Noise Modeling Circuit of Quantum Structure Type of Infrared Photodetectors

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Noise Modeling Circuit of Quantum Structure 3Type of Infrared Photodetectors

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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 toevaluate 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 aswhich 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


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4 Mohamed B. El_Mashade & M. El_Hanash

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

balanced by the trapping or capture of electronsinto 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 acrossone 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 = +,+ -, barrier thickness


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= ./- and0 = .2. 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,/ 3

1'4-(. 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 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 7 6' is the total absorption quantum efficiency, is the

number of wells, and 89is 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 :;


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(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*.?@denotes the measurement's bandwidth.

In the above formula, it is assumed thatC;


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(16)

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

(17)

Because := : C;


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(22)

In the above formula, JKis the dark-to-noise current ratio. Substituting C


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(27)

Substituting C.

CONCLUSIONS

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


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4. M. Z. Tidrow and W. R. Dyer, "Quantum We11 Infrared Focal Plane Arrays for Ballistic Missile Defense and

Space Applications", RTO SET Symposium on Space-Based Observation Technology, held on the Island of

Samos, Greece, 16-18 October 2000, pp.29-1_29-6.

5.

Levine, B.F, "Quantum-well infrared photodetector" J. Appl. Phys. 74, R1R81 (1993).

6. Harald Schneider and Hui Chun Liu, "Quantum Well Infrared Photodetectors Physics and Applications",

Springer-Verlag Berlin Heidelberg 2007.

7.

K. K. Cho, "Detection wavelength of quantum well infrared photodetectors", J. Appl. Phys. 73 (lo), May 1993.

8. N. Sclar, "Properties of doped silicon and germanium infrared detectors", Prog. Quant. Electr. 9, 149-257

(1984).

9.

Thomas R. Hickey, "TEMPERATURE DEPENDENCE OF DARK CURRENT IN QUANTUM WELL INFRARED

DETECTORS", NAVAL POSTGRADUATE SCHOOL, Monterey, California,June 2002.

10. V. D. Shadrin, V. V. Mitin, and V. A. Kochelapb, "Photoconductive gain and generation-recombination noise in

quantum well infrared photodetectors", J. Appl. Phys. 77 (4), February 1995.

11.

Robert H. Kingston, "Optical Sources, Detectors, and Systems Fundamentals And Applications", by ACADEMIC

PRESS, INC.1995.

12. L. Li D. Y. Xiong J. Wen Q. C. Weng, "An equivalent circuit model for the long-wavelength quantum well

infrared photo-detectors", Opt Quant Electron, (2013), Vol. 45, pp. 649656.

APPENDICES

Figure 1: The Dark Current Paths

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


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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 JKon Number of Quantum Wells


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Figure 7: Dependence of JdKon Number of Quantum Wells

Noise Modeling Circuit of Quantum Structure Type of Infrared Photodetectors

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