1. Lecture-13 • Current flow at a junction • Carrier injection
• Forward/Reverse Biases
• Junction Breakdowns

2. Forward & Reverse Biased Junctions; Steady State
One useful feature of a p-n junction:
Current flows quite freely in the p to n direction when p region has a positive external voltage bias relative to n region: forward bias and forward current !
Whereas, virtually no current flows when p region is made negative relative to n region: reverse bias and reverse current !
Applications of a p-n junction:
Asymmetry of the current flow makes the p-n junction diode very useful as a rectifier.
Biased p-n junctions can be used as voltage-variable capacitors, photocells, light emitters, many more devices which are basic to modern electronics.
Two or more junctions can be used to form transistors and controlled switches.

3. Figure 5—13
Effects of a bias at a p-n junction; transition region width and electric field, electrostatic potential, energy band diagram, and particle flow and current directions within W for (a) equilibrium, (b) forward bias, and (c) reverse bias.

4. Diffusion current is sensitive to the height of potential barrier:
Equilibrium (V = 0) : energy barrier = qV0
Forward Bias (V = Vf) : energy barrier = q(V0-Vf)
Reverse Bias (V = -Vr) : energy barrier = q(V0+Vr)
Drift current is insensitive to the height of the potential barrier:
Drift current is limited not by how fast carriers are swept away down the barrier,
but rather how often.
For example, minority carrier electrons on the p side which wander into the
transition region (W) will be swept down the barrier by the electric field. This
gives rise to the electron drift current ! However, this current is small not because
of the size of the barrier, but because there are very few minority carrier electrons
in the p side to participate. Every electrons on the p side which diffuses to the
transition region will be swept down the potential energy hill regardless of the size
of the hill. The electron drift current does not depend on how fast an individual
electron is swept from p to n, but rather on how many electrons are swept down the
barrier per second.
Similar comments may be applied regarding the drift of the minority carrier
holes from the n side to the p side of the junction. Approximately, electron and
hole drift currents at the junction are independent of the applied voltage.

5. I–V characteristic of a p-n junction.
On each side of the junction, the minority carriers required to participate in the drift current is generated by thermal excitation of electron-hole pairs (EHPs). The resulting current due to the drift of the generated carriers across the junction is commonly called the “generation current” since its magnitude depends entirely on the rate of the generation of EHPs. Negative generation current is called “reverse saturation current”.
Figure 5—14
I–V characteristic of a p-n junction.

6. (equilibrium)
Total current = Idiff –I0

7. 
(from Eq. 4-35)

8. (Eq. 4-40)

9. Total Current
For V = -Vr (Vr >> kT/q) :

10. Figure 5—15
Forward-biased junction: (a) minority carrier distributions on the two sides of the transition region and definitions of distances xn and xp measured from the transition region edges; (b) variation of the quasi-Fermi levels with position.

11. On either side of the junction, the minority carrier quasi-Fermi level varies significantly while the majority carrier concentration is not affected much.
Thus, the majority carrier quasi-Fermi level is so close to the original EF and also the quasi-Fermi levels are somewhat flat within the depletion region. For an ideal diode, within the depletion region, the product of the gradient of the quasi-Fermi level and carrier concentration must be independent of position.
For a given constant current, the gradient in the quasi-Fermi level must be large for minority carriers since the carrier concentration is small.
On the other hand, for majority carriers, very small gradient is needed in the quasi-Fermi level. Within W, there is an intermediate situation, where the carrier concentration is changing from majority on one side to minority on the other. Note: Although there is some variation in Fp and Fn within W, it does not show up on the scale in Fig

12. Figure 5—16
Two methods for calculating junction current from the excess minority carrier distributions: (a) diffusion currents at the edges of the transition region; (b) charge in the distributions divided by the minority carrier lifetimes; (c) the diode equation.

13. Another way of calculating the total current
This is the same as what was calculated from the diffusion currents (eq. 5-33).
Two ways to calculate the current at a p-n junction :
From the slopes of the excess minority carrier distributions at the two edges of the transition regions.
From the steady state charge stored in each distribution.

14. Total current
Minority carrier current
Majority carrier current

15. (Nd < Na) Total current
Figure 5—17
Electron and hole components of current in a forward-biased p-n junction. In this example, we have a higher injected minority hole current on the n-side than electron current on the p side because we have a lower n doping than p doping.

16. Reverse Bias When V = - Vr < 0 & Vr >> kT/q
Excess minority carrier concentrations in neutral regions
Depletion of carriers below the equilibrium values extends approximately a diffusion length beyond each side of the transition region.

17. This reverse-bias depletion of minority carriers can be thought of as minority carrier extraction. Physically, the extraction occurs because minority carriers at the edges of the depletion region are swept down the barrier at the junction to the other side and are not replaced by an opposing diffusion of carriers. The steady state hole distribution in the n-region has the inverted exponential shape (Fig. 5-18a).
It is important to remember that although the reverse saturation current occurs at the junction by drift of carriers down the barrier, this current is fed from each side by diffusion of minority carriers (toward the junction) in the neutral region. The rate of carrier drift across the junction (reverse saturation current) depends on the rate at which holes arrive at xno (and electrons at xpo) by diffusion from the neutral region.
These minority carriers are supplied by thermal generation, and the expression for the reverse saturation current represents the rate at which carriers are generated thermally within a diffusion length of each side of the transition region.

18. More p-type More n-type
Figure 5—18
Reverse-biased p-n junction: (a) minority carrier distributions near the reverse-biased junction; (b) variation of the quasi-Fermi levels.

19. In reverse bias, we have fewer carriers than in equilibrium, unlike the forward bias where we have an excess of minority carriers.

20. Reverse-Bias Breakdown
A p-n junction biased in the reverse direction exhibits a small, essentially voltage-independent saturation current, which is true until a critical reverse bias is reached where reverse breakdown occurs. At this critical voltage (Vbr), the reverse current through the diode increases sharply, and relatively large currents can flow with little further increase in voltage (Fig. 5-19).
Reverse breakdown can occur by two mechanisms, each of which requires a critical electric field in the junction transition region.
- Zener Breakdown (or Effect): operative at low voltage (a few volts reverse bias)
Avalanche Breakdown: operative at higher voltage (a few to thousands of volts)

21. Figure 5—19
Reverse breakdown in a p-n junction.

22. Zener Breakdown
Zener Effect :
When a heavily doped junction is reverse biased, the energy bands become crossed at relatively low voltages (Fig. 5-20). The crossing of the bands aligns the large number of empty states in the n-side conduction band opposite the many filled states of the p-side valence band. If the barrier separating these two bands is narrow, tunneling of electrons can easily occur. The tunneling of electrons from p-side valence band to the n-side conduction band constitutes a reverse current from n to p.

23. Figure 5—20
The Zener effect: (a) heavily doped junction at equilibrium; (b) reverse bias with electron tunneling from p to n; (c) I–V characteristic.

24. Impact Ionization & Avalanche Process :
Avalanche Breakdown
Impact Ionization & Avalanche Process :
For lightly doped junctions, electron tunneling is negligible, and instead, the breakdown mechanism involves the “impact ionization” of host atoms by energetic carriers. Normal lattice-scattering events can result in the creation of EHPs (electron hole pairs) if the carrier being scattered has sufficient energy. If the electric field in the transition region is large, an electron entering from the p-side may be accelerated to high enough kinetic energy to cause an ionizing collision with the lattice (Fig. 5-21). A single such interaction results in carrier multiplication; the original electron and the generated electron are both swept to the n-side of the junction, and the generated hole is swept to the p-side.
In this way, an incoming electron may have a collision with the lattice and create an EHP; each of these carriers has a chance of creating a new EHP, and each of those can also create an EHP, and so forth. This is an avalanche process, since each incoming carrier can initiate the creation of a large number of new carriers.

25. Avalanche Breakdown p n + + - - Figure 5-21
Electron-hole pairs created by impact ionization :
(a) band diagram of a p-n junction in reverse bias showing (primary) electron gaining kinetic energy in the field of the depletion region, and creating a (secondary) electron-hole pair by impact ionization, the primary electron losing most of its kinetic energy in the process;
(b) a single ionizing collision by an incoming electron in the depletion region of the junction;
c) primary, secondary and tertiary collisions. p n + + - -

26. nin : Electron number entering from p-side
P : Probability of having an ionizing collision with lattice
nin : Electron number entering from p-side
Electron Multiplication (Mn) :
Carrier Multiplication factor (M):
n = 3 ~ 6
Empirical relation !

27. Figure 5—22
Variation of avalanche breakdown voltage in abrupt p+- n junctions, as a function of donor concentration on the n side, for several semiconductors. [After S.M. Sze and G. Gibbons, Applied Physics Letters, vol. 8, p. 111 (1966).]

28. Piecewise-linear approximations of junction diode characteristics:
Figure 5—23
Piecewise-linear approximations of junction diode characteristics:
(a) the ideal diode; (b) ideal diode with an offset voltage; (c) ideal diode with an offset voltage and a resistance to account for slope in the forward characteristic.

29. Figure 5—24
Beveled edge and guard ring to prevent edge breakdown under reverse bias:
(a) diode with beveled edge; (b) closeup view of edge, showing reduction of depletion region near the bevel; (c) guard ring.

30. p+ - n - n+ junction diode
Figure 5—25
A p+- n - n+ junction diode: (a) device configuration; (b) zero-bias condition; (c) reverse-biased to punch-through.