The current-voltage (IV) characteristics of the ideal diode are modeled by the ideal diode equation. First we will start with a qualitative explanation of the IV characteristics. We will begin with the equilibrium band diagram of a pn junction
The filled and empty dots in this figure represent a crude approximation of the carrier distribution (e- filled, h+ open) on the two sides of the junction. All of these carriers have thermal energy above 0 K. We start by considering the n side e-, most of these have insufficient energy required to “climb” over the potential hill that results from the electric field that is pushing the e- back into the n region (opposing e- diffusion). Most of the time, when an e- makes it from the n-side into the scr it will be reflected back into the n-side because of this energy barrier. A few of the higher energy e- can make it over the (reduced) energy barrier and they will diffuse into the p region (and quickly recombine with the majority carrier h+).
On the other hand, any e- in the p side that moves to the junction and survives up to the edge of the scr region, sees no energy barrier at all and is quickly swept into the n region by the electric field in the scr. The few number of e- that drift from the p side to the n side (remember they are minority carriers in the p side) will be exactly matched by the few e- in the n side that have sufficient energy in which to diffuse over the energy barrier into the p side (at equilibrium DRIFT e- = DIFFUSION e-).
The situation with the h+ is exactly the same, except the energy barrier is reversed. The h+ see an energy barrier when they try to diffuse from the p side to the n side, but any h+ that make it to the edge of the scr on the n side will be quickly swept into the p side by the electric field (at equilibrium DRIFT h+ = DIFFUSION h+).
Now what happens when we apply a forward bias to the pn junction (NOTE – a forward bias is when we make the p side of the junction MORE positive and n side MORE negative). See figure below. What forward bias does is to move the bands closer together (i.e. using two hands on either side of the junction – we move them closer together under forward bias). What is the biggest change in the new band diagram? Now have a reduced energy barrier for e- wanting to diffuse from the n to p side and h+ in the opposite direction. The reduction in the energy barrier is linear with respect to the applied bias, but remember that carrier concentration increases exponentially as one moves away from the band edges, therefore we expect that any reduction in energy barriers means a corresponding exponential increase in e- or h+ flow.
So the diffusion current greatly increases, but what about the drift current? About the same number of minority carriers make it to the edge of the scr as before (and are swept away), but since they never saw an energy barrier at equilibrium, the reduction in the energy barrier does not increase their flow much. So drift current remains about the same as before.
Now we have net current flow and its direction is from the p to the n side of the diode Inet = In + Ip. We also expect that the forward current will exponentially increase with the applied forward bias. Now what happens during reverse bias? The situation is now
Note that we have made the energy barrier higher than at equilibrium, therefore we expect that the diffusion currents will be much reduced. Very few majority carriers will have sufficient energy in which to overcome this high barrier (i.e big decrease in diffusion). But once again, the drift current remains about the same as before because it is not sensitive to the energy barrier.
Even a reverse bias as small as a few KT/q volts will reduce the diffusion current down to a negligible amount. The net result is a small net current (due primarily to drift) which flows in the opposite direction as the net current under forward bias. Since this reverse bias current is based on minority carrier flow, we expect the net current to be quite small. A good analogy for the drift current in a pn junction is to consider a waterfall. The height of the waterfall has no affect on how much water flows over it. We also expect that the reverse current will be insensitive to the actual reverse bias that is being applied (up to a point of course). We end up postulating a qualitative IV curve for the pn junction as shown below
The equation for this type of behavior is
Eq. 6.1
and if we set Vref to KT/q, then we get the ideal diode equation. From our prior knowledge of how a diode works, all of this should make sense, i.e. a diode passes large amounts of current in only one bias direction and is essentially off for the other bias direction.
Now we need to consider the more subtle problem of what is happening in the bulk of the pn junction (outside the scr). Up until now, we have only considered what is happening at the edges of the scr. First consider the forward bias situation
At the either of the pn junction we have an ohmic contact. Remember that the majority forward bias activity in the vicinity of the scr is diffusion. We have now added some RG traps at the edges of the scr (ET). Under forward bias, we see that the excess number of minority carriers in each side is decreased by an increase in RECOMBINATION at the traps (remember that during recombination we are also losing majority carriers so we get a small electric field pushing the minority carriers towards the contacts) but some minority carriers will make it all the way to the ohmic contacts (remember there is a high positive voltage at the p contact under forward bias which strongly attracts e- and vice versa at the n contact), and e- at the p side contact will be pushed into the external wire and flow CCW through it, and at the n side contact they will recombine with excess minority h+ that have traversed the n side of the diode all the way to the n contact.
Next look at the diagram of the reverse bias situation
Remember that the majority reverse bias activity in the vicinity of the scr (i.e. minority carriers being swept away due to drift) is pictured in this figure. We again note the presence of RG traps at the edges of the scr (ET). Whenever an e- on the p side drifts over to the n side we are left with a charge imbalance and in order to reduce this imbalance a new carrier ehp is GENERATED in the p side scr region usually at one of the RG trap sites, i.e. a valence e- is caught at a trap site and is eventually elevated up into the CB. The same is happening with the h+. When a h+ makes it from the n side to the p side, a new ehp is created at a trap around the scr in the n side.
But these ehp generation events have created an additional e- in the n side and an additional h+ in the p side from this pair of RG events. We now have an excess of MAJORITY carriers on each side of the diode, which creates a small E field that pushes MAJORITY carriers away from the scr towards the ohmic contacts. So on the n side we see a net movement of e- towards the n side ohmic contact. The e- at the ohmic contact are pushed out into the external wire at the contact and flow through the circuit to the p side ohmic contact where the e- recombine with the excess h+ which have migrated away from the p side scr towards the p ohmic contact (just like the majority carrier e- did in the n side). Note that h+ do not travel in external wires, only e-. The situation is the opposite to what we just saw under forward bias.
An interesting note is that the current in the scr region is caused by the net flow of e- and h+, but in the bulk of the diode, the currents are caused only by majority carrier motion, but since the net current is the same everywhere in the circuit, we know that the e- and h+ components of this net current must therefore vary with respect to position inside the diode.
Our final diode IV equation looks like
Eqs. 6.28-30
where
This last equation is the ideal diode equation and is also known as the Schockley equation.
Now we will examine our results. We note that for reverse biases > a few kT/q (only a few tenths of a volt at room temperature), the exponential voltage term becomes negligible and the current approaches –Io. In this ideal case, the reverse saturation current is observed for all reverse biases. But what actually happens? We will discuss departures from ideality in the next section.
In forward biasing beyond a few kT/q, the exponential term dominates and I -> Io exp(qVA/kT). We often plot the IV char on a semi-log scale as shown below
Then our equation becomes
Eq. 6.31 if VA > several kT/q
Here we see that for VA0, we get a linear plot with slope of q/KT and an intercept of ln(Io).
Now look at the saturation current Io. Note that its size can vary by orders of magnitude depending on the semiconductor material due to ni (intrinsic carrier concentration with its dependency on the band gap) being in the equation. Now compare a Si and a Ge diode. Remember that Si ni =1e10 and Ge ni =1e13 cm-3 at room temperature. Because of the term, we would expect that Ge diodes would have 1e6 times more reverse bias saturation current than Si diodes.
Now we know that in reality, actual diode IV curves do not look ideal. We see differences at both high reverse and a figure highlighting the reverse deviations is shown below
The important thing to note under reverse bias is a breakdown region where we begin to get a large amount of current flow. The interesting thing to note about this region is that a diode can operate here WITHOUT permanent damage (up to the point where you get heat damage). Two types of diodes operate in these reverse regions; zener and avalanche diodes.
Very briefly we discuss devices based on pin diodes shown in the figure below (photodiodes, solar cells etc.). The key to these devices is the center intrinsic region, and what happens to an ehp created in the intrinsic region.
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EE 329 Introduction to Electronics