1. Outline Chap. 1 Introduction Chap. 2 Basics of Semiconductor Physics
Chap. 3 P-N Junctions
Chap. 4 Metal-Semiconductor Junctions
Chap. 5 Semiconductor Heterojunctions
Chap. 6 Semiconductor solar cells & Photodiodes
Chap. 7 Light Emitting Diodes & Semiconductor Lasers
Chap. 8 Quantum Dots for Biological Fluorescent Probes

2. Chapter 3
P-N Junctions

3. 3.1 Junction Formation
Junction: metallurgical contacts (or atomic contacts) of any two materials (except insulators).
p-n junction: metallurgical contacts of a p-type and an n-type semiconductors. The elementary units of almost all of the semiconductor devices.
Isotype homojunction: p-Si and p-Si.
Isotype heterojunction: p-Si and p-Ge
Anisotype homojunction: p-Si and n-Si
Anisotype heterojunction: p-Si and n-Ge
Common techniques of junction formation: ion implantation, diffusion, epitaxial growth, lithography, vacuum deposition, oxidization, testing and packaging technology.

4. Fabrication process of a p-n junction with Si single crystals

5. Fabrication process of a p-n junction with Si single crystals

6. linearly graded junction one-sided abrupt junction
3.1 Junction Formation
The most common technique of junction formation is impurity diffusion.
In practice, diffusion junctions can be approximately described by abrupt junctions and linearly graded junctions.
P+N
低表面浓度的深扩散结
高表面浓度的浅扩散结 NA ND
linearly graded junction
diffusion junction
one-sided abrupt junction

7. p  n 3.2 p-n junctions under equilibrium conditions p n +
Space Charge
When a p- and n-type semiconductors are joined, the large concentration gradient of holes from the p- to the n-side and vice versa for electrons results in the diffusion of free carriers.
Immobile positively ionized donor atoms and negatively ionized acceptor atoms are left behind in the n- and p- region respectively.
space charge p n _ +
Built-in electric field
p  n

8. 3.2 p-n junctions under equilibrium conditions
Band Diagram P N
When junction is formed, electrons transfer from n-region (high EF) to p-region (low EF), vice versa for holes.
EF increases in p-region and decreases in n-region, until they are equal on both sides.
Space-charge region is also called barrier region.
qVD=EFn - EFp

9. 3.2 p-n junctions under equilibrium conditions
Built-in field generates drift currents in opposite direction of diffusion currents.
At thermal equilibrium, drift current = diffusion current.  no net current flow. VD + -
Neutral zone: p- and n-regions far from the space-charge region. No space charge, high density of carriers, low resistance.
Depletion region: space-charge region. Immobile charges, no free carriers, high resistance.
Boundary zone: area between neutral and depletion regions.

10. 3.3 p-n junctions under bias
Forward Bias
Forward bias reduce the built-in electric field, equivalent to reducing space charges  barrier region width reduces and potential barrier lowers.
Drift current is reduced and diffusion current is favorable  large current.
Low-resistance current path is created by applied forward bias. VD

11. 3.3 p-n junctions under bias
Reverse Bias
Barrier region width increases and potential barrier increases.
Diffusion current is reduced and drift current dominates.
Very low current passing through the junction  high resistance.
A p–n junction only allows current in one direction. rectification.  VD

12. 3.3 p-n junctions under bias
Electrical injection of non-equilibrium carriers
Forward bias generates net diffusion current, electrons moving from N to P, holes from P to N, leading to non-equilibrium minority carriers in N and P. Electrical injection of non-equilibrium carriers
The majority carrier densities are hardly affected.
The density of non-equilibrium minority is very high in the boundary zone, decreases as recombination happens, and finally drops to zero.
In LEDs or laser, injected minority carriers recombine with the background majority carriers and produce photons.
nn=nn0
pp=pp0

13. 3.3 p-n junctions under bias
Quasi-Fermi level under electrical injection
Under forward bias, quasi Fermi levels are
present in the areas where non-equilibrium
minorities exist.
In hole diffusion region, the Fermi level of electrons is unchanged.
Large change in the hole density  Quasi-Fermi level is a diagonal line and approaching the Fermi level when hole injection is zero.
Changes of quasi-Fermi levels at the barrier region can be ignored.
Electron
Diffusion
Region
Hole
Diffusion
Region
Barrier
Region V + - P N

14. 3.3 p-n junctions under bias
Extraction of minority carriers
Under reverse bias, the holes in the boundary region of N side are forced to move to the P side, introducing hole diffusion current in the neutral region of N side Extraction of minority carriers

15. 3.4 I-V characteristics for ideal diodes
Diode: a two terminal rectifier. One p-n junction for one diode.
DC current-voltage relation of p-n junctions ---- I-V characteristic
Basic assumptions for ideal p-n junctions:
（1）Ignore the bulk and contact resistances in the neutral region.
The applied voltage completely drops across the depletion region;
（2）Homogeneous doping;
（3）Small injection;
（4）No recombination and generation currents in the depletion
region;
（5）Degenerate semiconductor (low doping).

16. 3.4 I-V characteristics for ideal diodes
Under forward bias, the injected minority carriers recombine with the majority carriers.
The hole (electron) current dissipates exponentially in the p (N) side.
Since current continuity requires total current unchanged, the majority current increases exponentially. Ip In P N P N Ip In In Ip

17. 3.4 I-V characteristics for ideal diodes
Under reverse bias, the strengthened electric field in the barrier region could sweep away any minority carrier diffused into the barrier region.
Reverse current: generated in the vicinity of the space charge region and related to the diffusion of minority carriers to the space charge region.
Since the minority carrier densities are very low, the reverse current is small and will be saturated. P N N P
|In|
|Ip|

18. 3.4 I-V characteristics for ideal diodes
Unidirectional conduction of an ideal p-n junction: forward current increases exponentially with applied voltage, and reverse current is very low and will be saturated. I0 I
Shockley equation:
I0 : Saturated current.

19. 3.5 Recombination and generation current in the depletion region
In real diodes, the I-V characteristics deviate from the Shockley equation, due to the recombination and generation of carriers in the depletion region and external contact resistance.
The injected carriers by forward bias move across the depletion region, pn>ni recombination of non-equilibrium carriers.
Under reverse bias, due to thermal excitation, in the depletion region, pn<ni generation of non-equilibrium carriers.
Recombination and generation currents will be generated by the recombination and generation of non-equilibrium carriers.

20. 3.5 Recombination and generation current in the depletion region
Recombination current under forward bias
Recombination of non-equilibrium carriers at the recombination centers in the depletion region. h+ e-
ABCD: injected electron current; A’B’C’D’: injected hole current.
EFGH：recombination current at the recombination center.

21. 3.5 Recombination and generation current in the depletion region
Recombination current under forward bias
（Maximum recombination）
For P+N (one-side injection), diffusion current due to injection V. S. recombination current in the depletion region:
For semiconductors with larger band gap, ni is smaller, so Irec is larger. Eg., Irec in Si is larger than that in Ge, for small injection.
For light doped region with higher impurity density, Irec is larger.
For smaller forward bias, Irec is larger.

22. Id Irec I-V characteristics of a Si diffusion junction
Effect of series resistance
I-V characteristics of a Si diffusion junction
For a low forward bias, recombination current in the depletion region dominates.
As the forward bias increases, the slope also goes up, indicating larger diffusion current.
For a higher current, the series resistance causes a large Ohm voltage drop.
Experimental data Id
Slope = q/KBT
Irec
Slope = q/2KBT

23. 3.5 Recombination and generation current in the depletion region
Generation current under reverse bias h+ e-
Due to thermal excitation
CBAD: reverse electron diffusion current; C’B’A’D’: reverse hole diffusion
current.
EFGH：generation current due to the recombination centers in the depletion region.

24. 3.5 Recombination and generation current in the depletion region
Generation current under reverse bias I0
Ideal
Non-ideal
A: cross section of the junction.
W: depletion region width.
1/0: capture probability in the
combination center.
As W increases with reverse bias, Ig also gets higher with increasing reverse bias. Thus, the reverse current of a real diode can not be saturated.

25. 3.6 Breakdown in a p-n junction
One of the most important problems that should be considered in device designing.
Junction breakdown：Sudden increasing of reverse current when the reverse bias exceeds a certain value. Breakdown bias VBR.
VBR I V
Breakdown
Mechanisms
Thermal
Avalanche
Zener

26. 3.6 Breakdown in a p-n junction
Zener Breakdown (tunnel breakdown)
Earlieat model.
Under the high E field, covalent bonds break in the depletion region and generate e-h pairs (tunneling effect)  Reverse tunnel current.
Non-destructively reversible breakdown.
Dominated in heavily doped diodes.
Zener breakdown is applicable for low voltages. Eg., Si p-n junction, VBR< 4.5 V.
Avalanche breakdown is applicable for high voltages. Eg., Si p-n junction, VBR > 6.7 V.

27. 3.6 Breakdown in a p-n junction
Avalanche Breakdown
High reverse bias  Carriers gains energy from the electric field 
Carriers collide with the lattice in the depletion region  For high enough energy, electrons will be excited from VB to CB, leading to e-h pairs  E-h pairs are accelerated by the E field, and collisions give rise to more e-h pairs  The carriers multiply.
The electric field for avalanche breakdown in a Si based p-n junction is V/cm N P
Non-destructive breakdown.

28. Localized Temperature Rise
3.6 Breakdown in a p-n junction
Thermal Breakdown
Very important for narrow-band-gap Ge p-n diodes at room temperature.
Heat Loss
Localized Temperature Rise
Current Increasing
Destructive breakdown !

29. Outline Chap. 1 Introduction Chap. 2 Basics of Semiconductor Physics
Chap. 3 P-N Junctions
Chap. 4 Metal-Semiconductor Junctions
Chap. 5 Semiconductor Heterojunctions
Chap. 6 Semiconductor solar cells & Photodiodes
Chap. 7 Light Emitting Diodes & Semiconductor Lasers
Chap. 8 Quantum Dots for Biological Fluorescent Probes

30. Metal-Semiconductor (M-S) Junctions
Chapter 4
Metal-Semiconductor (M-S) Junctions

31. Introduction
M-S Junction: metallurgical contacts of metals and semiconductors.
Point-contact: pressing metal pins on the semiconductor crystals.
Surface-contact: evaporation of metal films on the semiconductors.
Schottky contacts: rectification effect, rectifying junction
Ohm contacts: Ohm effect, non-rectifying junction
Properties of ideal M-S contacts:
1. Atomic contacts between metal and semiconductor, no layers in between.
2. No mutual diffusion or mixing between metal and semiconductor.
3. No impurities or charges on the interface of metal and semiconductor.

32. Introduction
In 1970s, the devices based on M-S junctions were developing promptly, due to the reproducibility in making M-S contacts by using semiconductor planar process and vacuum technology.
Schottky diodes are unipolar devices, where the current is predominantly due to the thermionic emission of carriers over the potential barrier.
Non-rectifying diodes (Ohm contacts): equal and large currents flow in both forward and reverse bias directions with small resistance. All of the devices need Ohm contacts to connect to other devices.
Primary M-S devices: Schottky diodes, Schottky field effect transistors.

33. 4.1 Schottky Barriers 4.1.1 Formation of Schottky Barriers
Assume no surface states  flat band till the surface of semiconductor
E0：vacuum level
After contacts, electrons in the semiconductor transfer to the metal, to flatten out the Fermi levels.  Positive space charges on the surface of semiconductor, and negative space charges on the surface of metal.
－work function of semiconductor
- work function of metal
- electron affinity of semiconductor

34. 4.1 Schottky Barriers 4.1.1 Formation of Schottky Barriers
The space charge region is very thin on the surface of metal (~0.5nm), and much thicker on the semiconductor side.
Under thermal equilibrium, the band of semiconductor bends upwardly —— built in potential
Metal
Semiconductor
Schottky barrier: or
Where,

35. 4.1 Schottky Barriers 4.1.2 Under forward bias
Forward bias: negative voltage applied on the semiconductor.
The barrier reduces to ,
and changed to
The space charge is very thin in the depletion region, b unchanged.
The Fermi level of metal is lower than that of semiconductor, by qV.
As the barrier is lowered, it is easier for the electrons in the semiconductor to move to the metal. large current. 金属
半导体 金属
半导体
No Bias
Forward Bias

36. Schottky barrier has rectification property.
4.1 Schottky Barriers
4.1.3 Under reverse bias
Reverse bias: positive voltage applied on the semiconductor
The barrier increases to , is changed to
The space charge layer is very narrow on the metal sizeb is unchanged.
The Fermi level of metal is higher than that of semiconductor, by ~qVR.
The electron current from metal to semiconductor dominates, while the barrier is so high that the reverse current is small and can be saturated.
Schottky barrier has rectification property.
Metal
Semiconductor
metal
Semiconductor
No Bias
Reverse Bias

37. 4.2 Effect of Interface States on the Barrier Height
For a given semiconductor,  is fixed. Based on , the height of Schottky barrier will change with the work function of metal.
But actual measurements reveal that the work function of metal does not affect the barrier height, due to the presence of surface states on the surface of semiconductor.

38. 4.2 Effect of Interface States on the Barrier Height
What are interface states? - + - +
In real Schottky diodes, the break of crystal lattice of semiconductor at the interface introduces a large amount energy states in the forbidden band, so called interface states or surface states.
Properties of surface states.
The interface states have a distribution in the forbidden band, which can be characterized by a neutral level , below which, all the interface states are filled by electrons and the interface is electrical neutrality.
If , the interface is positively charged, similar to the donors.
If , the interface is negatively charged, similar to the acceptors.
If , the interface is electrical neutrality. No net charges.

39. 4.2 Effect of Interface States on the Barrier Height
If ,
The interface is positively charged, similar to the donors. W
Potential forms in the tiny gap between metal and semiconductor, due to the charges on the surface of metal and semiconductor.
LESS ionized donors are needed in the depletion region to reach equilibrium.
Built-in potential is greatly reduced, and b also lowers. Ef is closer to E0 .

40. 4.2 Effect of Interface States on the Barrier Height
If ,
The interface is negatively charged, similar to the acceptors.
MORE ionized donors are needed in the depletion region to reach equilibrium.
Built-in potential increases, and b also greatly increases. Ef is closer to E0 .

41. 4.2 Effect of Interface States on the Barrier Height
Interface charges has inverse feedback effect, which makes
close to .
If density of interface states is very high, the Fermi level will be pinned at , so called Pinning Effect of Fermi level. And is not related to the work functions of metal and semiconductor.
In most of the real Schottky diodes, the interface states predominantly decide , and the barrier height has nothing to do with the work functions and the doping density in semiconductors.

42. 4.3 I-V Charateristics of Schottky Diodes
The current in the Schottky barrier is dominated by the carrier flow from the edge of the depletion region of semiconductor to the metal.
The forward bias reduces the E field and potential in the depletion region, leading to electron diffusion current across the depletion region, and the emission of electrons to the metal.
At room temperature, the carrier transport is limited by the electron emission process in most real Schottky diodes, and the electron diffusion effect can be ignored.
Metal
Semiconductor
Forward Bias

43. 4.3 I-V Charateristics of Schottky Diodes
Hot electrons and hot carrier diodes
When electrons on the top of the barrier emit to the metal, their energy is higher (by ~ ) than that of the electrons in the metal.  Hot electrons. After entering the metal, the hot electrons will collide with other electrons and release the excess energy.
The Schottky diodes are also called hot carrier diodes.
The equilibrium will be shortly (< 0.1 ns) reached between the hot electrons and other electrons in the metal.
Metal
Semiconductor
Forward Bias

44. W-Si和W-GaAs肖特基二极管正向电流密度与电压的对应关系
4.3 I-V Charateristics of Schottky Diodes
I-V characteristics
Richardson-dushman equation:
n=1.02
where,
n=1.04
Effective Richardon constant
n is ideality factor, induced by non-ideal effects. For ideal Shnokky diodes, n=1.
W-Si和W-GaAs肖特基二极管正向电流密度与电压的对应关系

45. 4.3 I-V Charateristics of Schottky Diodes
The thermionic emission corresponds to the majority carrier current.
Minority carrier current: electron current from the top of the valence band of the semiconductor to the empty states below EF of the metal, and can be considered as hole current from the metal to the semiconductor.
where,
The current of the Schottky diodes is primarily conveyed by the majority carriers, and the minority carrier current can be ignored.
Metal
Semiconductor
Forward Bias

46. 4.4 M-I-S Schottky Diodes Basic Structures M I S
In reality, there has been always a thin layer ( nm) of oxides between the metal and semiconductor, forming a M-I-S structure.
In MIS Schottky diodes, the current is generated by the tunneling effect of carriers across the oxide layer.
If applied voltage is unchanged, the oxide layer (<2nm) only reduces majority carrier current and does not affect the minority carrier current.  Increasing ratio of minority to majority carrier current.  Increasing injection ratio of minority carriers, good for solar cells and LEDs. M I S

47. 4.5 Schottky Diodes V.S. P-N Diodes
Schottky diodes: thermionic emission current, majority carrier devices;
P-N diodes: diffusion current, minority carrier devices.
Forward bias converts abruptly to reverse bias  Switching speed of p-n diodes are limited by the storage effect of minority carriers, but Schottky diodes do not have minority carrier storage.
Schottky diodes is applicable to high-frequency and fast-switching devices.
Al-Si(N) Si
The saturated current of a Schottky diode is much higher than that for a p-n diode. And under the same current, forward voltage drop and threshold voltage are much lower than those for a p-n diodes.

48. 4.5 Schottky Diodes V.S. P-N Diodes
Schottky diodes are more stable at different temperatures.
Schottky diodes have lower noises.
Schottky diodes are easier to fabricate.

49. 4.6 Ohm Contact：Non-Rectifying M－S Junction
Ohm contact: no large spurious impedance which cannot change the equilibrium carrier density and affect the performance of devices.
Before contact
After contact
Almost no barriers in the junction and currents can flow freely in both directions.

50. 4.6 Ohm Contact：Non-Rectifying M－S Junction
Schottky contact and Ohm contact
Metal－n-type semiconductor:
: Schottky contact, rectifying junction
: Ohm contact, non-rectifying junction
Metal－ p-type semiconductor:
Due to the charge effect in the interface states, M-S junctions are usually not Ohm contacts, especially for low doping.

51. 4.6 Ohm Contact：Non-Rectifying M－S Junction
For heavy-doping (>1019 cm-3), the space charge region is so narrow that carriers can penetrate the barrier due to tunneling effect. Symmetric I-V curve for forward and reverse biases  Ohm contacts, non-rectifying barrier, low resistance.
In practice, heavily doped substrates are used to realize ohm contacts to the metal electrodes.