Question

A diode operates in forward bias, in which it is described by equation iD≅Isexp(vD/(nVT)) , with VT = 0.024 V . For vD1 = 0.600 V , the current is iD1 =1 mA . For vD2 = 0.670 V , the current is iD2 = 12 mA . Determine the value of Is . n = 1.17. Express your answer using three significant figures.

Answer 1

The corrected value of
`\(I_s\)` is approximately
`\(0.018 \, \text{mA}\)` (to three significant figures)

How did we get the value?

The given diode equation is:

`\[ i_D \approx I_s \exp\left((v_D)/(nV_T)\right) \]`

where:

-
`\( i_D \)` is the diode current,

-
`\( I_s \)` is the reverse saturation current,

-
`\( v_D \)` is the voltage across the diode,

-
`\( n \)` is the ideality factor,

-
`\( V_T \)` is the thermal voltage
`(\( V_T = 0.024 \)`V in this case).

We are given two data points
`(\(v_(D1), i_(D1)\) and \(v_(D2), i_(D2)\))`:

1. For
`\(v_(D1) = 0.600\) V, \(i_(D1) = 1\) mA`

2. For
`\(v_(D2) = 0.670\) V, \(i_(D2) = 12\) mA`

Let's use these points to form two equations and solve for
`\(I_s\)`:

For the first point:

`\[ i_(D1) = I_s \exp\left((v_(D1))/(nV_T)\right) \]`

`\[ 1 = I_s \exp\left((0.600)/(1.17 * 0.024)\right) \]`

For the second point:

`\[ i_(D2) = I_s \exp\left((v_(D2))/(nV_T)\right) \]`

`\[ 12 = I_s \exp\left((0.670)/(1.17 * 0.024)\right) \]`

We have the equations:

1.
`\(1 = I_s \exp\left((0.600)/(1.17 * 0.024)\right)\)`

2.
`\(12 = I_s \exp\left((0.670)/(1.17 * 0.024)\right)\)`

Let's denote x as the common term in the exponentials:

1.
`\(1 = I_s \exp(x_1)\)`

2.
`\(12 = I_s \exp(x_2)\)`

Now, solve for
`\(x_1\) and \(x_2\)`:

`\[x_1 = (0.600)/(1.17 * 0.024) \approx 20.08\]`

`\[x_2 = (0.670)/(1.17 * 0.024) \approx 22.30\]`

Now substitute these values back into the equations:

1.
`\(1 = I_s \exp(20.08)\)`

2.
`\(12 = I_s \exp(22.30)\)`

Solve for
`\(I_s\)`:

`\[I_s = (1)/(\exp(20.08)) \approx 0.018 \, \text{mA}\]`

`\[I_s = (12)/(\exp(22.30)) \approx 0.018 \, \text{mA}\]`

Therefore, the corrected value of
`\(I_s\)` is approximately
`\(0.018 \, \text{mA}\)` (to three significant figures).