CN112434485A - Semiconductor device resistor mismatch model correction method - Google Patents

Semiconductor device resistor mismatch model correction method Download PDF

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CN112434485A
CN112434485A CN201910785194.3A CN201910785194A CN112434485A CN 112434485 A CN112434485 A CN 112434485A CN 201910785194 A CN201910785194 A CN 201910785194A CN 112434485 A CN112434485 A CN 112434485A
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resistor
resistance
value
rend
mismatch
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周天舒
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Suzhou Nexun High Energy Semiconductor Co ltd
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Suzhou Nexun High Energy Semiconductor Co ltd
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Abstract

The invention discloses a correction method of a resistor mismatch model, which comprises the following steps of firstly, introducing 5 resistor process mismatch parameters; secondly, introducing random deviation amount of the 5 mismatch parameters; thirdly, setting random deviation correction factors of the 5 mismatch parameters; through simplification and correction of the parameters, correction representation of a resistor device mismatch model is realized, and therefore the influence of the resistor width W, the resistor length L and the resistor distance D on the resistor device mismatch is obtained.

Description

Semiconductor device resistor mismatch model correction method
Technical Field
The invention relates to the technical field of microelectronics, in particular to a resistance mismatch model improvement method of a semiconductor device.
Background
In the design and production process of integrated circuits, due to uncertainty, random error, gradient error, etc., some semiconductor devices that are identical in design have deviations after production, which is called mismatch of semiconductor devices (mismatch). Device mismatch can cause device structural and electrical parameters to change, greatly affecting the characteristics of analog circuits. As semiconductor manufacturing processes evolve, device dimensions continue to shrink, and device mismatches are mainly caused by random errors that are typically caused by integrated circuit manufacturing processes. Especially for new compound semiconductor processes (GaN MMICs), the mismatch of rf devices is particularly important since they are mainly various rf devices (including resistors) and are more susceptible to random errors in the integrated circuit manufacturing process.
The current SPICE (simulation Program with Integrated Circuit Emphasis) model lacks a device mismatch model of improved resistance. The technical problem to be solved by the invention is as follows: the model can better simulate the mismatch condition of the resistor caused by random errors in the use process of the SPICE model, and improves the simulation precision of simulation, particularly radio frequency circuits.
Disclosure of Invention
In view of this, the present invention provides a method for improving a resistance mismatch model of a semiconductor device, so as to solve a circuit simulation error caused by a resistance error in the prior art, thereby improving the simulation accuracy of a radio frequency circuit in the prior art.
The invention provides a resistance mismatch model correction method, which is characterized by comprising the following steps:
firstly, the width of a resistor is W, and the length of the resistor is L;
secondly, determining 5 resistor process mismatch parameters which are a square resistor RS, a terminal resistor REND, a resistor width offset delta W, a resistor length offset delta L and a resistor value R respectively;
wherein, the characterization relational expression of the resistance is as follows:
Figure BDA0002177823410000021
further, the random deviation factors of the mismatch parameters of the 5 resistance processes are respectively: the random deviation factor of the resistance value R is
Figure BDA0002177823410000022
The square resistance RS random deviation factor is
Figure BDA0002177823410000023
The random deviation factor of the terminal resistor REND is
Figure BDA0002177823410000024
The random deviation factor of the deviation amount Delta W of the resistance width is
Figure BDA0002177823410000025
The random deviation factor of the offset amount Delta L of the resistance length is
Figure BDA0002177823410000026
And the random deviation of the mismatch parameters of the 5 resistor processesThe following relation is satisfied between the factors:
Figure BDA0002177823410000027
further, the random deviation correction factors of the mismatch parameter of the resistance process are respectively: the random deviation correction factor of the square resistor RS is SRS、TRSThe random deviation correction factor of the terminal resistor REND is SREND、TRENDThe random deviation correction factor of the deviation amount delta W of the resistance width is SW、TWThe random deviation correction factor of the offset amount Delta L of the resistance length is SL、TL(ii) a And satisfies the following relation:
Figure BDA0002177823410000028
Figure BDA0002177823410000029
Figure BDA0002177823410000031
Figure BDA0002177823410000032
wherein D is the distance between the resistors.
Further, the corrected resistance value R satisfies:
Figure BDA0002177823410000033
wherein R _ original is the original resistance value, TALLAs a random deviation correction factor of the resistance value R, agauss (0,1,3) indicates an expected value of 1 and a standard deviation of 1/3The random numbers in the value range of normal distribution.
Further, the random offset correction factor SRS、TRS、SREND、、TREND、SW、TW、SL、TLAnd TALLOnly with respect to the resistor width W, the resistor length L and the spacing D between the resistors.
Further, the random offset correction factor SRS、TRS、SREND、、TREND、SW、TW、SL、TLAnd TALLThe calculation of (a) includes:
selecting data with the largest resistance length L value from device mismatch data of the resistance obtained through actual test, selecting a group of data with the largest resistance width W value from the data, substituting the group of data into a relational expression of a random deviation factor and a random deviation correction factor of a resistance process mismatch parameter, and obtaining the product through simplified approximate operation:
Figure BDA0002177823410000034
Figure BDA0002177823410000041
Figure BDA0002177823410000042
Figure BDA0002177823410000043
Figure BDA0002177823410000044
further, the resistance length L and the resistance width W are maximum
Figure BDA0002177823410000045
Respectively substituting the R values into the simplified approximate relational expression to obtain random deviation correction factors T corresponding to different D valuesRS、TREND、TW、TLAnd TALLThe value of (a).
Further, T is addedRSValue substitution formula
Figure BDA0002177823410000046
Obtaining S corresponding to different values of W and LRSValue, SRSOnly related to W and L;
will obtain TRENDValue substitution formula
Figure BDA0002177823410000047
Obtaining S corresponding to different values of W and LRENDValue, SRENDOnly related to W and L;
will obtain TWValue substitution formula
Figure BDA0002177823410000048
Obtaining S corresponding to different L valuesWValue, SWOnly related to L;
will obtain TLValue substitution formula
Figure BDA0002177823410000049
Obtaining S corresponding to different W valuesLValue, SLOnly related to W.
The invention provides a resistor mismatch model improvement method according to the physical mechanism of resistor device mismatch, and firstly, 5 resistor process mismatch parameters are introduced; secondly, introducing random deviation factors of the 5 mismatch parameters; thirdly, setting random deviation correction factors of the 5 mismatch parameters; through simplification and correction of the parameters, the device mismatch model of the resistor is corrected and represented, so that the influence of the resistor width W, the resistor length L and the resistor distance D on the mismatch of the resistor is obtained, the circuit simulation error caused by the resistor error is reduced, and the simulation precision of the radio frequency circuit in the prior art is improved.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention are fully described by specific embodiments. It is obvious that the described embodiments are a part of the embodiments of the present invention, not all embodiments, and all other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without inventive efforts fall within the scope of the present invention.
In order to solve the above technical problem, the method for correcting the mismatch model of the semiconductor device resistor provided by the present invention comprises:
first, in the resistance mismatch model, the resistance width is W, the resistance length is L, and 5 new resistance process mismatch parameters are introduced into the mismatch model of the present invention, which are the square resistance RS (sheet-resistance), the terminal resistance red (end-resistance), the offset Δ W (resistance width offset value) of the resistance width, the offset Δ L (resistance length offset value) of the resistance length, and the resistance r (resistance).
According to the role of the 5 resistance mismatch parameters and the resistance self parameters in the model, the following physical relationship is provided:
Figure BDA0002177823410000051
secondly, random deviation factors of the 5 mismatch parameters are additionally introduced, wherein the random deviation factors of the resistance values are respectively
Figure BDA0002177823410000052
The random bias factor of the square resistance is
Figure BDA0002177823410000053
Random offset factor of termination resistance of
Figure BDA0002177823410000054
The random deviation factor of the offset of the resistor width is
Figure BDA0002177823410000055
The random deviation factor of the offset of the resistor length is
Figure BDA0002177823410000056
The following relation is satisfied between the random deviation factors of the 5 resistances:
Figure BDA0002177823410000061
again, the D parameter of the spacing between the introduced resistors, for example, (D1, D2, D3 and D4) is the spacing between the upper, lower, left and right resistors of the semiconductor device, respectively, and D ═ Max (D1, D2, D3, D4).
Then set SRS、TRS、SREND、TREND、SW、TW、SL、TLRespectively, random bias correction factors in the resistance model. Specifically, the random deviation correction factor of the square resistor RS is SRS、TRSThe random deviation correction factor of the terminal resistor REND is SREND、TRENDThe random deviation correction factor of the deviation amount delta W of the resistance width is SW、TWThe random deviation correction factor of the offset amount Delta L of the resistance length is SL、TL。
Setting a random bias factor of the sheet resistance to
Figure BDA0002177823410000062
It satisfies the following relation:
Figure BDA0002177823410000063
setting a random bias factor of the termination resistance to
Figure BDA0002177823410000064
It satisfies the following relation:
Figure BDA0002177823410000065
setting a random deviation factor of the amount of shift of the resistor width to
Figure BDA0002177823410000066
It satisfies the following relation:
Figure BDA0002177823410000067
setting a random deviation factor of the amount of shift of the resistor length to
Figure BDA0002177823410000068
It satisfies the following relation:
Figure BDA0002177823410000069
finally, the invention carries out mismatch improvement on the resistance value of the semiconductor device according to the introduced resistance mismatch parameter and the random deviation factor of the resistance, and the obtained resistance value R after being corrected by the resistance mismatch model meets the following relation formula:
Figure BDA0002177823410000071
wherein R _ original is the original resistance value, TALLAgauss (0,1,3) represents a random number within a normal distribution range having an expected value of 1 and a standard deviation of 1/3, which is a random deviation correction factor for the resistance value R. The agauss (absolute _ val, abs _ variation, sigma) function is a normal distribution function using absolute variables in SPICE software, where nominal _ val is the nominal value of the normal distribution, and abs _ variation is the absolute offset of the normal distribution, sigma is a specified level of absolute offset (specifiedlevel) of the normal distribution. The value of the agauss function ranges from nominal _ val _ abs _ variation to nominal val + abs variation. For example, if sigma is 3, the standard deviation of the normal distribution is abs _ variation/3.
In the embodiment of the present invention, it is,
Figure BDA0002177823410000072
and R can be obtained by actual testing. When the simulation of the SPICE model of the device mismatch model is carried out, S can be continuously adjustedRS、TRS、SREND、、TREND、SW、TW、SL、TLAnd TALLThe values of these random bias correction factors are such that the simulation results of the SPICE model of the device mismatch model (i.e., the calculation results of the above equations) are equal to the actual mismatch data (i.e., the data obtained from the actual test). Through the above adjustment process, S can be obtainedRS、TRS、SREND、、TREND、SW、TW、SL、TLAnd TALLThe value of the random offset correction factor. These random bias modifiers are only related to functions of W, L and D (D1, D2, D3, and D4), and each set W, L and D corresponds to a set of values for the random bias modifier.
Wherein the random offset correction factor SRS、TRS、SREND、、TREND、SW、TW、SL、TLAnd TALLThe calculation comprises the following steps:
step 1, selecting data with the largest resistance length L value from the mismatch data of the devices of the resistors obtained through actual tests, and selecting a group of data with the largest resistance width W value (referred to as a group of actual measurement data with the largest L and W values for short) from the data, wherein the value of D is not limited.
In practical situations, the resistance length L is much longer than the resistance width W, when L is the largest and W is the largest on the premise of the largest L, when L,
Figure BDA0002177823410000081
W×L、
Figure BDA0002177823410000082
When the parameters all appear on the denominator term, the denominator term values corresponding to the parameters can be approximate to zero. Therefore, according to the above principle, the method can obtain
Figure BDA0002177823410000083
The simplified approximate relationship for R is as follows:
Figure BDA0002177823410000084
Figure BDA0002177823410000085
Figure BDA0002177823410000086
Figure BDA0002177823410000087
Figure BDA0002177823410000088
a set of actual measurements maximizing the values of L and W
Figure BDA0002177823410000089
The R values are respectively substituted into the simplified approximate relational expression, so that random deviation correction factors T corresponding to different D values can be obtainedRS、TREND、TW、TLAnd TALLIs a value of, and TRS、TREND、TW、TLAnd TALLThe value of (D) is only related to D.
Step 2And (3) taking the value of any D obtained in the step (1) as the corresponding TRS、TREND、TW、TLAnd TALLRandom offset correction factors, respectively substituted into the un-simplified resistance-related random offsets
Figure BDA0002177823410000091
And the relation formula of R can respectively obtain S corresponding to different values of L and WRS、SREND、、SW、SLThe value of each random deviation correction factor under different W, L and D conditions is obtained.
Illustratively, will TRSValue substitution formula
Figure BDA0002177823410000092
Obtaining S corresponding to different values of W and LRSValue, SRSOnly W and L are relevant.
Will obtain TRENDValue substitution formula
Figure BDA0002177823410000093
Obtaining S corresponding to different values of W and LRENDValue, SRENDOnly W and L are relevant.
Will obtain TWValue substitution formula
Figure BDA0002177823410000094
Obtaining S corresponding to different L valuesWValue, SWOnly with respect to L.
Will obtain TLValue substitution formula
Figure BDA0002177823410000095
Obtaining S corresponding to different W valuesLValue, SLOnly related to W.
Through the calculation of the step 2, S corresponding to different values of L and W is obtainedRS、SREND、SW、SLThe value of each random deviation correction factor under different W, L and D conditions is obtained.
According to the physical mechanism of the mismatch of the resistor device, 5 mismatch parameters are given for representation, and firstly, 5 resistor process mismatch parameters are introduced; secondly, introducing random deviation amount of the 5 mismatch parameters; thirdly, setting random deviation correction factors of the 5 mismatch parameters; through simplification and correction of the parameters, correction and representation of a resistor device mismatch model are achieved, so that the influence of the resistor width W, the resistor length L and the resistor distance D on the resistor device mismatch is obtained, an improvement method of the device mismatch is provided, the device mismatch of the resistor can be optimized in SPICE software, and the simulation precision of the resistor of the semiconductor device is improved.
It is to be noted that the foregoing is only illustrative of the preferred embodiments of the present invention and the technical principles employed. It will be understood by those skilled in the art that the present invention is not limited to the particular embodiments described herein, but is capable of various obvious modifications, rearrangements, combinations and substitutions without departing from the scope of the invention. Therefore, although the present invention has been described in greater detail by the above embodiments, the present invention is not limited to the above embodiments, and may include other equivalent embodiments without departing from the spirit of the present invention, and the scope of the present invention is determined by the scope of the appended claims.

Claims (8)

1. A resistor mismatch model correction method is characterized by comprising the following steps:
firstly, determining the width of a resistor as W and the length of the resistor as L;
secondly, determining 5 resistor process mismatch parameters which are a square resistor RS, a terminal resistor REND, a resistor width offset delta W, a resistor length offset delta L and a resistor value R respectively;
wherein, the characterization relational expression of the resistance is as follows:
Figure FDA0002177823400000011
2. the method for correcting the resistor mismatch model according to claim 1, wherein the random deviation factors of the 5 resistor process mismatch parameters are respectively: the random deviation factor of the resistance value R is
Figure FDA0002177823400000012
The square resistance RS random deviation factor is
Figure FDA0002177823400000013
The random deviation factor of the termination resistance REND is
Figure FDA0002177823400000014
The random deviation factor of the deviation amount Delta W of the resistance width is
Figure FDA0002177823400000015
The random deviation factor of the offset amount Delta L of the resistance length is
Figure FDA0002177823400000016
And the random deviation factors of the mismatch parameters of the 5 resistance processes meet the following relational expression:
Figure FDA0002177823400000017
3. the method for correcting the resistor mismatch model according to claim 2, wherein the random deviation correction factors of the resistor process mismatch parameters are respectively: the random deviation correction factor of the square resistor RS is SRS、TRSThe random deviation correction factor of the terminal resistor REND is SREND、TRENDThe random deviation correction factor of the deviation amount delta W of the resistance width is SW、TWThe random deviation correction factor of the offset amount Delta L of the resistance length is SL、TL(ii) a And satisfies the following relation:
Figure FDA0002177823400000018
Figure FDA0002177823400000021
Figure FDA0002177823400000022
Figure FDA0002177823400000023
wherein D is the distance between the resistors.
4. The method for correcting the resistor mismatch model according to claim 3, wherein the corrected resistance value R satisfies the following condition:
Figure FDA0002177823400000024
wherein R _ original is the original resistance value, TALLAgauss (0,1,3) represents a random number within a normal distribution range having an expected value of 1 and a standard deviation of 1/3, which is a random deviation correction factor for the resistance value R.
5. The method of claim 4, wherein the random bias correction factor S isRS、TRS、SREND、、TREND、SW、TW、SL、TLAnd TALLOnly with respect to the resistor width W, the resistor length L and the spacing D between the resistors.
6. According to claim 4The method for correcting the resistor mismatch model is characterized in that the random deviation correction factor SRS、TRS、SREND、、TREND、SW、TW、SL、TLAnd TALLThe calculation of (a) includes:
selecting data with the largest resistance length L value from device mismatch data of the resistance obtained through actual test, selecting a group of data with the largest resistance width W value from the data, substituting the group of data into a relational expression of a random deviation factor and a random deviation correction factor of a resistance process mismatch parameter, and obtaining the resistance mismatch data through simplified approximate operation:
Figure FDA0002177823400000031
Figure FDA0002177823400000032
Figure FDA0002177823400000033
Figure FDA0002177823400000034
Figure FDA0002177823400000035
7. the method of claim 6, wherein the resistance length L and the resistance width W are maximized for a set of actual measurements
Figure FDA0002177823400000036
Respectively substituting R values into the simplified valuesObtaining random deviation correction factors T corresponding to different D valuesRS、TREND、TW、TLAnd TALLThe value of (a).
8. The method of claim 7, wherein T is adjustedRSValue substitution formula
Figure FDA0002177823400000037
Obtaining S corresponding to different values of W and LRSValue, SRSOnly related to W and L;
will obtain TRENDValue substitution formula
Figure FDA0002177823400000038
Obtaining S corresponding to different values of W and LRENDValue, SRENDOnly related to W and L;
will obtain TWValue substitution formula
Figure FDA0002177823400000039
Obtaining S corresponding to different L valuesWValue, SWOnly related to L;
will obtain TLValue substitution formula
Figure FDA00021778234000000310
Obtaining S corresponding to different W valuesLValue, SLOnly related to W.
CN201910785194.3A 2019-08-23 2019-08-23 Semiconductor device resistor mismatch model correction method Withdrawn CN112434485A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113569516A (en) * 2021-07-30 2021-10-29 上海华虹宏力半导体制造有限公司 Method and system for obtaining BJT mismatch model with random proportional number

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113569516A (en) * 2021-07-30 2021-10-29 上海华虹宏力半导体制造有限公司 Method and system for obtaining BJT mismatch model with random proportional number
CN113569516B (en) * 2021-07-30 2024-02-27 上海华虹宏力半导体制造有限公司 Method and system for obtaining BJT mismatch model with arbitrary proportion number

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