Electrical TCAD Simulations and Modeling in Germanium

Abstract

Chapter 4 extends a TCAD device simulator to allow electrical simulations of scaled Ge MOSFETs.

Appendix

4.1.1 A.1 TCAD Model Parameters

This appendix contains the model parameters used in this work. Each time, both the name of physical phenomenon and the name of the parameter set is given (e.g. SRH-recombination is modeled using the Scharfetter dataset in Sentaurus Device) together with the default silicon values. If different values apply for electrons and holes, both values are given in this order, separated by a comma. Note that the definition of these parameters below applies solely to their specific implementation in Sentaurus Device. The literature references on which these models are based may use slightly different definitions. For this reason, the parameters below are not included in the general list of symbols of this book.

4.1.2 A.2 Recombination

SRH-recombination (Scharfetter)

Parameter	Units	Si (e, h)	Ge (e, h)
τ min	s	0, 0	0, 0
τ max	s	1×10−5, 3×10−6	4×10−5, 4×10−5
N ref	cm−3	1016, 1016	1014, 1014
γ	–	1, 1	0.85, 0.85
T α	–	−1.5, −1.5	−1.5, −1.5
T coeff	–	2.55, 2.55	2.55, 2.55
E trap	eV	0.0, 0.0	0.0, 0.0
Note (1)—E trap refers to the SRH reference trap energy w.r.t mid-bandgap (e.g. E trap =0.0 corresponds to E V +0.33 eV in Germanium)
Note (2)—τ max was taken from [47] and then decreased slightly to correspond with the leakage measurements on our Ge p+/n diodes
Note (3)—The temperature dependence for Ge was not investigated. Instead, Si defaults are still used. Further research is required for this dependency

TAT (HurckxTrapAssistedTunneling)

Parameter	Units	Si (e, h)	Ge (e, h)
m t	–	0.5, 0.5	0.12, 0.34

BTBT (Band2BandTunneling)

Parameter	Units	Si	Ge
A	cm s−1 V−2	8.977×1020	8.977×1020
B	eV−3/2 V cm−1	2.147×107	1.6×107

4.1.3 A.3 Mobility

Phonon Scattering (ConstantMobility)

Parameter	Units	Si (e, h)	Ge (e, h)
μ max	cm2 V−1 s−1	1417, 470.5	3900, 1900
exponent	–	2.5, 2.2	2.5, 2.2

Impurity Scattering (DopingDependence)

Parameter	Units	Si (e, h)	Ge (e, h)
μ min1	cm2/Vs	52.2, 44.9	60, 60
μ min2	cm2/Vs	52.2, 0.0	0, 0
μ 1	cm2/Vs	43.4, 29	20, 40
P c	cm−3	0, 9.23×1016	1017, 9.23×1016
C r	cm−3	9.68×1016, 2.23×1017	8×1016, 2×1017
C s	cm−3	3.34×1020, 6.10×1020	3.43×1020, 1020
α	–	0.68, 0.719	0.55, 0.55
β	–	2.0, 2.0	2.0, 2.0

High Lateral Field Mobility (HighFieldDependence)

Parameter	Units	Si (e, h)	Ge (e, h)
v sat0	cm/s	1.07×107, 8.37×106	8×106, 6×106

High Transversal Field Mobility (EnormalDependence (holes only))

Parameter	Units	Si	Ge
B	cm/s	9.925×106	1.993×105
C	cm5/3 V−2/3 s−1	2.947×103	4.875×103
N 0	cm−3	1	1
λ	–	0.0317	0.0317
k	–	1	1
δ	cm2/Vs	2.0546×1014	1.705×1011
A	–	2	1.5
α ⊥	cm3	0	0
N 1	cm−3	1	1
ν	–	1	1
η	V2 cm−1 s−1	2.0546×1030	2.0546×1030
l crit	cm	10−6	10−6