Sspd_chapter 3_solid state diode physics.  (Page 5/5)

As already discussed, forward bias lowers the built-in barrier potential hence though up-hill for majority carriers, majority carriers cross it with ease. Hence diffusion current component carried by majority carriers increases mani-folds and diode is turned on. As seen in Figure 3.7. Depletion layer shrinks and Majority carriers are injected into the other side across the depletion layer. Hence minority carrier profile is perturbed near the edge of the depletion width on both sides of the junction.The perturbation of minority carrier profile leads to identical perturbation in the majority carrier profile for maintaining the space-charge neutrality. The perturbed profile in the minority carrier leads to the diffusion of minority carriers away from the junction to the ohmic contact.As minority carriers diffuse away they recombine with the majority carriers along the way. Hence majority cariers rush in as recombination current from the ohmic contact towards the depletion layer.

For the continuity of the current flow, at every section of the bulk:

Within the depletion layer as shown in Figure 3.7, electron and hole currents are constant and there is no recombination within the depletion layer.

Deduction of Shockley Equation or Ideal Diode Equation.( Optional )

William Shockley, who invented BJT along with Bardeen and Braittain, made two important assumptions while deriving Ideal Diode Equation:

Assumption 1: There is no recombination within the depletion region and both electron and hole current are constant while crossing the depletion region;

Assumption 2:The two bulk regions are quasi-neutral and the forward applied voltage drops across the depletion region causing the built-in barrier potential to drop from φ _BO to (φ _BO -V _F ). During reverse bias, the built-in barrier potential increases from φ _BO to (φ _BO +V _R ).

The total diode current J _D (forward)referring to Figure 3.7:

By Boltzmann Relationship:

Substituting Equation (3.2.2.4) in Equation(3.2.2.3):

Equation 3.2.2.5 gives the Ideal Diode Equation by multiplying current density ‘J’ by cross-sectional area ‘A’ of the device:

In Equation (3.2.2.5), Diffusion Coefficient and Diffusion Lengths are strongly dependent on the ambient temperature as well as the doping concentration of the P and N-Bulk.

Table 3.2.2.1. gives the typical values of Diffusion Lengths for different samples.

Table 3.2.2.1.Typical values of Diffusion Lengths for typical ssamples.

3.2.2.1. Wide-Bulk Diode .

When the Bulk Widths are much greater than Diffusion Lengths of the minority carriers then the minority carriers perturbation have exponential decay and these Diodes are called Wide-Bulk Diode. The surface contacts or ohmic contacts donot influence the diode forward-bias current and donot effect the turn-on time.

Table 3.2.2.2. gives the typical parameters of an abrupt junction Wide-Bulk Diode.

Table 3.2.2.2.The fabrication parameters and the electrical parameters of a Wide-Bulk Abrupt Junction Diode.

Table 3.2.2.3. gives the reverse saturation current or reverse leakage current in a Wide-Bulk Diode.

Table 3.2.2.3.The carrier transport parameters and reverse saturation current of a Wide-Bulk diode with N-Type Doping 10 16 /cc and P-Type Doping 10 18 /cc and life-time τ n = τ p =1μs, cross-sectional area A= 10 -3 cm 2 .

For this Diode if we adopt Ideal Diode Equation then I-V characteristic is the following:

Plotting Equation 3.2.2.7. we get Figure 3.8 and Figure 3.9.

We clearly see that in Figure 3.9, the cut-in voltage of an Ideal Diode is 0.5V.

3.2.2.1. Narrow-Bulk Diode.

When N-Bulk and P-Bulk is much shorter than the corresponding minority carrier Diffusion Lengths then we have Narrow-Bulk Diode. In such a case we have linear decay of the minority carrier perturbation under forward bias condition as shown in Figure 3.10.

As can be seen in Figure 3.10, these new perturbations p _n (0) at the edge of the depletion layer on N-side and n _p ( 0) at the edge of the depletion layer on P-side decay linearly to thermal equilibrium values on their respective sides over the Bulk-width up to the ohmic contact where excess carrier is zero.

Under the condition shown n Figure 3.10. the ideal diode equation becomes:

Equation 3.2.2.8 is identical to Equation 3.2.2.5 except for the length constant. The Diffusion Lengths of minority carriers have been replaced by effective Bulk-Widths on the respective sides.This results in the increase of reverse saturation current by a factor of 6.

If we take W _BP =W _BN =5μm which is much less than the diffusion lengths as can be seen in Table 3.2.2.3 then we get I _D0 = 5.6×0.01pA. But this gives a superior turn-on time as we will see in Diode Transients therefore narrow-bulk diode have applications.

The theorization of narrow-bulk diode also helps understand the modern day BJT which are shallow junction and narrow bulk devices.

In the advanced version of Diode Physics we will discuss this narrow-bulk diode in a greater detail.