Single Electronics

Abstract

Operational principle of single electron transistor is outlined. Based on energy band diagram, the influence of the gate voltage on the drain-source voltage for tunneling from source to drain is expounded. Derivation of the equation for total energy stored in the capacitors comprising a single electron transistor is presented. From energy viewpoint, necessary conditions favoring electron tunneling are deduced. These electron tunneling processes take place from one tunnel junction into the quantum dot island, and thereafter from this island across the other tunnel junction. Considering opposite sequences of operation of electron tunneling across tunnel junctions into and away from the quantum dot island, symmetrically placed triangular regions are sketched and combined to show Coulomb diamonds. Logic circuit operation based on single electron transistors is introduced. The reader is familiarized with voltage-based logic and charge-based logic used with SETs . Restrictions on increasing the low voltage gain of SETs are discussed. Elimination of the requirement of separately fabricating complementary SETs is both an advantage and a disadvantage. Difficulties faced in straightway adoption of CMOS logic circuits for SET logic are indicated. Operation of voltage-logic-based SET AND, NOT, and OR gates is described. Other applications of SETs as a supersensitive electrometer, as a standard of direct current and for IR detection are briefly touched upon.

Review Exercises

• 14.1 What is single electronics? What does a single electron transistor do? How many terminals does this device have? What are the functions of these terminals? Is the gate terminal connected to the quantum dot by a tunneling capacitance? How does the single electron transistor differ from a quantum dot circuit ?

• 14.2 From the energy band diagram of a single electron transistor, explain how the gate voltage determines the drain-source voltage required for electron tunneling from source to drain?

• 14.3 Derive the equation for the total energy stored in the capacitors C _a , C _b , and C _g of a single electron transistor:

  $$ E_{\text{se}} = \left\{ { C_{a} C_{\text{{g}}} \left( {V_{\text{{s}}} - V_{\text{{g}}}^{i} } \right)^{2} + C_{a} C_{b } V_{\text{{s}}}^{2} + C_{b } C_{\text{{g}}} V_{\text{{g}}}^{{i^{2} }} + Q^{{i^{2} }} } \right\}/\left( {2C_{\text{{s}}} } \right) $$

  where $Q^{i}$ is the total charge on the quantum dot island, $V_{\text{{g}}}^{i}$ is the gate voltage, V _s is the supply voltage and $C_{\text{{s}}} = C_{a} + C_{b} + C_{\text{{g}}}$.

• 14.4 Show that an electron will tunnel into the quantum dot through TJ _b if

  $$ q_{\text{{e}}} \left( {n + 1/2} \right) + C_{a} V_{\text{{s}}} + C_{\text{{g}}} V_{\text{{g}}} > 0 $$

  where q _e is the electronic charge and n is the initial number of electrons on the quantum dot island, C _a is the capacitance of tunnel junction TJ _a , V _s is the supply voltage, C _g is the gate capacitance and V _g is the gate voltage.

• 14.5 Prove that an electron will tunnel off the quantum dot through TJ _a if

  $$ q_{\text{{e}}} \left( { - n + 1/2} \right) + \left( {C_{b} + C_{\text{{g}}} } \right)V_{\text{{s}}} - C_{\text{{g}}} V_{\text{{g}}} > 0 $$

  where q _e is the electronic charge and n is the initial number of electrons on the quantum dot island, C _b is the capacitance of tunnel junction TJ _b , V _s is the supply voltage, C _g is the gate capacitance and V _g is the gate voltage.

• 14.6 Show that for n = 0, an electron will tunnel across the junction TJ _b into the quantum dot if

  $$ V_{\text{{s}}} >- \left( {1/C_{a} } \right)\left( {q_{\text{{e}}} /2 + C_{\text{{g}}} V_{\text{{g}}} } \right) $$

  Draw the region of V _s-V _g plane defined by this equation.

  For n = 1, show that the electron will tunnel off the quantum dot across the junction TJ _a if

  $$ V_{\text{{s}}} > \left\{ {1/\left( {C_{b} + C_{\text{{g}}} } \right)} \right\}\left( {q_{\text{{e}}} /2 + C_{\text{{g}}} V_{\text{{g}}} } \right) $$

  Draw the corresponding region of V _s-V _g plane. Mark the resultant triangular region of the V _s-V _g plane satisfying both the above equations.

  Considering the opposite sequence of tunneling operations in which an electron tunnels across the junction TJ _a into the quantum dot and then tunnels off the quantum dot across the junction TJ _b , similar triangular regions are defined which are located symmetrically opposite on the V _g axis to the previously obtained triangular regions. What are the regions drawn by shading the symmetrically placed triangles called? What do they indicate and what do they represent?

• 14.7 Bring out the differences between SET and CMOS devices, which do not allow straightway adoption of CMOS logic circuits for implementation by SET devices.

• 14.8 What restrictions forbid raising the voltage gain of a single electron transistor? What value of voltage gain is generally used?

• 14.9 Is it necessary to fabricate complementary SETs separately? How is complementary behavior realized in SETs?

• 14.10 Explain the statement, “The availability of identical complementary SET transistors is both a blessing and a curse.”

• 14.11 Why is static power consumption high in SET logic circuits? How does charge-based logic decrease power consumption? How does this logic work?

• 14.12 Draw and explain the operation of a voltage-logic based SET NOT gate .

• 14.13 Draw the circuit diagram of a SET AND gate . Identify the SETs identical to P-channel and N-channel transistors, and hence explain the operation of this circuit in analogy to CMOS AND gate.

• 14.14 Draw the circuit diagram of a SET OR gate . Point out differences in connections of transistors from the SET AND gate, and explain the working of the gate.

• 14.15 Explain how a SET acts an ultrasensitive electrometer ? Cite some applications of this capability of SET?

• 14.16 Explain the use of SET as a standard of direct current. Why are SET arrays used as IR detectors ?