CN102385642B - Correction method for device dismatch of resistor - Google Patents

Abstract

The invention discloses a corrosion method for device dismatch of a resistor. The procedure is that: firstly defining the number of the technological dismatch parameters as four, namely a square resistance parameter, a terminal resistance parameter, a resistor width offset parameter and a resistance value parameter; secondly, setting the random deviation of the four parameters, and thirdly correcting the device dismatch of the resistor. The correction method for device dismatch of the resistor can perform simulation analysis to the device dismatch of the resistor in simulation program with integrated circuit emphasis (SPICE) software, and the influence to the device dismatch of the resistor of resistor width W, resistor length L and device distance D is fully considered.

Description

The modification method of the device mismatch of resistance

Technical field

The present invention relates to a kind of mismatch modification method of semiconductor devices.

Background technology

In integrated circuit (IC) design and production run, owing to reasons such as uncertainty, stochastic error, gradient errors, but there is deviation after the identical semiconductor devices production during some designs, this just is called the mismatch (mismatch) of semiconductor devices.Device mismatch can cause that device architecture parameter and electrical parameter change, thereby greatly affects the characteristic of mimic channel.Along with the production process of semiconductor development, device size constantly dwindles, and device mismatch is mainly caused by stochastic error, and this stochastic error is normally caused by the integrated circuit production technology.

SPICE(Simulation Program with Integrated Circuit Emphasis) be a general integrated circuit simulating software.Because device mismatch is very large on the impact of integrated circuit, is necessary to find early and revised by software emulation.Lack at present the device mismatch model for resistance in the SPICE software.

Summary of the invention

Technical matters to be solved by this invention provides a kind of device mismatch model of resistance, and the mismatch that this model can cause owing to stochastic error resistance in SPICE software is carried out emulation and revised.

For solving the problems of the technologies described above, the modification method of the device mismatch of resistance of the present invention is:

At first, the technique mismatch parameter of determining resistance is 4, is respectively side-play amount (resistance width offset value), the resistance value (Resistance) of square resistance (sheet resistance), terminal resistance (end resistance), resistance width;

Secondly, set the random deviation of square resistance

The random deviation of setting terminal resistance

Set the random deviation of the side-play amount of resistance width

Set the random deviation of resistance value

${\mathrm{\σ}}_{\mathrm{\ΔR}}^2={\mathrm{\σ}}_{\mathrm{\ΔRS}}^2\×\frac{L^2}{{(W+\mathrm{\ΔW})}^2}+{\mathrm{\σ}}_{\mathrm{\ΔREND}}^2\×\frac{1}{{(W+\mathrm{\ΔW})}^2}+{\mathrm{\σ}}_{\mathrm{\ΔW}}^2\×{[\frac{L\×\mathrm{RS}}{{(W+\mathrm{\ΔW})}^2}+\frac{\mathrm{REND}}{{(W+\mathrm{\ΔW})}^2}]}^2;$

Wherein W is that resistance width, L are that resistance length, D are that spacing, RS between the resistance is that square resistance, REND are that terminal resistance, Δ W are the side-play amount of resistance width, S _{Δ RS}, T _{Δ RS}, S _{Δ REND}, T _{Δ REND}, S _{Δ W}, T _{Δ W}Be the random deviation modifying factor;

Again, the device mismatch of resistance is revised, is specifically comprised:

$R=R\_\mathrm{original}\×[1+\frac{L}{(W+\mathrm{\ΔW})}\×\frac{S_{\mathrm{\ΔRS}}}{\sqrt{W\×L}}\×\mathrm{agauss}\left(\mathrm{0,1,3}\right)+\frac{1}{(W+\mathrm{\ΔW})}\frac{S_{\mathrm{\ΔREND}}}{\sqrt{W\×L}}\×\mathrm{agauss}\left(\mathrm{0,1,3}\right)$

$+(\frac{L\×\mathrm{RS}}{{(W+\mathrm{\ΔW})}^2}+\frac{\mathrm{REND}}{{(W+\mathrm{\ΔW})}^2})\×\frac{S_{\mathrm{\ΔW}}}{\sqrt{L}}\×\mathrm{agauss}\left(\mathrm{0,1,3}\right)+D\×T_{\mathrm{\ΔALL}}\×\mathrm{agauss}\left(\mathrm{0,1,3}\right)]$

Wherein R is revised resistance value, and R_original is original resistance value, T _{Δ ALL}Be the random deviation modifying factor;

Described agauss (0,1,3) expression expectation value is 1, standard deviation (standard deviation) is the random number in 1/3 the normal distribution span;

Described random deviation modifying factor S _{Δ RS}And S _{Δ REND}Only relevant with W and L, described random deviation modifying factor S _{Δ W}Only relevant with L, described random deviation modifying factor T _{Δ RS}, T _{Δ REND}, T _{Δ W}And T _{Δ ALL}Only relevant with D;

Described random deviation modifying factor S _{Δ RS}, T _{Δ RS}, S _{Δ REND}, T _{Δ REND}, S _{Δ W}, T _{Δ W}, T _{Δ ALL}Calculating comprise the steps:

The 1st step, test the device mismatch data of the resistance that obtains from reality, pick out the data of L value maximum, select again one group of data of W value maximum;

Should organize data substitution formula ${\mathrm{\σ}}_{\mathrm{\ΔRS}}^2=D^2\×T_{\mathrm{\ΔRS}}^2,$ ${\mathrm{\σ}}_{\mathrm{\ΔREND}}^2=D^2\×T_{\mathrm{\ΔREND}}^2,$ ${\mathrm{\σ}}_{\mathrm{\ΔW}}^2=D^2\×T_{\mathrm{\ΔW}}^2,$ $R=R\_\mathrm{original}\×[1+(\frac{L\×\mathrm{RS}}{{(W+\mathrm{\ΔW})}^2}+D\×T_{\mathrm{\ΔALL}}\×\mathrm{agauss}\left(\mathrm{0,1,3}\right)];$ Obtain the corresponding T of different D values _{Δ RS}, T _{Δ REND}, T _{Δ W}And T _{Δ ALL}Value;

In the 2nd step, go on foot the corresponding T of any D value that obtains with the 1st _{Δ RS}Value substitution formula

Obtain different W and the corresponding S of L value _{Δ RS}Value;

Go on foot the corresponding T of any D value that obtains with the 1st _{Δ REND}Value substitution formula Obtain different W and the corresponding S of L value _{Δ REND}Value;

Go on foot the corresponding T of any D value that obtains with the 1st _{Δ W}Value substitution formula

Obtain the corresponding S of Different L value _{Δ W}Value.

The present invention can the device mismatch to resistance carry out simulation analysis in SPICE software, and fully takes into account resistance width W, resistance length L and device pitch D to the impact of the device mismatch of resistance.

Embodiment

The modification method of the device mismatch of resistance of the present invention is:

At first, determine that the technique mismatch parameter of resistance is 4, be respectively offset Δ W, the resistance value R of square resistance RS, terminal resistance REND, resistance width.Why adopting these four parameters as the technique mismatch parameter of resistance, is owing to have the physical significance that following formula is expressed between these four parameters:

This is formula 0.Wherein W represents the resistance width, and L represents resistance length.

Secondly, based on research and analysis to the device mismatch data of a large amount of resistance, the random deviation of finding above-mentioned 4 parameters all is to be inversely proportional to resistance width W and resistance length L, is directly proportional with space D between the resistance, obtain thus the stochastic error of each technique mismatch parameter, comprising:

The random deviation of square resistance RS

This is formula 1.

The random deviation of terminal resistance REND

This is formula 2.

The random deviation of the offset Δ W of resistance width

This is formula 3.

The random deviation of resistance value C

${\mathrm{\σ}}_{\mathrm{\ΔR}}^2={\mathrm{\σ}}_{\mathrm{\ΔRS}}^2\×\frac{L^2}{{(W+\mathrm{\ΔW})}^2}+{\mathrm{\σ}}_{\mathrm{\ΔREND}}^2\×\frac{1}{{(W+\mathrm{\ΔW})}^2}+{\mathrm{\σ}}_{\mathrm{\ΔW}}^2\×{[\frac{L\×\mathrm{RS}}{{(W+\mathrm{\ΔW})}^2}+\frac{\mathrm{REND}}{{(W+\mathrm{\ΔW})}^2}]}^2,$

This is formula 4.Formula 4 is after formula 1, formula 2, formula 3 are gathered, and by summary of experience formula 0 is differentiated and is got.

Wherein W is that resistance width, L are that resistance length, D are the spacing between the resistance, S _{Δ RS}, T _{Δ RS}, S _{Δ REND}, T _{Δ REND}, S _{Δ W}, T _{Δ W}Be the random deviation modifying factor.

Again, the device mismatch of resistance is revised, is specifically comprised:

$R=R\_\mathrm{original}\×[1+\frac{L}{(W+\mathrm{\ΔW})}\×\frac{S_{\mathrm{\ΔRS}}}{\sqrt{W\×L}}\×\mathrm{agauss}\left(\mathrm{0,1,3}\right)+\frac{1}{(W+\mathrm{\ΔW})}\frac{S_{\mathrm{\ΔREND}}}{\sqrt{W\×L}}\×\mathrm{agauss}\left(\mathrm{0,1,3}\right)$

$+(\frac{L\×\mathrm{RS}}{{(W+\mathrm{\ΔW})}^2}+\frac{\mathrm{REND}}{{(W+\mathrm{\ΔW})}^2})\×\frac{S_{\mathrm{\ΔW}}}{\sqrt{L}}\×\mathrm{agauss}\left(\mathrm{0,1,3}\right)+D\×T_{\mathrm{\ΔALL}}\×\mathrm{agauss}\left(\mathrm{0,1,3}\right)]$

This is formula 5.Wherein R is revised resistance value, and R_original is original resistance value, T _{Δ ALL}Be the random deviation modifying factor.Described agauss (0,1,3) expression expectation value is 1, standard deviation is the random number in 1/3 the normal distribution span.

Above-mentioned five functions that formula all is W, L and D.The application is based on the device mismatch statistics of a large amount of resistance, through summarizes, finally obtains the funtcional relationship of above-mentioned five formula.

In above-mentioned five formula,

R can obtain by the reality test.When the SPICE emulation of carrying out the device mismatch model, can constantly adjust S _{Δ RS}, T _{Δ RS}, S _{Δ REND}, T _{Δ REND}, S _{Δ W}, T _{Δ W}, T _{Δ ALL}The numerical value of these random deviation modifying factors, thus make the SPICE simulation result (being the result of calculation of above-mentioned formula) of device mismatch model equal actual mismatch data (i.e. the data that actual test obtains).And the process by above adjustment can obtain random deviation modifying factor S _{Δ RS}, T _{Δ RS}, S _{Δ REND}, T _{Δ REND}, S _{Δ W}, T _{Δ W}, T _{Δ ALL}Numerical value.These random deviation modifying factors are only relevant with W, L and D, the value of the corresponding one group of random deviation modifying factor of value of each group W, L and D.

The below provides a kind of computing method of random deviation modifying factor as example.

The 1st step, the device mismatch data of the resistance that obtains from reality test, pick out the data of L value maximum, select again one group of data (referred to as one group of actual measurement data of L and W value maximum) of W value maximum, to the value of D without limits.Above-mentioned formula 1, formula 2, formula 3, formula 5 are reduced to respectively:

${\mathrm{\σ}}_{\mathrm{\ΔRS}}^2=D^2\×T_{\mathrm{\ΔRS}}^2,$ This is formula 1a.

${\mathrm{\σ}}_{\mathrm{\ΔREND}}^2=D^2\×T_{\mathrm{\ΔREND}}^2,$ This is formula 2a.

${\mathrm{\σ}}_{\mathrm{\ΔW}}^2=D^2\×T_{\mathrm{\ΔW}}^2,$ This is formula 3a.

$R=R\_\mathrm{original}\×[1+(\frac{L\×\mathrm{RS}}{{(W+\mathrm{\ΔW})}^2}+D\×T_{\mathrm{\ΔALL}}\×\mathrm{agauss}\left(\mathrm{0,1,3}\right)],$ This is formula 5a.

With one group of actual measurement of described L and W value maximum

The R value is substitution formula 1a, formula 2a, formula 3a, formula 5a respectively.

The principle of simplified formula is: in formula 1, formula 2, formula 3, formula 5 L,

W * L,

All appear on the denominator term, because L is much larger than W, maximum and when the W value was maximum under the prerequisite of maximum L value, these item numbers can be approximated to be zero when the L value.

For formula 1a,

Be actual measurement, thereby can obtain the corresponding T of different D values _{Δ RS}Value, T _{Δ RS}Only relevant with D.

For formula 2a,

Be actual measurement, thereby can obtain the corresponding T of different D values _{Δ REND}Value, T _{Δ REND}Only relevant with D.

For formula 3a,

Be actual measurement, thereby can obtain the corresponding T of different D values _{Δ W}Value, T _{Δ W}Only relevant with D.

For formula 5a, R, RS, Δ W are actual measurements, and R_original is design load thereby is known that W and L are that described maximum occurrences is known, and agauss (0,1,3) is a known function, thereby can obtain the corresponding T of different D values _{Δ ALL}Value, T _{Δ ALL}Only relevant with D.

Through the calculating of the 1st step, obtained the corresponding T of different D values _{Δ RS}, T _{Δ REND}, T _{Δ W}And T _{Δ ALL}Value.

In the 2nd step, go on foot the corresponding T of any D value that obtains with the 1st _{Δ RS}Value substitution formula 1 obtains different W and the corresponding S of L value _{Δ RS}Value, S _{Δ RS}Only relevant with W and L.

Go on foot the corresponding T of any D value that obtains with the 1st _{Δ REND}Value substitution formula 2 obtains different W and the corresponding S of L value _{Δ REND}Value, S _{Δ REND}Only relevant with W and L.

Go on foot the corresponding T of any D value that obtains with the 1st _{Δ W}Value substitution formula 3 obtains the corresponding S of Different L value _{Δ W}Value, S _{Δ W}Only relevant with L.

Through the calculating of the 2nd step, the Different L of having got back and the corresponding S of W value _{Δ RS}, S _{Δ REND}And S _{Δ W}Value, namely obtained the value of each random deviation modifying factor in different W, L and the D situation.

Agauss (nominal_val, abs_variation, sigma) function is the normal distyribution function of the absolute variable of usefulness in the SPICE software, wherein nominal_val is the nominal value (nominal value) of normal distribution, abs_variation is the absolute offset values (absolute variation) of normal distribution, and sigma is the specified level (specified level) of the absolute offset values of normal distribution.The span of agauss function is from nominal_val-abs_variation to nominal_val+abs_variation.Sigma=3 for example, then the standard deviation of this normal distribution is abs_variat ion/3.

The present invention has provided 4 parameters and has been characterized, and provided the modification method of device mismatch according to the Physical Mechanism of the device mismatch of resistance, finally can the device mismatch to resistance carry out simulation analysis in SPICE software.

Claims (1)

1. the modification method of the device mismatch of a resistance is characterized in that:

At first, determine that the technique mismatch parameter of resistance is 4, be respectively square resistance, terminal resistance, the side-play amount of resistance width, resistance value;

Secondly, set the random deviation of square resistance

The random deviation of setting terminal resistance

Set the random deviation of the side-play amount of resistance width

Set the random deviation of resistance value

${\mathrm{\σ}}_{\mathrm{\ΔR}}^2={\mathrm{\σ}}_{\mathrm{\ΔRS}}^2\×\frac{L^2}{{(W+\mathrm{\ΔW})}^2}+{\mathrm{\σ}}_{\mathrm{\ΔREND}}^2\×\frac{1}{{(W+\mathrm{\ΔW})}^2}+{\mathrm{\σ}}_{\mathrm{\ΔW}}^2\×{[\frac{L\×\mathrm{RS}}{{(W+\mathrm{\ΔW})}^2}+\frac{\mathrm{REND}}{{(W+\mathrm{\ΔW})}^2}]}^2;$

Wherein W is that resistance width, L are that resistance length, D are that spacing, RS between the resistance is that square resistance, REND are that terminal resistance, Δ W are the side-play amount of resistance width, S _{Δ RS}, T _{Δ RS}, S _{Δ REND}, T _{Δ REND}, S _{Δ W}, T _{Δ W}Be the random deviation modifying factor;

Again, the device mismatch of resistance is revised, is specifically comprised:

$R=R\_\mathrm{original}\×[1+\frac{L}{(W+\mathrm{\ΔW})}\×\frac{S_{\mathrm{\ΔRS}}}{\sqrt{W\×L}}\×\mathrm{agauss}\left(\mathrm{0,1,3}\right)+\frac{1}{(W+\mathrm{\ΔW})}\frac{S_{\mathrm{\ΔREND}}}{\sqrt{W\×L}}\×\mathrm{agauss}\left(\mathrm{0,1,3}\right)$

$+(\frac{L\×\mathrm{RS}}{{(W+\mathrm{\ΔW})}^2}+\frac{\mathrm{REND}}{{(W+\mathrm{\ΔW})}^2})\×\frac{S_{\mathrm{\ΔW}}}{\sqrt{L}}\×\mathrm{agauss}\left(\mathrm{0,1,3}\right)+D\×T_{\mathrm{\ΔALL}}\×\mathrm{agauss}\left(\mathrm{0,1,3}\right)]$

Wherein R is revised resistance value, and R_original is original resistance value, T _{Δ ALL}Be the random deviation modifying factor;

Described agauss (0,1,3) expression expectation value is 1, standard deviation is the random number in 1/3 the normal distribution span;

Described random deviation modifying factor S _{Δ RS}And S _{Δ REND}Only relevant with W and L, described random deviation modifying factor S _{Δ W}Only relevant with L, described random deviation modifying factor T _{Δ RS}, T _{Δ REND}, T _{Δ W}And T _{Δ ALL}Only relevant with D;

Described random deviation modifying factor S _{Δ RS}, T _{Δ RS}, S _{Δ REND}, T _{Δ REND}, S _{Δ W}, T _{Δ W}, T _{Δ ALL}Calculating comprise the steps:

The 1st step, test the device mismatch data of the resistance that obtains from reality, pick out the data of L value maximum, select again one group of data of W value maximum;

Should organize data substitution formula ${\mathrm{\σ}}_{\mathrm{\ΔRS}}^2=D^2\×T_{\mathrm{\ΔRS}}^2,$ ${\mathrm{\σ}}_{\mathrm{\ΔREND}}^2=D^2\×T_{\mathrm{\ΔREND}}^2,$ ${\mathrm{\σ}}_{\mathrm{\ΔW}}^2=D^2\×T_{\mathrm{\ΔW}}^2,$

$R=R\_\mathrm{original}\×[1+(\frac{L\×\mathrm{RS}}{{(W+\mathrm{\ΔW})}^2}+D\×T_{\mathrm{\ΔALL}}\×\mathrm{agauss}\left(\mathrm{0,1,3}\right)];$ Obtain the corresponding T of different D values _{Δ RS}, T _{Δ REND}, T _{Δ W}And T _{Δ ALL}Value;

In the 2nd step, go on foot the corresponding T of any D value that obtains with the 1st _{Δ RS}Value substitution formula

Obtain different W and the corresponding S of L value _{Δ RS}Value;

Go on foot the corresponding T of any D value that obtains with the 1st _{Δ REND}Value substitution formula

Obtain different W and the corresponding S of L value _{Δ REND}Value;

Go on foot the corresponding T of any D value that obtains with the 1st _{Δ W}Value substitution formula Obtain the corresponding S of Different L value _{Δ W}Value.