Spring 2001 6.012 Microelectronic Devices and Circuits Prof. J.A.del Alamo March 14, 2001 - Quiz #1 problem grade Name: Recitation: total General guidelines (please read carefully before starting): • Make sure to write your name on the space designated above. • Open bo ok: you can use any material you wish. • All answers should be given in the space provided. Please do not turn in any extra material. If you need more space, use the back page. • You have 120 minutes to complete your quiz. • Make reasonable approximations and state them, i.e. quasi-neutrality, depletion approxima-tion, etc. • Partial credit will be given for setting up problems without calculations. NO credit will be given for answers without reasons. • Use the symbols utilized in class for the various physical parameters, i.e. µn, ID, E,etc. • Every numerical answer must have the proper units next to it. Points will be subtracted for answers without units or with wrong units. • Use φ =0 at no = po = ni as potential reference. • Use the following fundamental constants and physical parameters for silicon and silicon dioxide at room temperature: −3ni =1 × 1010 cm kT /q =0.025 V q =1.60 × 10−19 C s =1.05 × 10−12 F/cm ox =3.45 × 10−13 F/cm 1234561. (10 points) Compute the equilibrium electron and hole concentrations, no and po, for silicon at room temperature doped with: −3(1a) (2 points) Boron (B) concentration = 1017 cm . (1b) (2 points) Phosphorus (P) concentration = 5 × 1016 cm−3 and Antimony (Sb) concentration = −35 × 1016 cm . −3(1c) (2 points) Arsenic (As) concentration = 1017 cm−3 and Boron (B) concentration = 1016 cm . (1d) (4 points) In (1a) above, what is the magnitude of the electric field that must be applied to the sample for the magnitude of the majority carrier drift velocity to be equal to 106 cm/s?2. (10 points) An engineer is told that a region of silicon of length 20 µm,width 5 µm and thickness 1 µm is uniformly doped with a single kind of dopant with a concentration of 1020 cm−3.Ohmic contacts are formed at the ends of the region and she measures the I-V characteristics given in the table below. Is the sample n-type or p-type? Explain how you reach this conclusion. [Hint: think about the sample r esistance.] W=5 µm voltage (V) current (A) 0 0 1 0.025 2 0.05 + _ V L=20 µm t=1 µm3. (10 points) In a certain n-type region of a semiconductor in thermal equilibrium, there is a hole concentration with the following spatial distribution: −3 po(x)=103(1 − 9 × 103 x) cm for 0 ≤ x ≤ 10−4 with x in cm Assume that in this region, the electron mobility and hole mobilities are µn = 500 cm2/V · s and µp = 200 cm2/V · s, respectively. (3a.) (5 points) Derive an expression for and sketch the hole diffusion current density in this region.(3b.) (5 points) Derive an expression for and sketch the electric field distribution in this region.−34. (20 points) Consider an abrupt pn junction with Na =1017 cm−3 and Nd =1016 cm ,as sketched below. N Na Nd x0 4a) (6 points) Compute the value of the electrostatic potential at x = 0 in thermal equilibrium (numerical answer expected).4b) (4 points) Compute no and po at x = 0 in thermal equilibrium (numerical answer expected). 4c) (5 points) Compute the value of x for which no = po = ni in thermal equilibrium (numerical answer expected).4d) (5 points) Compute the total amount of charge per unit area on the p side of the junction when a reverse bias voltage of 5 V is applied to the diode (numerical answer with appropriate sign expected).� 5. (30 points) Consider the following MOS structure: VGB n+ polySi oxide p-Si (Na=6x1017 cm-3) contactcontact x0-tox The oxide thickness is tox =5 nm =5 × 10−7 cm. To save you time, for this structure: 1 γ = 2sqNa =0.65 V 1/2 Cox (5a) (5 points) Compute the threshold voltage of the structure (numerical answer with appropriate sign expected).(5b) (5 points) What is the value of VGB that leads to a sheet charge density in the inversion layer of Qn = −10−6 C/cm2?(numerical answer expected). (5c) (5 points) What is the magnitude of Eox (electric field across the oxide) for a condition in which QG = −2 × 10−7 C/cm2? (numerical answer expected).(5d) (5 points) What is the magnitude of Es = E(x =0+) (electric field on semiconductor side of oxide-semiconductor interface) at threshold? (numerical answer expected). (5e) (10 points) What is the capacitance of the MOS structure at a bias point for which the total charge in the semiconductor is equal to −2 × 10−7 C/cm2? (numerical answer expected).6. (20 points) Consider a MOSFET made out of the MOS structure of problem 5. The gate length is L =1 µm. The gate width is W =10 µm. The electron mobility in the channel is 200 cm2/V · s. The MOSFET is biased with VDS =0.1 V , VGS =1 V and VBS =0 V . If you did not compute the threshold voltage of this structure in section (5a), assume it to be 0.5 V . (6a) (10 points) Compute the magnitude of the inversion layer charge density at the source-end of the channel: |Qn(y =0)| (numerical answer expected).(6b) (10 points) Compute the magnitude of the electron velocity at the source-end of the channel: |vy(y =0)| (numerical answer
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