Contact Resistance and Schottky Barriers

Question 1

List the four requirements for ohmic contacts.

Answer 1

1. linear or quasi-linear
2. supply necessary current with minimal voltage drop (drop across contacts should be much smaller than drop across active device)
3. contacts should not degrade the device
4. contacts should not inject minority carriers

Question 2

In the Figure, please give the following assuming a n-type semiconductor:

1. List the barrier type of each
2. Draw the energy bands after contact
3. Give the equation for the Schottky barrier height (ϕ_B) and what it is dependent on

Answer 2

1. Left - accumulation (ϕ_M < ϕ_S), middle - neutral (ϕ_M = ϕ_S), right - depletion (ϕ_M > ϕ_S)
2. See Figure
3. ϕ_B = ϕ_M - χ (where χ is the electron affinity of the semiconductor) - ϕ_B does not depend on ϕ_S and is therefore not dependent on doping density. However, in reality, it is difficult experimentally to change ϕ_B by using a different ϕ_M.

Question 3

1. What are the preferred type of contacts to form ohmic contact?
2. What type of contacts are actually used and what is the typical ϕ_B associated with them?
3. Draw an energy band schematic of these actual contact types on n- and p-type substrates.

Answer 3

1. Accumulation contacts are preferred because carriers encounter the least barrier to flow into the semiconductor
2. It is very difficult to form accumulation contacts because of Fermi level pinning, so depletion contacts are actually used. For n-type substrates, ϕ_B ≈ 2E_g/3 and for p-type substrates, ϕ_B ≈ E_g/3.
3. See Figure of depletion contacts.

Question 4

Explain why and how tunneling contacts are used in semiconductor devices.

Answer 4

Since accumulation-type contacts are hard to create, depletion contacts are used. However, ϕ_B should be lowered to create ohmic contacts. By adjusting the doping density of the semiconductor, a transition from thermionic to field emission occurs via narrowing of the space-charge region width as shown in the Figure. This reduces the barrier for carriers to flow into the semiconductor.

Question 5

Delineate the differences between contact resistance, specific contact resistivity and specific interfacial resistivity.

Answer 5

Question 6

1. Give the equations for total resistance for the vertical (a) and lateral (b) two-terminal contact resistance test structures shown.
2. Outline how the semiconductor resisivity is accounted for for the various geometries

Answer 6

1. (a) R_T = R_c + R_sp + R_cb + R_p; (b) R_T = 2R_c + R_sp + R_p. R_c is the contact resistance of the top contact, R_sp the spreading resistance in the semiconductor directly under the contact, R_cb the contact resistance of the bottom contact, and R_p the probe or wire resistance. The bottom contact usually has a large contact area with a concomitant small resistance. Consequently, R_cb and R_p are often neglligible and can be neglected.
   probe resistance is usually negligible.
2. See Figure.

Question 7

1. Explain why the two-terminal two-contact island structure shown is used instead of measurements on an undoped substrate.
2. What is the equation for total resistance?
3. Explain and show how and why this concept can be implemented into a contact chain (or contact string).

Answer 7

1. Current is confined to the diffused region, allowing for simpler extraction of the semiconductor resistivity component of R_T
2. R_T = (R_sheetd)/W + R_d + R_w + 2R_c. R_sheet is the sheet resistance of the n-layer, R_d the resistance due to current crowding under the contacts, R_w a contact width correction if Z < W.
3. The contact chain structure is shown in the Figure. It is a coarse measurement method, but can be useful as a process monitor. R_T = (NR_sheetd)/W + 2NR_c. N is the number of islands and 2N the number of contacts.

Question 8

What is the advantage of the TLM structures over the typical multiple-contact two-terminal test structure?

Answer 8

Allows for extraction of ρ_c in addition to R_c.

Question 9

1. For the test structure shown, explain how R_c can be extracted.
2. Why is this advantageous over the two-contact two-terminal method?
3. How are TLM structures better than this simple version of the multiple-contact two-terminal method?

Answer 9

1. See Figure.
2. In this case, ρ of the semiconductor and/or R_sheet aren’t needed.
3. In this simple variation, only R_c can be extracted, not ρ_c. In TLM structures, both can be extracted.

Question 10

What is the transfer length (L_T) and why is it needed in TLM measurements?

Answer 10

See Figure.

Question 11

Draw the following three-terminal linear TLM structures and describe each.

• (a) Contact front resistance (CFR)
• (b) Contact end resistance (CER)
• (c) Cross bridge Kelvin resistance (CBKR)

Answer 11

See Figure.

Question 12

1. Describe the use of circular TLM structures and give the relevant equations for extracting R_T.
2. How are R_c and L_T extracted?
3. What is the primary advantage of circular TLM structures over linear ones?

Answer 12

1. See Figure.
2. By plotting the linear relationship of R_T vs. d for various values of d (gap thickness), 2R_c is extracted at d = 0 and 2L_T at R_T = 0.
3. It is not necessary to isolate the area that is to be measured, which is why the issue of W ≠ Z isn’t as much of a concern.

Question 13

Explain how the transfer length method test structure shown can be used to extract R_c and L_T (and therefore ρ_c).

Answer 13

Assuming L ≥ 1.5L_T, the equation for R_T is:

R_T = R_sheetd/Z + 2R_c ≈ (R_sheet/Z)·(d + 2L_T)

The method of extraction is shown in the Figure.