V-l Characteristics Equation of a Diode

V-l Characteristics Equation of a Diode

AU : Dec.-03, May-09

• The mathematical representation of V-I characteristics of diode is called V-I characteristic equation or diode current equation. It gives the mathematical relationship between applied voltage V and the diode current I. It is given by,

I = I₀ [e^{V/η VT} – 1] A  … (1.9.1)

where          I₀ = Reverse saturation current in amperes, V = Applied voltage

η = 1 for germanium diode and 2 for silicon diode

V_T = Voltage equivalent of temperature in volts.

• The factor η is called emission coefficient or ideality factor. This factor takes into account the effect of recombination taking place in the depletion region. The effect is dominant in silicon diodes and hence for silicon η = 2. The range of factor is from 1 to 2.

• The voltage equivalent of temperature indicates dependence of diode current on temperature. The voltage equivalent of temperature V_T for diode at temperature T is calculated as,

V_T = kT volts  …(1.9.2) .

Where         k = Boltzmann's constant

= 8.62 × 10^-5 eV/°K

T = Temperature in °K.

• At room temperature of 27 °C i.e. T = 27 300 °K and the value of V_T is 26 mV, as seen earlier.

• The value of V_T also can be expressed as,

Key Point : The diode current equation is applicable for all the conditions of diode i.e. unbiased, forward biased and reverse biased.

• When unbiased, V = 0 hence we get,

I = I₀ [e° - 1] = 0 A

• Thus there is no current through diode when unbiased.

Key Point : For forward biased, V must be taken positive and we get current I positive which is forward current. For reverse biased, V must be taken negative and we get negative current I which indicates that it is reverse current.

1. Nature of V-I Characteristics from Equation of Diode

• Consider a current equation of diode as,

I = I₀ (e^V/ηVT - 1)

• Now for a forward biased condition, the bias voltage V is considered positive and hence exponential index has positive sign. Due to this, 1 << e^V/ηVT  hence neglecting 1 we get the equation for a forward current as,

I_f = I₀ e^V/ηVT

• This indicates that once bias voltage exceeds cut in voltage, the forward current increases exponentially. In reverse biased condition, the bias voltage V is treated negative and due to this exponential index has negative sign. So e^-V/ηVT << 1, hence neglecting exponential term we get,

αI_R ≅  I₀ (-1) ≅  - I₀

• The above equation indicates that under reverse biased condition, the current is reverse saturation current which is negative indicating that it flows in opposite direction to that of forward current and almost constant. Such nature of diode characteristics is already been discussed and it is as shown in Fig. 1.9.1. The dashed portion represents breakdown region.

• As mentioned earlier, I₀ is due to minority carriers generated due to thermal energy and hence IQ is temperature dependent. While V_T, the voltage equivalent of temperature is kT is also temperature dependent. Hence the forward current which depends on I₀ and V_T is also temperature dependent, hence we can conclude that in all, the entire V-I characteristics of a p-n junction diode depends on the temperature.

• The diode current equation is applicable for both forward and reverse biased conditions and completely describes the V-I characteristics of p-n junction diode.

Ex. 1.9.1 A diode operating at 300 °K at a forward voltage of 0.4 V carries a current of 10 mA. When voltage is changed to 0.42 V, the current becomes twice. Calculate the value of reverse leakage current and ʼn for the diode. Sol. At V1 = 0.4 V, I1 = 10 mA and at V2 = 0.42 V, 1221120 mA

Ex. 1.9.2 Determine the Germanium p-n junction diode current for the forward bias voltage of 0.22 V at room temperature 25 °C with reverse saturation current equal to 1 mA. Take 1= 1 for Germanium.

Sol. : V = 0.22 V, I₀ = 1 mA, η = 1

V_T = kT = 8.62 × 10^-5 × (25 + 273)

= 0.02568

I = I₀ [e^V/η V_T -1]

= 1 × 10^-3 [e^{0.22/l×0.02568} -1]

= 5.25 A     ... Forward current 

Ex. 1.9.3 A silicon diode conducts 5 mA at room temperature in forward bias condition at 0.7 V. Calculate its reverse saturation current. If the forward voltage is increased to 0.75 V calculate the new current through the diode. (Take η = 2 and V_T =26 mV) at room temperature.

Sol.

Review Questions

1. State the diode current equation explaining the meaning of each term involved in it.

2. The current of germanium diode is 100 μA at a voltage of 1 V, at room temperature. Determine the magnitude of the current for the voltages of ±0.2 V at room temperature.

(Ans.: 291 mA, 99.95 μA)

3. A silicon diode has a reverse saturation current of 60 nA. Calculate the voltage at which 1 % of the rated current will flow through the diode, at room temperature if diode is rated for 1 A.

(Ans. : 0.6252 V)