Effect of gauss doping profile on electric potential of p-n diode

Effect of Gauss Doping Profile on Electric Potential of p-n Diode

by:A.A.N. Gde Sapteka

T. Abuzairi D. Hartanto

P.S. PriambodoH. Sudibyo

The 13th International Conference on QiR (Quality in Research), 2013

Outline

• Motivation

• Theory

• Simulation Procedure

• Result and Discussion

• Conclusion

• Acknowledgment


Motivation


Modelling the Soft Dead Space Effect on Mean Gain of Si/Ge Avalanche Photodiode

Monte Carlo Method

Si/Ge Avalanche Photodiode Fabrication

Avalanche Photodiode Simulation Using COMSOL and MATLAB Software

Outline

• Motivation

• Theory



• Conclusion

• Acknowledgment


Theory


where

Theory


Outline

• Motivation

• Theory



• Conclusion

• Acknowledgment


Simulation Procedure

• We simulate the doping concentration of five Gauss Doping profile (GDP) of p-n diodes, i.e., GDP 1 with dfc = 0.46599 μm; GDP 2 with dfc = 0.37279 μm; GDP 3 with dfc = 0.27959 μm; GDP 4 with dfc = 0.18640 μm; GDP 5 with dfc = 0.046599 μm . In this study, the p-n diodes have p-type doping NA (1 x 1018; 1 x 1017; 1 x 1016; 1 x 1015) cm-3 and n-type doping ND (1 x 1016; 1 x 1015; 1 x 1014; 1 x 1013) cm-3.

• We set NA is 100 times of ND. The diodes have different doping fall-off constant (dfc) in accordance with Gauss function. The involved parameters are listed in Table I.

• The relationship between GDP, NA and built-in voltage of p-n diode is determined using MATLAB.


Simulation Procedure

• We analyzed the result to find the relationship between dfc with Gauss built-in potential (VGbi), and also with maximum junction voltage (Vjmax) and minimum junction voltage (Vjmin).

• The research conducted by means of simulation of p-n diodes with Gauss Doping Profile (GDP) using COMSOL.

• The last step was to determine conclusions obtained from the analysis.


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Table I. Definition and Description of Parameters

Parameter Description

N Concentration of free electron (cm-3)

P Concentration of free hole (cm-3)

NA Maximum p-type doping (cm-3)

ND Maximum n-type doping (cm-3)

ni Intrinsic concentration for Si = 1.46 x 1010 (cm-3)

N Doping concentration

Wp Maximum p-type doping thickness (μm)

VAbi, VGbi Abrupt built-in potential (V), Gauss built-in potential (V)

WDp Depletion width in n-type material (cm)

WDn Depletion width in p-type material (cm)

V(x) Electric Potential (V) at depth x

s Relative permittivity for Si = 11.8

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Table I. Definition and Description of Parameters (cont’d)

Parameter Description

ju Junction depth = -2 μm

y1 Diode dimension = -7 μm

x1 Diode dimension = 5 μm

ac Anode dimension = 2 μm

dfc Doping fall-off constant (μm)

k Boltzmann's constant = 1.3 x 10-23 J/K

T Room temperature = 300 K

q Elementary charge = 1.602 x 10-19 C

Vjmax Maximum junction voltage (V)

Vjmin Minimum junction voltage (V)

Gf Gauss function

Outline

• Motivation

• Theory



• Conclusion

• Acknowledgment


Result and Discussion

Fig. 1. Gauss Function



Fig. 2. p-n Diode with NA = 1 x 1017 cm-3 and ND = 1 x 1015 cm-3 using GDP 1
















GDP dfc (μm) N1 N2 N3 N4

GDP 1 0.465990 0.813 V 0.695 V 0.575 V 0.456 V

GDP 2 0.372790 0.813 V 0.695 V 0.575 V 0.456 V

GDP 3 0.279590 0.813 V 0.695 V 0.575 V 0.456 V

GDP 4 0.186400 0.813 V 0.695 V 0.575 V 0.456 V

GDP 5 0.093198 0.813 V 0.695 V 0.575 V 0.456 V

Table II. Gauss Doping Profile Built-In Voltage (VGbi)

Where N1 : NA = 1 x 1018 cm-3 ; ND = 1 x 1016 cm-3

N2 : NA = 1 x 1017 cm-3 ; ND = 1 x 1015 cm-3

N3 : NA = 1 x 1016 cm-3 ; ND = 1 x 1014 cm-3

N4 : NA = 1 x 1015 cm-3 ; ND = 1 x 1013 cm-3


Fig. 7. Electric Potential of GDP 1 with NA =1 x 1018 cm-3 and ND =1 x 1016 cm-3













NA (cm-3) ND (cm-3) VAbi VGbi % diff

1 x 1018 1 x 1016 0.8135 V 0.8130 V 0.06

1 x 1017 1 x 1015 0.6945 V 0.6950 V 0.07

1 x 1016 1 x 1014 0.5747 V 0.5750 V 0.08

1 x 1015 1 x 1013 0.4565 V 0.4560 V 0.11

Table III. Built-In Voltage Comparison

We propose an equation of built-in voltage for Gauss

Doping Profile as a function of log (NA):

,


Fig. 11. Relationship of dfc, NA and VGbi.




Fig. 12. Junction voltage of GDP 1 using NA = 1x1018 cm-3; ND = 1x1016 cm-3



GDP dfc N1 N2

Vjmax Vjmin Vjmax Vjmin

GDP 1 0.465990 -0.0402 V -0.0794 V -0.0709 V -0.1344 V

GDP 2 0.372790 -0.0468 V -0.0925 V -0.0813 V -0.1516 V

GDP 3 0.279590 -0.0565 V -0.1122 V -0.0955 V -0.1750 V

GDP 4 0.186400 -0.0734 V -0.1445 V -0.1185 V -0.2078 V

GDP 5 0.093198 -0.1109 V -0.2082 V -0.1615 V -0.2590 V

Table IV. Junction Voltage Vjmax and Vjmin



GDP dfc N3 N4

Vjmax Vjmin Vjmax Vjmin

GDP 1 0.465990 -0.1095 V -0.1778 V -0.1541 V -0.1946 V

GDP 2 0.372790 -0.1207 V -0.1924 V -0.1606 V -0.2034 V

GDP 3 0.279590 -0.1360 V -0.2102 V -0.1686 V -0.2134 V

GDP 4 0.186400 -0.1570 V -0.2329 V -0.1784 V -0.2255 V

GDP 5 0.093198 -0.1885 V -0.2641 V -0.1909 V -0.2419 V

Table IV. Junction Voltage Vjmax and Vjmin (con’t)


Fig. 13. Relationship of dfc, NA, and Vjmin



Fig. 14. Relationship of dfc, NA, and Vjmax




We propose equations for Vjmax as a function of dfc and log NA as stated in equation (11)

where



We propose equations for Vjmin as a function of dfc and log NA as stated in equation (12)

where

Outline

• Motivation

• Theory



• Conclusion

• Acknowledgment


Conclusion

We achieve the relationship between dfc, NA, and VGbi of p-n Diode with Gauss Doping Profile in which NA is 100 times of ND as stated in (10) using MATLAB and COMSOL software. We also propose equations for Vjmax and Vjmin

as a function of dfc and log (NA) as stated in (11) and (12).


Outline

• Motivation

• Theory



• Conclusion

• Acknowledgment


Acknowledgment

We would like to thank to Pusat Komputer FT UI for their permission to use MATLAB software version R2012 and also to the reviewers for their suggestions and improvements.


Thank You


Date post:	08-Jul-2015
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Effect of gauss doping profile on electric potential of p-n diode

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