# JEE Main & Advanced Physics Semiconducting Devices Characteristic Curves of a Diode

## Characteristic Curves of a Diode

Category : JEE Main & Advanced

A graph represents the variation of ${{i}_{p}}$ with ${{V}_{p}}$ at a given filament current $({{i}_{f}})$ is known as characteristic curve.

The curve is not linear hence diode valve is a non-ohmic device.

(1) Space charge limited region (SCLR) : In this region current is space charge limited current.

Also ${{i}_{p}}\,\propto \,V_{p}^{3/2}$$\Rightarrow$${{i}_{p}}=kV_{p}^{3/2}$; where k is a constant depending on metal as well as on the shape and area of the cathode. This is called child?s law.

(2) Linear region (LR) : In this region ${{i}_{p}}\,\propto \,{{V}_{p}}$

(3) Saturated region (SR) or temperature limited region (TLR) : In this part, the current is independent of potential difference applied between the cathode and anode. ${{i}_{p}}\ne f({{V}_{p}})$, ${{i}_{p}}=f$ (Temperature) The saturation current follows Richardson Dushman equation i.e. $i=AS{{T}^{2}}{{e}^{-{{\varphi }_{0}}/kT}}$;  Here A = Emission constant =$\frac{4\pi \ me{{k}^{2}}}{{{h}^{3}}}amp/{{m}^{2}}-{{k}^{2}}$ S = Area of emitter in ${{m}^{2}}$;  T = Absolute temperature in K ${{\varphi }_{0}}$= Work function of metal in Joule; k =Boltzmann constant   The small increase in ${{i}_{p}}$ after saturation stage due to field emission is known as Shottkey effect.

(4) Diode resistance

(i) Static plate resistance or dc plate resistance : ${{R}_{p}}=\frac{{{V}_{p}}}{{{i}_{p}}}$.

(ii) Dynamic or ac plate resistance : If at constant filament current, a small change $\Delta {{V}_{P}}$ in the plate potential produces a small change $\Delta {{i}_{p}}$ in the plate current, then the ratio $\Delta {{V}_{p}}/\Delta {{i}_{p}}$ is called the dynamic resistance, or the 'plate resistance' of the diode ${{r}_{p}}=\frac{\Delta {{V}_{p}}}{\Delta {{i}_{p}}}$.

(iii) In SCLR : ${{r}_{p}}<{{R}_{p}}$,

(iv) In TLR  :${{R}_{p}}<{{r}_{p}}$ and ${{r}_{p}}=\infty$.

(5) Uses of diode valve

(i) As a rectifier

(ii) As a detector

(iii) As a transmitter

(iv) As a modulator

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