The PN Junction Diode
2.2 Diode Current
We can now describe the currents that flow in equilibrium. The built-in fieldεcauses car- riers in the transition region to drift. In addition there are substantial carrier concentration gradients across the junction. For electrons, the high electron (majority carrier) concentra- tion in the n-side falls to a low electron (minority carrier) concentration in the p-side. This electron concentration gradient as well as an analogous hole concentration gradient drive diffusion currents across the junction.
There are now four currents to consider:
In drift Electrons (minority carriers) on the p-side that enter the transition region will drift to the right towards the n-side. This current is driven by the built-in electric field.
Ip drift Holes on the n-side (minority carriers) that enter the transition region will drift to the left towards the p-side. This current is driven by the built-in electric field.
In diffusion Electrons on the n-side (majority carriers) will diffuse to the left. This current is driven by the electron concentration gradient.
Ip diffusion Holes on the p-side will diffuse to the right. This current is driven by the hole concentration gradient.
p-side n-side In diffusion
Ec
Ev Ef
Ip diffusion
In drift
Ip drift
ε
Figure 2.3 Flow directions of the four p-n junction currents. The two diffusion currents are driven by concentration gradients of electrons or holes across the junction and the two drift currents are driven by the electric field. Note that the electron currents flow in the direction opposite to the flux or flow of electrons. The electron diffusion flux is to the left and the electron drift flux is to the right
These four currents can be viewed schematically in Figure 2.3. The electron currents are reversed in direction from the directions of electron flow since electrons carry negative charge.
If the p-n junction is in equilibrium we can conclude that the following equalities apply:
Ip drift+Ip diffusion=0 (2.2a)
In drift+In diffusion=0 (2.2b)
We will show in Section 2.5 that both drift and diffusion currents may be very large;
however, the net current is the observed diode current.
If we apply a voltage to the diode by connecting an external voltage source to the p-n junction, the currents will no longer cancel out, and the diode is no longer in an equilibrium state. This is illustrated in Figure 2.4. This external voltage is called a bias voltage.
Let us first consider the application of a forward bias with V >0 in which the p-side is connected to the positive output of the voltage source and the n-side to the negative output.
The applied voltage V will fall across the transition region of the p-n junction and will decrease the energy barrier height as well as the electric fieldεas shown in Figure 2.5. The decrease in barrier height will result in a net current because the opposing drift current will no longer be sufficient to cancel out all the diffusion current. The net current flow results from a net majority carrier diffusion current to become
I =Ip diffusion+In diffusion−Ip drift−In drift>0 (2.3)
metal p-type n-type metal anode semiconductor semiconductor cathode
contact contact
p n
+ –
V
Figure 2.4 A p-n junction diode with external voltage source connected. The external bias voltage will modify the built-in electric field
Note that in Figure 2.3 the electron and hole diffusion currents flow in the same direction and may therefore be added in together in Equation 2.3 to obtain the total diode current, whereas hole and electron diffusion fluxes flow in opposite directions but they carry opposite charge polarities. The electron and hole drift currents also flow in the same direction and are both negative in Equation 2.3.
If we now consider the application of a reverse bias with V <0 the applied voltage will again fall across the transition region of the p-n junction, which will increase the magnitude of both the potential barrier and ε, as shown in Figure 2.6. The increase in the energy barrier will cause drift current to effectively oppose diffusion current. There is,
Transition region
p-side n-side
Ec
q(V0–V)
Ev
ε
Figure 2.5 Diode band model with the application of a forward bias. The energy barrier across the transition region is smaller resulting in much higher currents dominated by diffusion currents. In the depletion regionεwill be smaller and drift currents no longer compensate for diffusion currents. Note that the applied voltage V (in volts) must be multiplied by the electron charge q (in coulombs) to obtain energy (in joules)
Transition region
p-side n-side
Ec
Ev
q(V0 – V)
ε
Figure 2.6 Diode band model with the application of a reverse bias. Since the applied voltage V is negative, the energy barrier as well as electric fieldεbecome larger across the transition region virtually eliminating diffusion currents
however, a remaining current due to thermally generated minority carriers. This constitutes a small net minority carrier drift current and it is assisted by the electric field. The net current flow is dominated by thermally generated minority carrier drift currents. From Equation 2.2 we obtain
I =Ip diffusion+In diffusion−Ip drift−In drift<0
The total current I is now small and virtually independent of applied voltage V because I is controlled by the supply of thermally generated minority carriers available to drift and the magnitude ofεis not important. This is analogous to varying the height of a waterfall in a river – the amount of water flowing down the waterfall will depend on the available flow of the water approaching the waterfall and will not be affected by the height of the waterfall. The magnitude of this current is known as the reverse saturation current, I0, and hence I0is the net thermally generated drift current supplied by minority carriers.
The diode current may now be plotted as a function of the applied voltage, as shown in Figure 2.7. We will treat diode current quantitatively in Section 2.5.