Consider p-type silicon in thermal equilibrium with an intrinsic carrier concentration ni=1.5xE10 cm-3 and a hole concentration of Po=3.0xE16 cm-3 . The lifetime of the minority carrier electrons is Tno=3.0xE-17. Calculate the recombination rate of electrons Rno. Give the answer in cm.
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3E-3
To calculate the recombination rate of electrons (Rno) in cm-3, we need to use the formula:
Rno = Po / Tno
Given:
ni = 1.5 x 10^10 cm-3 (intrinsic carrier concentration),
Po = 3.0 x 10^16 cm-3 (hole concentration),
Tno = 3.0 x 10^-17 (lifetime of minority carrier electrons).
Substituting the given values into the formula, we get:
Rno = (3.0 x 10^16 cm-3) / (3.0 x 10^-17)
To simplify the calculation, we can express the denominator in scientific notation:
Rno = (3.0 x 10^16 cm-3) / (3.0 x 10^-17) = (3.0 x 10^16 cm-3) / (3.0 / 10^17)
Dividing the numerator by the denominator:
Rno = (3.0 x 10^16 cm-3) / (3.0 / 10^17)
= (3.0 x 10^16 cm-3) × (10^17 / 3.0)
≈ 1.0 x 10^33 cm-3
Therefore, the recombination rate of electrons (Rno) is approximately 1.0 x 10^33 cm-3.
To calculate the recombination rate of electrons (Rno) in p-type silicon, we can use the formula:
Rno = (Pn)/(Tno)
Where Pn is the concentration of minority carrier electrons, and Tno is the lifetime of the minority carrier electrons.
Given:
ni = 1.5 x 10^10 cm^-3 (intrinsic carrier concentration)
Po = 3.0 x 10^16 cm^-3 (hole concentration)
Tno = 3.0 x 10^-17 s (lifetime of minority carrier electrons)
To find Pn, we need to use the charge neutrality condition, which states that the product of the electron concentration (n) and the hole concentration (p) is equal to the square of the intrinsic carrier concentration (ni):
n * p = ni^2
Since the material is p-type silicon, the electron concentration (n) is much smaller than the hole concentration (p), so we can approximate the equation as:
n * Po ≈ ni^2
Solving for n:
n ≈ (ni^2) / Po
Substituting the given values:
n ≈ (1.5 x 10^10 cm^-3)^2 / (3.0 x 10^16 cm^-3)
n ≈ 2.25 x 10^20 cm^-3
Now, we can substitute the values of n and Tno into the formula for Rno:
Rno = (2.25 x 10^20 cm^-3) / (3.0 x 10^-17 s)
Rno ≈ 7.5 x 10^36 cm^-3 s^-1
Therefore, the recombination rate of electrons (Rno) is approximately 7.5 x 10^36 cm^-3 s^-1.