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Using Equation (3.3.1) and (3.3.2), the built-in barrier potentials and the depletion widths are tabulated in Table 3.3.2.

Table 3.3.2. The built-in barier potential,depletion widths and Emax at zero bias for Classical Diodes(10^16/cc), Zener Diodes(10^20/cc) ,Back-ward Diodes(10^21/cc) and Tunnel Diodes(10^22/cc).

N 10 16 /cc 10 19 /cc 10 20 /cc 10 21 /cc 10 22 /cc
Φ BO 0.718V 1.077V 1.197V 1.317V 1.437V
d 0 4236.7A° 164A° 54.7A° 18.0A° 5.74A°
E max0 (V/cm) 33939.75 1.3×10 6 4.38×10 6 14.4×10 6 46×10 6

In Figure 3.20. I show that there is no possibility of Quantum Mechanical Tunneling.This is the usual classical case. In this under zero-bais, diffusion of majority carriers is exactly balanced by drift of minority carriers and detailed charge balance is maintained.Under forward bias, depletion width shrinks and potential barrier is reduced by forward bias hence the charge balance is heavily tipped in favour of majority carriers diffusing in the forward direction and it exponentially increases. Under reverse bias, diffusion of majority carriers is fully prevented because of higher potential barrier. Potential barrier has increased by reverse bias and only limited number of minority carriers are drifting down the potential gradient as reverse leakage current.Here the electrons from the top of the Valence Band cannot do Band-to-Band tunneling from Valence to Conduction Band. This is because the potential barriers thickness is thicker than 4236.7A° and Potential Barrier height is greater than 1V hence there is no possibility of tunneling asa is evident from Table 3.3.1.

In Forward Bias and Reverse Bias, thermal equilibrium is disturbed hence we donot have Fermi Level but we have IMREF levels and IMREF levels are not aligned.

Now we examine the case of Zener diode with doping density of 10 20 /cc. As seen from Table 3.3.2. the built –in barrier potential is 1.077V which means that Fermi level is very near the band edge in P-Type as well as in N-Type.The Potential Barrier Width is 164A°.

Figure 3.21 gives the Energy Band diagram of Zener Diode.Let us assume that its Zener Breakdown is 4V. As seen in the diagram, at reverse bias of 4V, the built-in Barrier Potential= (1.077+4)V=5.077V and the Barrier Width= depletion Width = 356A°. As seen from case (b) of Figure 3.21, Valence Band in P-Type faces empty permissible energy states across the barrier into the conduction band of N-Type.Since Barrier Width is thin and Barrier height is moderate, quantum mechanical tunneling occurs and Zener Breakdown occurs. In addition to the minority carriers drifting across the barrier the electrons from P-Side tunnel to the N-Side adding to the reverse current and leading to Zeber Breakdown.

When forward bias is done, forward current can flow only through diffusion across the lowered barrier potential.There is no possibility of tunneling.

3.3.1. Design of Zener Diode for a given breakdown between 0V to 4V.

Experimentally it has been found that just as we have a critical field of 5×10 5 V/cm for Avalanche Breakdown similarly we have a crtical field for Zener Breakdown . This E critical_Zener =1.2×10 6 V/cm.

Hence if I am designing for a Breakdown Voltage of V Z Volts then the following Design Rule holds good:

Therefore:

From depletion width consideration:

Built-in Barrier Potential:

Combining the Equations (3.3.1.1),(3.3.1.2) and (3.3.1.3) we get;

Using the Design Formula (3.3.1.4) we tabulate the Fabrication Parameters of Zener Diode of V Z = 4V,3V,2V and 1V in Table 3.3.1.1.

Table 3.3.1.1.Doping Density for Zener Diode of Zener Breakdown Voltage=4V,3V.2V and 1V.

V Z N A (No.per cc) N D (No. per cc)
-4V 1.81×10 20 1.81×10 20
-3V 2.235×10 20 2.235×10 20
-2V 2.91×10 20 2.91×10 20
-1V 4.18×10 20 4.18×10 20

3.3.2. Comparison between Zener Break-down Voltage and Avalanche Break-down Voltage.

The following Table brings out the major differences between two kinds of Breadowns.

Table 3.3.2.1. Salient features of Avalanche Breakdown and Zener Breakdown.

Avalanche Breakdown Zener Breakdown
E critical 5×10 5 V/cm 1.2×10 6 V/cm
Mechanism Impact collision and ionization Covalents are strained and broken
Voltage Range Above 6V Below 4V
Between 4V and 6V the mechanism is partially Avalanche and partially Zener.
Sharpness of Breakdown Soft BreakdownSlope resistance 40Ω Sharp BreakdownSlope Resistance lower than 10Ω
Temperature Coefficient Positive Temperature Coefficient Negative Temperature Coefficient

It is possible to design a Zener Diode between 4V and 6V which has Zero Temperature Coefficient. This will act as an ideal Voltasge Source as well as an ideal Reference Voltage.

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Source:  OpenStax, Solid state physics and devices-the harbinger of third wave of civilization. OpenStax CNX. Sep 15, 2014 Download for free at http://legacy.cnx.org/content/col11170/1.89
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