FOREIGN MATTER REDUCTION IN HIGH DENSITY PLASMA CHEMICAL VAPOR DEPOSITION PROCESS

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International Journal of Semiconductor Science & Technology (IJSST) ISSN(P): 2250-1576; ISSN(E): 2278-9405 Vol. 4, Issue 2, Dec 2014, 1-12 © TJPRC Pvt. Ltd.

NOISE MODELING CIRCUIT OF QUANTUM STRUCTURE

TYPE OF INFRARED PHOTODETECTORS

MOHAMED B. EL_MASHADE & M. EL_HANASH

Department of Electrical Engineering, Faculty of Engineering, Al Azhar University, Nasr City, Cairo, Egypt

ABSTRACT

Noise is a general property of electrical conductors where it introduces random fluctuations in their currents.

Studies of these fluctuations are of great interest because they give information about the charge carriers in the system and

their mutual interactions.

Quantum well infrared photodetectors QWIPs are very successful devices. They have been developed very

quickly and demonstrated large format focal plane arrays with low noise equivalent irradiance, high uniformity, and high

operability. Therefore, it is of interest to model its noise behavior under different operating conditions to show to what

extent the noise can affect the operation of that attractive device. Our scope in this paper is to derive the noise modeling

circuit of QWIP. As a tool for this achievement, it is intuitive to calculate all different current's components, which include

dark current, photocurrent, thermal noise current and shot noise currents (generation-recombination noise). Finally,

we represent all these noise currents in a simplified electrical circuit to become a one of its basic characteristics.

KEYWORDS: QWIP Detectors, Dark Current, Photocurrent, Thermal Noise Current, Photo Shot Noise Current and

Dark Shot Noise Current

INTRODUCTION

The technology of band gap engineering has led to significant advances in the development of new infrared

photodetectors. In a bulk type of semiconductor materials, electrons are free to move in any of the three spatial directions.

A confining structure may be made by embedding a limited region of one material within another. The difference between

allowed electronic states for the two materials forms a barrier to free electron movement. If any dimension of the structure

approaches the wavelength of an electron, quantum effects will arise. Quantum structures of semiconductor materials have

the property of confining the mobility of electrons. Each one of the three dimensions of the bulk material may be thinned

conceptually to yield the three classes of quantum structures. Making the structure thin along only one axis results in a two

dimensions layer called a quantum well. If thinned along any two of three axes, a one dimension quantum wire is

produced. Thinning along the final axis leads to a zero dimension structure known as quantum dot.

The design of quantum well devices was originated from the suggestion that a hetero structure consisting of

alternating ultrathin layers of two semiconductors with different band gaps should exhibit some novel useful properties

[1, 2]. The band-edge potential varies from layer to layer as a result of the difference in the band gaps and a periodically

varying potential is produced in the structure with a period equal to the sum of the widths of two consecutive layers [3].

This is because of the importance of the developed device in achieving novel characteristics in the fields of optical

communications, thermal imaging and sensor networking, etc. Recently infrared photo detectors have been the focus of

2 Mohamed B. El_Mashade & M. El_Hanash

Impact Factor (JCC): 3.8869 Index Copernicus Value (ICV): 3.0

much attention due to their potential use in far-infrared imaging as well as room temperature operation, which is of interest

from user’s point of view.

Quantum Well Infrared (IR) Photo detectors (QWIP) have been developed very quickly and demonstrated large

format focal plane arrays with low noise equivalent irradiance, high uniformity, and high operability. Through the using of

high quality GaAs material systems, QWIPs have the potential for high production with low cost and low power

consumption. On the other hand, Infrared focal plane array (IRFPA) technology is very important to ballistic missile

defense (BMD) and space-based applications, as well as other military and commercial applications. These arrays are

widely used in tactical applications for surveillance, target detection, target tracking, and discrimination. On the other

hand, important FPA characteristics for future BMD FPAs will include large format, high sensitivity, low l/f noise, good

uniformity, and high operability [4]. Such applications require accurate measurement and subtraction of background

irradiance to detect the target’s signal. Although QWIPs have lower sensitivity than mercury cadmium telluride FPAs at

MWIR and LWIR wavelengths, its performance at low temperature and VLWIR makes it especially attractive for IR space

systems. In addition, multicolor capabilities are highly desirable for advance IR sensor systems. FPA stability,

reproducibility, cost, maintenance, and manufacturability are also very important issues. From this point of view, superior

multicolor capability has been demonstrated in QWIP manufacture.

With the increasing demand for new optical application of QWIPs at a wide variety of wavelength from mid to far

infrared, the need for low noise structure becomes an urgent necessity. The absorption of long wavelength light in QW is

due to transition from a quasi bound state to the continuum in a narrow well or intersubband transition in a wide well [5].

QWIPs exhibit very fast operation. Their intrinsic high speed is considered as one of the advantages of the QWIPs over

standard detectors made of narrow-gap semiconductors. Because of the performance of QWIP is enhanced when number

of the wells is increased, so a multiple QWIP structure is preferred. A multiple-quantum-well (MQW) structure with only

one bound state in each well is found to be optimum in detecting infrared radiation [6, 7].

The figure of merit used to evaluate the performance of most QWIPs is the specific detectivity which is a measure

of the signal-to-noise ratio (SNR). In calculating such important characteristic at a certain electrical frequency, the output

noise current at that frequency must be known. Additionally, noise information is required to optimize the operating bias

voltage. From the operation point of view, QWIP is a photoconductive device which means that its conductivity increases

with incident infrared power. Under normal conditions of operation, QWIP photoconductivity increases linearly with

power and this in turn leads to making the responsivity constant. However, the high infrared power, nonlinear

photoconductivity effects can take place giving rise to a decrease of responsivity. This effect is very important in some

practical applications, for example, in heterodyne detection where a weak infrared signal is mixed with a strong infrared

radiation from a laser system.

Here, we present a theoretical calculation of all possible currents that are generated inside QWIP and are induced

by noise. For the dark current case, our calculation can be carried out not only by using the flow of electrons above the

barriers but also by employing the emission and capture of electrons in the wells. Due to the physical structure of the last

method, we will use it in calculating the noise component introduced by the dark current. Photoconductivity phenomena in

solids are well known. From this point of view, the device operation of the photoconductive QWIPs is similar to that of

extrinsic semiconductor detectors [8].The distinct feature of QWIPs in contrast with the conventional intrinsic and extrinsic

photoconductors is the discreteness. This means that incident photons are only absorbed in discrete quantum wells which

Noise Modeling Circuit of Quantum Structure 3 Type of Infrared Photodetectors


are normally much narrower than the inactive barrier regions. We will analyze the photocurrent caused by intersubband

excitations in a QWIP and consider only the case of positive photoconductivity; the effect of which is to have smaller

resistance against the incident of IR light. Negative photoconductivity is possible, if one has a device with a negative

differential resistance region [6].

THEORETICAL BACKGROUND

QWIPs belong to the category of the so-called photon detectors; the absorption of an infrared photon results

directly in some specific quantum event, such as the photoelectric emission of electrons from a surface, or electronic inter

band transitions in semiconductor materials. Therefore, the output of photon detectors is governed by the rate of absorption

of photons and not directly by the photon energy. Photon detectors typically require cooling down to cryogenic

temperatures in order to get rid of excessive dark current, but in return their general performance is high. QWIPs are most

often used as photo-conductive detectors. In this type of detectors photo-generated charge carriers increase the conductivity

of the device material.

The physical structure of QWIPs is the main key of changing or modulating its characteristics such as dark

current, photocurrent, noise currents, responsivity, and detectivity. Our scope in the following sections is to show to what

extent the physical structure can affect the characteristics of dark, photo and noise currents. The theoretical procedure of

calculations of these currents is based on capture and escape probabilities for the electrons. These probabilities are

dependent on capture, transit, escape, and intersubband relaxation time. However, all these parameters vary from one of

QWIP structures to another. In the condition of designing of an optimum QWIP, we must be careful when we choose

QWIP parameters such as doping density in the well, the mole fraction and the barrier width. This is due to the role that

these parameters can play on determination of the capture and escape probabilities. For these reasons, we are going to

evaluate the basic formulas which are very useful in comparing the different structures of QWIP devices.

It is generally assumed that each well in a QWIP can be regarded as a discrete generation-recombination (GR)

noise source. Within this approach, a good agreement between theoretical models and experimental QWIP noise results has

been achieved.

Dark and Photo Currents

A QWIP is a photoconductor. Unlike a photodiode, it does not contain an internal electric field. Thus an external

electric field must be applied across the detector to induce current flow. With the incident optical flux, photoelectrons are

generated in the conduction band. Thus, the conductance of the detector changes with incident flux. Since the detector has

a finite conductance, there will always be a dark current associate with the photocurrent. For effective imaging, the dark

current must be significantly less than the photocurrent.

The dark current in a typical photoconductive QWIP is controlled by the flow of electrons above the barriers, and

by the emission and capture of electrons in the wells [6]. It is the current that flows even without the presence of incident

light. This current is the source of noise that represents the main factor limiting the performance of QWIPs. Figure 1 shows

the dark current paths. In the barrier regions, the current flows in a three-dimensional (3D) fashion, and the current density

is labeled as which equals the dark current density. In the vicinity of each well, the emission of electrons from

the well contributes to the dark current. This current, which tends to lower the electron density in the well, must be



balanced by the trapping or capture of electrons into the well, so under steady state = [5] since the dark current

is the same throughout the structure. If we define a trapping or capture probability for an electron traversing a well with

energy larger than the barrier height, we must have

(1)

And the sum of the captured and uncaptured fractions must equal the current in the barrier region, so the escape

current density can be written as

(2)

Where is a 2D electron density which only includes electrons on the upper part (with energy greater than the

barrier height) of the ground state suband and is the scattering time to transfer these electrons from the 2D sub and

to the non confined continuum on top of the barrier. The capture probability is related to the relevant time constants by [6]

(3)

is the capture time of an excited electron back into the well and is the transit time for an electron across

one quantum well region including the surrounding barriers. Practically, ≪ 1 ≫ , as is true for

actual devices at operating electric fields, the dark current density will be

(4)

"" denotes the drift velocity and is the period length of the multiple quantum well structure, which is the sum

of the well and the barrier width = + ". Thus,

(5)

"A" represents the device area.

Because is a function of temperature and is a function of electric field or applied biasing voltage, so the

dark current is a function of both the bias and the temperature [9]. Figure 2 illustrates the theoretical calculations of three

samples. The main difference between these samples is the doping density in the well. The sample structure consists

of 100 periods of #$%&'(%#)/&#) quantum wells with well width = 6.6-, barrier thickness



" = 25- and0 = 20%. The variation of the dark current, generated by this sample, as a function of the electric

field for different values of operating temperatures is plotted in Figure 3 when the well's doping density is = 1.5 ×

10'4-(. On the other hand, when IR light is incident on the detector, all the dark current paths remain unchanged [6]

as Figure 4 demonstrates.

Let us now turn our attention to the photocurrent to show to what extent its presence can affect the behavior of the

QWIP detector. There is a direct photoemission of electrons from the well, and this, of course, contributes to the observed

photocurrent in the collector. The photoconductive gain is a result of the extra current injection from the contact necessary

to balance the loss of electrons from the well due to photoemission. The amount of the extra injection must be sufficiently

large in such a way that its fraction trapped in the well equals the direct photoemission current. The total photocurrent

consists of contributions from the direct photoemission and the extra current injection [10]. The photoemission current

directly ejected from one well is

(6)

where Φ is the rate of incident photons, the superscript (1) indicates quantities for one well, is the escape

time, 5% is the intersubband relaxation time, 6 ≡ 6'is the total absorption quantum efficiency, is the

number of wells, and89 is the escape probability for an excited electron from the well is.

The derivation of Eq. (6) is straight-forward from a rate equation consideration which relates the rate of change of

the number of excited electrons % to the other system parameters as:

(7)

As shown in Figure 3, for each well, the injection current :;<<' / which refills the well to balance the loss due

to emission :;<<'

equals the observed photocurrent. The photocurrent is then given by

(8)

Using Eq. (6), we immediately get

(9)

and the photoconductive gain will be:



(10)

Shot (Generation-Recombination) Noise Current

The basic principle of photodiode operation is when photons strike photodiode surface, they generate free

electrons and the movement of free electrons results in a measurable current. Shot noise in the current is due to the

statistical nature of the generation of the free electrons. In given time interval, there will be random fluctuations in the

number of free electrons generated as the photons strike that surface. These fluctuations will follow Poisson statistics,

which tells us the uncertainty in the number of events"", that occur in a given time interval is given simply by the square

root of, or = = √. During a measuring time interval of∆@, the number of events (creation of free electrons), is given

by:

(11)

A represents the external circuit current. Shot noise current is based on Poisson statistics, so the standard

deviation of the current is

(12)

where∆B = 1/2∆@ denotes the measurement's bandwidth.

In the above formula, it is assumed thatC;<< = C<D = 1, so shot noise current (square average) is given by:

(13)

Here :,;< consists of two contributions: fluctuations in:: . The shot noise caused by the dark

current becomes:

(14)

Where: = × :'

. From Eq. (13), the shot noise current (square average) due to the fluctuation in the

emission dark current can be expressed as,

(15)

and the shot noise current (square average) due to the fluctuation in the capture dark current can be formulated as,



(16)

So the total fluctuations in the dark current can be calculated by adding Eqs. (15) and (16).

(17)

Because : = : C;<< = C<D ≅'

GH as a good approximation for ≅ 1,

(18)

An expression for the shot noise current caused by the photocurrent can be easily obtained by replacing A in

Eq. (18) with photocurrent (A;<<).

(19)

Johnson noise

Johnson noise is inherent to all resistive devices and the noise mean square current is [11]

(20)

As previously stated,∆Bis the bandwidth of the measuring channel and R refers to the device differential

resistance. Johnson noise is easily calculated once the device I–V curve is known. A photoconductor has 1/B noise but

for GaAs QWIPs, experiments show that 1/B noise seldom limits the detector performance. So, the contribution of 1/B

noise can be neglected [6].

Now, we can easily draw the equivalent circuit of photoconductive (QWIP) as shown in Figure 5, where I" is the

biasing voltage.

Comparison of Dark and Noise Currents

From the dark current point of view, the total mean square noise current is given by:

(21)

The normalization of the above formula to the standard noise current will give a ratio:



(22)

In the above formula, JK is the dark-to-noise current ratio. Substituting C<D ≅'

GH into Eq.(22), we

get

(23)

Figure 6 illustrates the dependence of JK on the number of quantum wells. It is well-known that the dark

current is independent on N. However,JKis enhanced as N increases. This is due to the inverse proportionality of

the shot noise currents with N. It is of importance to note that the sample structure; for which the displayed results in

Figure 6 were obtained; consists of #$%&'(%#)/&#) quantum wells with well width = 6.6- , barrier

thickness " = 25- and0 = 0.2 , = 1.5 × 10'4-( , L = 90NO,# = 200P- ∗ 200P-,

∆B = 1RST, = 7), = 31.6 × 10(), K = 20Ω under applied biasing voltage with electric field

of intensity4000I/4-.

Let us now turn our attention to the condition of photo operation; the total measured current is the contribution of

the dark current and photocurrent [12], so the total current is given by

(24)

The amount of noise in this current is given by

(25)

If we refer to "the dark and photo currents-to-noise current ratio" with DPNR, we have

(26)

Therefore,



(27)

Substituting C<D ≅'

GH into Eq.(27) yields:

(28)

Using the same previous parameter values and6' = 0.5%, we evaluate the dependence of DPNR on the

number of quantum well and the results are depicted in Figure 7.

From the last two figures, Figures 6 & 7, we note that ]^_] and`abc enhanced significantly with

increasing N in this range (1-200) and this significant enhancement decreases gradually as N is increased beyond that range

and tends to be constant for larger densities of wells. This is because of the dependence of ]^_] and`abc on some

function of N which is practically predicted as √ .

CONCLUSIONS

Thanks to their wavelength diversity and to their excellent uniformity, QWIP detectors emerge as potential

candidates for many practical applications; especially in the very long wavelength infrared (VLWIR) spectral domain.

This paper is concerned with calculating all different currents that are generated by several sources of noise. These currents

include dark, shot noise, thermal noise, and photocurrent component. From our calculations, it is noted that the absorption

6 is directly proportional to N while C;<< is inversely proportional to it. So, the product of them, which gives the

photocurrent, is independent of N. However, the detector performance is dependent upon the number of quantum wells

owing to the inverse proportionality of the shot noise currents on N. As a final conclusion, there are several remarks that

may be taken into account in designing such types of optical devices. The more important one is that the photocurrent and

dark current are independent on the number of quantum wells, whilst the shot noise current is inversely proportional to it.

Thus, increasing the number of quantum wells results in decreasing the shot noise currents and this in turn leads to enhance

the performance of the quantum well infrared photodetector.

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APPENDICES

Figure 1: The Dark Current Paths

Figure 2: Dark Current Density Plots with Applied Field for Different Doping Densities in the Wel



Figure 3: Dark Current Density Plots with Applied Field for Different Temperatures

Figure 4: The Dark Current Paths and the Collected Total Photocurrent

Figure 5: The Equivalent Circuit of Photoconductive (QWIP)

Figure 6: Dependence of JK on Number of Quantum Wells



Figure 7: Dependence of JdK on Number of Quantum Wells

FOREIGN MATTER REDUCTION IN HIGH DENSITY PLASMA CHEMICAL VAPOR DEPOSITION PROCESS

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