Pure silicon crystal of length $$l (0.1m)$$ and area $$A$$($$10^{-4}m^2$$) has the mobility of electrons ($$\mu_e$$) and holes ($$\mu_h$$) as $$0.135 m^2/Vs$$ and $$0.048 m^2/Vs$$ , respectively. If the voltage applied across it is $$2V$$ and the intrinsic charge concentration is $$n_i = 1.5 \times 10^6 m^{-3}$$, then the total current flowing through the crystal is
Given:
$$l = 0.1m$$
$$A = 10^{-4} m^{-2}$$
$$\mu_e = 0.135 m^2 (Vs)^{-1}$$
$$\mu_h = 0.048 m^2 (Vs)^{-1}$$
$$n_i = 1.5 \times 10^{6} m^{-3}$$
$$E = 2 V$$
The conductivity is:
$$\sigma = n_i(\mu_e + \mu_h) e$$
$$\sigma = 1.5 \times 10^{6} (0.135 + 0.048) 1.6 \times 10^{-19}$$
$$\sigma = 1.5 (0.183) 1.6 \times 10^{-13}$$
$$\sigma = 0.4392 \times 10^{-13} Sm^{-1}$$
Now, the resistance is given by,
$$R = \dfrac{l}{\sigma (A)}$$
$$R = \dfrac{0.1}{0.4392 \times 10^{-13} (10^{-4})}$$
$$R = 0.2276 \times 10^{17} \Omega$$
Hence, the current is:
$$I = \dfrac{V}{R} = \dfrac{2}{0.2276 \times 10^{17}}$$
$$I = 8.787 \times 10^{-17} A$$
Let $$\Delta \,E$$ denote the energy gap between the valence band and the conduction band. The population of conduction electrons (and of the holes) is roughly proportional to $$e^{-\Delta \, E /2kT}$$. Find the ratio of the concentration of conduction electrons in diamond to that in silicon at a room temperature 300 K. $$\Delta \,E$$ for silicon is $$1\cdot1\, eV$$ and for diamond is $$6\cdot 0\, eV$$.
The conductivity of an intrinsic semiconductor depends on temperature as $$\sigma =\sigma _0 e^{-\Delta \, E/2kT}$$, where $$\sigma _0$$, is a constant. Find the temperature at which the conductivity of an intrinsic germanium semiconductor will be double of its value at T= 300 K. Assume that the gap for germanium is $$0\cdot 650\, eV$$ and remains constant as the temperature is increased.
In an intrinsic semiconductor the energy gap $$E_g$$ is $$1.2\ eV$$. Its hole mobility is much smaller than electron mobility and independent of temperature. What is the ratio between conductivity at $$600\ K$$ and that at $$300\ K$$? Assume that the temperature dependence of intrinsic carrier concentration $$n_i$$ is given by $$n_i = n_o exp \left(- \dfrac{E_g}{2 k_B T} \right)$$ Where $$n_0$$ is a constant.
Find the angle between the planes whose vector equations are $$\vec { r } .\left( 2\hat { i } +2\hat { j } -3\hat { k } \right) =5$$ and $$\vec { r } .\left( 3\hat { i } -3\hat { j } +5\hat { k } \right) =3$$
The probability of electrons to be found in the conduction band of an intrinsic semiconductor at a finite temperature :-
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