Sample Problems from the Annual International Microelectronics Olympiad of Armenia

Problem 1 Problem 1. (10 points)

Using the following parameters, define the current through series connected transistors.
Kp'=25 mkA/V2, VT0=1.0V, γ=0.39V1/2, 2|ΦF|=0.6V, W/L=1.
Consider the body bias effect. Several iterations will be needed for the solution.

Problem 2. (10 points)

The first inverter of the presented buffer is of minimal size, input capacitance is Cin=10 fF, delay 70 ps. The load capacitance of the buffer is CL=20 pf.

Problem 2

a. Define the sizes of the other two inverters with respect to the minimal one. Use minimum delay condition, consider that input capacitances are proportional to sizes.
b. Add any number of inverters to get minimum delay. Define the total delay.
c. Define the power consumption of the circuit if the supply voltage is 2.5V and operating frequency is 200 MHz.

Problem 3. (10 points)

Suppose 2-input, 1-output combinational circuit is given, it depends on input variables A, B and Z* output variable implementing the function of disjunction Z=A v B. Let T(F) be a test set for a single fault F, a set of all possible input patterns detecting F.
Definition: Faults F1 and F2 are called equivalent faults if T(F1)⊆T(F2) and T(F2)⊆T(F1), i.e., T(F1) = T(F2).
Find the faults that are equivalent to the fault "line A stuck-at-1" mentioned in the figure.

Problem 4. (10 points)

A circuit of flip-flop with combined logic is shown. Define values of S1, S2, S3 signals, for which this circuit will operate as:
  • Positive edge-triggered D-flip-flop with synchronous reset
  • Positive edge-triggered T- flip-flop with synchronous reset
  • D-latch
  • Transfer of input signal data to output
Problem 4

Problem 5. (10 points)

Suppose we have a given "data_in" signal which is a one hot logic vector of 8-bit of width. And the goal is to calculate the encoded decimal value of the bit index having value of 1'b1 (shown 'casez' statemens implements the required logic). Note, 'one hot logic vector' means that this vector will have only one 1 value in its bits. E.g.: 0001, 0010, etc.

Please provide an optimal gate-level logic equivalent to this case statement (using only logical AND, OR and NOT gates). The answer may be provided in either VerilogHDL or schematic drawing interpretation. Provide the gate level derivation logic for data_out[1].

Problem 5

Problem 6 Problem 6. (15 points)

Find Av=dVout/dVin small signal gain.
gm1, gm2, gm3, R1 values are known. Ignore the secondary effects.

Problem 7. (10 points)

Calculate the drain current of n-MOS Si transistor according to the following conditions:
threshold voltage Vt=1 V, gate width W=10 μm, gate length L=1 μm, thickness of oxide layer tox=10 nm, VGS=3 V and VDS=5 V. For calculation, use square model, surface mobility is 300 cm2/V and VBS=0 V. Also calculate gm transconductance.

Problem 8. (15 points)

In the given directed graph, realize search according to depth starting from the 2nd vertex.

Problem 8

Problem 9. (10 points)

Estimate an accuracy of the rectangle's symmetric rule,supposing that the function ƒ is two times continuously differentiable on the segment [a,b].

Problem 9

Problem 10. (10 points)

Let n≥2 be an integer. A partition of n is a representation of n as a sum of positive integers without taking into account the order of them. For example, the partitions of 3 are: 1+1+1; 2+1; 3. Develop a pseudo code for an algorithm generating the list of all the partitions of the given n.

Problem 11 Problem 11. (10 points)

What is the value of free term of characteristic polynomial for the following matrix?

Problem 12. (15 points)

The sequence x(n)=cos(πn/4) is obtained in the result of time sampling of analog signal u(t)=cos(2πƒ0t) with sampling frequency fs=1000 Hz:x(n)=u(n)Δt, where Δt=1/fs.

a. Find the two minimum values of the frequency f0, for which it is possible.
b. For sampling frequency fs=800 Hz, find the two minimum values of the frequency f0200 Hz for which it is possible.

Problem 13. (15 points)

The nanostructure of field type transistor consists of quantum dot which is connected to two current conductors by tunnel current – electron's source and drain.

When VSD voltage is applied between the source and drain, current starts to flow through the net which is conditioned by the tunnel transition of electrons from the source into the quantum dot, and then from the quantum dot to the drain.

The second electrode of transistor – the gate, is connected to the quantum point by capacitive link Cg and it is possible to control the current that flow through the circuit source-quantum point – drain by the applied voltage Vg.

Considering that the quantum point has a radius r=10nm, and the current cross section of source and observer are of the same order, estimate, due to Coulomb blockage, how much it is necessary to change the gate voltage such that after one electron tunnel transition from source to the quantum dot, the second, the third and other electrons transitions are possible, due to which I-V dependence will look like a stairway.

Problem 13

Problem 14. (10 points)

Assume given two rectangles – with left, top, right and bottom coordinates. Implement a program that will calculate and print the intersection of those rectangles. Print "Has no intersection!" if they are not intersected.

Problem 14

Problem 15. (13 points)

It is known that colloidal solutions (sols), for example, quantum dots, can agglomerate, forming composite complexes, consisting of 2 or more particles.
One reason for this phenomenon is the excess surface energy and the power of molecular attraction, forcing other small particles to unite. To prevent agglomeration, it is possible to report the charge of the same name sign to nanoparticles, which will lead to their repulsion.
How can nanoparticles be charged in a colloidal solution? What could be the minimum and maximum charge of nanoparticles?

Suppose, for example, each of the forming sols of silicon nanocrystals (Si), having a spherical shape with a radius R = 1 nm, and a positive charge q, equal in magnitude to twice the electron charge was reported.
Will these particles form agglomerates in a collision in a colloidal solution in benzene at room temperature? Will the result change if benzene is replaced with water? Does the probability of agglomeration depend on size of the nanoparticle, their concentration, the temperature of the solution?

      Charged colloidal nanoparticles