GaAs Gunn Diode Parameters Calculation

This solution details the calculation of essential parameters for an n-type GaAs Gunn diode. We will determine the current density and electron mobility using the provided drift velocity, doping concentration, and electric field values.

Calculating Current Density for GaAs Gunn Diode

The current density ($J$) represents the flow of electrical current per unit cross-sectional area. For a semiconductor like the GaAs Gunn diode, assuming uniform doping, it is calculated using the formula:

$J = n \cdot q \cdot V_d$

Where:

• $n$ denotes the charge carrier concentration (specifically, the doping concentration for an n-type semiconductor).
• $q$ represents the elementary charge, which is the magnitude of the charge of an electron ($q \approx 1.602 \times 10^{-19}$ Coulombs).
• $V_d$ is the drift velocity of the charge carriers (electrons in this case).

Given Parameters for Calculation:

• Doping concentration ($n$): $2 \times 10^{14}$ cm$^{-3}$
• Drift velocity ($V_d$): $10^7$ cm/s
• Elementary charge ($q$): $1.602 \times 10^{-19}$ C

Step-by-step Calculation:

Plugging the given values into the current density formula:

$J = (2 \times 10^{14} \text{ cm}^{-3}) \times (1.602 \times 10^{-19} \text{ C}) \times (10^7 \text{ cm/s})$

First, multiply the numerical values:

$2 \times 1.602 = 3.204$

Next, combine the powers of 10:

$10^{14} \times 10^{-19} \times 10^7 = 10^{(14 - 19 + 7)} = 10^2$

Combine these parts to find the current density:

$J = 3.204 \times 10^2 \text{ A/cm}^2$

$J \approx 320 \text{ A/cm}^2$

This calculated value closely matches the statement in Option A.

Calculating Electron Mobility for GaAs Gunn Diode

Electron mobility ($\mu_e$) quantifies how efficiently electrons move within the semiconductor material when subjected to an electric field. The relationship is defined as:

$V_d = \mu_e \cdot E$

To find the electron mobility, we rearrange the formula:

$\mu_e = \frac{V_d}{E}$

Given Parameters for Calculation:

• Drift velocity ($V_d$): $10^7$ cm/s
• Electric field ($E$): 3200 V/cm

Step-by-step Calculation:

Substitute the known values into the mobility formula:

$\mu_e = \frac{10^7 \text{ cm/s}}{3200 \text{ V/cm}}$

Perform the division:

$\mu_e = \frac{10,000,000}{3200} \text{ cm}^2/\text{V} \cdot \text{s}$

$\mu_e = \frac{100000}{32} \text{ cm}^2/\text{V} \cdot \text{s}$

$\mu_e = 3125 \text{ cm}^2/\text{V} \cdot \text{s}$

This calculated electron mobility is approximately 3125 cm²/V·s. This value is very close to the value stated in Option B (3100 cm²/v-s), suggesting it is a correct approximation.

GaAs Gunn Diode Results Summary

Our calculations confirm the following:

• The calculated current density ($J$) is approximately 320 A/cm², supporting the statement in Option A.
• The calculated electron mobility ($\mu_e$) is approximately 3125 cm²/V·s, which is consistent with the statement in Option B.

Therefore, statements A and B are accurate based on the provided parameters and standard semiconductor physics principles.