Solution:

The statement "At absolute zero temperature, it behaves like a conductor" is wrong for a semiconductor.

Explanation:

• At absolute zero (0 K), intrinsic semiconductors (like silicon and germanium) do not have free charge carriers (electrons and holes) because all the electrons occupy the valence band, and there is no thermal energy available to promote them to the conduction band.
• Therefore, intrinsic semiconductors behave like insulators at absolute zero, not conductors.

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Solution:

At absolute zero temperature (0 K), intrinsic germanium and silicon behave like insulators due to the following reasons:

1. No Free Charge Carriers: At absolute zero, all the electrons in the material occupy the lowest energy states, and there are no thermally excited electrons available to conduct electricity. This means there are no free charge carriers (electrons or holes).
2. Wide Band Gap: Both germanium and silicon have a band gap (about 0.66 eV for germanium and 1.1 eV for silicon). At absolute zero, the thermal energy is insufficient to excite electrons across this band gap from the valence band to the conduction band.

As a result, intrinsic germanium and silicon cannot conduct electricity at absolute zero, behaving as insulators.

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Solution:

When a conducting wire of Copper and Germanium is cooled from room temperature to 80K:

• Copper (metal): Its resistance will decrease because metals have lower resistance at lower temperatures due to reduced electron scattering.
• Germanium (semiconductor): Its resistance will increase because the number of charge carriers (electrons and holes) decreases at lower temperatures, leading to higher resistance.

Thus, Copper's resistance decreases, while Germanium's resistance increases when cooled to 80K

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Solution:

Both N-type and P-type germanium are electrically neutral because, while they have an imbalance of charge carriers (electrons or holes), the overall number of positive and negative charges remains equal.

- **N-type**: Donor atoms add extra electrons (negatively charged carriers), but the atoms themselves become positively charged ions. This ensures charge neutrality.

- **P-type**: Acceptor atoms create holes (positively charged carriers) by accepting electrons, but the atoms become negatively charged ions. This balances the charge.

In both cases, the total positive and negative charges cancel each other out, keeping the material electrically neutral.

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Solution:

Resistance of conductor increases with increasing temperature and resistance of semiconductor decreases with increasing temperature.

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Solution:

The resistivity (ρ) of a pure (intrinsic) semiconductor is given by the formula:

$$\rho = \frac{1}{q (n_i) (\mu_n + \mu_p)}$$

ρ=q(ni​)(μn​+μp​)1​

Where:

• 
  $\rho = 0.5 \, \Omega\text{m}$ 

  $\rho =0.5\Omega \text{m}$ (resistivity),

• 
  $q = 1.6 \times 10^{-19} \, \text{C}$ 

  q=1.6×10−19C (charge of an electron),

• 
  $n_i$ 

  ni​ = intrinsic carrier concentration (to be calculated),

• 
  $\mu_n = 0.39 \, \text{m}^2/\text{V-s}$ 

  μn​=0.39m2/V-s (electron mobility),

• 
  $\mu_p = 0.19 \, \text{m}^2/\text{V-s}$ 

  μp​=0.19m2/V-s (hole mobility).

Rearranging the formula to solve for

$n_i$

ni​:

$$n_i = \frac{1}{q \rho (\mu_n + \mu_p)}$$

​

Substitute the values:

$$n_i = \frac{1}{(1.6 \times 10^{-19})(0.5)(0.39 + 0.19)}$$

​

$$n_i = \frac{1}{(1.6 \times 10^{-19})(0.5)(0.58)}$$

$$n_i=\frac{1}{4.64\times 10^{-20}}=2.16\times 10^{19}{\text{m}}^{-3}$$

Thus, the intrinsic carrier concentration

$n_i$

ni​ is

$2.16 \times 10^{19} \, \text{m}^{-3}$

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Solution:

The ratio of electron to hole currents is given by:

$$\frac{I_n}{I_p} = \frac{7}{4}$$​The ratio of electron to hole concentrations is:

$$\frac{n}{p} = \frac{7}{5}$$Using the current formula

$I = q n v A$

I=qnvA, the ratio of drift velocities (

$\frac{v_n}{v_p}$

vp​vn​​) can be found as:

$$\frac{I_n}{I_p}=\frac{n{v}_n}{p{v}_p}$$Substitute the given ratios:$$\frac{7}{4} = \frac{\frac{7}{5} \cdot v_n}{v_p}$$Simplifying:

$$\frac{v_n}{v_p}=\frac{5}{4}$$

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Solution:

GaAs (Gallium Arsenide) with a band gap of 1.5 eV can emit light in the infrared region of the electromagnetic spectrum.

The energy of a photon emitted by an LED is related to its wavelength by the equation:

$$E = \frac{hc}{\lambda}$$Solving we get 

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Solution:

Majority charge carrier in N-type semiconductor is electrons and in P-type semiconductor is holes

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Solution:

In N type semiconductor number of electrons is more than number of holes

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