618 326

1. 618 326 Physics of electronic materials and devices I Lecture 11

2. Ohmic contact • This contact is defined as a junction that will not add a significant parasitic impedance to the structure on which it is used and will not sufficiently change the equilibrium-carrier densities within the semiconductor to affect the device characteristics.

3. Ohmic contact • The I-V characteristic of ohmic contact is linear for an ideal case.

4. Ohmic contact • A specific contact resistance RC is given by • A good ohmic contact should have a small specific contact resistance about 10-6 Ω.cm2.

5. Ohmic contact • When the semiconductor is heavily doped with an impurity density of 1019 cm-3 or higher, the depletion layer of the junction becomes very thin so that carriers can tunnel instead of going over the potential barrier.

6. 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.

7. 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)

8. Ohmic contact • The specific contact resistance for high doping is

9. Ohmic contact Upper inset shows the tunneling process. Lower inset shows thermionic emission over the low barrier.

10. Example 1 • 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.

11. Example 1 • SolnThe contact resistance for the ohmic contact is RC/Area = 10-6/ 10-5 = 0.1 Ω.

12. Example 1

13. 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.

14. Transistor • The BJT was invented by Bell laboratories in 1947. 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.

15. Bipolar Junction Transistor (BJT)

16. 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.

17. Bipolar Junction Transistor (BJT)

18. BJT

19. Active mode • 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.

20. Active mode • 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.

21. Active mode • 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. It equals to IEp – ICp.

22. Active mode • 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.

23. Active mode (4) (5) (6)

24. Common-base • The crucial parameter called “common-base current gain” 0 is defined by (7) • Substituting (4) into (7) yields (8)

25. Common-base • γ is the emitter efficiency written as (9) • T is the base transport factor written as (10)

26. 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)

27. 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)

28. 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.

29. BJT • Minority carrier distribution in various regions of a p-n-p transistor under the active mode of operation.

30. 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.

31. BJT • Now the minority-carrier distributions are known, the current components can be calculated. The emitter current can be found by (16)

32. BJT • The collector current is expressed by (17)

33. BJT • The ideal base current is IE – IC or (18)

34. Example 2 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.

35. Example 2 • Soln

36. Example 2

37. BJT • The general expressions of currents for all operational modes are (19)

38. IV 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.

39. IV 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 VECand IC are the output parameters.

40. Common-Emitter • The collector current for this configuration can be found by substituting (6) into (12) (20)

41. Common-Emitter • We define β0 as the common-emitter current gain as (21) • Then, ICE0 can be written as (22)

42. Common-Emitter • 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.

43. 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).

44. 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.

45. 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 low-frequency common-base current gain and fα is the common-base cutoff frequency.

46. 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.

47. Frequency response • Normally, fT is pretty close to but smaller than fα.