A 2cm long bar of n-type Ge has a cross sectional area of 0.1 square centimeters and resistivity of 10 ohms - cm. A 10V battery is connected across the bar.
a). long does it take for an electron to drift across the bar?
b). How much energy does an electron deliver to the lattice during its transit through the bar?
To find the time it takes for an electron to drift across the bar (a), we need to calculate the drift velocity of the electron in the material. The drift velocity can be determined using the formula:
v = I / (n * A * q)
Where:
- v is the drift velocity.
- I is the current.
- n is the charge carrier concentration.
- A is the cross-sectional area.
- q is the charge of the electron.
In this scenario, we have the following information:
- The length of the bar (L) is given as 2 cm.
- The cross-sectional area (A) is 0.1 square centimeters.
- The resistivity (ρ) is given as 10 ohms - cm.
- The voltage (V) applied is 10V.
To calculate the current (I), we can use Ohm's Law:
I = V / R
Where:
- I is the current.
- V is the voltage.
- R is the resistance.
Since the length (L) and resistivity (ρ) are given, we can find the resistance (R) using:
R = (ρ * L) / A
Now we can calculate the current (I) by substituting the given values into Ohm's Law.
Next, we need to find the charge carrier concentration (n). In intrinsic semiconductors like Ge, the charge carrier concentration is equal to the intrinsic carrier concentration (ni). The value of ni for Ge is approximately 2.4 × 10^13 per cubic centimeter.
Finally, we substitute all the obtained values into the drift velocity formula to find the drift velocity (v).
To calculate the time (t) it takes for an electron to drift across the bar, we can use the formula:
t = L / v
Now, let's calculate the answers.
a) How long does it take for an electron to drift across the bar?
1. Calculate the resistance (R):
R = (ρ * L) / A
2. Calculate the current (I) using Ohm's Law:
I = V / R
3. Calculate the charge carrier concentration (n):
n = ni
4. Calculate the drift velocity (v) using the drift velocity formula:
v = I / (n * A * q)
5. Calculate the time (t) it takes for the electron to drift across the bar:
t = L / v
b) How much energy does an electron deliver to the lattice during its transit through the bar?
To calculate the energy (E) delivered to the lattice, we can use the formula:
E = q * V
Where:
- E is the energy delivered to the lattice.
- q is the charge of the electron.
- V is the voltage.
Now, let's calculate the answer for (b).