# US 11,442,097 B2 · Method and apparatus for calculating kink current of SOI device

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- Number: US 11,442,097 B2
- Document ID: US11442097B2
- Status: Granted
- Kind: B2
- Application number: 16/959,633
- Filed: 2019-06-10
- Published: 2021-12-30
- Granted: 2022-09-13
- Earliest claimed: 2019-05-31
- Assignees: Soochow University
- Applicants: Soochow University
- Inventors: Mingxiang Wang; Yanyan Chen; Dongli Zhang; Huaisheng Wang
- Web page: https://patentgrep.com/patent/US11442097B2

## CPC

- G01R 31/2623: {for measuring break-down voltage therefor}
- G01R 31/2601: {Apparatus or methods therefor (G01R31/2607, G01R31/2642 take precedence)}
- G01R 31/2621: {for testing field effect transistors, i.e. FET's}
- G01R 31/275: {for testing individual semiconductor components within integrated circuits}
- G01R 31/2884: {using dedicated test connectors, test elements or test circuits on the IC under test (G01R31/2855 takes precedence)}
- G06F 30/398: Design verification or optimisation, e.g. using design rule check [DRC], layout versus schematics [LVS] or finite element methods [FEM] (optical proximity correction [OPC] design processes G03F1/36)
- G01R 31/2637: {for testing other individual devices (G01R31/2608 - G01R31/2632, G01R31/27 take precedence)}
- G01R 31/2642: {Testing semiconductor operation lifetime or reliability, e.g. by accelerated life tests}
- G01R 31/2831: {Testing of materials or semi-finished products, e.g. semiconductor wafers or substrates (G01R31/318511 takes precedence; testing during manufacture H10P74/00)}
- G01R 31/3004: {Current or voltage test}
- G06F 2119/10: Noise analysis or noise optimisation
- H10D 86/201: {the substrates comprising an insulating layer on a semiconductor body, e.g. SOI (H10D86/40 take precedence)}
- G01R: MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES (indicating correct tuning of resonant circuits H03J3/12)
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- H10D: INORGANIC ELECTRIC SEMICONDUCTOR DEVICES

## Abstract

The present application discloses a method and apparatus for calculating the kink current of SOI device, which is used to solve the problem that the kink current calculation in the prior art is not accurate and is not suitable for circuit simulation. The method includes: obtaining the impact ionization factor, the parasitic transistor effect factor, and the drain saturation current of the SOI device respectively; and calculating the kink current of the SOI device according to the impact ionization factor, the parasitic transistor effect factor, and the drain saturation current.

## Claims

### Claim 1

A kink current calculation method for SOI device, comprising:
obtaining impact ionization factor, parasitic transistor effect factor, and drain saturation current of the SOI device respectively;
calculating the kink current of the SOI device according to the impact ionization factor, the parasitic transistor effect factor, and the drain saturation current,
wherein obtaining the parasitic transistor effect factor of the SOI device specifically includes: obtaining channel length and carrier diffusion length in body region of the SOI device, and calculating the parasitic transistor effect factor of the SOI device according to the channel length and the carrier diffusion length in the body region.

### Claim 2 (depends on 1)

The method according to claim 1, wherein the parasitic transistor effect factor of the SOI device has a hyperbolic secant dependence on channel length and carrier diffusion length in body region of the SOI device.

### Claim 3 (depends on 1)

The method according to claim 1, wherein the impact ionization factor of the SOI device has an exponential relationship with threshold field FI characterizing the impact ionization, depletion region width ld, drain voltage VD, and interpolation function VDse related to drain saturation voltage of the SOI device;
alternatively, the impact ionization factor of the SOI device has an exponential relationship with drain voltage VD, voltage parameter Vk associated with kink effect, and interpolation function VDse related to drain saturation voltage of the SOI device.

### Claim 4 (depends on 1)

The method according to claim 1, wherein the calculation method for kink current Ikink of the SOI device is:
I
kink
=
C
⁢
(
V
D
-
V
D
⁢
s
⁢
e
)
l
d
⁢
exp
⁡
(
-
F
I
⁢
l
d
V
D
-
V
D
⁢
s
⁢
e
)
⁢
sech
⁡
(
L
L
b
)
⁢
I
D
⁢
s
⁢
a
⁢
t
;
(
1
)
where C is a parameter related to material and geometry of the SOI device, L is channel length of the SOI device, VD is drain voltage of the SOI device, VDse is interpolation function related to the drain saturation voltage, ld is depletion region width of the SOI device, FI is threshold field for impact ionization of the SOI device, Lb is carrier diffusion length in body region of the SOI device, and IDsat is drain saturation current of the SOI device;
alternatively, the calculation method for kink current Ikink of the SOI device is:
I
kink
=
C
k
⁢
(
V
D
-
V
D
⁢
s
⁢
e
)
V
k
⁢
exp
⁡
(
-
V
k
V
D
-
V
D
⁢
s
⁢
e
)
⁢
sech
⁡
(
L
L
b
)
⁢
I
D
⁢
s
⁢
a
⁢
t
;
(
2
)
where Ck is a parameter related to material and geometry of the SOI device, L is channel length of the SOI device, VD is drain voltage of the SOI device, VDse is interpolation function related to the drain saturation voltage, Vk is voltage parameter associated with the kink effect, Lb is carrier diffusion length in body region of the SOI device, and IDsat is drain saturation current of the SOI device.

### Claim 5 (depends on 4)

The method according to claim 4, wherein the method further comprises:
parameter extraction of the threshold field FI:
obtaining drain current ID and drain saturation current IDsat of multiple long-channel SOI devices with fixed channel width but varied channel lengths at multiple gate voltages;
using equation (1) to establish function with the threshold field FI as slope in long-channel SOI devices;
according to the drain current ID and drain saturation current IDsat of the multiple long-channel SOI devices at multiple gate voltages, and the function with the threshold field FI as the slope in long-channel devices, calculating the threshold fields for impact ionization of the multiple long-channel SOI devices at multiple gate voltages.

### Claim 6 (depends on 5)

The method according to claim 5, wherein the method further comprises:
averaging the threshold fields for impact ionization of each long-channel SOI device at multiple gate voltages, respectively, and obtaining the initial fitting value of the threshold field FI in equation (1) of each long-channel SOI devices.

### Claim 7 (depends on 4)

The method according to claim 4, wherein the method further comprises:
extraction of the parameter Vk:
obtaining drain current ID and drain saturation current IDsat of multiple long-channel SOI devices with fixed channel width but varied channel lengths at multiple gate voltages;
using equation (2) to establish the function with Vk as the slope in long-channel SOI devices;
according to the drain current ID and drain saturation current IDsat of the multiple long-channel SOI devices at multiple gate voltages, and the function with Vk as the slope in long-channel devices, calculating Vk values of the multiple long-channel SOI devices at multiple gate voltages.

### Claim 8 (depends on 1)

An electronic apparatus, comprising:
one or more processors; and
one or more computer memory devices arranged to store computer-executable instructions, wherein the one or more processors execute the computer-executable instructions to implement the kink current calculation method for an SOI device according to claim 1.

### Claim 9 (depends on 2)

The method according to claim 2, wherein the parasitic transistor effect factor is:
sech
⁢
(
L
L
b
)
where L is the channel length of the SOI device and Lb is the carrier diffusion length in the body region of the SOI device.

### Claim 10 (depends on 3)

The method according to claim 3, wherein the impact ionization factor is:
(
V
D
-
V
D
⁢
s
⁢
e
)
l
d
⁢
exp
⁡
(
-
F
I
⁢
l
d
V
D
-
V
D
⁢
s
⁢
e
)
;
alternatively, the impact ionization factor is:
(
V
D
-
V
D
⁢
s
⁢
e
)
V
k
⁢
exp
⁡
(
-
V
k
V
D
-
V
D
⁢
s
⁢
e
)
.

### Claim 11 (depends on 5)

The method according to claim 5, wherein the method further comprises:
parameter extraction of the carrier diffusion length Lb in the body region:
using equation (1) to establish function with
-
1
L
b
as the slope in long-channel SOI devices;
calculating average value of the threshold fields for impact ionization of each long-channel SOI device at multiple gate voltages, respectively;
according to the average value of the threshold fields for impact ionization of each long-channel SOI device at multiple gate voltages, and the function with
-
1
L
b
as the slope in long-channel devices, calculating the carrier diffusion lengths in the body region of the multiple long-channel SOI devices at multiple gate voltages.

### Claim 12 (depends on 11)

The method according to claim 11, wherein the method further comprises:
averaging the carrier diffusion lengths in the body region of the multiple long-channel SOI devices at multiple gate voltages, and obtaining the fitting value of the carrier diffusion length Lb in the body region in equation (1).

### Claim 13 (depends on 11)

The method according to claim 11, wherein the method further comprises:
extraction of the parameter C:
calculating average value of carrier diffusion lengths in the body region of the multiple long-channel SOI devices at multiple gate voltages;
according to the average value of carrier diffusion lengths in the body region of the multiple long-channel SOI devices at multiple gate voltages, and the average value of the threshold fields for impact ionization of each long-channel SOI device at multiple gate voltages, calculating the parameter C in equation (1) of the multiple long-channel SOI devices at multiple gate voltages.

### Claim 14 (depends on 13)

The method according to claim 13, wherein the method further comprises:
taking average value of the parameter C of the multiple long-channel SOI devices at multiple gate voltages as initial fitting value of the parameter C in equation (1);
substituting the initial fitting value of the parameter C into equation (1), and according to average value of the carrier diffusion lengths in the body region of the multiple long-channel SOI devices at multiple gate voltages, determining the threshold field for impact ionization of each SOI device at multiple gate voltages, respectively, as fitting value of the threshold field FI in equation (1) of each long-channel SOI device;
repeating the parameter C extraction steps to obtain the fitting values of the parameter C in equation (1) for the multiple long-channel SOI devices at multiple gate voltages.

### Claim 15 (depends on 7)

The method according to claim 7, wherein the method further comprises:
parameter extraction of carrier diffusion length Lb in the body region and Ck:
using equation (2) to establish function with
-
1
L
b
as slope and ln(2Ck) as intercept in long-channel SOI devices;
calculating Vk average value of each long-channel SOI device at multiple gate voltages, respectively;
according to the Vk average value of each long-channel SOI device at multiple gate voltages, and the function with
-
1
L
b
as the slope, ln(2Ck) as the intercept in long-channel devices, calculating the carrier diffusion length Lb in the body region and Ck of the multiple long-channel SOI devices at multiple gate voltages.

### Claim 16 (depends on 15)

The method according to claim 15, wherein the method further comprises:
averaging Ck values of the multiple long-channel SOI devices at multiple gate voltages, and obtaining the fitting value of Ck in equation (2); and/or,
averaging the carrier diffusion lengths in the body region of the multiple long-channel SOI devices at multiple gate voltages, and obtaining the fitting value of the carrier diffusion length Lb in the body region in equation (2); and/or,
substituting the average value of parameter Ck and the carrier diffusion length Lb in the body region of the multiple long-channel SOI devices at multiple gate voltages into equation (2), respectively, and obtaining the Vk fitting values in equation (2) of the multiple long-channel SOI devices at multiple gate voltages.