The way to QDIP

The way to QDIP

Report (2)

Outline

1. Photodetectors

2. Infrared Photodetectors

3. QDIP

1. Photodetectors

1.1 Definition

It is an essential component of any optical communication system

where optical signal into an electrical signal to be subsequently by the

receiver electronics.

Figure 1.1: Front end photoreceiver

1.2 Main performance criteria for good photodetectors

1) High sensitivity at the operating wavelength.

2) High fidelity.

3) Large optical to electrical conversion efficiency.

4) Fast response.

5) Large SNR at the output.

6) High reliability.

7) Stability

8) Compatibility.

1.3 Parameters of photodetectors

1.3.1 Quantum efficiency

The quantum efficiency is a measure of how many electron-hole pairs

are created and then collected by the contacts to the external circuit per

incident photon.

1.3.2 Responsivity

An alternative figure-of-merit that may be used is responsivity (ℜ)

that is defined as the ratio of the primary photocurrent (without internal

gain) Iopt to the incident optical power Pi and ℜ is related to η as follows

1.3.3 Bandwidth

The bandwidth is known as the “3-dB frequency” of a photodetector,

is a measure of how fast the photodetector can respond to a series of

light pulses.

1.3.4 Gain

The gain of the photodetector is defined as the ratio of the number of

collected e-h pairs to the number of primary photogenerated pairs and it

expresses the photodetector sensitivity at the operating wavelength.

1.3.5 Noise

Noise is defined as the fluctuations of the electrical signal. Sources of

the noise are in the dark current, leakage currents and shunt

conductance and they must be minimized.

1.4 Conventional photodetectors

Conventional photodetectors can be classified into two classes

A) PD’s without internal gain

1. PN photodiode. 2. PIN PD.

3. Schottky barrier PD. 4. metal-semiconductor-metal PD.

B) PD’s with internal gain

1. Photoconductors. 2. Phototransistors.

3. Avalanche PD (APDs).

1.4.1 PD’s without internal gain

1.4.1.1 PN photodiode

A P-N photodiode is simply a P-N junction diode operating under a reverse

bias as shown in figure 1.2(a). The incident photons may be absorbed in both of the

depletion and the diffusion regions, where the number of the generated electron-

hole (e-h) pairs is proportional to the optical power.

1.4.1.2 PIN PD

The basic PIN-PD consists of three regions, heavily doped P+ and N+ layers and

an intrinsic layer that is sandwiched between them. This intrinsic layer may have a

small residual n or p type background carrier concentration. The photon absorption

takes place mainly in the intrinsic region that is depleted when reverse bias voltage

is applied to its terminals. The collection process for the generated carriers is

therefore fast and efficient.

Figure 1.2: (a) PN photodiode (b) PIN PD

1.4.1.3 Schottky barrier PD

Schottky barrier photodiodes are made of metal-semiconductor-metal

rectifying junctions rather than PN semiconductor junctions. Schottky

photodiodes have narrow active layers compared to PIN-PD and hence the transit

time of Schottky photodetectors is very small, resulting in a very high bandwidth.

But this narrow active layer also results in poor quantum efficiency.

Figure 1.3: schottky barrier PD

1.4.1.4 Metal-Semiconductor-Metal PD

A basic MSM-PD uses a layer of semiconductor material that is sensitive to

the wavelength of interest. On the top of this layer, the metal electrodes are

deposited as interdigitated fingers to form back-to-back Schottky diodes with

a suitable anti-reflection coating between them. Each set of electrodes forms a

Schottky barrier contact with the semiconductor, and is connected to a large

pad for connection to the external circuit.

Figure 1.4: MSM PD

1.4.2 PD’s with internal gain

1.4.2.1 Photoconductors

An absorptive semiconductor layer together with two electrical terminals.

Under illumination, the electrical conductivity increases because of the photo

generated carriers. The internal gain mechanism arises from the space charge

neutrality.

1.4.2.2 Phototransistors

It is similar to a bipolar transistor, but with only two terminals with electrical

contacts to the collector and the emitter. The base and the base-collector junction

are used as the absorption layer. The photogenerated holes in the absorption region

accumulate in the base. This excessive charge results in electrons injected from the

emitter and the current gain mechanism is the same as in a BJT.

Figure 1.5: (a) photoconductor (b) phototransistor

1.4.2.3 Avalanche PD (APDs)

The avalanche photodetectors (APDs) are the most important photodetectors

with internal gain that have been widely used in optical communication systems.

The APD’s internal gain is realized by the avalanche multiplication process that is

achieved through impact ionization. APDs are operated under a sufficiently high

reverse voltage to generate highly energized e-h pairs. Under a high electric field in

the conduction band, the high energy electrons initially scatters with an electron in

the valence band and knocks it out into the conduction band, resulting in

multiplication of the number of electrons in the conduction band.

Figure 1.6: APD

2. Infrared radiations systems

2.1 Infrared radiation

Infrared radiation is simply a region of the electromagnetic spectrum. It

differs only in wavelength or frequency from other well-known regions of the

electromagnetic spectrum such as visible, ultraviolet, or microwave

radiation. The IR portion of the electromagnetic spectrum extends in

wavelength above that detectable by the human eye (~700 nm) to 1 mm. The

electromagnetic spectrum, with an expanded view of the infrared region, is

shown in Figure 2.1.

Figure 2.1 : EM spectrum

The infrared portion of the electromagnetic spectrum was discovered by

English astronomer Sir William Herschel in 18003 by using a thermometer

to measure the temperature difference between areas of light separated by a

prism.

Later it was discovered experimentally, that every object emits radiation

with a range of wavelengths that depend on the temperature of the object. A

blackbody radiation versus temperature plot is shown in Figure 2.2. It is the

relationship between temperature and the distribution of emission

wavelength that was first accurately described empirically by Planck in 1900.

The consequence of Planck’s Law was that energy is not continuous, but

rather has discrete values or quanta. This initiated the development of

quantum physics.

Today, it is understood that every object emits radiation proportional to its

temperature because of atomic oscillations. Most simply, the hotter the

object, the faster the frequency of the atoms oscillations and therefore the

higher the frequency of radiation emitted by the object.

Figure 2.2: blackbody radiation versus temperature

2.2 Applications of Infrared Systems

Referring back to Figure 2.2, it is apparent that all but the hottest objects

have peak emission wavelengths in the infrared. This is one reason infrared

lasers and detectors have countless numbers of applications. Applications

using infrared lasers and detectors can be classified into three groups of users

having different requirements: industrial, military, and medical. A number of

these applications are described in detail to provide background for the

operating characteristics required by each application. The heat signature of

the fighter planes and missiles has made the infrared seeker one of the best

choices for the target detection systems. Several new military applications are

using coupled infrared detectors and emitters. One Example of such systems

is smart bombs, which follow the infrared reflection of the target illuminated

by an infrared laser tracking system.

Another example is the infrared active countermeasure systems, using an

infrared laser beam to jam the seeker of a missile by actively reading its

chopper signal and tuning the jamming laser beam to the chopper pattern.

Both of these applications take advantage of the two infrared atmospheric

transmission windows: between 3-5 μm and 8-12 μm. In the atmospheric

transmission windows, infrared light can propagate with very little

attenuation, thereby requiring only a small amount of power to travel a long

distance.

Infrared thermal imaging has found many industrial applications especially in

nondestructive testing and inspection techniques8. Fast and easy detection of

hidden cracks and nonuniformity is one of the examples of this technique

which is based on the change of thermal resistance of the fractured area. This

technique has been successfully used for the detection of hidden cracks under

the airport runways and detection of knots in the wood industry. Infrared

spectroscopy is also widely used in many industries for continuous monitoring

of chemical quality and process control.

Infrared detectors have also found many medical applications, based on the

facts that many kinds of malfunctions and abnormal situations can change the

blood flow pattern in the tissues which leads to a change in their temperature

characteristics. Therefore, thermal imaging has provided a relatively reliable

and safe method for early diagnosis of breast cancer, dental and thyroid

diseases.

Several new noninvasive techniques have been developed in recent years due

to the rapid improvement of the infrared detectors and emitters. Non-invasive

measurement of the oxygen level in the organs during surgery and blood sugar

monitoring1are examples of these recently available methods, which are based

on the infrared spectroscopy techniques.

Besides these applications, the low absorption rate in the atmospheric 3-5μm

and 8-12μm windows makes the infrared detectors an attractive choice for

many other applications such as range finding , remote sensing, and free space

communication.

2.3 Types of Semiconductor Infrared Photodetectors

Infrared semiconductor Photodetectors can be divided into four categories:

intrinsic interband, extrinsic, type-II, and intrinsic intersubband. This is

shown with material system used in Table 2.1.

MWIR and LWIR Semiconductor photodetectors

Intrinsic

Interband

Extrinsic Type-II

QWIP QDIP

IV-Vi

(PbSnTe)

Si:In

Ge:Cu

GaSb/AlSb/InAs In(Ga)As/GaAs

or

In(Ga)As/GaInP/InP

In(Ga)As/GaAs

or

In(Ga)As/InP II-VI

(HgCdTe)

III-V (Sb-

based)

2.3.1 Intrinsic Interband

The optical absorption in this type of photodetector leads to an interband

transition in which the electrons of the valance band of a semiconductor are

excited to the conduction band. The required energy for such transition is

higher than the bandgap of the semiconductor. Therefore, narrow gap

semiconductors are of particular interest for infrared detection since the

longest wavelength that the material can absorb is inversely proportional to its

bandgap. The optically generated electron-hole pairs can make an electrical

signal if one applies an electrical field to sweep them to the electrodes of the

device. Based on the origin of this electrical field, there are two types of

intrinsic photodetectors: photoconductors and photodiodes. In the first type,

the voltage bias of a thin layer of the narrow gap semiconductor can attract

the excess electrons to the positive contact and the excess holes to the negative

contact. In a photodiode, however, there is an internal electrical field that

sweeps the generated electrons and holes to the electrodes.

The internal electrical field is due to the space-charge area of a p-n or p-i-n

structure. Narrow gap semiconductors are the key material system for

intrinsic photodetectors. Compound semiconductors are of particular interest

due to their direct gap and IV-VI, II-VI, and III-V compound semiconductors

are the commonly used material for infrared systems.

2.3.1.1 Intrinsic IV-VI

The lead-chalcogenide materials (PbS, PbSe, PbTe) were one of the first used

materials for infrared detectors. In the mid- 1960s it was discovered at Lincoln

Laboratories that PbTe and SnTe and also PbSe and SnSe form solid solutions

in which the energy gap varies continuously through zero, so that it is possible,

by selecting the appropriate composition, to obtain any required small energy

gap. The detectors made of these IV-VI material system show high quantum

efficiency and detectivities of mid 1010

cm Hz 1/2

/W at 77K at 10 μm.

However, due to their lower thermal expansion coefficient and permittivity, II-

VI Mercury Cadmium Telluride (MCT) rapidly replaced the IV-VI material

system.

2.3.1.2 Intrinsic II-VI

HgCdTe or MCT is perhaps the most developed material for infrared

detectors. In 1959 Lawson et al. reported that the alloy system Hg1-xCdxTe

exhibited semiconductor behavior over a large range of its composition. In less

than ten years the intensive research on this material system led to high

quality HgCdTe detectors in the entire short, mid, and long wavelength

infrared range. However, even today the low uniformity and yields of about

10% are drawbacks of this technology. The usual growth method for single

crystal MCT is a modified Bridgman technique

However, the epitaxial growth techniques such as Liquid Phase Epitaxy

(LPE), Metal organic Chemical Vapor Deposition (MOCVD) , and Molecular

Beam Epitaxy (MBE) have provided crystals with lower native defects, higher

uniformity, and abrupt heterojunction interfaces for HgCdTe heterojunction

devices.

Specific examples of 0.1eV lightly doped n-type Hg1-xCdxTe detectors have

been developed intensively because of its application in the 8-12mm region.

Device performance has approached the theoretical limits. The devices were

fabricated from bulk Hg0.795Cd0.205 Tewith n=2-5×10 14

cm -3

which is

passivated with native oxide and coated with a ZnS anti -reflection coating

layer. The 77K detectivity reaches a value of about 10 12

cm Hz 1/ 2/W at about

10 μm, which is close to the theoretical background limited performance

(BLIP). At present, commercially available 3-5mm photoconductors also

exhibit BLIP performance.

Near-BLIP performance can also be achieved at elevated temperatures, up to

about 200K. Recently new multi-heterojunction photovoltaic HgCdTe has

been designed for near room temperature operation. The device shows a

considerably higher detectivity than the detectivity of conventional HgCdTe

detectors at 10.6 μm at 230 K. Unfortunately, the high 1/f noise of this

structure, reported by Ashley et. al, prevents its application for imaging

systems.

2.3.1.3 Intrinsic III-V

III-V compound semiconductors are the most widely used compound

semiconductors due to their lower permittivity and higher mechanical

hardness over IV-VI and II-VI material systems. The narrowest gap III-V

binary is InSb whose semiconducting properties were first revealed by H.

Welker in 1952. InSb arrays are the main competitor of HgCdTe for imaging

systems below 5mm since it can provide higher uniformity and mechanical

strength than HgCdTe. Currently very high quality Focal Plane Arrays

(FPAs) of InSb with 1024x1024 resolution are available.

Although InSb FPAs are highly developed, there is a new trend in InSb

photodetector and FPA research. InSb films are directly grown on GaAs or

GaAs-coated Si substrates. Such structures would take advantage of both the

high quantum efficiency of narrow-gap semiconductors and advanced

integrated circuit technologies thus providing a challenge for traditional

hybrid technologies. High performance InSb infrared photodetectors on Si

and GaAs substrates have been demonstrated that can operate from 77 K to

room temperature.

Due to the bandgap bowing, even narrower bandgap can be achieved with the

ternary InAsxSb1-x. The minimum bandgap is about 0.1 ev at room

temperature which corresponds to 35% arsenic. High performance uncooled

detectors have been demonstrated using AlInSb/InAsSb double

heterostructures. The detectivity of these detectors are about 10 8

cm Hz1/2

/W at 8 µm without any optical immersion or anti-reflection coating

2.3.2 Extrinsic

The optical absorption in this type of photon detector leads to the excitation of

an electron from a n-type impurity level to the conduction band (or excitation

of a hole from a p-type impurity level to the valance band). The longest

detectable wavelength for this type of detector is inversely proportional to the

activation energy of the impurity. In this phenomenon, which has been known

for more than 40 years, the excitation of the electron to the conduction band

(or the hole to the valance band) leads to a higher free carrier concentration

and hence higher conductivity. Therefore, this type of detector is similar to an

intrinsic photoconductor and needs an external bias source.

In order to prevent the thermal ionization of the impurities, the detector

should be operated at very low temperatures. The operating temperature is

proportional to the activation energy of the impurity or inversely proportional

to the optimum wavelength of the detector. This value is about 5K for an

arsenic doped silicon (Si:As) detector with 25mm optimum wavelength.

Extrinsic photovoltaic detectors have also been achieved using an impurity

band. The device which is commonly known as Blocked Impurity Band (BIB)

detector has a highly doped section which leads to the formation of an energy

band. The band is blocked from one side with a low doping section, so the

optically generated holes in the impurity band cannot diffuse to the negative

contact. Such hole buildup at the positive contact leads to the photovoltaic

effect, and the device can operate at zero bias mode.

2.3.3 Type-II

Type-II structures allow the electronic band structure to be engineered by

simply changing the thickness or composition of the constituent layers.

Therefore, the Auger recombination rate and other losses can be reduced thus

reducing the threshold current density and increasing the maximum operation

temperature. The detecting wavelength of type-II detectors can be adjusted to

a wide range, by simply changing the thickness of the layers.

Type-II detectors also have advantages of excellent carrier confinement,

suppression of Auger loss, and large gain. The disadvantages of these detectors

are inherent in the structure. First is the complexity of the structure. Each

layer in the superlattice is around tens of Anstrong thick and so the active

region usually consists of approximately hundreds of layers. Efficient

manufacturing and maintaining tolerances and uniformities on the order of

the superlattice layer thickness has yet to be proven. Additionally, the electron

and hole wave functions do not overlap spatially and therefore the radiative

recombination efficiency is reduced.

2.3.4 Intersubband

Although the benefits of low dimension semiconductor nanostructures such as

quantum wells, quantum wires and quantum dots were predicted decades ago,

they were only realized after the advancement of epitaxial growth techniques

such as MBE and MOCVD. Many different detectors have been designed and

realized based on these nanostructures, however two of the most commonly

used structures are Quantum Well Infrared Photodetectors (QWIP) and

Quantum Dot Infrared Photodetectors (QDIP).

The overall principle of operation of QWIP is explained here. The operation

of QDIP is very similar to QWIP, however with much better predicted

characteristics and performance.Quantum well infrared photodetectors are

based on intersubband absorption by confined carriers in multiple quantum

wells. The process is very similar to an extrinsic photoconductor, except that

the electrons are excited from a confined energy state rather than an impurity

level.

An extension of QWIPs is the quantum dot infrared photodetector (QDIP)

which utilize intersubband absorption between bound states in the

conduction/valence band in quantum dots. Given high uniformity and high

density quantum dot layer, QDIPs are predicted to outperform QWIPs due to

their inherent sensitivity to normal incidence radiation and reduced phonon

scattering. Higher temperature operation and lower dark current are also

expected for this type of device. So far, most of QDIPs reported showed

inferior performance than that of QWIPs with similar parameters. The major

challenges facing QDIPs are quantum dots growth. To justify its potential

advantages, QDIPs need high uniform and high density quantum dots layers.

New device designs for QDIPs are also required to further improve its

performance as an infrared photodetector.

Figure 2.3: principle of QWIP operation

Finally, we sum up by comparison of current infrared photodetector technology given in

Table 2.2

Advantages Disadvantages

QWIP • Mature III-V growth technology.

• Wide-bandgap material is better for

radiation hard application.

• Excellent array uniformity.

• high R0A allows long integration

Time.

• VLWIR demonstrated using standard

QWIP technology, no unique steps.

• Multi-color arrays demonstrated.

• Lower quantum efficiency.

• Requires lower sensor

temperature than intrinsic

detector for λ<12 μm.

• Normal incidence detection

requires light coupling

scheme like grating.

HgCdTe

(MCT)

• Excellent quantum efficiency

• Very high detectivity

• Bandgap can be adjusted to vary

detection wavelength

• Multi-color arrays demonstrated

• Poor array operability and

uniformity

• Radiation-hard arrays are

difficult due to narrow

bandgap and defects

in material

• Low yield and high cost for

large area arrays

• Reproducibility is poor due

to sensitivity of bandgap to

material

InAs/GaSb

type II

superlattice

• Wide wavelength coverage (2~50 μm)

• Reduced Auger recombination rate

for higher operation temperature

• High detectivity

• Normal incidence absorption

• Single color imaging array

demonstrated

• Difficult material growth

technique

• Complex device structure

• Difficulty with device

passivation

QDIP • Normal incidence absorption

• High responsivity

• High temperature operation

• Lower dark current

• Multi-color detection capability

• Difficult to control

quantum dot formation

• difficult to achieve high

uniform dot and high

density

• low quantum efficiency

3. QDIP

3.1 QDIP parameters

3.1.1 Dark current

The dark current is one of the most important aspects regarding performance

optimization of QDIP device because it contributes to the detector noise and dictates the

operating temperature. It refers to the current flow through a QDIP under no

illumination. The dark current of a QDIP has been discussed in the literature and can

be expressed:

⟨ ⟩ (

⟨ ⟩)

⟨ ⟩

√ √

√ √ Where

where jm is the maximum current density which can be extracted from the emitter

contact, ε is the dielectric constant of QD, kB is the Boltzmann constant, T is the

temperature, ΣQD is the density of QD, ΣD is the doping density of each QD layer, NQD

is the maximum number of electrons which can occupy each QD, L is the width of QD

layer, K is the total number of QD layers inside a QDIP, V is the bias voltage,< N> is

the average number of electron belonging to each QD layer. This dark current formula

is derived by assuming not too low bias voltage so that eV is larger than ionization

energy of the ground state in QDs.

In dark conditions, the main mechanism of the electron escape from QDs is related with

their thermoemission and the transport of electrons across the QDIP active region is

due to their drift. The dark current of realistic QDIP increases exponentially with

increasing of applied bias as well as with increasing of doping level. The above dark

current equation can also explain why the dark current of most real QDIP is fairly

high, exceeding that in QWIPs with comparable parameters.

3.1.2 Photo current

Similarly as the dark current, the photocurrent density of QDIP can be

expressed as

All parameters in this equation have the same definition as in dark current

equation. From photocurrent density equation, it can be seen that higher QD

densities give larger photocurrent.

The ratio of photocurrent to dark current can be written as:

(⟨

⟩

⟨

⟩)

⁄

√

Where A is a constant. Parameter B can be treated as the electron density

induced in QDs by the applied bias. aQD is the lateral characteristic size of one QD.

From calculation of the ratio as a function of QD density Σ QD of QDIPs with

different doping level, it can be seen that QDIPs with lower QD density exhibit

significantly inferior performance as a photodetector.

3.1.3 Absolute absorption spectrum

For QDIPs made with self-assembly technique, the absorption spectra can be

modeled with a Gaussian line shape and is express as:

(

)

where A is the maximum absorption coefficient obtained from calculations

presented in the literature, n1 is the density of electrons in the QD ground state, EG

is the energy difference between ground and excited states in the QDs. σ QD and σ ens

are standard deviations in the Gaussian line shape for intersubband absorption in a

single QD and for the distribution in energies for the quantum dot ensemble,

respectively. The ratio of σ ens / σ QD represents the size non-uniformity of QDs.

From calculations, it is shown that larger absorption coefficient comparable to a

quantum well with similar peak can be achieved for a perfectly uniform QD

ensemble. For QDs with non-uniform sizes (larger ratio σ ens / σ QD), same absorption

coefficient is reached with much higher QD density. It’s clear that control over QD

size uniformity is necessary to provide acceptable absorption.

3.1.4 Responsivity

The current responsivity of an intersubband detector can be expressed as:

Where

where g is the gain of the device, η is the quantum efficiency, hv is the energy of

incident photons, τrecapture and τtransit are the recapture and transit time of the

carriers in the conduction band. Carrier transit time can be simply estimated of

transportation from emitter to collector of device as:

Where l is the distance from emitter to collector, V is the bias, and μ is the carrier

mobility.

τrecapture is determined by the quantum mechanical scattering process, which is

usually summarized in terms of Fermi’s Golden Rule: if any electron (hole) in a

state i of energy Ei experiences a time-dependent perturbation ̃ which could

scatter (transfer) it into any one of the final states f of energy Ef, then the lifetime

(recapture time) of the carrier in state i is given

∑|⟨ | ̃| ⟩|

The peak responsivity is a more common parameter used to compare detectors of

different wavelength. Peak responsivity assumes the detector only receive light in

only the wavelength where it is most sensitive. The peak responsivity of QDIP is

usually measured with a blackbody source and is given by:

(

)

k is given by:

∫

Where IPhoto is measured QDIP current, Ad is the detector area, DA is the blackbody

aperture diameter, and r is the distance between aperture and the QDIP, σ is the

Stefan-Boltzmann constant, and TBB is the temperature of blackbody. The k is the

correction factor due to the overlap of the relative spectral responsivity of the QDIP

S(λ) and the blackbody spectra M (TBB, λ).

3.1.5 Noise

There are several sources of noise in a QDIP detector: the 1/f noise, Johnson noise,

dark current noise, and photon noise. The physical mechanism of 1/f is still not fully

understood and it is related to the contact quality. For QDIP with good Ohmic

contact, 1/f noise is not a limiting factor of detector performance. Johnson noise

(thermal noise) is due to the random motion of thermally excited carriers and is

inherent to all conducting material; the noise mean square current can be expressed

as:

Where Δf is the bandwidth and Rd is the device differential resistance. The

contribution of Johnson noise is usually small in a QDIP device. The QDIP device

ultimate performance is often limited by its dark current noise and photon noise.

The dark current noise is generation-recombination (G-R) in nature. The noise

current should be expressed by the standard G-R noise form

Where gnoise is the noise gain and Idark is the device dark current.

The photon noise in a QDIP is related to the background radiation because it is

caused by the fluctuation in the number of background photons absorbed by QDIP

(ηΦ). Photon noise is given by:

where g is the photoconductive gain. In a conventional photoconductor, the noise

gain equals the photoconductive gain, at least as a very good approximation for the

practical purpose.

The total noise of a QDIP is

√

For a given QWIP and application, the background photon flux is often fixed.

The background limited infrared performance (BLIP) is defined as the regime

where the dominant noise source is due to the background photon fluctuations

(larger than dark current noise). The BLIP temperature (TBLIP) is the temperature

at which in,dark=i n,B.

3.1.6 Specific detectivity

The specific detectivity (now normally just called detectivity) is defined as:

√

Where A is the detector area, R is the responsivity, Δf is the bandwidth, and in is

the noise current.

3.2 Improvements of Characteristics in QDIP

3.2.1 High temperature operation

Most of the expected improvement in QDIP device performance originates from the

change in the density of states. For example, under the low carrier density limit

condition where electrons obey Boltzmann’s distribution, the energy distribution of

electrons in bulk, QW and QD are show in Figure 3.2. In the bulk structure, as the

density of states is proportional to the square root of electron energy, the energy

distribution of electron has a width of about 1.8 kT. In QWs, where electrons are the

density of states is like a staircase, at the band edge the density of states becomes

constant and independent of energy. The energy distribution of electrons becomes 0.7

kT, which is less than half that in the bulk structure. This reduction enables a

concentration of electrons into a narrower energy distribution. However, it should be

noted that as the energy distribution width is linearly proportional to the ambient

temperature, basic device performance is fundamentally dependent on temperature.

In QDs, the width of the electron energy distribution is zero in an ideal case. This

means that electrons in those structures are distributed in certain discrete energy

levels and the energy distribution width is fundamentally independent of

temperature. In real semiconductor structures, due to many interaction processes

such as electron-electron and electron-phonon scattering (which can also be reduced

by QDs, as will explained later), certain width in the electron energy distribution

exists. However are expected much smaller compared to bulk (1.8 kT) and QW (0.7

kT).

3.2.2 High responsivity

Since the phonons themselves inside crystal represent the motion of atoms which are

centers of electric charges, they also represent time-dependent perturbations of the

crystal potential and can therefore scatter charge carriers. For most practical

quantum dot applications, the majority of interest lies with the heterostructure made

from compound semiconductors, such as InAs/GaAs, InGaAs/InGaP, etc. These

materials are polar as the different electronegativities of the constituent atoms lead to

a degree of ionicity in the chemical bonds. In such materials, the dominant electron-

phonon interaction (scattering) is with the longitudinal optic photons, often referred

to as the LO phonon. For a given band a given number of electron-hole pairs in their

ground states, the maximum optical gain increases with decreasing dimensionality

due to the concentration of the oscillator strength in energy. In first order, such a k-

matched pair has the same strength, whatever the dimensionality, but occupied states

usually cover a range of some kBT, distributing the total oscillator strength according

to the density of states. Quantized degrees of freedom allow k matching of the electron

and hole states in the 1, 2, or 3 directions for quantum wells, wires, or boxes,

respectively, and increasingly concentrate the oscillator strength in a narrow line.

However, carriers first have to cascade down to the ground state through k-

unmatched excited states. If denote n, m, l as the standard (z, y, x) quantum numbers

of a quantum-well, -wire, or –box system in the infinite-square-well approximation.

Then, the usual Δk=0 selection rule of optical transitions become Δn,m,l=0. In typical 3D

and 2D systems, electrons “meet” holes both in real and k space. Elastic collisions

very quickly randomize k directions. Energy is lost first through LO phonon emission

and next through acoustic phonons still in the sub nanosecond range due to the 2D

continuum of final states.

Down to 0D, relaxation rates vanish, chiefly due to the scarcity of final states

satisfying both energy and momentum conservation. It is even more so for extreme

quantization (~15 nm) when the average energy level spacing exceeds the energy of

LO phonons. The reduced electron-LO phonon interaction results in much longer

carrier recapture time inside quantum dot energy states than that in quantum well

(This phenomenon is called “phonon bottleneck”). The predicted carrier capture time

is in the nanosecond range. 32 Measurements have shown that carrier recapture time

in quantum dot lasers are significantly longer than those measured for quantum

wells. The enhancement of carrier recapture lifetime leads to a dramatic increase in

responsivity for quantum dot (QD) devices.

3.2.3 Normal incidence detection

Since the wavelength of light corresponding the energy of single-particle

excitations of a quantum dot is much larger than the dot size (<1 μm), the

oscillations of the electromagnetic field induced by this radiation are almost

homogeneous over the area of the quantum dot.

Therefore, the interaction between the electron and electromagnetic wave can be

written in the dipole approximation and the oscillator strength is given by:

|⟨ | ⃗ ⃗| ⟩|

where F1 and F2 are the electron envelope functions, ⃗⃗ is the polarization vector

for the incident infrared light, ⃗⃗⃗⃗ the momentum operator. In the case of

quantum well, if we assume the quantum well growth direction is along the z-

axis, then the envelope functions should depend on z only, with F1=F1(z) and

F2=F2(z). It is seen readily that for normal incidence of infrared radiation, for

which ε=(εx,εy,0), results in zero absorption. For quantum dots,

however,F1=F1(x,y,z) and F2=F2(x,y,z), it’s obvious that the normal incident

light results in non-zero absorption. Normal incident light absorption is one of

major advantages of QDIPs compared

with QWIPs.

In order to have a meaningful absorption length, a QDIP structure usually requires

multilayer QDs. Like in QWIP, it’s desirable to have a large number of high density

QD layers to allow maximum photon interaction. However, since the QDs in QDIP

are mostly grown by self-assembly method, high strain builds up with the increase

of number of the QD layers. This strain sets a limit of the number of QD layers,

beyond which a high density of structural defects will occur. This limit may be lifted

or even totally removed by techniques such as strain balance.

Two types of devices structures can be used for QDIPs, depending on the transport

direction of the photo current. One is the conventional vertical transport scheme, in

which the photocurrent moves along the growth direction. The other is the lateral

transport scheme, in which the photocurrent moves parallel to the growth planes.

Both structures allow normal incidence detection. In the lateral devices,

photocurrent moves through a high-mobility channel, either the QD wetting layers

or the QW layers in the dot-in-well structure. Lateral transport QDIPs with a

modulation-doped heterostructure have demonstrated lower dark current and

operation near room temperature as a result of the fact that primary components of

the dark current originate from interdot tunneling and hopping conduction.

However, the vertical transport structure is compatible with the focal plane arrays

architecture. For this reason, most of the research to date has been on the vertical

transport QDIPs.