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tcsv018

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Hello,

I read a derivation for the width of the depletion region [itex]W[/itex] in "SEMICONDUCTOR DEVICE FUNDAMENTALS" by Robert F. Pierret in which at one point it says:

http://imageshack.com/i/ipbgKsK9p

Here again for better readability:

[itex]x_N = \sqrt{\frac{2 K_S \epsilon_0}{q}\frac{N_A}{N_D\cdot(N_A+N_D)}V_{bi}}[/itex]

[itex]x_P = \sqrt{\frac{2 K_S \epsilon_0}{q}\frac{N_D}{N_A\cdot(N_A+N_D)}V_{bi}}[/itex]

[itex]W = x_N + x_P = \sqrt{\frac{2 K_S \epsilon_0}{q}\frac{N_D+N_A}{N_A\cdot N_D}V_{bi}}[/itex]

Which is confusing to me as I would expect the same containing:

[itex]W = x_N + x_P = \sqrt{\frac{2 K_S \epsilon_0}{q}\frac{N_D^2+N_A^2}{N_A\cdot N_D\cdot(N_A+N_D)}V_{bi}}[/itex]This same outcome though is found on various places in the internet.

Does anyone know what I am missing?

Kind regards,

Name

Symbols:

[itex]x_N[/itex] length of n-doped region

[itex]x_P[/itex] length of p-doped region

[itex]N_A[/itex]density of acceptors

[itex]N_D[/itex]density of donors

[itex]V_{bi}[/itex] builtin potential

All the others are known constants

I read a derivation for the width of the depletion region [itex]W[/itex] in "SEMICONDUCTOR DEVICE FUNDAMENTALS" by Robert F. Pierret in which at one point it says:

http://imageshack.com/i/ipbgKsK9p

Here again for better readability:

[itex]x_N = \sqrt{\frac{2 K_S \epsilon_0}{q}\frac{N_A}{N_D\cdot(N_A+N_D)}V_{bi}}[/itex]

[itex]x_P = \sqrt{\frac{2 K_S \epsilon_0}{q}\frac{N_D}{N_A\cdot(N_A+N_D)}V_{bi}}[/itex]

[itex]W = x_N + x_P = \sqrt{\frac{2 K_S \epsilon_0}{q}\frac{N_D+N_A}{N_A\cdot N_D}V_{bi}}[/itex]

Which is confusing to me as I would expect the same containing:

[itex]W = x_N + x_P = \sqrt{\frac{2 K_S \epsilon_0}{q}\frac{N_D^2+N_A^2}{N_A\cdot N_D\cdot(N_A+N_D)}V_{bi}}[/itex]This same outcome though is found on various places in the internet.

Does anyone know what I am missing?

Kind regards,

Name

Symbols:

[itex]x_N[/itex] length of n-doped region

[itex]x_P[/itex] length of p-doped region

[itex]N_A[/itex]density of acceptors

[itex]N_D[/itex]density of donors

[itex]V_{bi}[/itex] builtin potential

All the others are known constants

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