##### 6.2 THE DIODE AS A SWITCH

Semiconductor and Zener diodes can be used in switching applications. To understand the working of a two-terminal device as a switch, we need to consider its V–I characteristic and switching times.

#### 6.2.1 Diode Characteristics

A *p-n* junction diode can be used as a switch. When the diode is forward-biased, the switch is said to be in the ON state and when it is reverse-biased, the switch is in the OFF state. Figure 6.1 shows the V–I characteristic of a *p–n* junction diode.

The diode current is given by the relation:

where, *V* is the bias voltage, *η* = 1 or 2 depending on whether it is a Ge or Si diode and *V _{T}* is the Volt-equivalent for temperature.

**FIGURE 6.1** The V–I characteristic of a *p–n* junction diode

where, *T* is the room temperature. If *e ^{V/ηVT} >>* 1, Eq. (6.1) reduces to:

When the diode is forward-biased, *V* is positive and *I* is a positive current that varies exponentially with the variation of *V*. When the diode is reverse-biased, *V* is a negative voltage and the current *I* now flows in the opposite direction (*I* = −*I _{o}*),

*I*almost remains constant and it is called the reverse saturation current. The reverse saturation current gets doubled for every 10°C rise in temperature. The leakage currents in Ge are significantly larger when compared to that in Si devices. Ge diodes develop large reverse currents at elevated temperatures whereas the increase in the reverse current in Si diodes is negligible.

_{o}When used as a switch, a diode can be either ON or OFF, depending on the polarity of the signal applied to change the state. Though the diode is expected to switch between these two states almost instantaneously, in case of a high-frequency switching signal, it may not be possible to drive the switch from one state to the other abruptly because of junction capacitances and there arises a finite time delay before the device switches its state.

#### 6.2.2 Transition Capacitance

When a *p–n* junction diode is reverse-biased, electrons from the *p*-side will move to the *n*-side, aided by the external field and the holes move away from the junction. As a result, negative charge is developed on the *p*-side and positive charge on the *n*-side. The width of the space-charge region increases with reverse-bias. This can be considered as the parallel plate condenser whose value changes with the width of the depletion region. This capacitance is called as transition capacitance or depletion-region capacitance and its value is given by:

where, *W* = Spacing between the plates of the capacitor (in m),

*A* = Area (in m^{2}), and

*ε* = permittivity of the material.

For some simplified geometries:

where, *λ* is a constant,

*V* is the external voltage applied,

*n* = 1/2 for an abrupt junction, and

*n* = 1/3 for a gradual junction.

#### 6.2.3 Diffusion Capacitance

In a forward-biased junction diode there is a junction capacitance—called the diffusion capacitance—due to the injected charges being proportional to the applied external voltage *V*. This is given by the relation:

where, *η* = 1 for Ge and *η* = 2 for Si,

*τ* = mean life time for holes,

*V _{T}* = Volt-equivalent for temperature, and

*I* = hole current.

The diffusion capacitance *C _{D}* is usually significantly larger than the transition capacitance

*C*. These junction capacitances influence the switching times of a diode. When the diode switches state, the response is accompanied by a transient.

_{T}#### 6.2.4 Junction Diode Switching Times

**Forward Recovery Time.** The forward recovery time, *t _{fr}* of a diode is defined as the time difference between the 10 per cent value of the diode voltage and the time when this voltage reaches and remains within 10 per cent of its final value, i.e., 110 per cent or 90 per cent of the steady-state value. The forward recovery time is typically of the order of a few tens of nanoseconds.

Let the diode be in the OFF state for some time. When it is switched into the ON state, there occurs a transient response before the diode recovers to the steady state. If a large current step, equal to or greater than the rated forward current of the diode, is applied, then the diode voltage will have an overshoot and the response will reach the steady-state value after a finite time interval. At large currents, the diode is represented as a combination of a resistor and an inductor. For a current step of smaller value, the diode is represented as a combination of a resistance and a capacitance. The resultant responses when the current is either large or small are shown in Fig. 6.2. Note that here we have assumed the rise time of the current pulse to be negligible.

**Reverse Recovery Time.** Initially, if the diode is in the OFF state due to reverse-bias voltage, then the resultant current is a reverse saturation current. When the diode is ON with a forward voltage for some time and turned OFF by reverse-biasing, then the current cannot reach the initial reverse saturation current instantaneously. The reverse recovery time of the diode is defined as the time taken for the diode current to reach its initial reverse saturation current, when the diode is turned OFF from the ON state. If the diode is ON for some time, then there is a large current due to injected hole or electron density, as shown in Fig. 6.3(a).

**FIGURE 6.2** Diode response for currents of different amplitudes

*I*_{4} > *I*_{3} > *I*_{2} > *I*_{1}

The dashed lines represent current step pulses

**FIGURE 6.3(a)** The minority carrier density distribution as a function of *x*, the distance from the junction when the diode is ON

*p _{no}* = density of holes on the

*n*-side at equilibrium

*n _{P0}* = density of electrons on the

*P*-side at equilibrium

*n _{P}* = density of electrons on the

*P*-side when forward-biased

*p _{n}* = density of holes on the

*n*-side when forward-biased

*p _{n} – p_{n0}* = injected or excess hole density on the

*n*-side

*n _{P} – n_{P0}* = injected or excess electron density on the

*P*-side

**FIGURE 6.3(b)** Minority carrier density distribution as a function of *x*, the distance from the junction when the diode is OFF

When the diode is ON, the number of minority carriers is large [see Fig. 6.3(a)]. When the polarity of the external voltage is suddenly reversed, the diode forward current is expected to reduce to a negligible reverse current. However, this does not happen as it takes a finite time delay for the minority carrier density distribution to take the form shown in Fig. 6.3(b). During this period, the injected minority carrier density will drop to zero and the minority carrier density reaches the equilibrium value.

Let us try to understand the situation when a diode, which is ON for sometime, is abruptly reverse-biased, as shown in Fig. 6.4. The voltage shown in Fig. 6.5(b) is applied to the diode circuit shown in Fig. 6.4.

- As long as the voltage
*v*=_{i}*V*(till_{F}*t*_{1}), the diode is ON. The forward resistance of the diode is negligible when compared to*R*. Thus,_{L} - At
*t*=*t*_{1}, the polarity of*v*is abruptly reversed:_{i}

This is the time at which the minority carrier density *p _{n}* at

*x*= 0 has reached the equilibrium value

*p*

_{n0}.

If the diode resistance now is *R _{d}*, the diode voltage falls slightly by an amount (

*I*+

_{F}*I*)

_{R}*R*but, the voltage still remains positive. At

_{d}*t*=

*t*

_{2}the charge carriers have been cleaned up, the polarity of the diode voltage reverses, and the diode current starts to decrease.

The time duration *t*_{1} to *t*_{2}, during which period the stored minority charge becomes zero, is called the storage time *t _{S}*. The time interval from

*t*

_{2}to the instant the diode has recovered (

*V*= −

*V*) is called the transition time,

_{R}*t*. The sum of the storage time,

_{t}*t*and the transition time,

_{s}*t*is called the reverse recovery time of the diode,

_{t}*t*.

_{rr}**FIGURE 6.4** Driving an ON diode into the OFF state

**FIGURE 6.5** The switching times of a diode

*t _{s}* is given by the relation:

#### 6.2.5 Piecewise Linear Diode Model

The diode characteristics in Fig. 6.1 is a non-linear characteristic. In the simplified analysis of a diode circuit, it is advisable that the diode be represented by its electrical equivalent. Hence, the non-linear characteristic of a diode is piecewise linearized so that the diode can be represented by an electrical equivalent. The practical V–I characteristic and the piecewise linear V–I characteristic of a *p–n* diode are shown in Figs. 6.6(a) and (b), respectively.

Figure 6.6(b) gives the piecewise linear V–I characteristic of the diode. When *V* ≥ *V _{γ}*, the diode is ON and when

*V < V*, the diode is OFF. Figures 6.6(c) and (d) show the forward-biased and reverse-biased diode equivalent circuits respectively for large signal conditions.

_{γ}**FIGURE 6.6** Diode characteristics (a) V–I characteristic of a practical diode; and (b) piecewise linear characteristic of a diode

**FIGURE 6.6(c)** The diode when forward-biased

**FIGURE 6.6(d)** The diode when reverse-biased

#### 6.2.6 Breakdown Diodes

Avalanche or Zener diodes are normally operated when reverse-biased. At a voltage called the breakdown voltage, the current abruptly rises to a large value but the voltage across the two terminals of the device remains almost constant. So, these devices are used as voltage reference or constant voltage devices. These breakdown diodes are used as voltage regulators. The V–I characteristic of a typical avalanche or Zener diode is shown in Fig. 6.7.

The maximum power dissipation in the Zener, *P*_{D(max)} = *V _{z}I*

_{z(max)}.

**FIGURE 6.7(a)** A reverse-biased Zener diode

Avalanche multiplication takes place when a sufficient reverse-bias voltage is applied to a diode and the charge carrier acquires sufficient kinetic energy due to the applied potential. This carrier, in turn, may collide with a crystal ion and, in the process, may transfer sufficient energy to break the covalent bond. Now a new electron–hole pair is generated which in turn may acquire sufficient energy, collide with another crystal ion and create a new electron–hole pair. This cumulative process of multiplication of electron–hole pairs is called avalanche multiplication, resulting in a large current in a reverse-biased diode.

**FIGURE 6.7(b)** The V–I characteristic of a Zener diode

On the other hand, Zener breakdown occurs due to the physical rupturing of covalent bonds due to a strong electric field and a large current flows in a reverse-biased Zener diode. The breakdown voltage can be controlled by adjusting the doping levels. Zener breakdown voltages are usually less than 6 V; and if the breakdown voltage is more than 6 V, the mechanism involved is an avalanche breakdown.

The breakdown voltage may also vary with the temperature. Normally, data sheets specify the temperature co-efficient as ±0.1 per cent/°C. The temperature co-efficient is taken as positive for avalanche breakdown and negative for Zener breakdown.

As temperature has a profound effect on *V _{Z}*, the change in breakdown voltage due to an increase in temperature can be calculated if the temperature co-efficient is known, as:

where, *α _{Z}* is the temperature coefficient, which is negative for Zener diode and is positive for an avalanche diode.

*V*at

_{Z}*T*

_{2}is given by:

For a Zener diode:

For an avalanche diode:

Let us consider Example 6.1.

##### EXAMPLE

*Example 6.1:* A Zener has a breakdown potential *V _{Z}* = 3.8 V. If

*α*= −0.1 per cent/°C and the temperature changes from 25°C to 100°C, calculate the Zener voltage at 100°C.

_{Z}*Solution:*

Using Eq. (6.8):

Using Eq. (6.9):

*V*_{Z(100°C)} = *V _{Z}* − 0.285

*V*_{Z(100°C)} = 3.8 − 0.285 = 3.515 V

##### EXAMPLE

*Example 6.2:* An avalanche diode has a breakdown potential *V _{Z}* = 12 V. If

*α*= 0.1 per cent/°C and the temperature changes from 25°C to 100°C, calculate the breakdown voltage at 100°C.

_{Z}*Solution:*

Given, *V _{Z}* = 12 V,

*α*= 0.1 per cent/°C and the temperature changes from 25°C to 100°C.

_{Z}Using Eq. (6.8):

Using Eq. (6.10):

*V*_{Z(100°C)} = 12 + 0.9 = 12.9 V