1. Basic Semiconductor Physics
Slides taken from:
A.R. Hambley, Electronics, © Prentice Hall, 2/e, 2000
A. Sedra and K.C. Smith, Microelectronic Circuits, © Oxford University Press, 5/e, 2004

2. Semiconductors (1) Electronic materials fall into three categories:
Insulators Resistivity () > 105 -cm
Semiconductors <  < 105 -cm
Conductors  < 10-3 -cm
Elemental semiconductors are formed from a single type of atom.
Compound semiconductors are formed from combinations of column III and V elements or columns II and VI.
Germanium was used in many early devices.
Silicon quickly replaced germanium due to its higher bandgap energy, lower cost, and easy oxidation to form silicon-dioxide insulating layers.

3. Semiconductors (1)

4. Semiconductors (1) Bohr model of the atom:
an atom contains a fixed nucleus having a positive charge (protons) and electrons with negative charges the move around the nucleus in elliptical paths (orbits).
These electrons distribute themselves in shells (quantistic energy levels).
Electrons in the outermost shell are called valence electrons.

5. Conduction in materials

6. Conduction in materials
Semiconductor
Bandgap Energy EG (eV)
Carbon (diamond)
5.47
Silicon
1.12
Germanium
0.66
Tin
0.082
Gallium arsenide
1.42
Gallium nitride
3.49
Indium phosphide
1.35
Boron nitride
7.50
Silicon carbide
3.26
Cadmium selenide
1.70

7. Figure 3.36 Intrinsic silicon crystal.
Silicon Intrinsic Crystal
Figure Intrinsic silicon crystal.

8. both of which can move freely through the crystal.
Free electrons & Holes
Figure Thermal energy can break a bond, creating a vacancy and a free electron,
both of which can move freely through the crystal.

9. Holes movement
Figure As electrons move to the left to fill a hole, the hole moves to the right.

10. carrier movement

11. carrier movement  = q(n n + p p) (cm)-1
At room temperature n = p = ni = 1010/cm3 for silicon.
q = 1.60 x (always – this is a physical constant).
n = 1350 cm2/Vs and p = 500 cm2/Vs at room temp. for silicon.
 = (1.60 x 10-19)[(1010)(1350) + (1010)(500)] (C)(cm-3)(cm2/Vs)
= 2.96 x 10-6 (cm) >  = 1/ = 3.38 x 105 cm
Intrinsic silicon is near the low end of the insulator resistivity range
( > 105) at room temperature.

12. n-type silicon
Figure n-type silicon is created by adding valence five impurity atoms.

13. In metals electron density is about: For n-type Semiconductors:
n-type silicon
In metals electron density is about:
For n-type Semiconductors:

14. p-type silicon
Figure p-type silicon is created by adding valence three impurity atoms.

15. If both Donor and Acceptor atoms added then:
p-type silicon
If both Donor and Acceptor atoms added then:
Example 1 (a): In room temperature, find holes and electrons densities in Silicon when:
Example 1 (b): If we only add donor atoms, how does Silicon conductivity change?

16. Career Mobility
Carrier mobility is not constant, it depends on T and doping densities.
m* : effective mass of the carrier
τ: mean free time (average time between collisions)
Drude model of electrical conduction
In solid state physics, a particle's effective mass is the mass it seems to carry in the semiclassical model of transport in a crystal. It can be shown that, under most conditions, electrons and holes in a crystal respond to electric and magnetic fields almost as if they were free particles in a vacuum, but with a different mass.

17. Electron effective mass
Career Mobility
Material
Electron effective mass
Hole effective mass
Group IV
Si (4.2K)
1.08 me
0.56 me Ge
0.55 me
0.37 me
III-V
GaAs
0.067 me
0.45 me
InSb
0.013 me
0.6 me
II-VI
ZnO
0.19 me
1.21 me
ZnSe
0.17me
1.44 me

18. Career Mobility
Carriers are scattered due to lattice and impurities scatterings:
Lattice scattering is due to carrier collision with lattice atoms that are vibrating at their equilibrium positions. This scattering increases with temperature.
Impurity scattering is caused by repulsion or absorption of carriers by ionized impurity atoms. A high energy carrier is less vulnerable to trajectory deviations.
We can approximate the combined effect as:

19. Career Mobility

20. Career Mobility
At high fields, carrier velocity saturates and places upper limits on the speed of solid-state devices.

21. Drift: Charged particle motion in response to an electric field
Drift Current
Drift: Charged particle motion in response to an electric field

22. Diffusion Current
In practical semiconductors, it is quite useful to create carrier concentration gradients by varying the dopant concentration and/or the dopant type across a region of semiconductor.
This gives rise to a diffusion current resulting from the natural tendency of carriers to move from high concentration regions to low concentration regions.
Diffusion current is analogous to a gas moving across a room to evenly distribute itself across the volume.

23. Diffusion Current
Diffusion: Particles tend to spread out or redistribute from areas
of high concentration to areas of lower concentration.

24. Diffusion Current
Dp and Dn are the hole and electron diffusivities with units cm2/s. Diffusivity and mobility are related by Einstein’s relationship:
The thermal voltage, VT = kT/q, is approximately 25 mV at room temperature.

25. Total Current in a Semiconductor
Total current is the sum of drift and diffusion current: Rewriting using Einstein’s relationship (Dn = μnVT):

26. Semiconductor Energy Band Model
Thermal energy breaks covalent bonds and moves the electrons up into the conduction band.
Semiconductor energy band model. EC and EV are energy levels at the edge of the conduction and valence bands.
Electron participating in a covalent bond is in a lower energy state in the valence band. This diagram represents 0 K.

27. Energy Band Model for a Doped Semiconductor
Semiconductor with donor or n-type dopants. The donor atoms have electrons with energy ED. Since ED is close to EC, (about eV for phosphorous), it is easy for electrons in an n-type material to move up into the conduction band.
Semiconductor with acceptor or p-type dopants. The donor atoms have unfilled covalent bonds with energy state EA. Since EA is close to EV, (about eV for boron), it is easy for electrons in the valence band to move up into the acceptor sites and complete covalent bond pairs.

28. Energy Band Model for Compensated Semiconductor
The combination of the covalent bond model and the energy band models are complementary and help us visualize the hole and electron conduction processes.
A compensated semiconductor has both n-type and p-type dopants. If ND > NA, there are more ND donor levels. The donor electrons fill the acceptor sites. The remaining ND-NA electrons are available for promotion to the conduction band.

29. Constructing a Diode
Figure If a pn junction could be formed by joining a p-type crystal to an n-type crystal, a sharp gradient of hole concentration and electron concentration would exist at the junction immediately after joining the crystals.

30. region to appear at the junction.
Unbiased PN junction
Figure 3.43a Diffusion of majority carriers into the opposite sides causes a depletion
region to appear at the junction.

31. Figure 3.44 Under reverse bias, the depletion region becomes wider.
Reverse biased PN junction (1)
Figure Under reverse bias, the depletion region becomes wider.

32. depletion region increases.
Reverse biased PN junction (2)
Figure As the reverse bias voltage becomes greater, the charge stored in the
depletion region increases.

33. Unbiased PN junction
A PN junction in thermal equilibrium with zero bias voltage applied. Under the junction, plots for the charge density, the electric field and the voltage are reported.

34. Built-in Potential

35. Example: Calculate the built-in-potential for a pn junction if

36. Electric Field in SCR

37. Depletion Width

38. Depletion Width Example: For a Silicon pn junction, if:
(a) Find width of depletion region, xp, xn, and Eo .
Solve (a) if we increase impurity densities by a factor of 10.
Solve (a) if, by applying an external voltage, we increase the junction potential by 10 V.
Solve (a) if, by applying an external voltage, we decrease the junction potential by 0.2 V.

39. Figure 3.46 Parallel-plate capacitor.
PN junction capacitance = Depletion Capacitance
Figure Parallel-plate capacitor.

40. Depletion Capacitance
Figure Depletion capacitance versus bias voltage for the 1N4148 diode.

41. Forward biased PN junction
p-type
n-type EC EC Ef Ei Ei Ef EV EV
Ef : Fermi Level, which is the highest occupied energy level at absolute zero, that is, all energy levels up to the Fermi level are occupied by electrons.
Ei : Intrinsic Fermi Level (Ef for intrinsic semiconductor)

42. Forward biased PN junction
Subscript “0” refers to
equilibrium conditions

43. Forward biased PN junction
Assumptions:
Abrupt depletion layer approximation
Low-level injection  injected minority carrier density much smaller than the majority carrier density
No generation-recombination within the space-charge region (SCR)

44. Forward biased PN junction
(a) Depletion layer:
Since (Vo – V) is the net voltage (or barrier) when a forwarded voltage is applied:
At low-level injection: pp= pp0; Recall that
Similarly:

45. Forward biased PN junction
(b) Quasi-neutral regions:
Using minority carrier continuity equations, one arrives at the following expressions for the excess hole and electron densities in the quasi-neutral regions:
Lp: diffusion length of holes in the n-region
Ln: diffusion length of electrons in the p-region
Forward bias
Reverse bias
Space-charge
region W

46. Forward biased PN junction
Corresponding minority-carriers diffusion current densities are:

47. Forward biased PN junction
(c) Total current density:
Total current equals the sum of the minority carrier diffu-sion currents defined at the edges of the SCR:
Reverse saturation current IS : I V Ge Si
GaAs

48. Forward biased PN junction
(d) Limitations of the Shockley model:
The simplified Shockley model accurately describes IV-characteristics of Ge diodes at low current densities.
For Si and Ge diodes, one needs to take into account several important non-ideal effects, such as:
 Generation and recombination of carriers within the depletion region.
 Series resistance effects due to voltage drop in the quasi-neutral regions.
 Junction breakdown at large reverse biases due to tun-neling and impact ionization effects.

49. Diode Capacitances (Reverse Biased)
The charge stored on either side of the depletion layer as a function of the reverse voltage VR.

50. Diode Capacitances (Reverse Biased)
Stored Charge at each side of the junction:
And as we saw earlier:
And thus junction capacitance (depletion capacitance) is equal to:

51. Diode Capacitances (Reverse Biased)
Or we can consider:
m is a function of impurity concentration changes in pn-junction (abrupt or gradual).

52. Diode Capacitances (Forward Biased)
1- Junction capacitance:
2- Diffusion capacitance:
In the steady state a certain amount of excess minority carrier charge is stored in each of the p and n regions. If the terminal voltage changes, this charge will have to change before a new steady state is achieved.

53. Diode Capacitances (Forward Biased)
where τ is the excess-minority- carrier lifetime and is equal to:
Similarly we have:
To consider the total effect of electron and hole charges, we write:

54. Diode Capacitances (Forward Biased)
Where τT is called the mean transit time.
For small changes around a bias point, we define the small-signal diffusion capacitance Cd as:

55. Figure 3.50 Small-signal linear circuits for the pn-junction diode.
Diode small signal circuit
Figure Small-signal linear circuits for the pn-junction diode.

56. Diode switching behavior (1)
Figure Circuit illustrating switching behavior of a pn-junction diode.

57. Figure 3.52a Waveforms for the circuit of Figure 3.51.
Diode switching behavior (2)
Figure 3.52a Waveforms for the circuit of Figure 3.51.

58. Figure 3.52b Waveforms for the circuit of Figure 3.51.
Diode switching behavior (3)
Figure 3.52b Waveforms for the circuit of Figure 3.51.

59. Diode switching behavior (4)
Figure Another set of waveforms for the circuit of Figure 3.51.
Notice the absence of a storage interval.