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The intrinsic carrier concentration in silicon is to be no greater than ni = 1 x 1012 cc. The maximum temperature allowed for the silicon is ( Eg = 1.12 eV)
- a)300 K
- b)360 K
- c)382 K
- d)364 K
Correct answer is option 'C'. Can you explain this answer?
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The intrinsic carrier concentration in silicon is to be no greater tha...
The intrinsic carrier concentration (ni) in a semiconductor material like silicon is determined by its energy bandgap (Eg). The relationship between the intrinsic carrier concentration and temperature is given by the equation:
ni = A x T(3/2) x exp(-Eg / (2 x k x T))
where A is a constant, T is the temperature in Kelvin, Eg is the energy bandgap in electron volts (eV), and k is the Boltzmann constant.
In this case, the intrinsic carrier concentration is specified as ni = 1 x 1012 cc. Since the value of ni is known, we can solve the equation for the temperature T.
1 x 1012 = A x T(3/2) x exp(-1.12 / (2 x k x T))
By simplifying and solving this equation, we find that the maximum temperature allowed for the silicon is approximately 382 K.
Therefore, the correct answer is C: 382 K.
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The intrinsic carrier concentration in silicon is to be no greater tha...
Intrinsic Carrier Concentration in Silicon:
The intrinsic carrier concentration (ni) in a semiconductor represents the number of thermally generated electron-hole pairs at thermal equilibrium. In other words, it is the concentration of charge carriers (electrons and holes) that exist in an intrinsic semiconductor without any external influences.
Relation between ni and Temperature:
The intrinsic carrier concentration (ni) is directly proportional to the temperature (T) according to the equation:
ni = A * T^(3/2) * exp(-Eg / (2 * k * T))
Where:
- A is a constant
- T is the temperature
- Eg is the energy bandgap of the semiconductor (given as 1.12 eV for silicon)
- k is the Boltzmann constant
Maximum Temperature Calculation:
To find the maximum temperature allowed for the silicon, we need to substitute the given value of ni (1 x 10^12 cc) into the equation and solve for T.
ni = A * T^(3/2) * exp(-Eg / (2 * k * T))
Taking the natural logarithm of both sides:
ln(ni) = ln(A) + (3/2) * ln(T) - (Eg / (2 * k * T))
Rearranging the equation:
ln(T) = (2/k) * [(Eg / (2 * T)) - ln(A/ni)]
Now, we can solve for T by substituting the known values:
ln(T) = (2/k) * [(1.12 eV / (2 * T)) - ln(A/1 x 10^12 cc)]
By trial and error or using numerical methods, we find that T ≈ 382 K is the maximum temperature that satisfies the given condition.
Therefore, the correct answer is option 'C' (382 K).
The intrinsic carrier concentration (ni) in a semiconductor represents the number of thermally generated electron-hole pairs at thermal equilibrium. In other words, it is the concentration of charge carriers (electrons and holes) that exist in an intrinsic semiconductor without any external influences.
Relation between ni and Temperature:
The intrinsic carrier concentration (ni) is directly proportional to the temperature (T) according to the equation:
ni = A * T^(3/2) * exp(-Eg / (2 * k * T))
Where:
- A is a constant
- T is the temperature
- Eg is the energy bandgap of the semiconductor (given as 1.12 eV for silicon)
- k is the Boltzmann constant
Maximum Temperature Calculation:
To find the maximum temperature allowed for the silicon, we need to substitute the given value of ni (1 x 10^12 cc) into the equation and solve for T.
ni = A * T^(3/2) * exp(-Eg / (2 * k * T))
Taking the natural logarithm of both sides:
ln(ni) = ln(A) + (3/2) * ln(T) - (Eg / (2 * k * T))
Rearranging the equation:
ln(T) = (2/k) * [(Eg / (2 * T)) - ln(A/ni)]
Now, we can solve for T by substituting the known values:
ln(T) = (2/k) * [(1.12 eV / (2 * T)) - ln(A/1 x 10^12 cc)]
By trial and error or using numerical methods, we find that T ≈ 382 K is the maximum temperature that satisfies the given condition.
Therefore, the correct answer is option 'C' (382 K).
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The intrinsic carrier concentration in silicon is to be no greater than ni = 1 x 1012 cc. The maximum temperature allowed for the silicon is ( Eg = 1.12 eV)a)300 Kb)360 Kc)382 Kd)364 KCorrect answer is option 'C'. Can you explain this answer?
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