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Microwave Effects in a Silicon Single Donor Quantum Dot

Enrico Prati, Rossella Latempa, and Marco Fanciulli

Laboratorio Nazionale Materiali e Dispositivi per la Microelettronica,

Consiglio Nazionale delle Ricerche - Istituto Nazionale per la Fisica della Materia,

Via Olivetti 2, I-20041 Agrate Brianza, Italy

Abstract

Single donors in semiconductor nanostructures represent a key element to develope quantum

functionalities in atomic scale devices. The behaviour of a Single Donor Quantum Dot (SDQD)

under microwave irradiation is addressed through quantum transport characterization. The system

consists of an isolated dopant lying in the channel of a silicon decanano flash memory, which

provides two well resolved energy levels below the conduction band edge attributed to a single

Arsenic donor. Similarly to other quantum dots the microwave irradiation produces photon assisted

tunneling. Two different regimes of coupling are observed as a function of the microwave power.

Furthermore, zero bias spectroscopy of excited levels is made possible using microwave irradiation

at sufficiently high power. Level crossing as a function of a static magnetic field is also observed

by means of such microwave spectroscopy.

1

Single and double atoms in a semiconductor nanostructure are of major interest for their

key role in atomic scale devices for electronics and spintronics [1, 2, 3, 4, 5, 6]. The first

observation of a single As atom in a Silicon nanostructure [7, 8] opened the route to its

characterization through new experimental techniques. Isolated dopants in a nanoMOSFET

channel behave as atomic-like systems with one or two electrons in a central 1/r attracting

Coulomb potential. Donors can be characterized in terms of energy levels associated to

the D0 and D− states, whose values are known in bulk Silicon [10]. A direct measure of

the degree of hybridization of the electron wavefunction between the donor potential and

the interfacial well has been recently performed in a Si nanostructure [8]. The separation

of the conduction peaks, observed by applying a gate voltage to a nanostructure, and the

threshold voltage, is proportional to the energy level position in the respect of the conduction

band edge [7, 8]. An isolated, diffused dopant embedded in the Si inversion layer of a

nanostructure acts as a quantum dot (Single Donor Quantum Dot, SDQD) at cryogenic

temperatures [7, 11]. A microwave field, in force of the variety of its couplings with the single

atom and its environment provides an unique tool to explore quantum tranport and spin

properties. In a SDQD the electron spin qubits are based on Zeeman state doublets, coupled

by microwave irradiation at the resonance frequency. Microwave irradiation should drive

spin resonance and manipulation with pulses of appropriate duration as already observed in

GaAs systems [12]. In Si the observation and the control of single electron spin resonance

is still unaddressed because of the extremely small linewidth (expected to be less than one

gauss) [13] if compared to GaAs where the spin orbit effect broadens the line to tens of gauss

[12, 14, 15], and of the competition of such effect with photon assisted tunneling. When

a quantum dot is irradiated by a microwave source, the electromagnetic vector potential

provides excitation of electrons in the leads [16] and in the dot [17], and an electromotive

potential at the leads [16, 18, 20]. The combination of the two effects goes under the name of

photon assisted tunnelling (PAT). Such study has been previously carried out only in GaAs

split gate quantum dot samples [16] and double dots [22], and later in a lithographically

defined single electron transistor(SET) based on Si/SiGe technology [23]. Investigation and

control of microwave irradiated quantum dots should lead to an improvement of nanodevices

architecture [21]. Here we show that the microwave irradiation is able to produce photon

assisted tunneling through a silicon SDQD like in other confined 0-dimensional systems and

that appropriate field powers make possible an accurate energy level spectroscopy of the

2

single dopant.

In order to charaterize electronic transport without and with microwave irradiation in

a Si nanoMOSFET at 300 mK, we measured the conductance below the conduction band

edge, where Coulomb blockade peaks appear. These peaks are due to resonant tunneling

through discrete energy levels [7]. Approximately one sample every ten shows a well isolated

pair of peaks which can be related to the energy levels of an As donor, as explained in the

following.

The samples were commercial flash memories based on Si technology with nominal n-

channel dimensions of 50 nm width and an effective lenght of less than 70 nm, as revealed by

TEM analysis and simulations [9]. The contacts are doped with arsenic and the channel with

boron. Few As atoms can also diffuse in the channel. From the current-voltage characteristics

IDS(VG) of the device between 8 K and 77 K we measured a threshold gate voltage of 2.850

V. The electronic structure of the dot is first characterized by dc transport spectroscopy, i.e.

by measuring the Coulomb-blocked oscillations in conductance in absence of any external

field. At 300 mK the conductance pattern develops well isolated peaks due to the Coulomb

blockade (Figure 1). In the subthreshold region two current peaks are measured.

We now turn to the identification of such peaks, which, as discussed in the following, are

attributed to channels opened by a single Arsenic atom, like in Ref.[7, 8]. We measured

the charging energy (energy difference bewteen peaks 1 and 2) U = E2 − E1 and the

binding energy EC − E1 energies from the stability diagram shown in Fig. 1. There, the

conductance is plotted in color scale and units of e2/h versus gate and bias voltage at 0.3

K. VDS was varied from -7.5 mV to 7.5 mV, while control gate polarization between 2.2

and 3 V. Conductance variations develop typical triangular sectors both at positive and

negative drain-source voltages. Maximum values of conductance are evidenced in white.

The calculated coupling factor, which allows to traslate the applied gate voltages in the

corresponding energies, is α=0.14. The charging energy of the donor U is 35 meV, while

the spacing between the first peak and the band edge EC − E1 is 61 meV. Such results are

close to those reported by Selleir and coauthors [7] where U=32 meV and EC −E1=52 meV

for As in a Si FinFET with As implantations in the source/drain regions. The magnetic

spectroscopy of the two peaks has been characterized up to 2 T. The peaks linearly shift as

a function of the magnetic field B according to the Zeeman splitting gµB of a S = 1/2 spin

for g ≈ 2, as in Ref. [7]. We attribute the two peaks visible below the band edge to the

3

tunneling through an As atom occupied by N = 0 (peak number 1) and N = 1 (peak number

2) electrons. In other words, the first and second peak correspond to first (N = 0 → 1 ) and

second (N = 1 → 2 ) charge state of the impurity (D0 and D− respectively).

When a microwave field is applied, the additional time-varying potential V cosωt allows

inelastic tunnelling events due to energy exchanges between the electrons and photons. At

40 GHz quantum regime is achieved since kT ≤ hν < ∆E << U where ∆E is the energy

separation of the donor levels which is of the order of few meV (as measured by the Coulomb

blockade diamonds of each peak), the charging energy U is about 35 meV and the thermal

broadening ≈ 3kT = 75µeV. The intrinsec linewidth of the conduction peaks Γ is of about

1 meV so hν < Γ.

Also in a SDQD, according to the theory of electron tunneling in a QD under microwave

irradiation [24, 25, 26], the rf field can be modeled as a potential V cos ωt added to static

voltage across the leads. Such general ac coupling to three leads can be reduced without loss

of generality to only two [18, 19]. To include the asymmetry of the ac coupling, we model

the microwave amplitude by two parameters, αi = eVi/h̄ω, where i = D,S, and Vi are the

ac voltage drops across the source and drain reservoirs. Following Refs. [16] and [23] the

expression of the drain-source current through the SDQD in the channel is:

Γ̃(E) =+∞∑

−∞

J2

n(αi)Γi(E ± nh̄ω). (1)

.

In Eq.(1) Jn’s are Bessel function of the first kind and Γi is the tunnel rate in absence of

applied field

Γi(E) = (Gi/e2)E/(1− e−βE) (2)

where β = 1/kT , Gi is the characteristic conductance of the barrier, and E is the resonant

energy level. The net current is determined by the difference in the forward and backward

rates through the source and drain barriers.

The sample was cooled in a 300 mK cryostat while the 1-40 GHz continuous wave radia-

tion was supplied by a coaxial line UT-141 berillium in stainless steel, having a diameter of

3.5 mm. A dipole antenna was used at the end of the line to irradiate the sample, located

at a distance of about 3 mm.

The effect of microwave irradiation is clearly visible by measuring the conductance at zero

source-drain bias. In Fig. 2 a set of experimental IDS (∆ECG) characteristics of the first

4

conductance peak is shown for VDS = 0, where ∆ECG is the control gate energy shift from

the arbitrary center of the sweep, which is Vcg = 2.7 V. The shape of current oscillations

depends on the asymmetry of the coupling between both source and drain reservoirs with

microwave field [23]. Current peaks increase both in amplitude and width as a function

of the power Prf , while they do not significantly depend on frequency, like in single dots

with random microwave field coupling [23]. The absolute power at the sample is unknown

and changes randomly by several orders of magnitude at different frequencies. Indeed, the

electromagnetic environment of the sample strongly depends on the impedence load of the

end of the coaxial line which terminates in the 3He pot. In the inset of Fig. 2 a plot of the

maximum peak current as a function of the microwave power is shown. Experimental data

at low power are well fitted by the function c√

Prf (continuous line) as expected [23].

We increased the output power of the rf microwave generator and measured the tunnel

conductance as a function of its nominal value. The maximum peak current as a function

of microwave power is reported in Fig. 3 for the (1 → 2) peak. A double regime of coupling

is observed at different power scale. Typical√

Prf behaviour [23] holds at low power, where

photon assisted tunneling occurs, while a linear trend in Prf ( expressed in dBm in Fig. 3)

occurs at higher microwave power, where the pure voltage fluctuation pumping effect at the

leads dominates [19, 20, 27, 28]. The crossover between the two regimes occurs at about -5

dBm.

We now describe how microwave irradiation may provide an accurate tool for the spec-

troscopy of excited states at zero bias. Analogously to spectroscopy on real atoms, PAT can

be used as a probe to electrically reveal internal excitation energies on artificial atomic-like

systems, such as SDQDs.

In Fig. 4 a colour plot of the transconductance ∂IDS/∂(αeVCG) variation in the plane

(Prf , ECG) is reported for the (0 → 1) transport. Derivative maxima are evidenced in

white, while dark zones refer to minima. Conductance variations develop a triangular sector

evidenced by black lines with slopes following the positive (left, white zone) and negative

(blue, rigth zone) values. The bold vertical lines mark the energy values where the maximum

of conduction occurs. In correspondence of a nominal power of about -2 dBm, an excited

state is detected at energy 1.4 meV higher.

The second state of Fig. 4 is identified with an excited state of the donor, accessed at

zero bias only in the high power regime, when the voltage oscillations of the leads increase

5

in amplitude. The existence of such excited state at 1.4 meV state has been observed also

by means of second derivative stability diagrams.

Because of the small energy scale associated to the microwave frequency (of the order of

hν), the zero bias microwave spectroscopy (ZBMS) has a much higher resolution if compared

to the method of stability Coulomb blockade diagrams to isolate excited states. Indeed, only

a second derivative study of the stability diagram allows the detection of such excited level

at 1.4 meV, being the width of the Lorentzian peak Γ of the order of 1 meV for small bias.

Moreover, by measuring Coulomb diamond diagrams, excited states transport is accessed

only at non zero bias and always in parallel to the ground state.

An intriguing application of the ZBMS of the energy levels in the donor quantum dot

has been exploited by observing a level crossing of the same donor levels in presence of

a static magnetic field parallel to the channel otherwise not detectable by the stabiltiy

diagrams. In Fig. 5 the first derivative of the current Ids with respect to the gate voltage

Vcg as a function of the gate energy Ecg is plotted. The current was generated by a 40 GHz

microwave irradiation at -2 dBm at zero bias in correspondance of the energy level (0 → 1).

The magnetic field B varies along the vertical axis. Bright and dark zones correspond to

positive and negative values of the derivative. The two energy levels probed by microwave

transport at zero bias are positioned where the contrast from bright to dark zones occurs

and they are evidenced by a white line.

The two peaks move parallel as a function of the magnetic field B according to Zeeman

splitting for g = 2 up to about 1 T. Above, a crossing between the two levels is observed

in correspondance of 1.601 T. The origin of such level crossing requires a detailed analysis

which will be discussed elsewhere [29].

To conclude, we demonstrated that microwave irradiation induces transport in Single

Donor Quantum Dots like in any other quantum dot systems. Furthermore, we identify two

separate regimes of coupling, according to photon assisted tunneling and quantized charge

pumping effects respectively. The microwave irradiation, at sufficiently high power, allows

the detection of excited states at zero bias with a resolution which is much higher than by

means of stability diagrams, at least for SDQD. The powerfullness of zero-bias microwave

spectroscopy has been exploited to reveal an intriguing level crossing versus static magnetic

field, not otherwise observable with the same resolution using more conventional techniques.

6

Acknowledgments

The authors thank Dr. Cappelletti (STMicroelectronics) for providing the samples.

I. FIGURE CAPTIONS

Figure 1 Stability diagram in the subthreshold region. Two clearly isolated peaks lies

below the conduction band edge. The charging energy U is 35 meV, while the difference

EC − E1 is 61 meV, in agreement with As donors in Si nanostructures as reported in Ref.

[7, 8]

Figure 2 Current-Voltage characteristics of the first conductance peak at zero bias and

base temperature of 300 mK for different rf powers. The control gate voltage Vcgt is converted

into the corresponding energy shift ∆Ecg from the arbitrary center of the sweep, positioned

at 2.7 V. Inset: the square root dependence of the peak height, typical of photon assisted

tunneling [23].

Figure 3 Maximum current peak as a function of nominal applied microwave power.

Depending on the applied power, the regime changes from a square root trend P1/2rf (low

power) where photon assisted tunneling dominates, to a linear trend Prf (high power), where

the voltage fluctuation in the leads is the only responsible of electron pumping.

Figure 4 Transconductance variations as a function of microwave power. Above -2 dBm

the power is sufficient to access an excited state 1.4 meV higher than the ground energy E1.

Figure 5 Colour plot of the derivative of the zero bias microwave induced current at the

ground state (E1) and its excited state probed at 40 GHz and -2 dBm. A static magnetic

field is applied up to 2 T. Both ground and excited state energy levels shift under the field

according to g=2 Zeeman splitting. A level crossing between the ground and the excited

state is observed at around 1.6 T.

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8

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9

320 360 400

-5

0

5

35 meV61 meV

Ec

Ecg(meV)

V d (m

V)

1.000E-5

5.574E-5

3.107E-4

0.001732

0.009655

0.05382

0.3000

G(e2/h)

-42 -39 -36 -33

0

1

2

3

0.0 0.1 0.20.5

1.0

1.5

2.0

2.5

3.0

Vds=0

I ds(

nA)

Ecg (meV)

0.251 mW 0.158 mW 0.100 mW 0.063 mW 0.040 mW 0.025 mW 0.016 mW 0.010 mW

40 GHz

Max

. Cur

rent

(nA

)

Prf (mW)

-10 -5 0 5

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IPP(nA)

Prf (dBm)

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)

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