1. ENE 311
Lecture 10

2. Ohmic Contact
For metal-semiconductor contacts with low doping concentration, the thermionic-emission current dominants the current transport.
Rc can be written as
(1)
* As seen from equation (1), in order to have a small value of Rc, a low barrier height should be used.

3. Ohmic Contact
For metal-semiconductor contacts with high doping concentration, the barrier width becomes very narrow and the tunneling current becomes dominant.
The tunneling current can be found by
(2)

4. Ohmic Contact Upper inset shows the tunneling process.
The specific contact resistance for high doping is
Upper inset shows the tunneling process.
Lower inset shows thermionic emission over the low barrier.

5. Ohmic Contact
Ex. An ohmic contact has an area of 10-5 cm2 and a specific contact resistance of 10-6 Ω-cm2. The ohmic contact is formed in an n-type silicon. If ND = 5 x 1019 cm-3 and b = 0.8 V, and the electron effective mass is 0.26m0, find the voltage drop across the contact when a forward current of 1 A flows through it.

6. Ohmic Contact
Soln The contact resistance for the ohmic contact is RC/Area = 10-6/ 10-5 = 0.1 Ω.

7. Ohmic Contact
Soln

8. Transistor
Transistor (Transfer resistor) is a multijunction semiconductor device.
Generally, the transistor is used with other circuit elements for current gain, voltage gain, or even signal-power gain.
There are many types of transistors, but all of them are biased on 2 major kinds: bipolar transistor and unipolar transistor.

9. Bipolar Junction Transistor (BJT)
The BJT was invented by Bell laboratories in It is an active 3-terminal device that can be used as an amplifier or switch.
It is called bipolar since both majority and minority carriers participate in the conduction process.
Its structure is basically that 2 diodes are connected back to back in the form of p-n-p or n-p-n.

10. Bipolar Junction Transistor (BJT)

11. Bipolar Junction Transistor (BJT)
(a) A p-n-p transistor with all leads grounded (at thermal equilibrium).
(b) Doping profile of a transistor with abrupt impurity distributions.
(c) Electric-field profile.
(d) Energy band diagram at thermal equilibrium.

12. Bipolar Junction Transistor (BJT)
Operational Mode
Emitter-base junction
Collector-base junction
Active (normal)
Forward
Reverse
Cutoff
Saturation
Inverse

13. Bipolar Junction Transistor (BJT)
When the transistor is biased in the active mode, holes are injected from the p+ emitter into the base and electrons are emitted from the n base into the emitter.
For the collector-base reverse biased junction, a small reverse saturation current will flow across the junction.

14. Bipolar Junction Transistor (BJT)
However, if the base width is very narrow, the injected holes can diffuse through the base to reach the base-collector depletion edge and then float up into the collector.
This is why we called them “emitter” and “collector” since they emit or inject the carriers and collect these injected carriers, respectively.

15. Bipolar Junction Transistor (BJT)
IEp is the injected hole current. Most of these injected holes survive the recombination in the base, they will reach the collector giving ICp.
There are three other base current: IBB, IEn, and ICn. IBB is the electrons that must be supplied by the base to replace electrons recombined with the injected holes. IBB = IEp – ICp.

16. Bipolar Junction Transistor (BJT)
IEn is the injected electron current (electrons injected from the base to the emitter.).
ICn corresponds to thermally generated electrons that are near the base-collector junction edge and drift from the collector to the base.

17. Bipolar Junction Transistor (BJT)
(4)
(5)
(6)

18. Bipolar Junction Transistor (BJT)
The crucial parameter called “common-base current gain” α0 is defined by
(7)
Substituting (4) into (7) yields
(8)

19. Bipolar Junction Transistor (BJT)
γ is the emitter efficiency written as
(9)
αT is the base transport factor written as
(10)

20. Bipolar Junction Transistor (BJT)
For a well-designed and fabricated transistor, IEn is small compared to IEp and ICp is close to IEp.
Therefore, γ and α are close to 1 and that makes α0 is close to unity as well. Thus, the collector current can be expressed by
(11)

21. Bipolar Junction Transistor (BJT)
Normally, ICn is know as ICB0 or the leakage current between the collector and the base with the emitter-base junction open.
Thus, the collector current can be written as
(12)

22. Bipolar Junction Transistor (BJT)
In order to derive the current-voltage expression
for an ideal transistor, we assume the following:
The device has uniform doping in each region.
The hole drift current in the base region and the collector saturation current is negligible.
There is low-level injection.
There are no generation-combination currents in the depletion regions.
There are no series resistances in the device.

23. Bipolar Junction Transistor (BJT)
Minority carrier distribution in various regions of a p-n-p transistor under the active mode of operation.

24. Bipolar Junction Transistor (BJT)
The distributions of the minority carriers can be found by
pn0, nE0, and nC0 are the equilibrium minority-carrier concentrations in the base, emitter, and collector, respectively. LE and LC are emitter and collector diffusion lengths, respectively.

25. Bipolar Junction Transistor (BJT)
Now the minority-carrier distributions are known, the current components can be calculated. The emitter current can be found by
(16)

26. Bipolar Junction Transistor (BJT)
The collector current is expressed by
(17)

27. Bipolar Junction Transistor (BJT)
The ideal base current is IE – IC or
(18)

28. Bipolar Junction Transistor (BJT)
Ex. An ideal Si p+-n-p transistor has impurity concentrations of 1019, 1017, and 5 x 1015 cm-3 in the emitter, base, and collector regions, respectively; the corresponding lifetimes are
10-8, 10-7, and 10-6 s. Assume that an effective cross section area A is 0.05 mm2 and the emitter-base junction is forward-biased to 0.6 V. Find the common-base current gain of the transistor. Note: DE = 1 cm2/s, Dp = 10 cm2/s, DC = 2 cm2/s, and W = 0.5 μm.

29. Bipolar Junction Transistor (BJT)
Soln

30. Bipolar Junction Transistor (BJT)

31. Bipolar Junction Transistor (BJT)

32. Bipolar Junction Transistor (BJT)
The general expressions of currents for all operational modes are
(19)

33. Current-Voltage Characteristics of Common-Base Configuration
In this configuration, VEB and VCB are the input and output voltages and IE and IC are the input and output currents, respectively.

34. Current-Voltage Characteristics of Common-Emitter Configuration
In many circuit applications, the common-emitter configuration is mostly used where VEB and IB are the input parameters and VEC and IC are the output parameters.

35. Current-Voltage Characteristics of Common-Emitter Configuration
The collector current for this configuration can be found by substituting (6) into (12)
(20)

36. Current-Voltage Characteristics of Common-Emitter Configuration
We define β0 as the common-emitter current gain as
(21)
Then, ICE0 can be written as
(22)

37. Current-Voltage Characteristics of Common-Emitter Configuration
Therefore, (20) becomes
(23)
Since α0 is generally close to unity, β0 is much larger than 1.
Therefore, a small change in the base current can give rise to a much larger change in the collector current.

38. Frequency response
(a) Basic transistor equivalent circuit (low frequency).
(b) Basic circuit with the addition of depletion and diffusion capacitances (higher frequency).
(c) Basic circuit with the addition of resistance and conductance (high frequency).

39. Frequency response
For a high frequency, we expect to have these following components:
CEB = EB depletion capacitance, Cd = diffusion capacitance, CCB = CB depletion capacitance, gm = transconductance = iC/vEB, gEB = input conductance = iB/vEB, gEC = iC/v = output conductance, rB = base resistance, and rC = collector resistance.

40. Frequency response
The current gain will decrease after the certain frequency is reached. The common-base current gain α can be expressed by
(24)
where α0 is the lowest frequency common-base current gain and fα is the common-base cutoff frequency.

41. Frequency response
(25)
where fβ is the common-emitter cutoff frequency given by (1-α0) fα.
Whereas fT is the cutoff frequency when β = 1.
(26)
fT is pretty close to but smaller than fα.

42. Frequency response
fT is pretty close to but smaller than fα.