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Quantum Dot Structures for Multi-band Infrared and Terahertz Radiation Detection 679

interface (top contact layer), which has about 30% reﬂ ectivity. The DWELL detector showed two

response peaks at 6 and 10 μ m. The resonant optical cavity was active at 9.5 μ m; consequently,

the RC-DWELL showed an enhance response at 9.5 μ m (see Fig. 22.19b ). A peak responsivity of

0.76 A/W, detectivity of 1.4  1 0

c m H z

/W and 10% conversion efﬁ ciency at 1.4 V bias and

77 K were reported for RC-DWELL, while DWELL showed only 1.25% conversion efﬁ ciency at

1 0 μ m under the same conditions. The detectivity of the RC-DWELL was 3  1 0

cmHz

at 77 K under a 1.2 V bias, showing a factor of 3 improvement compared to the conventional

DWELL detector. Another important feature of incorporating an RC into a DWELL structure is

the increase in photocurrent without increasing the dark current.

(a)

GaAs 500 Å

0.15

0.85

As 50 Å

InAs(

n = 3  10

2

) 2.4 MLs

0.15

0.85

As 60 Å

GaAs 500 Å

GaAs(

n  2  10

3

) 1257 nm

0.98

0.02

As 1726 nm

GaAs 757 nm

0.98

0.02

As 1726 nm

GaAs S.I. substrates

GaAs Buffer 2000 Å

GaAs (n  2  10

3

) 1245 nm

 8

Photon reflector

Figure 22.19 (a) Schematic structure of an RC-DWELL detector with eight-period QD active layers (InAs/

0.15

0.85

As). (b) A comparison of the spectral responsivity of an RC-DWELL detector and a standard DWELL

0.6

0.5

0.1

0.2

0.3

0.4

0.9

0.7

0.8

RC-DWELL

DWELL

Resonant

cavity

peak

11 137935

Wavelength (m)

Normalized spectral response (a.u.)

(b)

22.5 Present performance capabilities of QDIPs

A summary of speciﬁ cations for several recently reported QDIPs is given in Table 22.2 . Pal et al.

[103] reported a super-lattice QDIP with 50-period InAs/GaAs QD active layers and an AlGaAs

current-blocking layer to suppress the dark current. The spectral responsivity and detectivity of

this detector is shown in Fig. 22.20a and b. Gunapala et al. [11] have demonstrated up to 1 A/W

response at 77 K for a DWELL detector coupled with a grating. A two-colour DWELL detector

with response peaks at 3.2 and 4.1 μ m operating up to room temperature was demonstrated by

Lim et al. [22] . Several other QDIPs [75, 104] operating at high temperatures are also listed in

the table. A historical analysis of the QDIP development shows rapid progression towards high-

performance detectors capable of room temperature operation.

In a recent investigation by Jayaweera et al. [105] , a new concept for developing photon detec-

tors, based on the displacement currents in a QD-embedded dielectric media, operating at room

temperature, has been reported. A preliminary detector structure along with its photoresponse

results were also reported. The detector structure consists of PbS QDs embedded in a dielec-

tric thin ﬁ lm, which is sandwiched between two conducting glass contacts. The dielectric thin

ﬁ lm was made of parafﬁ n wax, which has a high dielectric constant. The incident photons are

absorbed in QDs, generating an electron–hole pair. When an electric ﬁ eld is applied across the

contacts, the electrons drift towards the positive contact, while holes drift towards the negative

contact. Since carrier transport through the dielectric medium is not possible, there will be a

charge separation in the medium. This polarizability with photon absorption, which changes the

capacitance of the device, is the key detection mechanism in the structure proposed by Jayaweera

et al. QDs in a dielectric medium have shown several orders of magnitude higher polarizability

than atoms and molecules. The incident radiation is modulated and the photogenerated displace-

ment current is measured under an applied bias across the contacts. The displacement current

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680 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics

Table 22.2 A summary of recently reported QDIPs along with their ﬁ gures of merit. λ

, λ

, T , η , g , D *, and T

max

stand for peak wavelength, zero response wavelength threshold, peak

responsivity, operating temperature, quantum efﬁ ciency, photoconductive gain, detectivity, and

maximum reported operating temperature, respectively.

Ref. Description

( μ m) λ

( μ m)

(A/W)

@ T (K)

η  g

(%)

D * (Jones)

@ T ( K)

max

(K)

[10] DWELL

⬃ 10 ⬃ 12 ⬃ 0.67 @ 120

8.3

2.6  1 0

@ 78

240

[11] DWELL 8.1

⬃ 10 ⬃ 1 @ 77

1  1 0

@ 77

–

[22] DWELL 4.1

⬃ 4.75 ⬃ 0.67 @ 120

2.8  1 0

@ 120

300

[42] DWELL 10.5

⬃ 13

0.125 @ 80 1.5

1.5  1 0

@ 80

[43] T-QDIP 5.7

⬃ 8

0.75 @ 80 16

2.4  1 0

@ 80

300

[75] 70 InAs/GaAs QDs

⬃ 3.5 ⬃ 6 ⬃ 0.12 @ 100

1  1 0

@ 100

150

[103] 50 InAs/GaAs QDs 4.9,5.8 ~8 4.3 @ 100 91

2  1 0

@ 100

220

[104] DWELL 9.3 ~10 0.7 @ 78 9

3  1 0

@ 78

100

Figure 22.20 (a) Spectral responsivity of a QDIP with a current-blocking layer composed of an Al

0.3

0.7

As layer.

This enabled operation up to 220 K. (b) Variation of the peak detectivity with temperature. The photoconductive gain

as a function of bias at 100 K is shown in the inset. After [103] .

4.0

3.0

2.0

1.0

284106

Wavelen

th (m)

Photoresponse (Amp/W)

100 K

220 K

175 K

200 K

 10

 15

 20

(a)

432

Bias (V)

4.5

2.0

0.0

0.5

1.0

1.5

2.5

3.5

3.0

4.0

Bias V)

Peak responsivity (Amp/W)

100 K

Peak detectivity (cm Hz

1/2

/W)

(b)

is a direct measurement of the incident radiation intensity and does not contain any contribu-

tion from the dark current. Hence, this approach is suitable for developing room temperature

detectors. At 300 K and 40 V bias, the responsitivity and the detectivity at the peak absorption

( λ

 540 nm) were found to be 195 V/W and 3  1 0

c m H z

/W, respectively. As an advantage,

a sophisticated growth and fabrication techniques are not required for this type of detector devel-

opment. However, in this approach the incident light has to be modulated in order to obtained

a photoresponse. A closely related device structure, which operates in photocurrent mode, has

been reported by Konstantatos et al. [106] The device structure consists of spin-coating colloidal

PbS QDs fabricated onto interdigitated gold electrodes. A detectivity in the order of 10

c m H z

W has been reported at 1.3 μ m at room temperature. A high photoconductive gain ( ⬃ 10 000)

and consequently a high responsivity of 10

A/W were observed at room temperature.

22.6 Quantum dot focal plane arrays (FPAs)

The development of FPAs using successful single-element detector structures has remarkably

increased potential applications in IR imaging. Multi-colour FPAs would lead to additional detection

capabilities such as the construction of a true thermal map of a target. FPAs operating in atmos-

pheric windows (3–5 and 8–14 μ m) are required for a number of applications including night

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Quantum Dot Structures for Multi-band Infrared and Terahertz Radiation Detection 681

vision cameras and missile tracking, whereas FPAs operating in the FIR region are particularly

suited for applications in astronomy and space situational awareness [38] . Most high-performance

FPAs developed so far have been based on InSb, MCT and QWIPs; however, QD-based FPAs have

also attracted the attention of the infrared community due to the development of successful sin-

gle element QDIPs [22, 103, 107] . Krishna et al. [10] have reported a 320  256 pixel two-colour

FPA using an InAs/InGaAs DWELL detector. According to Krishna et al. one of the major draw-

backs in developing QD-based FPAs is the growth of thick active layers, providing sufﬁ cient absorp-

tion of radiation, without causing misﬁ t dislocations. The growth of self-assembled QDs needs

sufﬁ cient strain in the QD regions, reducing the possibility of growing thick QD layers. The two-

colour DWELL detector, which was used for the FPA, showed wavelength selectivity with applied

bias, where a 5.5 μ m peak was enabled at low bias and 8–10 μ m peak was activated by high biases.

This has a peak responsivity of 1 A/W and D* of 2 –7  1 0

cmHz

/W. Thermal imaging using the

FPA was demonstrated at 80 K with different optical ﬁ lters (3–5 and 8–12 μ m). Moreover, the oper-

ability of the FPA was reported to be greater than 99%, and the noise equivalent temperature differ-

ence (NEΔT) was estimated to be less than 100 mK for f /1 (for 3–5 μ m) and f /2 (5–9 μ m) optics.

Gunapala et al. [11] have demonstrated a 640  512 pixel QD-based IR imaging FPA operating

in the LWIR region. The detector was modelled on a DWELL structure, where InGaAs QDs were

placed in a GaAs/AlGaAs QW. The 30-stack DWELL detector has shown a peak absorption quan-

tum efﬁ ciency of 2.7%. Under normal incidence conﬁ guration, the detector had a much stronger

(almost one order of magnitude) responsivity compared to the responsivity of a typical QWIP

under 45° incidence conﬁ guration. In addition, it was found that the 45° incidence responsiv-

ity of the detector ( ⬃ 1 A/W) was 4–5 times stronger than the normal incidence responsivity,

as shown in Fig. 22.21a . DWELL detectors can be fabricated with a reﬂ ection grating to couple

normal incidence light to the z -polarization-sensitive absorption mechanism in the DWELL struc-

ture. A DWELL detector (reported by Gunapala et al. [11] ) fabricated with a reﬂ ecting grating

showed a factor of 3–4 enhancement in the responsivity, as shown in Fig. 22.21b . Peak detec-

tivity of 1  1 0

c m H z

/W at 8.1 μ m and 77 K was reported. Using this detector structure, a

640  512 pixel FPA has been fabricated. Additionally, an LWIR imagery system with a noise-

equivalent temperature difference of 40 mK at 60 K showing a high uniformity was constructed.

A 3-inch GaAs wafer with 12 640  512 pixels QDIP FPAs is shown in Fig. 22.22a , while an

image of a human target taken with the 640  512 pixels FPA camera is shown in Fig. 22.22b .

In a recent publication, Razeghi group demonstrated [12] a 320  256 pixel MIR focal

plane array operating at temperatures up to 200 K. The FPA was based on a DWELL structure

[22] , which consists of InAs QDs imbedded in a InGaAs/InAlAs QW. It was reported that the

detector has two-colour characteristics up to room temperature with response peaks at 3.2

and 4.1 μ m, as shown in Fig. 22.23 . The photoresponse peak at 4.1 μ m originated from bound-

to-bound intersubband transitions between delocalized mixed states in the QD and QW unlike

Figure 22.21 (a) A comparison between the spectral responsivity of a DWELL detector measured under normal

incidence and 45 ° incidence conﬁ gurations. (b) Normal incidence spectral responsivity with and without reﬂ ection

gratings. After [11] .

1.00

0.00

0.80

0.20

0.40

0.60

45 9101112867

Wavelength (m)

Responsivity (A/W)

2 V

45°-incident

Normal

incident

(a)

0.80

0.60

0.40

0.20

0.00

With

grating

5 6 11 1291078

DWELL-QDIP

normal incident

No grating

Wavelength (m)

Responsivity (A/W)

(b)

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682 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics

the bound-to-bound transitions between pure QD states and QW states for DWELL structures

reported in section 22.2. The detector had a peak responsivity of 34 mA/W and maximum D * of

2.8  1 0

c m H z

/W at 120 K, while a D * of 6  1 0

c m H z

/W was obtained at 300 K. The

DWELL FPA showed imaging capabilities at 120 and 200 K. A conversion efﬁ ciency of 1.1% and

a noise equivalent temperature difference of 344 mK at 120 K were observed. The FPA camera is

capable of imaging human targets up to 150 K. Images of a human target and a hot soldering

iron taken with the FPA camera at 130 and 200 K, respectively, are shown in Fig. 22.24 . Based

(a) (b)

Figure 22.22 (a) A 3-inch. GaAs wafer with 12 640  512 pixels QDIP FPAs. (b) An image of a human target

taken with the 640  512 pixels QDIP FPA camera. After [11] .

Figure 22.23 (a) Spectral responsivity of a DWELL detector at different temperatures under a (a)  1 V bias, and

(b)  5 V bias (response at room temperature (RT) was obtained under a  2 V bias). The variation of the response at

room temperature is shown in the inset. After [22] .

0.30

0.00

3.52.5

5.5

4.5 5.0

4.03.0

0.05

0.10

0.15

0.20

0.25

Bias   1V

77 K

120 K

150 K

200 K

240 K

InAs QD

InAsQD

AIInAS

GainAs

∼0.30

∼0.385

Wavelength (μm)

Photoresponse (a.u.)

(a)

120 K (5 V)

77 K (5 V)

180 K (5 V)

240 K (5 V)

RT (2 V)

Room

temperature

4.5

3.5

5.0 5.5

4.02.5

3.0

Wavelength (μm)

3.0 5.0 5.5 6.04.0 4.53.5

Wavelength (μm)

Photoresponse (a.u.)

2 V

1 V

(b)

(a)

(b)

Figure 22.24 Images taken with a 320  256 pixel QDIP FPA camera at (a) 130 and (b) 200 K. The maximum

operating temperature of the array is 200 K. After [12] .

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Quantum Dot Structures for Multi-band Infrared and Terahertz Radiation Detection 683

Table 22.3 QDIP FPA speciﬁ cations. Peak wavelength is given in the response range

column, when the range is not stated clearly.

Ref. Array size Cell pitch Response range @ T

NE Δ T

@ f #

Pixel operability

[10]

320  256

3 0 μ m 3 – 5 μ m @ 80 K

8–12 μ m @ 80 K

100 mK @ 1

100 mK @ 2

 99%

[11]

640  512

2 5 μ m 8 . 1 μ m @ 60 K

40 mK @ 2

 99%

[12]

320  256

3 0 μ m 4 μ m @ 120 K

344 mK @ 2 99%

on these results, it can be concluded that the development of QD-based FPAs is feasible, even

though the present QDIP FPAs show lower overall performance as compared to MCT and QWIP

FPAs. A summary of QDIP FPA speciﬁ cations is given in Table 22.3 . Major improvements in QDIP

FPAs include: high responsivity and low dark current at high temperatures, improved growth

quality, and uniformity in detector material for large wafer sizes and device processing.

22.7 Conclusion

The electronic transitions between energy states in the QD and QW give rise to multi-colour

response in DWELL detector structures. Response peaks experimentally obtained from each

detector correspond to the energy spacings calculated by theoretical models. By changing the

well width and the size of the QD, detectors can be designed to operate at different wavelength

regions depending on the application. The operating wavelength can be selected by varying the

applied bias. Advantages of DWELL detectors over typical n -type QWIPs include their ability to

operate under normal incidence and at high temperatures particularly in the VLWIR/FIR region.

In a different approach, T-QDIPs designed for room temperature operation and terahertz detec-

tion were reported. As evident from the results, T-QDIPs exhibit lower dark current, and higher

operating temperatures compared to typical QDIPs, which were made possible by the incorpora-

tion of double barriers into the structure. A 17 μ m T-QDIP that can operate at room temperature,

and a 6 terahertz detector operating at 150 K, were demonstrated. T-QDIPs are photon detectors,

which are inherently fast and do not use slower thermalization processes, which are the primary

detection mechanism in thermal detectors such as bolometer or TGS. In comparison with the Si

BIB detectors, the main advantage will be in the increase in operating temperature to 77 K or

higher, which will greatly reduce the cooling requirements. This would be an important feature

for space-based applications where moving from 20 K to higher temperatures is a major design

advantage. Furthermore, T-QDIP structures open up a wide range of possible modiﬁ cations and

designing options to aid in wavelength tuning and performance optimization. Promising results

have been observed for QD-based FPAs, even though the overall performance is low compared to

MCT and QWIP FPAs.

Acknowledgement s

This work is supported in part by the National Science Foundation under Grant ECCS: 0620688.

The authors acknowledge the contributions of Prof. P. Bhattacharya and his group at the

University of Michigan and Prof. S. Krishna and his group at the University of New Mexico, and

Ms Laura Byrum for her technical assistance in preparing this article.

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Optically Driven Schemes for Quantum Computation Based on

Self-assembled Quantum dots

I. D’Amico

and B.W. Lovett

Department of Physics, University of York, York YO10 5DD, United Kingdom

Department of Materials, University of Oxford, OX1 3PH, United Kingdom

23.1 Introduction and fundamentals of quantum information processing

Starting in the late 1990s, an increasing research effort has been devoted to the idea and prac-

tical implementation of the “ quantum computer ” [1] . While before, the quantum computer

was only a theoretical speculation put forward by Feynman and Deutsch [1] , in the late 1990s

micro- and nanotechnology started to develop further, boosted by practical necessities such

as the need for miniaturization and the speed-up of “ classical ” computers.

This improvement

follows Moore’s law, which states that the number of transistors per unit area on integrated cir-

cuits doubles-approximately every 18 months. Miniaturization and the related improvement of

experimental techniques have made dynamical control of a few particle quantum systems a near

reality, and with it ideas that the quantum computer could be transformed into actual devices.

Computation is a physical process and information has to be stored in a physical system and

manipulated using physical interactions. The smallest logical unit in classical computers is the bit,

which corresponds to a physical system characterized by two distinct states, labelled “ 0 ” and “ 1 ” .

We can think of them, for example, as the state of a capacitor (charged or discharged), or as a volt-

age pulse below or above a preﬁ xed threshold. In order to speed up calculations, increase storage

capacity and miniaturize computers, we can reduce the size of the physical system representing

the bit, but what can we do once such a system is reduced to a single electron? Moore’s law, which

has ruled for the last 43 years, predicts this will happen in about ten years. Quantum computation

provides one possible way forward, since it has been shown theoretically that such devices can sub-

stantially speed up the solution of problems such as factorization of large numbers and database

search, and allow for the simulation of complex many-particle quantum systems.

The logical unit of a quantum computer is called the “ qubit ” , or quantum bit. The qubit is a

two-level quantum system, with states called

|0 〉

and

|1〉

. Qubits can be in principle realized by any

two-level quantum system; for example, the horizontal or vertical polarization of a photon or

the up and down states of an electronic spin. The general state of a qubit is

01||〉〉

, a

and

being complex numbers. In contrast with the classical bit, the general state of a qubit is not

either 0 or 1, but a superposition of the two. This superposition property provides quantum com-

putation with natural parallelism and it allows the possibility of processing exponentially more

information than a classical computer of corresponding size. One qubit, as a superposition of

two states, is represented by 2

complex numbers ( a

and a

). A general two-qubit state is writ-

ten

aaaa

1234

00 01 10 11||||〉〉〉〉

; it is a superposition of 2

states, and is represented by 2

numbers. It is straightforward to extend this argument to N qubits: a general state is represented

CHAPTER 23

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688 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics

by 2

numbers and by careful design of algorithms and careful control of the system’s quantum

dynamics, operations can be performed on each of these numbers. This property is known as

quantum parallelism and provides a quantum computer with a signiﬁ cant advantage over its clas-

sical counterpart in certain situations.

23.1.1 Basic requirements for implementing quantum computation

A quantum computer is a physical system in which we can identify one or more collections of

well-deﬁ ned qubits. We refer to each of these collections as a quantum register. As an example,

an array of well-deﬁ ned self-assembled quantum dots (QDs), as depicted in Fig. 23.1 , is a poten-

tial quantum register. In order to perform actual computation, we must be able to address the

qubits in the quantum register and perform speciﬁ c logic gates. In analogy to classical computa-

tion, to perform universal quantum computation we must be able to drive a minimum, universal,

set of logic gates. A typical choice is composed of the set of all possible single-qubit gates and one

non-trivial (or entangling) two-qubit gate, e.g. a controlled-NOT (CNOT) or a controlled-PHASE

(CPHASE) gate. These are quantum gates which modify, in a controlled way, the state of one or

more two-level systems.

Figure 23.1 AFM image of a 2D regular array of InAs/GaAs self-assembled QDs. (From [11] , Fig. 12b , courtesy

of Oliver G. Schmidt and with kind permission of Springer Science and Business media.)

Single-qubit gates are represented by the set of unitary operators

which perform an arbi-

trary operation on the general single-qubit state Ψ ab||01〉〉

. They can be decomposed into

the 2  2 Pauli matrices { σ

, σ

} . Two-qubit gates are represented by speciﬁ c unitary

4  4 matrices, and examples will be given later in the chapter. Each quantum algorithm corre-

sponds to a well-deﬁ ned sequence of quantum gates. Finally, the results of the quantum com-

putation must be read out, i.e. a measuring apparatus must be connected to the quantum system

and must extract information from it. The readout may be performed in different ways, depend-

ing on the properties of the hardware and implementation scheme chosen. For example, a Stern–

Gerlach-type device may be used for deﬂ ecting spin-based qubits [2] or quantum point contacts

[3] may detect the variation of current due to the spatial displacement of charge qubits [4, 5] .

The readout can be performed on the entire qubit register or on only selected qubits, depending

on the overall computer architecture and available resources.

A general quantum computation scheme may be summarized as follows: (i) preparation of the

initial state (input), (ii) controlled quantum evolution of the system according to the sequence of

gates forming the quantum algorithm (actual quantum computation), and (iii) measurement of

the ﬁ nal state (readout).

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