Q1: Assume electronic charge (q) = 1.6 x 10^-19 C, kT/q = 25 mV and electron mobility (μn) = 1000 cm^2/V-s. If the concentration gradient of electrons injected into a P-type silico... Q1: Assume electronic charge (q) = 1.6 x 10^-19 C, kT/q = 25 mV and electron mobility (μn) = 1000 cm^2/V-s. If the concentration gradient of electrons injected into a P-type silicon sample is 1x10^21/cm^4, then find the magnitude of electron diffusion current density (in A/cm^2). Q2: Let’s consider a GaAs sample at T= 300K with doping concentration, Na = 0 and Nd = 10^16 cm^-3. Assume complete ionization with electron and hole mobilities as 8500 cm^2/V-s and 400 cm^2/V-s respectively. Calculate the drift current density if an electric field of E = 10 V/cm was applied.
Understand the Problem
The question involves calculating the electron diffusion current density in a P-type silicon sample due to a given concentration gradient and finding the drift current density in a GaAs sample under an electric field. This requires applying concepts from semiconductor physics and involves equations related to charge, mobility, and current density.
Answer
Q1: $4 \, \text{A/cm}^2$; Q2: $1.36 \, \text{A/cm}^2$.
Answer for screen readers
Q1: The magnitude of the electron diffusion current density is $4 , \text{A/cm}^2$.
Q2: The drift current density is $1.36 , \text{A/cm}^2$.
Steps to Solve
- Calculate the Electron Diffusion Current Density for Q1
The formula for the electron diffusion current density ($J_n$) is given by:
$$ J_n = -q D_n \frac{d(n)}{dx} $$
Where:
- $q = 1.6 \times 10^{-19}$ C (electron charge)
- $D_n$ is the diffusion constant, which can be found using the mobility ($\mu_n$) and the thermal voltage ($V_T$):
$$ D_n = \mu_n \cdot kT/q $$
For silicon:
- $\mu_n = 1000 , \text{cm}^2/\text{V-s}$
- Assuming room temperature, $kT/q \approx 25 , \text{mV} = 0.025 , \text{V}$
Now calculate $D_n$:
$$ D_n = 1000 , \text{cm}^2/\text{V-s} \cdot 0.025 , \text{V} = 25 , \text{cm}^2/\text{s} $$
Next, the concentration gradient $\frac{d(n)}{dx}$ is given as $1 \times 10^{21} , \text{cm}^{-4}$.
Now substitute these values into the equation for $J_n$:
$$ J_n = -1.6 \times 10^{-19} \cdot 25 \cdot (1 \times 10^{21}) = -4 , \text{A/cm}^2 $$
- Calculate the Drift Current Density for Q2
The drift current density ($J_d$) is given by:
$$ J_d = q n \mu_n E $$
For GaAs:
- The electron concentration, $n$, is equal to the donor concentration $N_d = 10^{16} , \text{cm}^{-3}$, as $N_a = 0$.
- $\mu_n = 8500 , \text{cm}^2/\text{V-s}$
- The electric field, $E = 10 , \text{V/cm}$
Now substitute these values:
$$ J_d = (1.6 \times 10^{-19}) \cdot (10^{16}) \cdot (8500) \cdot (10) = 1.36 , \text{A/cm}^2 $$
Q1: The magnitude of the electron diffusion current density is $4 , \text{A/cm}^2$.
Q2: The drift current density is $1.36 , \text{A/cm}^2$.
More Information
- The drift current is primarily due to electrons in the GaAs sample, driven by the applied electric field.
- The diffusion current density in the P-type silicon is significant when there is a concentration gradient.
Tips
- Confusing diffusion current density with drift current density; ensure to use the proper formulas.
- Forgetting to account for the negative sign in the diffusion current density formula, indicating direction.
- Not using correct units can lead to incorrect calculations; always check unit consistency.