperature generally causes the Fermi level to shift closer to the middle of the band gap in an intrinsic semiconductor. However, the increased effective mass of holes might counteract this effect by pulling the Fermi level upwards.

3. Fermilevel will be unaffected:

   • The Fermi level is unlikely to remain completely unaffected by these changes, as both temperature and effective mass are crucial factors that influence the Fermi level position.

4. Effective mass of hole will affect intrinsic Fermi level:

   • Yes, the effective mass of holes directly influences the intrinsic Fermi level because it alters the density of states in the valence band, thereby affecting the balance between electrons and holes.

Conclusion:

• The correct statements should be:
  • Fermilevel will go up
  • Effective mass of hole will affect intrinsic Fermi level

Would you like further details on this explanation or any related questions? Here are some additional questions to expand on this topic:

1. How does the Fermi level change with increasing temperature in a semiconductor?
2. What is the intrinsic carrier concentration, and how is it related to the Fermi level?
3. How does the effective mass of electrons affect the position of the Fermi level?
4. What happens to the Fermi level in a heavily doped semiconductor when the temperature changes?
5. How do the effective masses of electrons and holes affect the electrical conductivity of a semiconductor?
6. What is the significance of the Fermi level in determining the electrical properties of a semiconductor?
7. How does the band gap of a semiconductor relate to the position of the Fermi level?
8. Can the Fermi level be controlled or engineered in semiconductor devices? If so, how?

Tip: The position of the Fermi level is crucial in determining the electrical behavior of semiconductors and can be manipulated through doping, temperature, and changes in effective mass.