1-D Modeling of HgCdTe Photodetectors Operated at ... - nanoHUB

1-D Modeling of HgCdTe Photodetectors Operated at Low Temperatures

Pradyumna Muralidharan Dragica Vasileska

Computational Electronics

Outline • Motivation and need for Infrared Photodetectors • • • •

• • •

HgCdTe Properties Basic Photodetector Parameters The Drift-Diffusion Model Generation – Recombination Models - SRH - Radiative - Auger - Tunneling Rappture Interfacing Results Conclusions and Future Work

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NEED FOR IR PHOTODETECTORS

History of the development of photodetectors


Military Applications.
Communication Applications.
Bio-Medical Applications.

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HgCdTe Material Properties Intrinsic Carrier Concentration

• The above equation was developed by Hansen and Schmidt using the k.p approach with degenerate statistics.

•x

• 50K

0.7

T

300K

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• All material parameters in HgCdTe are very sensitive to the Cadmium Concentration ‘x’ and the temperature.

• For narrow bandgap HgCdTe the device is almost completely intrinsic near room temperature.

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Bandgap

• The above equation is provide by Hansen et al. • The equation is valid for 0 and 4.2 K T 300 K

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x

0.6

Effective Masses = 0.55

• Electrons have low effective mass as compared to the holes.

Permittivity

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Mobility

Electron Mobility

Hole Mobility

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PHOTODETECTOR PARAMETERS

• Quantum Efficiency • Response Times • Noise • Detectivity

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Quantum Efficiency • Quantum Efficiency :

d > Lp

d < Lp

Factors affecting Quantum Efficiency • Photosensitive Area (width of space – charge region) • Reflection Co-Efficient • Absorption Co-Efficient Computational Electronics

RESPONSE TIMES • Transit Time Average time taken by the electron to reach the contact after generation inside the space charge region.

1-D Node point visualization of the device.

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RC Constant Depletion Capacitance :

Diffusion Capacitance :

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NOISE • Shot Noise : The fluctuations in the velocities of free carriers due to their random motion and the random thermal generation rates jointly give rise to shot noise.

• Johnson Noise : The shunt resistance, load resistance and series resistance contribute to the Johnson noise.

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DETECTIVITY It is a primary figure of merit for any Infrared detector and is given by:

R is the effective dynamic resistance and is given by :

R0 is the zero bias resistance and RL is the load resistance.

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THE DRIFT DIFFUSION APPROACH Initialize Parameters • Mesh Parameters • Discretization Coefficients • Doping Density • Potential based on charge neutrality Equilibrium Solver Solve Equilibrium Poisson’s equation

Solve Electron Continuity equation

Solve Hole Continuity equation

Solve Non-Equilibrium Poisson’s equation Non-Equilibrium Solver Results

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POISSON’S EQUATION Poisson’s Equation :

Finite Difference Representation :

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CONTINUITY EQUATIONS Electron Continuity Equation :

Holes Continuity Equation :

Finite Difference Scheme : • Electrons

• Holes

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NUMERICAL METHODS • LU Decomposition Matrix representation of the equation :


Fast and efficient for 1-D device structures.
Does not converge for temperatures below 60 K with addition of impurity levels due to high oscillating error.

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• Successive Over Relaxation Method

is the relaxation parameter


Convergence is slower than LU.
Converges even at temperatures below 60 K.
The relaxation parameter can be used to over-damp or under damp the error which helps in convergence.

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GENERATION-RECOMBINATION MODELS • Shockley – Read – Hall Mechanism


In

with x = 0.225, SRH is a dominating factor at lower

temperatures.


SRH lifetimes depends on Trap concentrations and capture coefficient.

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SRH R-G TERM :

SRH Lifetimes :

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• Auger Mechanism


Auger generation is heavily dominant at higher temperatures.


Responsible for very high dark current at elevated temperatures.


Auger -1 mechanism is the dominant process in n type HgCdTe.


Auger -7 mechanism is the dominant process in p type HgCdTe.

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Auger Lifetimes :

Intrinsic Auger Lifetime :

Auger -1 Lifetime :

Auger - 7 Lifetime :

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Auger R-G TERM :

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• Radiative Mechanism
Band to Band type of recombination which involves direct annihilation of a conduction band electron with a valence band hole.
It is more significant at lower temperatures.

R-G Term

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Radiative Lifetime :

τ Rad

1 = B (no + po )

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• Band To Band Tunneling


Important mechanism in narrow bandgap HgCdTe at low temperatures.


Tunneling model based on W.K.B approximation.

Jozwikowski, K.; Kopytko, M.; Rogalski, A.; Jozwikowska, A.; , "Enhanced numerical analysis of current-voltage characteristics of long wavelength infrared n-on-p HgCdTe photodiodes," Journal of Applied Physics , vol.108, no.7, pp.074519-074519-11,Oct2010


This generation term can easily be integrated into the G-R terms of the continuity equation.

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• Trap Assisted Tunneling
This model is implemented by introducing a R-G term.


The


term in the standard ‘SRH’

terms are field effect functions.