Tunnel Diodes

Tunnel Diodes

• A normal p‒n junction has an impurity concentration of about 1 part in 10⁸. This much amount of doping has the depletion layer width of about 5 microns i.e. 5×10^‒4 cm.

• The diodes in which the concentration of impurity atoms is greatly increased upto 1 part in 10³, to get completely changed characteristics, are called tunnel diodes. These diodes are first introduced by Leo Esaki in 1958.

 

1. Construction

• The most common commercially available tunnel diodes are made from the germanium or gallium arsenide.

• The basic construction of an advanced design tunnel diode is shown in Fig. 3.4.1.

Fig. 3.4.1 Construction of tunnel diode

 

2. Tunneling Effect

• Let us consider an electron of total energy W (joules) moves in region 1, where the potential energy may be taken as zero, U = 0. At x = 0, there is a potential energy barrier of height U₀ and U₀ is greater than W. This is illustrated in Fig. 3.4.2 (a).

• Two regions, region 1 and region 2 having two different potential energy are shown separately in Fig. 3.4.2, and it is important to note that the potential energy remains constant in region 2 for x > 0. Now we apply the schrödinger equation for region 1 and region 2 to find the possibility that an electron will penetrate through the barrier.

Region 1:

Schrödinger equation is given as

d²Ψ/dx² + (8π²m/ h²)WΨ = 0

                ……….. (3.4.1)

For region 1 it takes the form:

Ψ = Cε^{±j(8π2mW/h2)1/2x}

      ……….(3.4.2)

where C is a constant.

• The product of Ψ and its complex conjugate Ψ* gives the probability of finding an electron between x and x + dx. Since ΨΨ* = |Ψ|² = C² = Constant, the electron has an equal probability of being found anywhere in the region 1. In other words, the electron is free to move in a region of zero potential energy.

Region 2:

In region 2, x > 0 and schrödinger equation is given as

d²Ψ/dx² – 8π²m/ h²(U₀-W)Ψ = 0

                ……….. (3.4.3)

Since U₀ > W the equation (3.4.3) takes the form :

  = A ɛ^{-x/2 d0}

            …………. (3.4.4)

where

A constant and

The solution of equation (3.4.3) is actually of the form

 Ψ= Aε^-x/2do +B ε^x/2do

              ………… (3.4.6)

• However, B = 0, since it is required that Ψ be finite energy where in the region 2. Again having the product of Ψ and its complex conjugate Ψ* to find the probability of the electron between x and x + dc in region 2 we have

 ΨΨ* = A²ε^-x/do

           ………... (3.4.7)

• From equation (3.4.7) we can observe following points.

An electron can penetrate a potential‒energy barrier.

The probability of penetrating a potential barrier by electron decreases exponentially with distance into the barrier region.

• Consider that the potential energy hill has a finite thickness d as shown in Fig. 3.4.2 (b). Then x = d and equation (3.4.8) becomes

ΨΨ* = A²ε^-d/do

           ………... (3.4.8)

• Now, if

1. d >> d₀: The probability that the electron will tunnel through the barrier is virtually zero.

2. d→d₀ (d approaches d₀): A²ε^-d/do becomes large enough to represent an appreciable number of electrons which have tunneled through the hill.

 

3. Energy Band Structure of Tunnel Diode

• We have seen that to achieve tunneling barrier, depth d should approach d₀. However, it is not the only condition to achieive tunneling. It is also required that occupied energy states exist on the side from which the electron tunnels and that allowed empty energy level. Hence we will now see the energy band structure when the impurity concentration is very high.

• We have seen that in the energy band structure for the lightly doped p‒n diode, the fermi level E_f lies inside the forbidden energy gap. In the heavily doped p‒n diode E_f lies outside the forbidden band.

We know that

 E_f = E_C ‒ kT In [N_C/N_D]      ……… (3.4.9)

• For a lightly doped semiconductor, N_D <N_C, so that In(N_C/N_D) is a positive number. Hence E_F <E_C, and the fermi level lies inside the forbidden band. For highly doped semiconductor donor concentrations are more so that N_D >N_C and InN_C/N_D is negative number. Hence E_F > E_C, and the fermilevel lies outside the forbidden band.

• For the similar reason, for heavily doped F region, N_A >N_V, and the fermi‒level lies in the valence band.

We have,

• When we compare above two equations for heavily doped p‒n diode we find that E₀ > E_G. Therefore, the contact difference of potential energy E₀ exceeds the forbidden energy gap voltage E_G. Hence, at open circuit condition the band structure for heavily doped p‒n junction is as shown in Fig. 3.4.3.

• As shown in Fig. 3.4.3, at open circuit, the fermi level in the p‒side is at the same energy as the fermi level E_f in the n‒side. It is important that there are no filled states on one side of the junction which are at the same energy as empty allowed states on the other side. Hence, at open circuit, there can be no flow of charge in either direction across the junction and the current is zero.

Fig. 3.4.3 Energy band in a heavily doped p‒n diode under open circuited condition

• When reverse bias is applied, the height of the barrier is increased above the open circuit value E_0. Hence the n‒side levels must shift downwards with respect to the p‒side levels, as shown in Fig. 3.4.4. Looking at Fig. 3.4.4, we can notice that there are some energy states (portion in dark black colour) in the valence band of the p‒side which lie at the same level as allowed empty states in the conduction band of the n‒side.

Fig. 3.4.4 Energy bands In a heavily doped p‒n diode under reverse bias

Hence these electrons will tunnel from the p to the n‒side, giving rise to a reverse diode current. As the reverse bias increases, the portion in dark black colour increases, causing the reverse current to increase, as shown in section 1 of Fig. 3.4.5.

• When forward bias is applied to the diode the barrier potential E₀ decreases. Hence the n‒side levels must shift upward with respect to those on the p‒side. This is illustrated in Fig. 3.4.6.

• Now, there are occupied states in the conduction band of the n‒material (the dark black colour area) which are at the same energy as allowed empty states (holes) in the valence band of the p‒side. Hence electrons will tunnel from the n to the p material, giving rise to the forward current as shown in section 2 of Fig. 3.4.5.

• As the forward bias is increased further, n‒side level shifts further upward, as shown in Fig. 3.4.7. In this situation the maximum number of electrons can leave occupied states on the left side, giving rise to the peak current I_P. If still more forward bias is applied, the situation shown in Fig. 3.4.8 (a) exists and the tunneling current decreases, giving rise to section 3 of Fig. 3.4.5.

• Finally, at an even larger forward bias, the band structure of Fig. 3.4.8 (b) is obtained. Since now there are no empty allowed states on one side of the junction at the same energy as occupied states on the other side, the tunneling current drops to zero. This is illustrated in Fig. 3.4.5.

 

4. Working Principle

• In tunnel diode, p and n regions are very heavily doped. Due to this, width of the depletion region reduces considerably.

• In normal p‒n junction, the width of the depletion region is about 5 × 10^‒4 cm while in tunnel diode it is about 1 × 10^‒6 cm which is about 1/100^th of normal diode.

• Due to such a thin depletion region, the charge carriers i.e. electrons can easily penetrate the depletion region due to their high kinetic energy.

• This penetration of electrons through the depletion region due to high velocities is called tunneling and the diode is called tunnel diode. This happens at very low forward bias voltages.

• Due to tunneling effect, the tunnel diode shows a negative resistance region.

 

5. Load Line for Tunnel Diode

• Consider a circuit as shown in Fig. 3.4.9. The supply voltage is V and R is the load resistance.

• The drop across the tunnel diode is V_T. Applying KVL,

  V = I_TR + V_T

 I_T = (‒1/R)V_T + V/R

                ………. (3.4.10)

• So when I_T = 0, V_T = V while when V_T = 0, I_T = V/R.

Using these two points a load line can be obtained on V‒I characteristics of tunnel diode as shown in Fig. 3.4.10.

• The load line intersects the characteristics at the three points A, B and C. The load line position and the slope is completely dependent on the network elements and tunnel diode characteristics.

• The points A and C are stable operating points as located in positive resistance region of characteristics. While point B is in the negative resistance region and hence unstable operating point.

• An important point regarding stable points A and C is that if there is slight change in the network conditions there will not be any change in the circuit behaviour and position of Q point for the circuit. If supply voltage increases then point C will move up on the curve as voltage across diode V_T will increase. When voltage decreases to original value, point C will regain its original position back.

• But if operating point is defined at point B in the unstable region and if supply voltage slightly increases then correspondingly V_T increases but I_T decreases due to negative resistance characteristics. This further reduces V_T and process continues till point shifts into stable region at point C. If supply voltage slightly decreases, point B moves up to achieve stable point A.

• Thus point B can be defined as an operating point using load line concept but in practice it will get stabilized at the locations A or C.

• This concept is used in a negative resistance oscillator using a tunnel diode.

 

6. Characteristics and Symbol

• Fig. 3.4.11 shows the volt‒ampere characteristics of a tunnel diode.

• For small forward voltages (upto 50 mV for germanium) the resistance remains small, of the order of 5 Ω and current increases.

• The current attains a peak value I_P corresponding to the voltage V_P which is about 600 mV. The I_P can vary from few micro amperes to several hundred amperes.

• At the peak point, the slope dI/dV of the characteristics becomes zero.

• If now the forward voltage is increased further, beyond V_p, then the current starts decreasing rather than increasing. Thus the dynamic conductance dl/dV becomes negative..

• Hence the dynamic resistance dV/dI is negative and it shows negative resistance characteristics. This negative resistance continues till a voltage V_V called valley voltage.

• At the valley voltage V_V, the current is I_V and slope dI/dV becomes again zero.

• After V_V, if the voltage is increased, the current again increases. Thus resistance again becomes positive and remains positive thereafter.

• At the so called peak forward voltage V_f, the current again reaches the value equal to peak current I_P.

• The value of current between I_P and I_V can be obtained with three different voltage values. For the value of current between I_P and I_V, the characteristics is triple valued.

• This multivalued feature makes the tunnel diode useful in the pulse and digital circuits.

• The circuit symbol of a tunnel diode is shown in Fig. 3.4.12 (a) while its equivalent circuit in the negative resistance region is shown in Fig. 3.4.12 (b).

• The negative resistance ‒ R_n has a minimum at the point of inflection between I_P and I_V.

• The series resistance R_S is due to ohmic contact resistance.

• The series inductance L_S depends upon the lead length and the geometry of the diode package.

• The junction capacitance C depends upon the bias represents the junction diffusion capacitance and is usually measured at the valley point.

 

7. Advantages of Tunnel Diode

• The advantages of a tunnel diode are:

1. Environmental immunity i.e. the peak point (V_P, I_P) is not a sensitive function of temperature.

2. Low cost.

3. Simplicity i.e. a tunnel diode can be used along with a d.c. supply and few passive elements to obtain various application circuits.

4. Low noise.

5. High speed i.e. the tunneling takes place at the speed of light hence the switching times of the order of a nanosecond are easily obtained and switching times as low as 50 psec also can be obtained.

6. Low power consumption.

• The only disadvantage of this diode are its low output voltage swing and it is a two terminal device. Hence there is no isolation between input and output. Hence transistor is used along with a tunnel diode for frequencies below 1 GHz.

 

8. Sinusoidal Oscillator using Tunnel Diode

• Fig. 3.4.13 (a) shows a tank circuit and a switch.

• The closing of the switch will result in a sinusoidal voltage that will decrease in amplitude with time. Thus it will produce damped output as shown in Fig. 3.4.13 (b).

• The damping of the oscillator output is due to the dissipative characteristics of the resistive elements in the tank circuit.

• The dissipative characteristics of the resistance must be compensated to produce pure sinusoidal output.

• A tunnel diode can be placed in series with the tank circuit as shown in Fig. 3.4.14 (a).

• It must be operated in its negative resistance region. This will compensate the resistive characteristics of the tank circuit to produce the undamped purely sinusoidal response as shown in Fig. 3.4.14 (b).

 

9. Other Applications of Tunnel Diode

• The various other applications of tunnel diode are,

1. As a high speed switch.

2. In pulse and digital circuits.

3. In negative resistance and high frequency (microwave) oscillator.

4. In switching networks.

5. In timing and computer logic circuitry.

6. Design of pulse generators and amplifiers.

 

10. Comparison of Tunnel Diode and Conventional Diode

• The comparison of tunnel diode and conventional p‒n junction diode is given below.

Tunnel diode

1. Impurity concentration is high about 1 part in 10³ atoms.

2. Depletion region width is about 5 microns, which is 1/100th the width of typical p‒n junction diode.

3. The carrier velocities are very high at low forward bias, hence can punch through the depletion region.

4. The V‒I characteristics shows the negative resistance region.

5. The V‒I characteristics is,

6. The materials used for construction are germanium or gallium arsenide.

7. The symbol is, 

8. The switching time is very low of the order of nano to picoseconds.

9. Used for high frequency oscillators, high speed applications such as computers, pulse and digital circuits and switching networks.

Conventional p‒n junction diode

1. Impurity concentration is low about 1 part in 10⁸ atoms.

2. The width of depletion region is high compared to the tunnel diode.

3. The carrier velocities are low at low forward bias, hence can not penetrate the depletion region.

4. The V‒I characteristics does not show the negative resistance region.

5. The VI characteristics is,

6. The silicon is most popularly used.

7. The symbol is, 

8. The switching time is high.

9. Used in rectifiers and other general purpose applications.

 

Review Questions

1. Describe the construction, the symbol, V‒I characteristics and applications of tunnel diode.

2. With energy band diagram, explain the theory and characteristics of tunnel diode.

3. Write short note on tunnel diode.

4. What is the difference between the Tunnel diode and ordinary PN diode ?