Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

The electron concentration in silicon at T = 300 K is given by
n(x) = 10^16 exp (-x/18) cm3
where x is measured in m and is limited to 0< or is equal to x < or is equal to 25 m. The electron diffusion coefficient is Dn = 25 cm2/s and the electron mobility is mun = 960 cm2/V-s. The total electron current density through the semi-conductor is constant and equal to Jn = 40 A/cm2. The electron current has both diffusion and drift current components. Determine the electric field as a function of x-bar which must exist in the semi-conductor.

Sagot :

oladayoademosu

Answer:

5.6 × 10⁻²[1 + 4.643 × 10⁻⁷exp (x/18)] V/cm

Explanation:

The total current density, J = drift current density, J' + diffusion current density, J"

J = J' + J"

J' = nμeE where n = electron concentration =  10¹⁶ exp (-x/18) cm³, μ = electron mobility = 960 cm²/V-s, e = electron charge = 1.602 × 10⁻⁹ C and E = electric field

J" = eDdn/dx where e = electron charge = 1.602 × 10⁻¹⁹ C, D = diffusion coefficient = 25 cm²/s and dn/dx = concentration gradient = d10¹⁶ exp (-x/18) cm³/dx = (-10¹⁶/18)exp (-x/18) cm³

So,

J = J' + J"

J = nμeE + eDdn/dx

E = (J - eDdn/dx)/nμe

Since J = 40 A/cm², substituting the values of the variables into the equation, we have

E = (J - eDdn/dx)/nμe

E = [40 A/cm² - 1.602 × 10⁻⁹ C × 960 cm/V-s × (-10¹⁶/18)exp (-x/18) cm²] ÷ (10¹⁶exp (-x/18) cm³ × 960 cm²/V-s × 1.602 × 10⁻⁹ C)

E = [40 A/cm² - 1537.92 × 10⁻⁹ C-cm/V-s × (-10¹⁶/18)exp (-x/18) cm²] ÷ (10¹⁶exp (-x/18) cm² × 1537.92 × 10⁻⁹  C-cm³/V-s)

E = [40 A/cm² + 85.44 × 10⁷ C-cm/V-s exp (-x/18) cm²] ÷ (exp (-x/18) cm² × 1537.92 × 10⁷  C-cm³/V-s)

E = [40 A/cm² ÷ (exp (-x/18) cm² × 1537.92 × 10⁷  C-cm³/V-s)] + [85.44 × 10⁷ C-cm/V-s exp (-x/18) cm² ÷ (exp (-x/18)  × 1537.92 × 10⁷  C-cm²/V-s]

E = [0.026 × 10⁻⁷ A/cm²exp (x/18)    V-s/C-cm³] + 0.0056]

E = [0.026 × 10⁻⁷exp (x/18) V/cm] + 0.0056]

E = 0.056[0.026 × 10⁻⁷exp (x/18) V/cm]/0.056 + 1]

E = 0.056[4.643 × 10⁻⁷exp (x/18) V/cm] + 1]

E = 5.6 × 10⁻²[1 + 4.643 × 10⁻⁷exp (x/18)] V/cm

Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.