When we put p-type and n-type semiconductors together as in Figure 4.2.1, we get a diode. When a voltage difference is applied across the diode, interesting behaviors can be observed.
(a)Forward-biased.
(b)Reverse biased.
Figure4.2.1. When the voltage is applied across the diode as in Figure 4.2.1.(a), we say the diode is forward-biased. Valence-band holes in the valence band of the p-type semiconductor and conduction-band electrons in the n-type semiconductor move toward the pn junction. At the junction, electrons in the n-type semiconductor fall across the pn junction into p-type semiconductor holes. Since the valence band is a lower energy level than the conduction band, this is accomplished easily. Electrons are also pulled out of the p-type into the wire, generating more valence-band holes. These electrons travel through the circuit and replenish the conduction-band electrons when they enter the n-type semiconductor. This process can proceed indefinitely, resulting in sustained current flow through the diode.
If the bias is reversed as in Figure 4.2.1.(b), we say the diode is reverse-biased. In this case, valence-band holes and conduction-band electrons move away from the pn junction in their respective semiconductors. While electrons can leave the n-type semiconductor, travel through the circuit, and fill the holes in the p-type semiconductor, this will quickly come to a halt because no new holes are formed at the p-n boundary.
Using the behaviors observed above, we find that diodes act similar to one-directional wires. The behavior is captured in Figure 4.2.2.
Figure4.2.2. In this figure, \(V_D\) is the voltage drop across the diode. When \(V_D \lt V_F\text{,}\) the diode is ‘off’ meaning no current flows through the diode and it acts as a circuit break. When \(V_D = V_F\text{,}\) the diode is ‘on’ meaning the diode starts acting like a wire, albiet with a voltage drop \(V_F\) in the direction of current. In this cartoon picture, the voltage drop across the diode will remain \(V_F\) as long as the diode is on regardless of the size of the current through the diode. Likewise, a diode that is off will allow no current regardless of the voltage change applied across the diode. Thus, a diode acts a bit like a unidirectional wire, allowing current to flow in one direction but not the other.
In the above discussion, we see that a diode turns on when the applied voltage drop across the diode reaches a value of \(V_F\text{,}\) which we call the forward turn-on voltage. More colloquially, it is often referred to as the diode voltage drop. The origin of this diode voltage drop will be developed below.
Both p-type and n-type semiconductors are neutral when the voltage applied across them is zero, meaning each semiconductor individually has no excess of positive or negative charges. Let’s now examine the situation in Figure 4.2.3 where we have a forward-biased diode.
Figure4.2.3. The p-n junction is used for the boundary between the semiconductors. The bias voltage creates an applied electric field \(\vec{E}_\text{applied}\) in the diode, accelerating charge carriers toward the p-n junction. Conduction-band electrons in the n-type semiconductor fall across the p-n junction into valence-band holes. It takes some finite time for the charge carriers to redistribute in each semiconductor, resulting in the formation of a thin depletion layer (indicated by dashed lines). Inside the boundary of this depletion layer, there is a deficit of electrons in the n-type semiconductor and a surplus of electrons in the p-type semiconductor, resulting in a second electric field \(\vec{E}_d\) within the depletion layer. If the depletion layer is characterized by thickness \(\Delta x\text{,}\) then this results in a voltage difference \(V_d = \\E_{d,x} \Delta x\text{.}\) In order for charge carriers to redistribute and maintain a current, we must have \(\left|\vec{E}_\text{bias}\right| \ge \left|\vec{E}_d\right|\text{.}\) This means that the applied voltage bias \(V_D = V_+ - V_-\) must be at least as large as some \(V_F\) in order to generate an applied electric field that is larger than \(\vec{E}_d\) and can sustain the requisite charge carrier motions to maintain a current through the diode. [CLEAN THIS LAST PART UP. How are \(V_d, V_D, \text{ and } V_F\) related? Be careful with definitions and be precise.]
The size of the diode voltage drop depends on the materials used in diode construction. In diodes constructed using silicon-based semiconductors, \(V_F\approx 0.6-0.7\)V. If germanium-based semiconductors are used to construct the diode, \(V_F\approx 0.3-0.4\)V. For the purposes of this text, we will assume that diodes are silicon-based with \(V_F=0.6\)V.
We can also be a bit more precise and realistic in our description of diode behavior. Instead of the behavior described in Figure 4.2.2, we can instead relate the current through the diode \(I_D\) in the forward direction to the voltage applied across the diode \(V_D=V_p - V_n\text{:}\)
where \(V_p\) and \(V_n\) are the voltages on the p-type and n-type semiconductor sides respectively, \(I_0\) is the saturation current, \(k_B\) is Boltzmann’s constant, and \(T\) is temperature. The value of \(n\) is dependent on the materials used to construct the diode. For silicon, \(n\approx 1\text{.}\) The diode behavior is graphically represented in Figure 4.2.4.
Figure4.2.4.More realistic diode behavior. The saturation current is the current that can bleed through the diode even when reverse-biased. This current is typically very small and can be found in the specifications for a real diode. For the purposes of this text, I will often assume that \(I_0 = 1\times 10^{-12}\)A. I will also typically assume room temperature \(T=293\)K.
Also discuss failure modes of diodes. Breakdown. Curve with fires.
