CHAPTER 3

1. CHAPTER 3 CONTACT RESISTANCE, SCHOTTKY BARRIERS, AND ELECTROMIGRATION

2. 3.2 Introduction

3. Ohmic contacts do not necessary to be linear. • Ohmic contacts should not inject minority carriers. • The contact should be able to supply sufficient current and has negligible voltage drop. • The contacts should have reproducible properties.

4. 3.2 METAL-SEMICONDUCTOR CONTACTS

5. METAL-SEMICONDUCTOR CONTACTS Metal-semiconductor contacts according to the simple Schottky model. The upper and lower parts of the figure show the metal-semiconductor system before and after contact, respectively.

6. The barrier height after contact for this model is given by Vbi=φm-φs φB=Vbi+(φs-χ) ψB is independent of semiconductor doping density. Accumulation contact is preferred Ohmic contact, because of the lower barrier height.

7. φm>φsn φm< φsp • Usually, φB =2Eg/3 for n-type substrate and φB = Eg/3 for p-type substrate

8. Surface states may cause Fermi level pinning, φB is independent of metals’ work function. • Ohmic contacts are defined as high recombination rate regions. • Highly damaged regions may serve as Ohmic contacts. However, highly damaged regions are not reproducible. • Barrier height is relatively independent of doping density but barrier width does. Heavily doped semiconductors have narrow scr, tunneling current can easily occur.

9. TE TFE FEDepletion-type contacts to n-type substrates with increasing doping concentration. The electron flow is schematically indicated by the electrons and their arrows.

10. TE: carriers are thermally excited over the barrier.TFE: carriers are thermally excited to an energy where the barrier is narrow enough for tunneling to occur.FE: the barrier is sufficiently narrow at the bottom of conduction band such that carriers can tunnel through directly.

11. Characristic energy Eoo and kT as a function of doping density for Si with m*tun/ m =0.3. T = 300 K.

12. TE: kT<<E00, E00 ≦0.2kT. TFE: kT≒ E00, 0.2kT< E00 <5kT. FE: kT>> E00, E00 >5kT

13. Usually, only the region directly under the metal is heavily doped, the real contact structure is The contact resistance RC=Rm-s+ Rn+-n If Rm-s dominates, then RCis independent of the n-region doping concentration. If Rn+-n dominates, then RC is inversely depends on the n-region doping concentration.

14. 3.3 CONTACT RESISTANCE

15. Contact Resistance

16. A schematic diagram showing two contacts to a diffused semiconductor layer , with the metal resistance, the contact resistances, and the semiconductor resistance indicated.

17. RS is determined by the sheet resistance of the diffused layer and the spreading resistance at the contact. • RC includes Rm-s, a portion of Rm immediately above the contact, part of the semiconductor below the contact, interfacial layer (oxide) between metal and semiconductor, and current crowding effect. • The current density of a metal- semiconductor contact depends on many parameters

18. Let ρc=M+ρi+S+current crowding effects, where is used in deriving theoretical expressions. The current density dominated by thermionic emission is where A=4πqk2m*/h3 is the Richardson’s constant.

19. C1 and C2 are functions of ND, T, and φB N is the doping density under the contact

20. Specific contact resistivity as a function of doping density for Si.

21. The specific contact resistivity normalized toT = 305K, as a function of temperature for (a) p-Si, (b) n-Si. The data for ND = 2 x 1018 cm-3 extend from T = 305 to 400 K only. The metal is tungsten .

22. 3.4 MEASUREMENT TECHNIQUES

23. There are four contact resistance measurements: • Two-contacts two-terminal method • Multiple-contacts two-terminal method • Four-terminal method Six-terminal method • All of the above methods measure ρc not ρi

24. Two-Terminal Contact Resistance Methods (a) A vertical two-terminal contact resistance structure, (b) a lateral two-terminal contact resistance structure.

25. Apply a current I and measure V gives RT = V/I Where Rp is the probe resistance

26. for 2t>>r where C is a correction factor, for widely separated contacts, C=1. If the current is vertically flow into the top contact, then For small Rs, Rcb, and Rp, Rc≒ RT-Rsp Accurate result is obtained if Rsp<< Rc , which implies that small radius contact should be used. One may use contacts with different r, plot RT vs. Ac, and ρc is proportional to the slope.

27. A lateral two-terminal contact resistance structure in cross section and top view. where Rd is the resistance due to current crowding under the contacts, Rw is a contact width correction if Z<W.

28. A contact string test structure ; cross section and top view. Usually, N is several hundred or more. This method is used as a process monitor, it is not useful for detailed evaluation.

29. Multiple Contact Resistance Methods Multiple-contact, two-terminal contact resistance test structure. The contact width and length are Z and L and the diffusion width is W.

30. Rc is independent of ρs • d1 and d2 may be the source of inaccuracy. • What has been determined is Rc not ρc because the contact area is not exactly known. • Only part of the contact length, about the diffused layer thickness, is active for current transfer.

31. Current transfer from semiconductor to metal represented by the arrows. The semiconductor / metal contact may be represented by the ρc一ρs equivalent circuit with the current choosing the path of least resistance. V(x) is the potential distribution under the contact, Z is the contact width, LT is the 1/e distance.

32. Normalized potential under a contact versus x as function of ρc , where x = 0 is the contact edge. L = 10 μm, Z = 50μm,ρs = 10 Ω/square.

33. Transfer length as a function of specific contact resistivity and semiconductor sheet resistance. A typical good contact has ρc ≦ 10-6Ω.cm2, which corresponds to an LT of about 1μm.

34. The above transmission line methods (TLM) are also called (a) the contact front resistance (CFR) structure, (b) the contact end resistance (CER) structure, and (c) the cross-bridge Kelvin resistance (CBKR) structure.

35. For Z=W, ρc>0.2ρst2, and V(0) measured at x=0 The above equation is not valid for Z<W. Now, call Rcf as Rc, for L≦0.5LT, coth(L/LT)=LT/L, so Ac,eff = LZ = Ac for L≧1.5LT, coth(L/LT)=1, so Ac,eff = LTZ < Ac

36. Front contact resistance-contact width product as a function of contact length and specific contact resistivity for ρs＝ 20Ω/ square andρsm = 0. RcZ reaches a minimum at about L = LT.

37. For CER structure, V is measured at x=L, and ρc>0.2ρst2 For short contacts, L<LT, the accuracy is determined by L. For long contacts, Rce is very small, the accuracy is limited by the instrument.

38. For CBKR structure, V is measured over the contact length, thus V is the average value as The contact resistance is

39. One dimensional current flow between contacts is true only when L≦LT, Z>>L, and δ=(W-Z)/2<<Z. • The problem of W≠Z is avoided by using circular structures. • No isolation for diffused or implanted layer is necessary for circular structures, since the current has no other path to flow.

40. Circular transmission line geometry test structure. C For

41. (a)Correction factor C versus d/L ratio for the circular transmission line method test structure, (b) total resistance for the circular TLM test structure before and after data correction. Rc = 0.75Ω,LT= 2um,ρc =4 x 10-6 Ω·cm2,Rsh=110ohms/square. Data courtesy of J.H. Klootwijk and C.E. Timmering, Philips Research Labs.

42. Transfer length method test structures. For L<<LT, current does not flow into the metal, in (a) contacts 2 and 3 have no effect on the measurement. For L>>LT, the current flows into the metal, in (b) the contact is effectively two contacts with length LT plus a metal conductor with length L-2LT.

43. A transfer length method test structure and a plot of function of contact spacing, d. Typical values might be L = 50μm, W = 100μm, W-Z = 5 μm ( should be as small as possible ) , d ＝5 to 50μm.

44. The above method gives ρs (if Z is known), 2Rc, and 2LT. • ρs under the contacts and between the contacts may not be identical due to the contact formation. Therefore, modify Rcf and RT as: where ρsc is the sheet resistance under the contact and LTc=(ρs/ ρsc)1/2

45. From the above equation, 2LTc is determined at RT=0, but ρsc and ρc are still unknown. • However, if Rce is also measured, then ρsc and ρc can be decided. • There is wafer level nonuniformity in these measurements

46. If silicide or polysilicon is used rather than metal, then conductor’s resistance must be counted in. where α= ρsm/ ρsc, ρsm isthe metal (polysilicon) sheet resistance, and LTcm = (ρc/ (ρsc+ρsm))1/2 = LTc/(1+ α) ½

47. Front contact rsistance-contact width product as a function of contact length and specific contact resistivity for ρc = 20 Ω/square and ρsm = 50 Ω /square. Note that there is a minimum for each curve.

48. The Correction of δ Uncorrected (solid points and lines ) and corrected (open points and dashed line ) total resistance versus spacing d for Au/Ni/Au/Ge/n-GaAs contacts annealed at 4000C for 20s.Reprinted after ref.72 by permission of IEEE(2002,IEEE)

49. Four-Terminal Contact Resistance Method A four-terminal or Kelvin contact resistance test structure. (a) Cross section through section A-A, (b) top view of the structure.

50. Four-terminal contact resistance test structures. (a) Ideal with only lateral current flow, (b) and (c) current flowing into and around the contact. The black area is the actual contact area. The measured ρc is higher than the actual value for δ≠ 0, the introduced error is high for low ρc and high ρs.