5.2 Sspd_chapter 3_sec3.2.4. reverse biaseddiode,3.2.5.real diodes  (Page 2/3)

Equation tells us that n _i ² increases by 15.48% for every 1K rise in Temperature.

But experimentally, n _i ² increases by 7% for every 1K rise in Temperature for both Si and Ge Diodes.

Hence we can assume that I _DO increases by 7% for every 1°C rise in Temperature.

Therefore:

If for 1°C rise in temperature, I _DO increases by 1.07 then for 10°C rise in temperature, I _DO increases by (1.07) ¹⁰ =1.969 ~ 2.

Therefore we can say that Reverse Saturation Current doubles for every 10°C rise in Ambient Temperature.

Hence the expression for Reverse Saturation Current is:

3.2.4.2.Temperature Dependence of Forward Bias Voltage V F for maintaining a constant forward current I F .

Since I _D0 doubles for every 10°C rise in temperature hence forward current also increases as shown in Figure 3.13. Therefore at Room Temperature, forward bias must decrease by 2.5mV for every 1°C rise in temperature to maintain forward current constant.

At Temperature T Kelvin:

At Temperature (T+1) Kelvin:

But I _D0 (T+1)=1.07I _D0 (T) hence if the current has to remain constant then V _D must reduce by ∆V.

Therefore Equation (3.2.4.2.2) is rewritten for constancy of the current:

Simplifying Equation (3.2.4.2.3) we get:

At T = 300K, 1/300<<1 therefore Equation (3.2.4.2.4) simplifies to:

Or

Theoretically forward voltage must decrease by 1.759mV/1°C to maintain I _D constant but exoerimentally:

3.2.5.Real Diode Equation.

Two simplifying assumptions were made while deriving Shockley Equation:

i.Bulk is quasi-neutral. This means the applied diode voltage drops across the depletion region only.

ii.There is no recombination in the depletion region.

In real diodes, at low voltages the depletion region is comparable to diffusion lengths hence while crossing the depletion region recombination does take place. As a result the current is not constant while crossing the depletion region.

Therefore an Ideality Factor has to be introduced in the Ideal Diode Equation. That is below 0.5mA, Ideal Diode Equation is not adequate to describe the real diode behavior.

Theefore at low currents:

Where Ideality Factor η =2 at low currents lower than 0.5mA.

At high currents, when we have high injection level then the bulk does not remain neutral. At high injection levels, perturbation in minority carrier becomes comparable to the majority carrier concentration that is:

Therefore the forward voltage where High Level Injection(HIL) occurs:

Under such a condition the carrier concentration profile as shown in Figure 3.14:

As seen in Figure 3.14. there is considerable field and hence voltage drop across the Bulk. Therefore V _D = V _dep is invalid now.

V _dep = V _D - (V _Bp +V _Bn ) ;

It will be shown through detailed analysis in the Appendix of Chapter 3 that

V _dep = (1/2)V _D . Since the drop across the depletion region decides the Shockley Equation hence at HIL the form of diode equation is:

Where η=2.

This discussion tells us that Real Diodes are described by Equation 3.2.5.1

where η=2 for currents less than 0.5mA(depletion region recombination dominates)

and η=2 for currents more than 5mA(the bulk does not remain quasi-neutral).