# US 10,769,339 B1 · Local band-to-band-tunneling model for TCAD simulation

> Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt

- Number: US 10,769,339 B1
- Document ID: US10769339B1
- Status: Granted
- Kind: B1
- Application number: 16/535,523
- Filed: 2019-08-08
- Granted: 2020-09-08
- Earliest claimed: 2018-08-09
- Assignees: Synopsys, Inc.
- Applicants: Synopsys, Inc.
- Inventors: Hiu Yung Wong; Rimvydas Mickevicius
- Web page: https://patentgrep.com/patent/US10769339B1

## CPC

- G06F 30/367: Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
- G06F 30/392: Floor-planning or layout, e.g. partitioning or placement
- G06F 2111/04: Constraint-based CAD
- G06F 2111/10: Numerical modelling
- G06F 2111/20: Configuration CAD, e.g. designing by assembling or positioning modules selected from libraries of predesigned modules
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

An improved local modeling function for estimating band-to-band tunneling currents RBBT in nanodevices and other low-voltage circuit elements during TCAD simulation, the model being represented by the equation: R B ⁢ B ⁢ T = - B ⁢  F  σ = exp ⁡ ( - F 0  F  ) ⁢ g where terms B, F, F0 and σ correspond to conventional terms used in Hurkx-based equations, and the term g is an exponential factor determined by the equation: g = ( F - F 1 F 1 ) 1 . 5 where the term F1 is the built-in electric field at a selected cell/point determined by the equation: F 1 = max ⁡ ( F ˜ 1 , C ⁢ 2 ⁢ q ⁢ E g ⁢ N n ⁢ e ⁢ t ɛ ) where {tilde over (F)}1 is the built-in electric field at zero bias, q is fundamental electronic charge, C is a fitting parameter, Eg is bandgap, Nnet is doping concentration, and E is dielectric constant. At low applied fields (F˜F0) the factor g biases the improved model toward the zero-field/zero-current origin in a way that closely matches non-local model results. At higher applied fields the factor g has less influence and the model is controlled by the conventional terms.

## Claims

### Claim 1

A computer implemented method for estimating a band-to-band tunneling (BBT) current in a circuit element, the method comprising:
generating, by a processor, a model of the circuit element including a plurality of cells, wherein each cell includes position data and material data corresponding with an associated portion of said circuit element such that said position data defines a spatial position of said each cell within said model corresponding to a spatial positional of said associated portion, and such that said material data operably defines a material composition and corresponding electrical characteristics of said associated portion of said circuit element;
simulating operation of the circuit element including applying a simulated external electric field to a selected cell of said plurality of cells; and
utilizing a local BBT modeling function to generate a BBT current estimate, the local BBT modeling function including an exponential factor having a value determined by a difference between said external electric field and a built-in electric field at said selected cell and raised to an exponential power greater than one,
wherein the built-in electric field is calculated using said position data and said material data of said plurality of cells,
wherein said local BBT modeling function implements said exponential factor such that the BBT current estimate becomes zero when the external electric field is equal to the built-in electric field.

### Claim 2 (depends on 1)

The method of claim 1, wherein said exponential factor of said local BBT modeling function is determined using the equation:
g
=
(
F
-
F
1
F
1
)
x
wherein g is said exponential factor,
wherein F is said external electric field applied to said selected cell,
where F1 is said built-in electrical force, and
wherein x is said exponential power having said value greater than one.

### Claim 3 (depends on 2)

The method of claim 2, wherein said exponential power has a value in the range of one and three.

### Claim 4 (depends on 3)

The method of claim 3, wherein said exponential power has a value equal to one-and-one-half.

### Claim 5 (depends on 1)

The method of claim 1,
wherein said exponential factor g has a value determined by said equation when the external electric field F is greater than the built-in electrical force F1, and
wherein said exponential factor g has a value equal to zero when the external electrical force F is less than or equal to the built-in electric field F1.

### Claim 6 (depends on 5)

The method of claim 5, wherein said built-in electric field F1 is determined by the maximum function:
F
1
=
max
⁡
(
F
~
1
,
C
⁢
2
⁢
qE
g
⁢
N
net
ɛ
)
where {tilde over (F)}1 is a built-in electric field occurring at said selected cell at zero bias,
wherein C is a fitting parameter determined by at least one of a structural configuration and an element type of said circuit element,
wherein Eg is a bandgap value of said selected cell,
wherein Nnet is a doping concentration of said selected cell, and
wherein ε is a dielectric constant of said selected cell.

### Claim 7 (depends on 2)

The method of claim 2, wherein utilizing said local BBT modeling function comprises generating said BBT current estimate using the equation:
R
BBT
=
-
B
·

F

σ
·
exp
⁡
(
-
F
0

F

)
·
g
wherein RBBT is said BBT current estimate,
wherein B is a temperature-independent pre-factor,
wherein F0 is a temperature-dependent bandgap force, and
wherein the exponent σ has a value in the range of two and two-and-one-half.

### Claim 8 (depends on 7)

The method of claim 7, wherein the temperature-independent pre-factor B is 4×1014 cm−1/2·v−5/2.

### Claim 9 (depends on 7)

The method of claim 7, wherein the temperature-dependent bandgap force F0 is proportional to Eg3/2, where Eg is the bandgap at the selected element.

### Claim 10

In an electronic design automation (EDA) tool implemented in a computer, a Technology Computer-Aided Design (TCAD) toolset configured to estimate band-to-band tunneling (BBT) current in a circuit element, said TCAD toolset including instructions that, when executed by a processor of said computer, cause the processor to perform operations comprising:
generating a model of the circuit element including a plurality of cells, wherein each cell includes position data and material data corresponding with an associated portion of said circuit element such that said position data defines a spatial position of said each cell within said model corresponding to a spatial positional of said associated portion, and such that said material data operably defines a material composition and corresponding electrical characteristics of said associated portion of said circuit element;
simulating operation of the circuit element including applying a simulated external electric field to a selected cell of said plurality of cells; and
utilizing a local BBT modeling function to generate a BBT current estimate, the local BBT modeling function including an exponential factor having a value determined by a difference between said external electric field and a built-in electric field at said selected cell and raised to an exponential power greater than one,
wherein the built-in electric field is calculated using said position data and said material data of said plurality of cells,
wherein said local BBT modeling function implements said exponential factor such that the BBT current estimate becomes zero when the external electric field is equal to the built-in electric field.

### Claim 11 (depends on 10)

The TCAD toolset of claim 10, wherein said exponential factor of said local BBT modeling function is determined using the equation:
g
=
(
F
-
F
1
F
1
)
x
wherein g is said exponential factor,
wherein F is said external electric field applied to said selected cell,
where F1 is said built-in electrical force, and
wherein x is said exponential power having said value greater than one.

### Claim 12 (depends on 11)

The TCAD toolset claim 11, wherein said exponential power has a value in the range of one and three.

### Claim 13 (depends on 12)

The TCAD toolset claim 12, wherein said exponential power has a value equal to one-and-one-half.

### Claim 14 (depends on 10)

The TCAD toolset claim 10,
wherein said exponential factor g has a value determined by said equation when the external electric field F is greater than the built-in electrical force F1, and
wherein said exponential factor g has a value equal to zero when the external electrical force F is less than or equal to the built-in electric field F1.

### Claim 15 (depends on 14)

The TCAD toolset claim 14, wherein said built-in electric field F1 is determined by the maximum function:
F
1
=
max
⁡
(
F
~
1
,
C
⁢
2
⁢
qE
g
⁢
N
net
ɛ
)
where {tilde over (F)}1 is a built-in electric field occurring at said selected cell at zero bias,
wherein C is a fitting parameter determined by at least one of a structural configuration and an element type of said circuit element,
wherein Eg is a bandgap value of said selected cell,
wherein Nnet is a doping concentration of said selected cell, and
wherein ε is a dielectric constant of said selected cell.

### Claim 16 (depends on 11)

The TCAD toolset claim 11, wherein utilizing said local BBT modeling function comprises generating said BBT current estimate using the equation:
R
BBT
=
-
B
·

F

σ
·
exp
⁡
(
-
F
0

F

)
·
g
wherein RBBT is said BBT current estimate,
wherein B is a temperature-independent pre-factor,
wherein F0 is a temperature-dependent bandgap force, and
wherein the exponent σ has a value in the range of two and two-and-one-half.

### Claim 17 (depends on 16)

The TCAD toolset claim 16, wherein the temperature-independent pre-factor B is 4×1014 cm−1/2·v−5/2.

### Claim 18 (depends on 16)

The TCAD toolset claim 16, wherein the temperature-dependent bandgap force F0 is proportional to Eg3/2, where Eg is the bandgap at the selected element.

### Claim 19

A computer implemented method for estimating a band-to-band tunneling (BBT) current in a circuit element, the method comprising:
generating, by a processor, a model of the circuit element including a plurality of cells;
simulating operation of the circuit element including applying a simulated external electric field to a selected cell of said plurality of cells; and
utilizing a local modeling function to generate a band-to-band tunneling (BBT) current estimate produced in said selected cell, said local BBT modeling function including an exponential factor g having a value determined by the equation:
g
=
(
F
-
F
1
F
1
)
1.5
wherein g is said exponential factor,
wherein F is said external electric field applied to said selected cell,
wherein F1 is a built-in electric field is determined by the maximum function:
F
1
=
max
⁡
(
F
~
1
,
C
⁢
2
⁢
qE
g
⁢
N
net
ɛ
)
where {tilde over (F)}1 is a built-in electric field occurring at said selected cell at zero bias,
wherein C is a fitting parameter determined by at least one of a structural configuration and an element type of said circuit element,
wherein Eg is a bandgap value of said selected cell,
wherein Nnet is a doping concentration of said selected cell, and
wherein ε is a dielectric constant of said selected cell.

### Claim 20 (depends on 19)

The method of claim 19, wherein utilizing said local BBT modeling function comprises generating said BBT current estimate using the equation:
R
BBT
=
-
B
·

F

σ
·
exp
⁡
(
-
F
0

F

)
·
g
wherein RBBT is said BBT current estimate,
wherein B is a temperature-independent pre-factor,
wherein F0 is a temperature-dependent bandgap force, and
wherein the exponent σ has a value in the range of two and two-and-one-half.