Performing statistical evaluations, coupling Schrödinger's equation and Poisson's equation self-consistently, and employing an iterative fitting process, we have obtained a simple parametric formula for the charge conductance of nonmagnetic two-phase porous and random alloys. The formula exhibits remarkable agreement in describing the response of a system to an applied voltage difference, system size, bandgap, and density of conductive grains as parameters. Exploiting the obtained formula, we parametrically determine the activation threshold functionality of each parameter to other parameters where the charge conductance switches “on” and “off.” The results of our study can be directly utilized to guide experiments.

1.
M.
O'Donovan
,
D.
Chaudhuri
,
T.
Streckenbach
,
P.
Farrell
,
S.
Schulz
, and
T.
Koprucki
, “
From atomistic tight binding theory to macroscale drift diffusion: Multiscale modeling and numerical simulation of uni-polar charge transport in (In,Ga)N devices with random fluctuations
,”
J. Appl. Phys.
130
,
065702
(
2021
).
2.
F.
Gebhard
,
A. V.
Nenashev
,
K.
Meerholz
, and
S. D.
Baranovskii
, “
Quantum states in disordered media. I. Low-pass filter approach
,”
Phys. Rev. B
107
,
064206
(
2023
).
3.
A. V.
Nenashev
,
S. D.
Baranovskii
,
K.
Meerholz
, and
F.
Gebhard
, “
Quantum states in disordered media. II. Spatial charge carrier distribution
,”
Phys. Rev. B
107
,
064207
(
2023
).
4.
R.
Finn
,
M.
O'Donovan
,
P.
Farrell
,
J.
Moatti
,
T.
Streckenbach
,
T.
Koprucki
, and
S.
Schulz
, “
Theoretical study of the impact of alloy disorder on carrier transport and recombination processes in deep UV (Al,Ga)N light emitters
,”
Appl. Phys. Lett.
122
,
241104
(
2023
).
5.
D.
Barettin
,
A. V.
Sakharov
,
A. F.
Tsatsulnikov
,
A. E.
Nikolaev
,
A.
Pecchia
,
M. A.
derMaur
,
S. Y.
Karpov
, and
N.
Cherkashin
, “
Impact of local composition on the emission spectra of InGaN quantum-dot LEDs
,”
Nanomaterials
13
,
1367
(
2023
).
6.
D.
Browne
,
B.
Mazumder
,
Y.-R.
Wu
, and
J.
Speck
, “
Electron transport in unipolar InGaN/GaN multiple quantum well structures grown by NH3 molecular beam epitaxy
,”
J. Appl. Phys.
117
,
185703
(
2015
).
7.
A.
Di Vito
,
A.
Pecchia
,
A.
Di Carlo
, and
M.
Auf der Maur
, “
Impact of compositional nonuniformity in (In,Ga)N-based light-emitting diodes
,”
Phys. Rev. Appl.
12
,
014055
(
2019
).
8.
M.
Sauty
,
N. M. S.
Lopes
,
J. Ph.
Banon
,
Y.
Lassailly
,
L.
Martinelli
,
A.
Alhassan
,
Y. Ch.
Chow
,
S.
Nakamura
,
J. S.
Speck
,
C.
Weisbuch
, and
J.
Peretti
, “
Localization effect in photoelectron transport induced by alloy disorder in nitride semiconductor compounds
,”
Phys. Rev. Lett.
129
,
216602
(
2022
).
9.
C.
Weisbuch
,
S.
Nakamura
,
Y.-R.
Wu
, and
J. S.
Speck
, “
Disorder effects in nitride semiconductors: Impact on fundamental and device properties
,”
Nanophotonics
10
,
3
21
(
2020
).
10.
L.
Fara
,
R.
Kumar
,
D.
Craciunescu
,
∅.
Nordseth
,
I. C.
Vasiliu
,
S.
Fara
,
I.
Chilibon
,
D.
Savastru
,
E.
Monakhov
, and
L.
Baschir
, “
Optimized Cu2O/C-Si tandem heterojunction solar cells: Experimental and modeling investigation for defect analysis
,” in
2nd International Conference on Photovoltaic Science and Technologies (PVCon)
,
Ankara, Turkey
(
IEEE
,
2020
), pp.
1
6
.
11.
C. K.
Wu
,
C. K.
Li
, and
Y. R.
Wu
, “
Percolation transport study in nitride based LED by considering the random alloy fluctuation
,”
J. Comput. Electron.
14
,
416
424
(
2015
).
12.
M.
O'Donovan
,
P.
Farrell
,
T.
Streckenbach
,
T.
Koprucki
, and
S.
Schulz
, “
Multiscale simulations of uni-polar hole transport in (In,Ga)N quantum well systems
,”
Opt. Quat. Elec.
54
,
405
(
2022
).
13.
J. B.
Varley
,
B.
Shen
, and
M.
Higashiwaki
, “
Wide bandgap semiconductor materials and devices
,”
J. Appl. Phys.
131
,
230401
(
2022
).
14.
R.
Finn
and
S.
Schulz
, “
Impact of random alloy fluctuations on the electronic and optical properties of (Al,Ga)N quantum wells: Insights from tight-binding calculations
,”
J. Chem. Phys.
157
,
244705
(
2022
).
15.
M.
O'Donovan
,
M.
Luisier
,
E. P.
O'Reilly
, and
S.
Schulz
, “
Impact of random alloy fluctuations on inter-well transport in I nGaN / GaN multi-quantum well systems: An atomistic non-equilibrium Green's function study
,”
J. Phys.: Condens. Matter
33
,
045302
(
2021
).
16.
G. D.
Mahan
,
Many-Particle Physics (Physics of Solids and Liquids)
,
2nd ed.
(
Springer
,
1990
).
17.
K. D.
Usadel
, “
Generalized diffusion equation for superconducting alloys
,”
Phys. Rev. Lett.
25
,
507
(
1970
).
18.
G.
Eilenberger
, “
Transformation of Gorkov's equation for type II superconductors into transport-like equations
,”
Z. Phys.
214
,
195
(
1968
).
19.
M.
Alidoust
and
K.
Halterman
, “
Spontaneous edge accumulation of spin currents in finite-size two-dimensional diffusive spin-orbit coupled SFS heterostructures
,”
New J. Phys.
17
,
033001
(
2015
).
20.
M.
Alidoust
and
K.
Halterman
, “
Long-range spin-triplet correlations and edge spin currents in diffusive spin-orbit coupled SNS hybrids with a single spin-active interface
,”
J. Phys.: Condens. Matter
27
,
235301
(
2015
).
21.
M.
Alidoust
, “
Critical supercurrent and φ 0 state for probing a persistent spin helix
,”
Phys. Rev. B
101
,
155123
(
2020
).
22.
A.
Zyuzin
,
M.
Alidoust
, and
D.
Loss
, “
Josephson junction through a disordered topological insulator with helical magnetization
,”
Phys. Rev. B
93
,
214502
(
2016
).
23.
I. V.
Bobkova
,
A. M.
Bobkov
,
A. A.
Zyuzin
, and
M.
Alidoust
, “
Magnetoelectrics in disordered topological insulator Josephson junctions
,”
Phys. Rev. B
94
,
134506
(
2016
).
24.
M.
Alidoust
and
H.
Hamzehpour
, “
Spontaneous supercurrent and φ 0 phase shift parallel to magnetized topological insulator interfaces
,”
Phys. Rev. B
96
,
165422
(
2017
).
25.
M.
Alidoust
, “
Self-biased current, magnetic interference response, and superconducting vortices in tilted Weyl semimetals with disorder
,”
Phys. Rev. B
98
,
245418
(
2018
).
26.
M.
Alidoust
,
M.
Willatzen
, and
A.-P.
Jauho
, “
Fraunhofer response and supercurrent spin switching in black phosphorus with strain and disorder
,”
Phys. Rev. B
98
,
184505
(
2018
).
27.
M.
Sahimi
,
Heterogeneous Materials: Linear Transport and Optical Properties
(
Springer
,
New York
,
2003
), Vol.
I
.
28.
A. A.
Snarskii
,
I. V.
Bezsudnov
,
V. A.
Sevryukov
,
A.
Morozovskiy
, and
J.
Malinsky
,
Transport Processes in Macroscopically Disordered Media: From Mean Field Theory to Percolation
(
Springer
,
NY
,
2016
).
29.
M.
Walschaers
,
F.
Schlawin
,
T.
Wellens
, and
A.
Buchleitner
, “
Quantum transport on disordered and noisy networks: An interplay of structural complexity and uncertainty
,”
Annu. Rev. Condens. Matter Phys.
7
,
223
(
2016
).
30.
E.
Pazhoohesh
,
H.
Hamzehpour
, and
M.
Sahimi
, “
Numerical simulation of ac conduction in three-dimensional heterogeneous materials
,”
Phys. Rev. B
73
,
174206
(
2006
).
31.
E.
Sharafedini
,
H.
Hamzehpour
,
S. F.
Masoudi
, and
M.
Sahimi
, “
Electrical conductivity of the films grown by ballistic deposition of rodlike particles
,”
J. Appl. Phys.
118
,
168
(
2015
).
32.
Z.
Ebrahiminejad
,
H.
Hamzehpour
, and
S. F.
Masoudi
, “
Electrical conductivity of thin films grown by deposition of random clusters of particles
,”
J. Mater. Sci.: Mater. Electron.
31
,
18297
(
2020
).
33.
A.
Yazdi
,
H.
Hamzehpour
, and
M.
Sahimi
, “
Permeability, porosity, and percolation properties of two-dimensional disordered fracture networks
,”
Phys. Rev. E
84
,
046317
(
2011
).
34.
H.
Hamzehpour
and
M.
Khazaei
, “
Effective permeability of heterogeneous fractured porous media
,”
Transp. Porous Med.
113
,
329
(
2016
).
35.
H.
Hamzehpour
,
A.
Atakhani
,
A. K.
Gupta
, and
M.
Sahimi
, “
Electro-osmotic flow in disordered porous and fractured media
,”
Phys. Rev. E
89
,
033007
(
2014
).
36.
H.
Hamzehpour
,
S.
Pazoki
,
M.
Khazaei
, and
M.
Sahimi
, “
Dependence of percolation and flow properties of fracture networks on the morphology
,”
Physica A
584
,
126361
(
2021
).
37.
A.
Di Vito
,
A.
Pecchia
,
A.
Di Carlo
, and
M.
Auf der Maur
, “
Simulating random alloy effects in III-nitride light emitting diodes
,”
J. Appl. Phys.
128
,
041102
(
2020
).
38.
M. A.
der Maur
,
G.
Penazzi
,
G.
Romano
,
F.
Sacconi
,
A.
Pecchia
, and
A.
Di Carlo
, “
The multiscale paradigm in electronic device simulation
,”
IEEE Trans. Electron. Devices
58
,
1425
1432
(
2011
).
39.
M. A.
der Maur
,
F.
Sacconi
,
G.
Penazzi
,
G.
Romano
,
M.
Povolotskyi
,
A.
Pecchia
, and
A.
Di Carlo
, “
Concurrent multiscale simulation of electronic devices
,”
J. Comput. Electron.
9
,
262
268
(
2010
).
40.
M. A.
Der Maur
, “
Multiscale approaches for the simulation of InGaN/GaN LEDs
,”
J. Comput. Electron.
14
,
398
408
(
2015
).
41.
S.
Schulz
,
M.
O'Donovan
,
D.
Chaudhuri
,
S. K.
Patra
,
P.
Farrell
,
O.
Marquardt
,
T.
Streckenbach
, and
T.
Koprucki
, “
Connecting atomistic and continuum models for (In,Ga)N quantum wells: From tight-binding energy landscapes to electronic structure and carrier transport
,”
International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD)
,
Turin, Italy
(
IEEE
,
2021
).
42.
M. A.
der Maur
, “
Multiscale approaches for the simulation of optoelectronic devices
,”
J. Green Eng.
5
,
133
156
(
2016
).
43.
M.
Auf der Maur
,
A.
Pecchia
,
G.
Penazzi
,
F.
Sacconi
, and
A.
Di Carlo
, “
Coupling atomistic and continuous mediamodels for electronic device simulation
,”
J. Comput. Electron.
12
,
553
(
2013
).
44.
C. K.
Li
,
M.
Piccardo
,
L. S.
Lu
,
S.
Mayboroda
,
L.
Martinelli
,
J.
Peretti
,
J. S.
Speck
,
C.
Weisbuch
,
M.
Filoche
, and
Y. R.
Wu
, “
Localization landscape theory of disorder in semiconductors. III. Application to carrier transport and recombination in light emitting diodes
,”
Phys. Rev. B
95
,
144206
(
2017
).
45.
E.
Sharafedini
,
H.
Hamzehpour
, and
M.
Alidoust
, “
Multiscale statistical quantum transport in porous media and random alloys with vacancies
,”
J. Appl. Phys.
133
,
035102
(
2023
).
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