To determine the change in diode voltage required to increase the forward bias diode current by 10 times, we need to consider the relationship between diode current and voltage in a forward biased diode.

The diode current-voltage relationship can be approximated by the Shockley diode equation:
I = I_s * (e^(V / (n * V_t)) - 1)
Where:
- I is the diode current
- I_s is the reverse saturation current
- V is the diode voltage
- n is the ideality factor
- V_t is the thermal voltage (approximately 25.85 mV at room temperature)

We want to find the change in voltage required to increase the current by 10 times. Let's denote the initial diode current as I1 and the initial diode voltage as V1, and the final diode current as I2 and the final diode voltage as V2.

Since we want to increase the current by 10 times, we can write:
I2 = 10 * I1

Now, let's substitute the current values into the diode equation:
10 * I1 = I_s * (e^(V1 / (n * V_t)) - 1)

To simplify the equation, we can take the natural logarithm of both sides:
ln(10 * I1) = ln(I_s * (e^(V1 / (n * V_t)) - 1))

Using logarithmic properties, we can rewrite the equation as:
ln(10) + ln(I1) = ln(I_s * (e^(V1 / (n * V_t)) - 1))

We can further simplify the equation:
ln(10) + ln(I1) = ln(I_s) + ln(e^(V1 / (n * V_t)) - 1)

Since ln(e^(V1 / (n * V_t)) - 1) is a small value compared to ln(10) + ln(I1), we can approximate the equation as:
ln(10) + ln(I1) ≈ ln(I_s)

Now, let's solve for the change in voltage required:
V2 - V1 = ΔV

Using the diode equation, we can write:
I2 = I_s * (e^(V2 / (n * V_t)) - 1)

Since we approximated ln(10) + ln(I1) ≈ ln(I_s), we can substitute ln(10) + ln(I1) for ln(I_s) in the equation above:
10 * I1 = I_s * (e^(V2 / (n * V_t)) - 1)

Dividing both sides by I_s and rearranging the equation, we get:
(e^(V2 / (n * V_t)) - 1) = 10 * I1 / I_s

Since ln(10) + ln(I1) ≈ ln(I_s), we can rewrite the equation as:
(e^(V2 / (n * V_t)) - 1) = e^(ln(10) + ln(I1))

Taking the natural logarithm of both sides, we get:
V2 / (n * V_t) = ln(10) + ln(I1)

Finally, rearranging the equation, we find:
ΔV = V2 - V1 = (n * V_t) *