The PN Junction Diode
2.6 Reverse Breakdown and the Zener Diode
I
Vbd
Measured
Predicted by diode equation
I0
V0 V
Figure 2.18 Measured current–voltage characteristics of a diode as well as predicted char- acteristics based on the diode equation. A very steep increase in current as applied voltage approaches the built-in potential V0is observed in practice as well as an abrupt onset of reverse breakdown current at Vbd
concentrations, and diode currents actually increase more rapidly with applied voltage predicted by the diode equation. This is illustrated in Figure 2.18 along with the predicted curve from the diode equation. Note that for forward bias the observed current–voltage characteristic rises very steeply as applied voltage V approaches V0. This is consistent with the band model of Figure 2.5, which shows that the potential barrier height for majority carrier injection will approach zero as V approaches V0. The reverse bias voltage Vbdwill be discussed in Section 2.6.
A quantitative model that includes strong bias conditions can be derived but will not be undertaken in this book. Additional effects including bulk resistances of the neutral semiconductor regions and contact resistances must also be considered for an accurate model of measured diode characteristics.
V0 – V
V0 Wbias
W0
ε0
εbias
ε V
x
x
Figure 2.19 Increase in depletion region width and increase in junction field with the appli- cation of a reverse bias for the p-n junction of Figure 2.13. The equilibrium conditions with depletion width W and peak electric fieldε0are shown with dotted lines. With the application of reverse bias V (V negative) the depletion width increases to Wbiasand the peak electric field increases toεbias
strength for a given semiconductor then bound electrons that normally do not contribute to current flow may become available for conduction. This occurs through field ionization of semiconductor atoms. Once a small number of normally bound electrons is released these electrons can increase in number by impact ionization of other atoms. Since the ionization energy for atoms in a given semiconductor is very specific to that semiconductor material, this process occurs at a specific reverse voltage and then increases rapidly with a further increase in voltage.
If a negative bias voltage V is applied the potential barrier increases to V0−V . The depletion region width Wbiasas well asεbiasalso increase, as shown in Figure 2.19. We can now modify the expressions we have for equilibrium conditions to calculate Wbiasas well asεbias
The integral of electric field across the depletion region (Equation 2.13) becomes the area under the newεversus x graph in Figure 2.19 and we obtain
V0−V = 1 2bh =1
2Wbiasεbias
From Equation 2.12 we can see thatεbiasincreases linearly with an increase in depletion region width on either side of the junction, which means that both Wbias andεpeak must be proportional to the square root of (V0−V ). Hence Equation 2.15a may be modified to
become
Wbias=
20r(V0−V ) q
1 Na+ 1
Nd
(2.23)
and from Equation 2.12 and Equation 2.15b or 2.15c we can write εbias= −q Wbias
0r
NaNd
Na+Nd
(2.24) Thus in reverse bias, the depletion region width as well as peak electric field increase with increasingly negative bias voltage untilεbiasreaches the breakdown field of the semicon- ductor. At this point, no further increase inεbiascan occur; however, electrons are generated at or near the junction, which are swept along by the electric field resulting in the reverse breakdown current.
From Equation 2.23 it is clear that the depletion width increases as the doping levels decrease. Since diodes often have much higher doping levels on one side than the other side we will consider a diode having NaNd. From Equation 2.23 we can simplify the expression for depletion region width to obtain
Wbias=
20r(V0−V ) q Nd
(2.25) We can now use Equation 2.24 to obtain the peak electric field as
εbias= −
2q Nd(V0−V ) 0r
(2.26) Hence the magnitude of the breakdown voltage may be increased by decreasing the doping level on at least one side of a diode. This is easy to visualize, since a decreased doping level leads to a wider depletion region with lower electric fields present for a given bias voltage V.
Another mechanism may also cause reverse breakdown current. This occurs in p-n junctions that have simultaneously high values of both n-type and p-type doping. From Equation 2.15a, if both Naand Nd are large then depletion width W will be small. This is illustrated in Figure 2.20. W may be small enough to allow tunnelling of electrons directly from the valence band on the p-side into the conduction band on the n-side. This differs from avalanche breakdown since neither field-ionization nor impact-ionization occur.
This tunnelling type of breakdown is properly referred to as Zener breakdown although the Zener diode has come to mean a diode used specifically for its reverse breakdown characteristics whether caused by avalanching or tunnelling processes. In practice, diodes with small breakdown voltages of a few volts involve tunnelling and diodes with higher breakdown voltages of 5 volts or more involve avalanching. There are often combinations of these two mechanisms occurring simultaneously in diodes with intermediate breakdown voltages.
e Transition
region
p-side n-side
Ec
Ev
V0 – V
Figure 2.20 Tunnelling of valence-band electron from valence band on p-side to conduction band on n-side upon application of a small reverse bias voltage. Note that there is a large supply of valence band electrons on the p-side. In comparison there is only a small supply of thermally generated minority carrier electrons that result in current I0. This explains how the reverse current can be much larger than I0as shown in Figure 2.18, when V exceeds the breakdown voltage Vbd