Silicon Electron Drift Time Calculation

To find the time an electron takes to drift across a distance under an electric field, we use the concepts of drift velocity and mobility.

Drift Velocity Calculation

The drift velocity ($v_d$) of an electron in a semiconductor is directly proportional to the applied electric field ($E$) and the electron mobility ($\mu_n$). The formula is:

$v_d = \mu_n E$

Drift Time Determination

Drift time ($t$) is the time taken to travel a distance ($d$) at the drift velocity ($v_d$). The relationship is:

$t = \frac{d}{v_d}$

Step-by-Step Calculation

First, ensure all units are consistent. We need to convert the drift distance to centimeters to match the mobility units.

• Given values:
  • Drift Distance, $d = 1 \mu m = 1 \times 10^{-6}$ m $= 1 \times 10^{-4}$ cm
  • Electric Field, $E = 100$ V/cm
  • Electron Mobility, $\mu_n = 1350 \text{ cm}^2/V-s$
• Calculate Drift Velocity ($v_d$):

  Substitute the given values into the drift velocity formula:

  $v_d = (1350 \text{ cm}^2/V-s) \times (100 \text{ V/cm})$

  $v_d = 135000 \text{ cm/s}$

• Calculate Drift Time ($t$):

  Now, use the drift velocity and distance to find the time:

  $t = \frac{d}{v_d} = \frac{1 \times 10^{-4} \text{ cm}}{135000 \text{ cm/s}}$

  $t = \frac{10^{-4}}{1.35 \times 10^5} \text{ s}$

  $t \approx 0.7407 \times 10^{-9} \text{ s}$

  Converting this to nanoseconds (ns), where $1 \text{ ns} = 10^{-9} \text{ s}$:

  $t \approx 0.74 \text{ ns}$

Conclusion

The calculated drift time is approximately $0.74$ ns, which matches Option A.