A Drift-Diffusion Model to Calculate Dark Current of InP

250

The 2nd Asian Symposium on Electromagnetics and Photonics Engineering

August 28-30, 2013, Tabriz, Iran

ASEPE 2013- Photodetector, OFrA5

A Drift-Diffusion Model to Calculate Dark Current

of InP/In0.53Ga0.47As/InP PIN Photodetector F.Roostaie *1,M.soroosh 2, R.talebi 3

Faculty of Electrical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran *1f-roostaie @mscstu.scu.ac.ir; 2m.soroosh @scu.ac.ir; [email protected]

Abstract- In this study, we employ a drift-diffusion model to characterize dark current of InP/In0.53Ga0.47As/InP PIN photodetector at low voltage bias. We also, investigate the dependence of multiplication layer parameters such as thickness and mobility of carriers on dark current. The results demonstrate that dark current is mostly affected by generation-recombination process than diffusion process. Our results are in good agreement with another model which prove the ability and success of this method in describing and anticipating dark current at low bias.

Keywords- Pin Photodetector; Dark Current; Drift-Diffusion Model (DDM); Heterostructure

I. INTRODUCTION

Optical detectors are the first part of the photoreceptor system, so their performance has crucial effect on the quality of the receiving data. Generally, optical detectors performance consists of three processes: carrier’s generation by incident light, carrier’s transportation and multiplication by current amplifying mechanisms and carrier extraction to form output signal. Carriers are generated in the high field depletion region in PIN photodetectors. The simplicity of PIN photoreceptors fabrication, their low power consumption and their low bias make them suitable for various applications. The very low doped depletion region sandwiched between p and n regions, causes electric field to be almost uniformly distributed in the i region and as a result, carriers behavior are very similar to each other [1]. A heterojunction is the interface that occurs between two materials with different energy band gap. Heterostructure is employed in PIN photodetectors to reduce dark current. In fact, in order to enhance recombination chance, a well which increases electrons and holes confinement together is formed in the path of the carriers and as a result, dark current is reduced. The dark current is an important factor in determining the minimum optical power that the detector is able to distinguish. Device manufacturing technology and quality of semiconductor crystal are effective on dark current too. In this paper we study dark current and propose a model to simulate it. Various devices with low dark currents were explored in the recent literatures. In [2] an InP/In0.53Ga0.47As/InP heterostructure was studied, in which its PIN detector was simulated using Synopsys 2008. Manufacturing technology and implantation quality of these detectors were also reported. M. Soroosh et al calculated dark current by neural network model in a microscopic view [3]. In the presented DDM, potential and electric distribution of device and also mean concentration, velocity and momentum of electrical carriers are derived by solving Boltzmann Transport Equation (BTE) in a macroscopic manner. After discretization the equations by finite difference method, Gummel numerical iteration method is applied to solve drift-diffusion equations. Then, these discrete equations are solved by upper and lower triangular Placement method. In this algorithm, first, the Poisson equation is solved, considering the initial conditions, and carrier distribution along the device is obtained. Then, the continuity equations are solved and a new value of potential distribution is calculated and this process goes on until we achieve the desired accuracy [4]. The function and structure of the PIN detector is introduced in section 2. The DDM and its numerical solutions are studied in Section 3. The effect of intrinsic region length and carrier mobility on dark current is explored in the final section. The results of the presented model are compared with others to verify the accuracy of our model.

II. PIN DETECTOR

A schematic of a PIN photodetector is shown in Fig 1. Low capacitance and high breakdown voltage in reverse bias are the results of a wide intrinsic layer of the detector [5]. The p-side or n-side illuminated light is absorbed in i region and generates several Electron and holes. Because of high electric field of i region, the generated carriers are drifted toward the lateral contacts. Electrical current of device can be varied by changing the intensity of optical input.

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Fig 1. Schematic of the InP/In0.53Ga0.47As/InP PIN.

III. DRIFT DIFFUSION MODEL

Solving the Boltzmann Transport Equations (BTEs) is the key to simulate the semiconductor device properties. One way to solve BTEs is DDM. In drift-diffusion, electron and hole continuity equations and carrier currents equations are solved simultaneity. This model is better than Monte Carlo and Hydrodynamics in simplicity and convergence speed respectively. Convergence in DDM is obtained by choosing proper initial and boundary conditions. However, it is required to solve poison equation with those equation mentioned above to catch transport properties. In heterostructures, revising some of the basic equations which were used for homojunctions is necessary [6-7].

In heterostructures, by changing the material used, the dielectric constant varies too. So, the Poisson equation in a heterostructure is expressed as:

2

D A2d q 1 d dp n N N

dx dxdx

(1)

Where in this equation, q is the charge of electron, n is free electron density, p is hole density, ND is the donor impurity density, NA is the acceptor impurity density and is the dielectric constant in semi-conductors. Continuity equations in heterostructures are similar to homojunctions and are:

n nn 1 .J U 0t q

(2)

n nn 1 .J U 0t q

(3)

Which Un and Up represent electrons and holes recombination rates respectively. Generation and recombination processes try to return a semiconductor back to its thermal equilibrium, ( 2

ipn n ), when it is out of it, 2ipn n . Here, Shockley-Read-Hall

and Auger recombination rates are considered in which, the continuity equation are defined for them as:

Shockley-Read–Hall recombination: 2i

SRHp t n t

np nU

(n n ) (p p )

(4)

i tt i

b

E Ep n exp( )

k T

(5)

t it i

b

E En n exp( )

k T

(6)

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Auger recombination: 2 2 2 2

Aug n i p iu c pn nn c np pn (7)

Where, in above equations, τp and τn are carriers life time, Et is the trap energy level, Ei is the middle energy level, ni is the intrinsic carrier density and cn and cp are the auger constants. Electric current terms of heterostructure are derived as:

n n n n nJ n q (V ) KT (8)

p p p p pJ n q (V ) KT (9)

In which, θn and θp are the band parameters in heterostructure and are:

c Cn 0

i

NKT lnq q n

(10)

Vp c g

i

N1 KT( E ) lnq q n

(11)

Where, χc is The electron affinity, gE is the band gap energy, in is intrinsic carrier concentration, T is the absolute

temperature, k is Boltzmann constant, cN and vN are the effective energy states density of conduction band and valence band respectively, is electrostatic potential and 0 is the reference potential which is a constant value.

IV. THE RESULTS OF SIMULATION

In order to investigate the accuracy of our simulation results and compare them, the parameters of a PIN detector from ref [2] is brought in table 1.

Table. 1 List of the material parameters used for simulations [2].

Parameters

Units InGaAs InP

Band gap

ev

0.78

1.34

Effective conduction band density of states

cm-3

2.75 × 1017

5.66 × 1017

Effective valence band density of states

cm-3

7.62 × 1018

2.03 × 1019

Electron mobility

cm2/vs

12000

4730

Hole mobility

cm2/vs

450

151

Electron Effective mass (relative)

0.0489

0.08

Hole Effective mass (relative)

0.45

0.86

Electron Auger coefficient

cm6/s

3.2 × 10-28

3.7 × 10-31

Hole Auger coefficient

cm6/s

3.2 × 10-28

8.7 × 10-30

Electron SRH lifetime

s

1 × 10-6

1 × 10-9

Hole SRH lifetime

s

1 × 10-6

1 × 10-9

Radiative recombination coefficient

cm3s-1

1.431 × 10-10

2 × 10-11

Structural parameters of device are brought in table 2.

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Table. 2 Structural parameters used for simulations [2].

Layer thickness (µm)

Injection density (cm-3)

Parameters Intended region

1

2 × 1018

Na

p

1.5

3 × 1016

Ni

i

0.6

2 × 1018

Nd

n

Conduction and valence bands energy level Alignment is an important subject in heterostructures. In these elements, the difference between electron affinity and layers band gap causes discontinuities in the conduction and valence bands. Energy band diagram for 0.5v bias is shown in Fig 2.

-2.5 -1.7 -0.9 -0.1 0.7 1.5 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

x [um]

Ener

gy [e

V]

Fig. 2 energy band diagram [2]. Fig 3 shows the current-voltage characteristics of a heterostructure device. Our results are in very good agreement with ref [2]. The proposed model contains an exponential behaviour and can calculate dark current very well even in very low voltages.

-0.6 -0.4 -0.2

10-12

10-10

10-8

10-6

Voltage (v)

Curr

ent (

A)

Fig. 3 current-voltage Characteristics. Dashed line represents data taken from [2].

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Current-voltage characteristic of device as a function of different thicknesses of absorption layer is shown in Fig 4. The dark current is the sum of the generation-recombination current in the absorption layer and diffusion current. Dark current increases as the absorption layer thickness increases from 0.1μm to 0.3μm. It is because of generation-recombination current dependence to the intrinsic layer width. The simulation results show small increment in dark current, when the intrinsic layer width increases above 3μm. This is due to significant decreasing of electric field in device, which increases recombination rate.

-0.6 -0.4 -0.210

-14

10-13

10-12

10-11

10-10

10-9

Voltage (v)

Curr

ent (

A)

Fig. 4 current–voltage characteristic of different absorption layer thicknesses [2]. Fig 5 shows the current-voltage characteristic of device as a function of different electron and hole mobility. The simulation results show that dark current varies a little by changing the mobility coefficients. It can be concluded that diffusion current can be neglected as is very low and the dominant component of dark current is the result of generation-recombination process.

-0.6 -0.4 -0.2

10-12

10-10

10-8

10-6

Voltage (v)

Curr

ent (

A)

(a)

-0.6 -0.4 -0.2

10-12

10-10

10-8

10-6

Voltage (v)

Cur

rent

(A)

(b)

Fig. 5 current–voltage characteristics for different mobility coefficients of (a) electrons and (b) holes [2].

V. CONCLUSION In this paper, employing Gummel method in DDM, we could simulate PIN heterostructure photodetector at low voltage. In the proposed model, energy band diagram and current-voltage characteristic of the detector was calculated by discretization Poisson equation, electron and hole concentrations continuity equations and electron and hole current equations using upper

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and lower triangular method. After that, current-voltage characteristic of heterostructure photodetector was obtained for different widths of absorption layer and different mobility coefficients. Comparing our results with Ref [2], demonstrates the accuracy of our model at low voltages. Impact ionization which happens in high electric field hasn't been studied and is the subject of our next paper.

ACKNOWLEDGMENT

The authors would like to express their appreciation of Shahid Chamran University due to its the moral support of this research. Also from National Oil Corporation (NOC) thanks for the financial support of this research through Contract No. 0744 - R -91.

REFERENCES

[1] Kwok K. Ng, Complete Guide to Semiconductor Devices, Academic Press, pp. 134-143, 2008.

[2] M. Soroosh, A. Zarifkar, M. Razaghi, and M. K. Moravvej-Farshi, “A Neural Network Model for Determination of Excess Noise Factor for Separate Absorption and Multiplication Region avalanche Photodiode (SAM-APD)”, International Conference: Optics & Photonics (ICO), pp. 403-404, 2004.

[3] D. L. Scharfetter and D. L. Gummel, “Large signal analysis of silicon read diode oscillator”, IEEE Transactions on Electron Devices, Vol.16, pp.64-77, 1999.

[4] S. M. Sze, “Physics of Semiconductor Devices, 3nd Edition”, Wiley, New York, 2007. [5] J. E. Sutherland and J. R. Hauser, “A computer analysis of heterojunction and graded composition solar cells,” IEEE Trans. Electron

Devices, vol. ED-24, pp. 363-372, 1972. [6] M.S. Lundstrom and R.J. Schuelke, “Numerical analysis of heterostructure semiconductor devices” IEEE Trans. Electron Devices, vol.

30, pp. 1151-1159, 1983.

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A Drift-Diffusion Model to Calculate Dark Current of InP