Question

what is the vi equation for a zener diode or a simple diode

Answer 1

what you mean in " vi equation"????
but what you mean as i think is "
for a normal diode the forward bias voltage is about " 0.6-0.7 volt"
for zener diode that will depend on its type and it could be ""5 volt, 8 volt"
or even higher...

Answer 2

For a typical diode the equation is:\[I_{D}=I_{S}(e^{V_{D}/V_{T}}-1)\]
And for the voltage it would be:
\[V_{D}=V_{T}Ln(1+I_{D}/I_{S})\]

Answer 3

Pay attention to the fact that when Vd<<0 then Id =-Is approximately, that is why Is is called Reverse Bias Saturation Current
Vd=Voltage in the diode
Vt=KT/e that is approximately 0.025 Volts at 300 Kelvin
Id is the current in the diode

For the Zener diode is the same equation, the only difference is the reverse behavior. You can make Vd<<0 and get Id=-Is until Vd<=-Vz(Zener Voltage) and then the reverse current takes a much higer value. That is why Zener diodes are used in Voltage/Current stabilization