##### 16.4 TUNNEL DIODES

In a *p*−*n* diode, the width of the depletion layer varies inversely as the square root of impurity concentration. Thus, the smaller the impurity concentration (doping), the larger the depletion region and vice-versa. The impurity concentration, in a *p*−*n* junction diode is of the order of 1 in 108. With this impurity concentration, the width of the depletion layer is typically 5 microns (5 × 10^{−6} m). If on the other hand, if this impurity concentration is increased to 1 in 103, the width of the depletion region may be as small as 0.01 microns (0.01 × 10^{−6} m) i.e., the depletion layer becomes very thin. Thus, if a *p*−*n* junction diode is formed with such high impurity concentrations, the barrier becomes very thin. When the depletion layer becomes thin, a large number of electrons may penetrate through this thin barrier. This phenomenon is called ‘tunneling’ and such *p*−*n* diodes are called ‘tunnel diodes’ or ‘Esaki diodes’. A tunnel diode can be used as a high speed switch as tunneling takes place at the speed of light. A tunnel diode is schematically represented as shown in Fig. 16.18(a).

**FIGURE 16.17(a)** The Schmitt trigger using 555 timers

A reverse-biased tunnel diode behaves like a resistance, the resistance value being very small. When a small forward-bias voltage is applied, the energy level on the *p*-side is lower when compared to the *n-*side. Hence, tunneling of the electrons from *n*-side to *p*-side takes place resulting in a forward current that increases with the applied forward-bias voltage and reaches a value of *I*_{P}. However, if more forward-bias voltage is applied, the energy level of the electrons on the *n*-side increases but that on the *p*-side reduces. So the tunneling current in the device decreases to *I*_{V}. Hence, a tunneling diode exhibits negative resistance characteristic between points *A* and *B*. Any further increase in the forward-bias voltage stops tunneling and the device behaves simply like a *p-n* junction diode. The V–I characteristic is shown in Fig. 16.18(b) and its ideal characteristic is shown in Fig. 16.18(c).

**FIGURE 16.17(b)** The waveforms of a Schmitt trigger using 555 timers

**FIGURE 16.18(a)** The schematic representation for a tunnel diode

**FIGURE 16.18(b)** The V–I characteristic of a tunnel diode

The V–I characteristic of a tunnel diode is a multi-valued function of the current (i.e., for a current *I*_{1}, we have three voltages *V*_{1}, *V*_{2} and *V*_{3}) but a single-valued function of the voltage (i.e., for a voltage *V*_{1} the current is *I*_{1}, for *V*_{2} it is *I*_{1} and for *V*_{3} it is *I*_{1}). Hence, the device is called a voltage controlled negative resistance device. The ideal characteristic of a tunnel diode is an *n*-shaped characteristic.

The electrical equivalent circuit of a tunnel diode is shown in Fig. 16.18(d). Here, *C* is the junction capacitance, *R*_{S} and *L*_{S} are the series ohmic resistance and series inductance respectively and –*R*_{n} is the negative resistance. The typical values for Ge tunnel diode are:

*R*_{S} = 1 Ω, *L*_{S} = 5 nH, *C* = 20 pF, *R*_{n} = −30 Ω, *V*_{P} = 50 mV, *I*_{P} = 10 mA, = 8,

**FIGURE 16.18(c)** The ideal characteristic of a tunnel diode

**FIGURE 16.18(d)** The electrical equivalent circuit of a tunnel diode

**FIGURE 16.19(a)** A monostable circuit using a tunnel diode

**FIGURE 16.19(b)** The characteristic that explains the circuit operation

*V*_{V} = 350 mV, maximum forward-bias voltage *V*_{F} = 500 mV.

#### 16.4.1 A Monostable Circuit Using a Tunnel Diode

A monostable circuit using a tunnel diode is shown in Fig. 16.19(a) and its characteristic is shown in Fig. 16.19(b). The characteristic shown in Fig. 16.19(b) can be redrawn using piece-wise linearization shown in Fig. 16.19(c).

**Operation of the circuit.** Assuming that the resistance associated with *L* is negligible; the dc load line is drawn (with *v*_{s} = 0) using the relation,

When *i* = 0, *v* = *V*.

**FIGURE 16.19(c)** The piecewise linear approximation to the V-I characteristic of a tunnel diode

**FIGURE 16.19(d)** The equivalent circuit

**FIGURE 16.19(e)** A modified circuit

When *v* = 0, *i* =

The load line intercepts the characteristic at *O*. *O* is the operating point with coordinates (*I*_{O}, *V*_{O}). The monostable multivibrator is initially in the stable state, as defined by the operating point. If a positive pulse of magnitude greater than or equal to (*V*_{P}-*V*_{O}) is applied, the multivibrator goes into the quasi-stable state. The operating point shifts from *O* to *A*. A tunnel diode is a voltage controlled negative resistance device, that is, there are multiple voltages at which the current is the same. At *A* the current is *I*_{p} and so is the current at *B*. The operation now shifts from *A* to *B* abruptly. The voltage at *B* is *V*_{F} and the current is *I*_{P}. Just prior to reaching *B*, if the pulse (*v*_{s}) is terminated, the operating point moves from *B* to *C*, and *C* to *D* and finally terminates at *O*. The multivibrator, at the end of the quasi-stable state, returns to the initial stable condition.

**Calculation of T**. The time period

*T*of the monostable circuit can be computed using the piece-wise linear characteristic, shown in Fig. 16.19(c).

Let

The resistance of the diode is *R*_{1} when operated in the region 0 to *A*^{′} and is *R*_{2} when operated in the region *C*^{′} to *B*, then

To calculate (*T*, the time during which *I*_{P} falls to *I*_{V}) the time period of the monostable circuit, let us replace the device by a battery voltage, from Fig. 16.19(c).

The equivalent circuit can be drawn as shown in Fig. 16.19(d).

In the above circuit,

and

Using Eq. (16.33)

Using Eq. (16.34) and Eq. (16.36) it is possible to redraw the circuit shown in Fig. 16.19(d) as shown in Fig. 16.19(e).

The variation of *i* as a function of *t* is given as:

At

*t* = 0, *i* = *i*_{i} = *I*_{P}

and

Therefore,

At

*t* = *T*, *i*(*t*) = *I*_{V}

We know 1n (1 + *x*) ≈ *x*

The waveforms are plotted as shown in Fig. 16.20.

#### 16.4.2 An Astable Multivibrator Circuit Using a Tunnel Diode

In the monostable circuit, the operating point is chosen such that the circuit initially is in the stable state. Then a trigger drives the multivibrator into the quasi-stable state and at the end of the time period, the multivibrator once again returns to the stable state. However, if the operating point is chosen in the negative resistance region, it is unstable, the circuit oscillates. Consider the piece-wise linear characteristic of the tunnel diode shown in Fig. 16.21(a).

As the operating point *O* is unstable, the operating point may move to point *A*, from there to *B*, from *B* to *C*, *C* to *D*, *D* to *A* and *A* to *B* and this process repeats. The variation of the voltage *v* and current *i* are shown in Fig. 16.21(b).

*T*_{1} is given by Eq. (16.38).

**FIGURE 16.20** The waveforms of the tunnel diode of a monostable circuit

**To calculate T_{2}**. From Fig. 16.21(b), it is seen that the diode current varies from

*I*

_{V}to

*I*

_{P}during

*D*to

*A*and the device can now be replaced by a resistance

*R*

_{1}. Proceeding as in the case of a monostable circuit:

= *R* + *R*_{1} *V*_{Y} = *V* − *V* = 0 − *V* = −*V*

The equivalent circuit is shown in Fig. 16.21(c).

**FIGURE 16.21(a)** The piece-wise linear tunnel diode characteristic with the operating point in the negative resistance region

**FIGURE 16.21(b)** The waveforms of an astable multivibrator

**FIGURE 16.21(c)** The equivalent circuit during *D* to *A*

We have,

*i*(*t*) = *i _{f}* − (

*i*−

_{f}*i*)

_{i}*e*

^{−t/τ}*I _{i} = I_{V}*

At *t* = *T*_{2}, *i*(*t*) = *I _{P}*

as ln (1 + *x*) ≈ *x*

*T* = *T*_{1} + *T*_{2} is the time period of the astable multivibrator.

**FIGURE 16.22** The operation of a tunnel diode of a bistable multivibrator

#### 16.4.3 A Bistable Multivibrator Using a Tunnel Diode

Consider the tunnel diode characteristic and the load lines shown in Fig. 16.22. The load line 1 intersects the device characteristic at two points *X* and *X"*. If the circuit is operating at point *X*, the bistable multivibrator is in one stable state. If the operation is to be shifted to the other stable operating point *X′*, then a positive trigger pulse *v*_{s} whose amplitude is reasonably good enough to shift the operating point beyond the valley region and on to the load line 2 should be applied as a trigger. A change of state occurs and the operating point shifts to *X′*. The multivibrator is now in the other stable state, at point *X′*. To once again drive into the initial stable at *X*, a negative trigger pulse *v*_{s} whose amplitude is large enough to clear the bottom of the characteristic is to be applied. The operation once again shifts to point *X*, resulting in the multivibrator operating as a bistable circuit.