Single Electron Devices for Single Electron Devices for Logic Applications Logic Applications Reza M. Rad Reza M. Rad UMBC UMBC Based on pages 425- Based on pages 425 -441 of 441 of “ “Nanoelectronics Nanoelectronics and and Information Technology” ”, Rainer , Rainer Waser Waser Information Technology
Introduction Introduction � Scaling down Scaling down MOSFETs MOSFETs has been has been � fundamental in improving the performance fundamental in improving the performance of ULSI circuits of ULSI circuits � Scaling of Scaling of MOSFETs MOSFETs is entering the deep is entering the deep � sub 50 nm regime sub 50 nm regime � Quantum mechanical effects are expected Quantum mechanical effects are expected � to be effective in these small structure to be effective in these small structure devices devices
Introduction Introduction � A new device having operation principles A new device having operation principles � effective in smaller dimensions which effective in smaller dimensions which utilizes quantum- -mechanical effects mechanical effects utilizes quantum � Single electron devices retain their Single electron devices retain their � scalability even on an atomic scale scalability even on an atomic scale � Single electron devices will reduce the Single electron devices will reduce the � power consumption because the number power consumption because the number of electrons transferred from voltage of electrons transferred from voltage source to ground is limited source to ground is limited
Single- -electron box electron box Single � A quantum dot connected with two A quantum dot connected with two � electrodes electrodes � One electrode connected to dot through a One electrode connected to dot through a � tunneling junction tunneling junction � The other electrode, gate, coupled with The other electrode, gate, coupled with � quantum dot via insulator, electron cannot quantum dot via insulator, electron cannot pass through tunneling pass through tunneling
Single- -electron box electron box Single � Electrons are injected/ejected to/from the dot Electrons are injected/ejected to/from the dot � through the tunneling junction (fig 1) through the tunneling junction (fig 1)
Single- -electron box electron box Single � Basic operation of single Basic operation of single- -electron box: electron box: � � As the size of quantum dot decreases, charging As the size of quantum dot decreases, charging � energy Wc Wc of a single excess charge on the dot of a single excess charge on the dot energy increases increases � If If Wc Wc is sufficiently larger than thermal energy, is sufficiently larger than thermal energy, � no electron tunnels to/from quantum dot no electron tunnels to/from quantum dot � Electron number in the dot takes a fixed value Electron number in the dot takes a fixed value � � The charging effect which controls The charging effect which controls � injection/ejection of a single charge to/from a injection/ejection of a single charge to/from a quantum dot is called Coulomb Blockade quantum dot is called Coulomb Blockade effect effect
Single Electron Devices Single Electron Devices � Condition for Coulomb blockade: Condition for Coulomb blockade: � 2 e = 2 >> W k T c B C � By applying a positive bias to the gate By applying a positive bias to the gate � electrode we could attract an electron to the electrode we could attract an electron to the quantum dot quantum dot � Further increase of the gate voltage causes an Further increase of the gate voltage causes an � electron to enter the dot electron to enter the dot � In single In single- -electron box, the electron number of electron box, the electron number of � the box is controlled, one by one, by utilizing the box is controlled, one by one, by utilizing the gate electrode the gate electrode
Single- -electron box electron box Single � Conditions for observing single Conditions for observing single- -electron electron � tunneling phenomena tunneling phenomena � First: charging energy of a single electron to First: charging energy of a single electron to � the dot must be greater than thermal energy the dot must be greater than thermal energy � Second: tunneling resistance Second: tunneling resistance R R t of the t of the � tunneling junction must be larger than tunneling junction must be larger than resistance quantum h/e 2 2 resistance quantum h/e � This is required to suppress the quantum This is required to suppress the quantum � fluctuations in electron number, n, of the dot fluctuations in electron number, n, of the dot
Single- -electron box electron box Single � This condition is obtained as follows: This condition is obtained as follows: � Uncertaini ty principle : ∆ ∆ > W . t h ∆ let W be the charging energy of the quantum dot : ∆ ≈ 2 W e / C ∆ let t be the lifetime of the charging : R C t = > 2 2 Then : ( e / C ). R C e R h t t h >> ≈ Ω R 25 . 8 k t 2 e
Single- -electron box electron box Single � Bias conditions for Coulomb Blockade Effects Bias conditions for Coulomb Blockade Effects � � The voltage range which keeps electron number at n, is The voltage range which keeps electron number at n, is � extracted by considering the free energy of the system extracted by considering the free energy of the system � F(n F(n) free energy having n electrons in the island ) free energy having n electrons in the island � � Wc(n Wc(n) : Charging energy ) : Charging energy � � A(n A(n) : Work done by the voltage source connected to gate in order ) : Work done by the voltage source connected to gate in order � to change the electron number from 0 to n to change the electron number from 0 to n � Polarization charge in capacitors: due to rearrangement of elect Polarization charge in capacitors: due to rearrangement of electrons rons � = − F ( n ) W ( n ) A ( n ) c − = − Q Q ne t g Q Q + = g t V Q and Q are the polarizati on g t g C C t g charge on the tunneling junction and gate capacitors
Single- -electron box electron box Single � Bias conditions .. Bias conditions .. � 2 2 2 2 2 Q C C V Q e n 1 = + = + = + g t g g t W ( n ) , C C C Σ c t g 2 C 2 C 2 C 2 C Σ Σ t g 2 C C C V ∫ = = = + g t g g A ( n ) I ( t ). V dt Q V en V g g g g C C Σ Σ To maintain electron number in quantum dot : 1 e 1 e < ± ⇒ − < < + F ( n ) F ( n 1 ) [ n ] V [ n ] g 2 C 2 C g g
Single- -electron box electron box Single � Bias conditions .. Bias conditions .. � Free energy change in the transitio n of electron + number from n to n 1 : e ∆ + = + − = − F ( n , n 1 ) F ( n 1 ) F ( n ) ( Q Q ) t c C t C e − = + g 1 Where : Q [ 1 ] c 2 C t
Single- -electron transistor electron transistor Single � Schematic structure of a Schematic structure of a � single- -electron transistor electron transistor single (SET) is shown in the (SET) is shown in the figure (fig 3) figure (fig 3)
Single- -electron transistor electron transistor Single � Operation of a single Operation of a single- -electron transistor electron transistor � � The circuit connected to the tunneling junction of source The circuit connected to the tunneling junction of source � is shown in the figure (fig4a) is shown in the figure (fig4a) � The condition for maintaining electron number at n is: The condition for maintaining electron number at n is: � + C V C V 1 e 1 e − < < + ⇒ g g d d [ n ] [ n ] + + + 2 C C C C 2 C C g d g d g d 1 e 1 e − − < < + − [ ne C V ] V [ ne C V ] g g d g g C 2 C 2 d d
Single- -electron transistor electron transistor Single � The circuit connected to the tunneling junction The circuit connected to the tunneling junction � of drain is transformed to the circuit shown in of drain is transformed to the circuit shown in the figure (fig 4b) the figure (fig 4b) � The condition to maintain the electron number The condition to maintain the electron number � at n is at n is 1 e 1 e − + + > > − − + [ ne C V ] V [ ne C V ] + + g g d g g C C 2 C C 2 s g s g
Single- -electron transistor electron transistor Single � Figure (fig 5a) shows the drain Figure (fig 5a) shows the drain- -gate voltage gate voltage � relation relation � Gray areas are coulomb blockade areas Gray areas are coulomb blockade areas � where electron number in the dot is fixed where electron number in the dot is fixed
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