UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences Fall 2005 EE143 Midterm Exam #1 Family Name First name SID Signature Make sure the exam paper has 7 pages (including cover page) + 3 pages of data for reference Instructions: DO ALL WORK ON EXAM PAGES This is a 90-minute exam (4 sheets of HANDWRITTEN notes allowed) Grading: The reader can only assess what you put down on the exam paper, not what is inside your brain. Please be concise with your answers. For answers requiring explanation, adding sketches can be very effective. To obtain full credit, show correct units and algebraic sign. Numerical answers orders of magnitude off will receive no partial credit. Problem 1 (25 points) Problem 2 (25 points) Problem 3 (25 points) Problem 4 (22 points) TOTAL (97 points) 1
Problem 1 Processing Modules and Simple Process Sequence (25 points total) The following schematic cross-section shows a MOSFET together with a tunneling ohmic contact to the substrate. The MOSFET part of the process sequence has been well described in your textbook [ Jaeger, Chapter 1]. MOSFET Tunneling Ohmic Contact to substrate CVD n+ poly Si CVD Al CVD CVD p+ n+ n+ p- substrate Gate oxide p+ p+ p+ (i) (5 points) Consider the whole process sequence. There are some sacrificial layers used during the process sequence which does not end up in the final structure. Quotes one example of such a sacrificial layer. (ii) (5 points) Starting with a blanket p- Si wafer, consider the whole process sequence. How many thermal oxidation steps are used to fabricate this structure? List all thermal oxidation steps used, and briefly describe the purpose. (iii ) (12 points) Starting with a blanket p- Si wafer, consider the whole process sequence. How many etching steps are used to fabricate this structure? List all etching steps used, and briefly describe the purpose. [ Do not count photoresist development as etching steps] (iv) (3 points) Which doped region will be subjected to the largest thermal budget for dopant diffusion? 2
Problem 2 Thermal oxidation (25 points total) (a) (15 points) The following structure is subjected to a steam oxidation step at 1000 o C for 3 hours. Sketch a roughly proportional cross-section after this oxidation step in the same figure. Label all regions and important thicknesses. Use the attached oxidation chart to generate numerical values of the different oxide thickness. 0.5 µm 0.2 µm Si3N4 Si (100) 0.1 µm (b) A Si wafer has an unknown initial oxide thickness x i. After thermal oxidation for 1 hour, the total oxide thickness is measured to be x µm. With an additional 3 hours of oxidation, the total oxide thickness becomes 2x µm. Given :Linear oxidation constant B/A =1µm /hour and parabolic oxidation constant B = 0.3 µm 2 /hour. (i) (5 points) Find the numerical value of x [Hint: The solution for the quadratic equation: ax 2 + bx +c = 0 is x = -b ± b2-4ac 2a ] (ii) (5 points) Find the numerical value of initial oxide thickness x i. 3
Problem 3 Ion Implantation (25 points total) Boron implantation (using B + ions) is performed to the following structure to a boron dose of 10 13 /cm 2. The B + ion energy is chosen such that the boron concentration at Location A is a maximum. For simplicity, let us assume the ion stopping powers and ion scattering characteristics are identical for both silicon and silicon dioxide. Boron Implantation 0.7 µm poly-si 0.05 µm x=0 B 0.6 µm A depth x n-type Si substrate (a) (4 points) What is the B+ ion energy? (b) (4 points) Calculate the maximum boron concentration at Location A? \ (c ) (4 points) Calculate the boron concentration at Location B? (d) (5 points) The n-type Si substrate has a uniform doping concentration = 10 15 /cm 3. Calculate the junction depth x j underneath Location B. 4
Problem 3 continued (e) (4 points) Now, let us consider ion channeling effect. Will you expect a longer channeling tail in the crystalline silicon substrate underneath Location A or Location B? Write down your reasoning. (f) (4 points) After the boron implantation, a high temperature drive-in diffusion step is performed with (Dt) drive-in = ( R p ) 2 of the boron implantation profile. Sketch qualitatively the boron concentrations (log scale) in the Si substrate versus depth x underneath Location B for: (i) before drive-in ( dash line), and (ii) after drive-in (solid line). Pay attention to slopes of the curves. C(x) log scale x =0 x 5
Problem 4 Dopant Diffusion (25 points total) (I) Consider the following Arsenic doping profiles. C(x) [log scale] Profile A 4 10 18 /cm 3 Profile B (Half-gaussian) x j = 2 µm p-type substrate (1 10 15 /cm 3 ) depth x (a ) (4 points) Calculate the sheet resistance of Profile A use the mobility curves. (b) (3 points) Use the Irvin s curves to find the sheet resistance of Profile B. (c ) Suppose Profile B is subjected to an additional drive-in diffusion step such that the (Dt) product of the half-gaussian profile is doubled. (i) (3 points) Calculate the new surface concentration. (ii) (3 points) Explain concisely why the sheet resistance of profile B is lower after the additional drive-in step. 6
Problem 4 continued (II) A microfabrication textbook use the following expression to calculate the diffusivity of Arsenic in Si at 1000 o C when the arsenic concentration is equal to 10 20 /cm 3. (i) (3points) What physical quantity does the number 7.14 10 18 represent? 4.15 (ii) (3 points) What physical quantity does the expression 31.0 exp ( k(1000+273) ) represent? (iii) (3 points) What physical quantity does the number 3.44 represent? 7
Information which may be useful 1 µm = 10-4 cm = 1000nm = 10 4 Å Electron charge q = 1.6 10-19 coulombs; Boltzmann constant k = 8.62 10-5 ev/k n i of Si = 3.69 10 16 T 3/2 exp [- 0.605eV/kT] cm -3 1 0.1 0.01 0.001 exp(-z^2) 0.0001 erfc(z) 0.00001 0.000001 0.0000001 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 z 8
R p =51.051+32.60883 E -0.03837 E 2 +3.758e-5 E 3-1.433e-8 E 4 R p =185.34201 +6.5308 E -0.01745 E 2 +2.098e-5 E 3-8.884e-9 E 4 Proj ected Range & Straggle in Angstrom 10000 1000 B 11 into Si R p R p 100 10 100 1000 Ion Energy E in kev R p =-7.14745 +12.33417 E +0.00323 E 2-8.086e-6 E 3 +3.766e-9 E 4 R p =24.39576+4.93641 E -0.00697 E 2 +5.858e-6 E 3-2.024e-9 E 4 10000 P 31 into Si Proj ected Range & Straggle in Angstrom 1000 100 R p R p 10 10 100 1000 Ion Energy E in kev 9
Irvins s Curves 10