CN101814100A - Method for carrying out image force compensation amendment on height of schottky barrier - Google Patents

Abstract

The invention discloses a kind of methods for carrying out image force compensating approach to the schottky barrier height extracted using J-V standard law, include: to combine GaN HEMT devices structure, derive without boundary layer or boundary layer within 20 angstroms can be considered ideal schottky barrier height because of image force caused by reduction amount

; Construction is about thermal equilbrium state schottky barrier height

Unitary higher order functionality, and according under forward voltage image force influence barrier height rule, determine equivalent potential barrier reduction amount come the approximate accumulative influence that potential barrier is reduced instead of a certain voltage range; Meet with the zero point of MATLAB Program unitary higher order functionality, in zero point and is greater than the barrier height value that standard J-V measurement obtains

Most recent value be modified schottky barrier height value. The present invention compensates for the reduction of the barrier height as caused by image force, reasonable to obtain thermal equilbrium state barrier height, is modified from completely new angle to barrier height.

Description

A kind of method of schottky barrier height being carried out image force compensation correction

Technical field

The present invention relates to Schottky characteristic parametric analysis techniques field, relate in particular to a kind of method of the barrier height in the Schottky characteristic parameter that adopts the extraction of J-V standard law being carried out image force compensation correction.

Background technology

During development GaN HEMT, in order to obtain very high mutual conductance, the quality of the Schottky junction structure that grid and semiconductor GaN form is very crucial, and the accurate extraction of Schottky electrical parameter has significance to device modeling, reliability evaluation etc., especially when the failtests data contrasted, the accurate measurement of Schottky electrical parameter was particularly important for result's influence.

Adopt the J-V standard law to extract schottky barrier height, inevitably can introduce the influence of image force, thereby reduce the schottky barrier height that extracts.And the GaN material is than Si, GaAs, and its high-frequency dielectric constant is less, and this potential barrier that makes image force cause reduces more obvious, for the accurate extraction of barrier height bring unfavorable.

In order to avoid the influence that image force reduces barrier height, Chinese scholars adopts flat-band voltage that the schottky barrier height that is extracted by the J-V standard law is revised usually, perhaps directly adopts the C-V tester to measure and extracts schottky barrier height.But comparatively speaking, the schottky barrier height that adopts the J-V standard law to extract, easy to operate simple, under the situation that does not have the C-V tester, be best choice.

Summary of the invention

(1) technical matters that will solve

Fundamental purpose of the present invention is to provide a kind of the schottky barrier height that adopts the J-V standard law to extract is carried out the method that the image force compensation is revised, to revise the influence of image force to barrier height, near obtaining the thermal equilbrium state schottky barrier height truly, and then the method that adopts the J-V standard law to extract the Schottky parameter improved and develop.

(2) technical scheme

For achieving the above object, the technical solution used in the present invention is:

A kind of method that the schottky barrier height that adopts the J-V standard law to extract is carried out image force compensation correction, this method comprises:

Step 1: in conjunction with GaN HEMT devices structure, derive no contact bed or contact bed at 20 dusts with the interior reduction amount that can be considered desirable schottky barrier height

This reduction amount Because of image force causes;

Step 2: structure is about the thermal equilbrium state schottky barrier height

The monobasic higher order functionality, and influence the rule of barrier height according to image force under the forward voltage, determine that equivalent potential barrier reduction amount is similar to the accumulative total influence that replaces a certain voltage range that potential barrier is reduced;

Step 3: find the solution zero point of monobasic higher order functionality with MATLAB programming, satisfy overgauge J-V in zero point and measure the barrier height value that obtains

Nearest value be the schottky barrier height value of correction.

In the such scheme, the reduction amount of the schottky barrier height of derivation described in the step 1

Specifically comprise: maximum field strength ε _MaxDetermine, the expression and the schottky barrier height of built-in potential derive.In the such scheme, structure is about the thermal equilbrium state schottky barrier height described in the step 2

The monobasic higher order functionality, specifically comprise: barrier height reduction amount is carried out iteration one time with the difference of ideal value and measured value, and be revised schottky barrier height the zero point of the higher order functionality of its structure just.

In the such scheme, determine described in the step 2 that equivalent potential barrier reduction amount is similar to a certain voltage range of replacement to the accumulative total influence that potential barrier reduces, and specifically comprises:, use in order to reflect the accumulative total influence of forward voltage to image force reduction amount

Integral mean to linear zone voltage replaces under the single voltage

In the such scheme, find the solution the zero point of monobasic higher order functionality described in the step 3 with MATLAB programming, specifically comprise: with the higher order functionality of structure as a function handle, with among the MATLAB zero point value finding function to its iterative, 2 real solutions can appear, consider

Nonnegativity, get separating greater than measured value; If meet to find the solution and to check V parameter ₀Value whether seriously greater than the reference value of built-in potential, if greater than, then Schottky barrier is the desirable Schottky of substantial deviation.

(3) beneficial effect

1, utilizes the present invention, influence the rule of barrier height by the analyzing prism image force, construct rational monobasic higher order functionality, choose appropriate forward voltage scope and equivalent barrier height reduction amount is revised the barrier height that measures, compensated because the reduction of the barrier height that image force causes reasonably obtains the thermal equilbrium state barrier height.

2, the present invention reduces compensation to the good image force of barrier height, is from brand-new angle barrier height to be revised.

Description of drawings

The present invention is described in detail below in conjunction with accompanying drawing.

Fig. 1 is the method flow diagram that the barrier height in the Schottky characteristic parameter that adopts the extraction of J-V standard law is carried out image force compensation correction provided by the invention;

Fig. 2 is that image force reduces the barrier height synoptic diagram;

Fig. 3 is the linear zone synoptic diagram that the J-V standard law is extracted barrier height.

Embodiment

For making the purpose, technical solutions and advantages of the present invention clearer, below in conjunction with specific embodiment, and with reference to accompanying drawing, the present invention is described in more detail.

The phenomenon that the potential energy that charge carrier produced when Schottky effect was added electric field reduces because of the effect of the image force of inducting.When an electronics and metal during at a distance of x, the positive charge of will inducting in the metal surface.The power that attractive force between the electronics and the positive charge of being inducted is equivalent to this electronics and can exists between an equal positive charge at-x place.This positive charge becomes image charge.Attractive force is called image force, can be expressed as:

Here ε _s' represent specific inductive capacity, because arriving semiconductor surface, electronics has the relaxation time, and the semiconductor perfact polarization that not necessarily is able to do in time during this period, so need to replace static dielectric with the high-frequency dielectric constant.

As described in Figure 1, Fig. 1 is the method flow diagram that the barrier height in the Schottky characteristic parameter that adopts the extraction of J-V standard law is carried out image force compensation correction provided by the invention, and this method comprises:

Step 1: in conjunction with GaN HEMT devices structure, derive no contact bed or contact bed at 20 dusts with the interior potential barrier reduction amount that can be considered desirable Schottky This reduction amount

Because of image force causes;

Step 2: structure is about the thermal equilbrium state schottky barrier height

The monobasic higher order functionality, and influence the rule of barrier height according to image force under the forward voltage, determine that equivalent potential barrier reduction amount is similar to the accumulative total influence that replaces a certain voltage range that potential barrier is reduced;

Step 3: find the solution zero point of monobasic higher order functionality with MATLAB programming, satisfy overgauge J-V in zero point and measure the barrier height value that obtains

Nearest value be the schottky barrier height value of correction.

As Fig. 2, when extra electric field E, the relation of total potential energy P and distance (from the right tolerance of X axis) is as follows:

Because image force only has the greatest impact to the surface, so use E _MaxIt is a kind of reasonably approximate replacing the electric field E in the following formula.By d[P (x)]/dx=0 ... (3) obtain

Following approximate ideal schottky interface maximum field expression formula is arranged in the n N-type semiconductor N of deriving in 1966 by Atalla and the relation of Metal Contact:

${E_{\max }}^2=\frac{2q}{{\mathrm{\ϵ}}_s}\{N_d(V_d-\frac{\mathrm{kT}}{q})+\frac{p_s\mathrm{kT}}{q}(1-\exp (-q{V}_d/\mathrm{kT}))+\frac{k{\mathrm{TN}}_d}{q}\exp (-q{V}_d/\mathrm{kT})\}\·\·\·\left(5\right)$

Wherein q is an electron charge, ε _sBe semiconductor static dielectric, N _dBe doping content, directly draw V by the surface density conversion or by hall measurement _dBe diffusion potential, k is a Boltzmann constant, and T is a kelvin degree, p _sBe surface voids concentration.Unless barrier height is too high, to such an extent as to surperficial transoid becomes the p type, otherwise second of 5 formula can be ignored.Work as qV _d＞＞kT,

With 6 formula substitutions, 4 formulas,

Constructed fuction

Energy band diagram according to Schottky contacts can get: Wherein V is an impressed voltage, and ξ is the poor of interior conduction band of semiconductor and Fermi level.Gain knowledge as can be known by semiconductor physics:

Wherein Nc is the equivalence density of states at the bottom of the GaN conduction band, and then complete constructed fuction is

The formula that extracts the Schottky parameter with the J-V standard law is

It during n=1 desirable Schottky model.It is generally acknowledged, when

The time, equation can be reduced to

A wherein ^*Be the Li Chaxun constant, A is the grid cross section, and T is a kelvin degree.Formula (2) is taken the logarithm and make the lnI-V curve map, then

Here

The grid section A is difficult to accurate measurement, but since its in logarithm the inside, the error that causes is very little to the influence of potential barrier, available grid are long to be the semi-cylindrical equivalence of radius.

But along with the increase of forward voltage, barrier height can raise gradually during actual measurement, and it is little to that is to say that forward voltage can make that the potential barrier that is caused by image force reduces quantitative change, and this can find out from 7 formulas.Potential barrier reduction amount when the image force influence that this feasible barrier height that is recorded by the J-V standard law is introduced can not simply in the end add thermal equilibrium.For of the accumulative total influence of reaction forward voltage, use now image force reduction amount Integral mean to linear zone voltage replaces

Constructed fuction becomes like this:

Wherein V0 is the linear zone upper limit (as Fig. 3).

With constructed fuction

Find the solution its zero point with MATLAB, be revised

Attention: real solution has 2 zero point, get greater than

Real number value.Now this method is used for the extraction of GaN HEMT device (band cap layer) Schottky characteristic, and contrasts with the C-V mensuration.Example is as follows: the doping content Nd of the GaN HEMT that hall measurement obtains is 1 * 10 ¹⁷Cm ^-3, the J-V standard law measure Equal 0.77eV, ln (I)-V figure (Fig. 3) neutral line district voltage is to 0.45V, and room temperature 300K measures, and available state density Nc is 2.53 * 10 at the bottom of the GaN conduction band ¹⁸m ^-3, GaN material static relative dielectric constant 8.9, high frequency relative dielectric constant 5.35, the C-V method records simultaneously Equal 0.88eV.Bring above numerical value into constructed fuction (16), solve with the MATLAB programming

The difference that it and C-V measure gained is because the Schottky electric current transport mechanism of GaN base also exists a large amount of defectives to assist to wear then composition, the potential barrier of measuring with the J-V standard law that is based upon the thermionic emission theory must than C-V method record low, this meets the otherness of theoretical model.

Above-described specific embodiment; purpose of the present invention, technical scheme and beneficial effect are further described; institute is understood that; the above only is specific embodiments of the invention; be not limited to the present invention; within the spirit and principles in the present invention all, any modification of being made, be equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (5)

1. the schottky barrier height that employing J-V standard law is extracted carries out the method that the image force compensation is revised, and it is characterized in that this method comprises:

Step 1: in conjunction with GaN HEMT devices structure, derive no contact bed or contact bed at 20 dusts with the interior potential barrier reduction amount that can be considered desirable Schottky

This reduction amount

Because of image force causes;

Step 2: structure is about the thermal equilbrium state schottky barrier height

The monobasic higher order functionality, and influence the rule of barrier height according to image force under the forward voltage, determine that equivalent potential barrier reduction amount is similar to the accumulative total influence that replaces a certain voltage range that potential barrier is reduced;

Step 3: find the solution zero point of monobasic higher order functionality with MATLAB programming, satisfy overgauge J-V in zero point and measure the barrier height value that obtains

Nearest value be the schottky barrier height value of correction.

2. the method that the schottky barrier height that adopts the J-V standard law to extract is carried out image force compensation correction according to claim 1 is characterized in that the reduction amount of the schottky barrier height of derivation described in the step 1

Specifically comprise: maximum field strength ε _MaxDetermine, the expression and the schottky barrier height of built-in potential derive.

3. the method that the schottky barrier height that adopts the J-V standard law to extract is carried out image force compensation correction according to claim 1 is characterized in that structure is about the thermal equilbrium state schottky barrier height described in the step 2 The monobasic higher order functionality, specifically comprise: barrier height reduction amount is carried out iteration one time with the difference of ideal value and measured value, and be revised schottky barrier height the zero point of the higher order functionality of its structure just.

4. method of the schottky barrier height that adopts the J-V standard law to extract being carried out image force compensation correction according to claim 1, it is characterized in that, determine described in the step 2 that equivalent potential barrier reduction amount is similar to the accumulative total influence that replaces a certain voltage range that potential barrier is reduced, specifically comprise:, use in order to reflect the accumulative total influence of forward voltage to image force reduction amount

Integral mean to linear zone voltage replaces under the single voltage

5. method of the schottky barrier height that adopts the J-V standard law to extract being carried out image force compensation correction according to claim 1, it is characterized in that, find the solution the zero point of monobasic higher order functionality described in the step 3 with the MATLAB programming, specifically comprise: with the structure higher order functionality as a function handle, with among the MATLAB zero point value finding function to its iterative, 2 real solutions can occur, consider

Nonnegativity, get separating greater than measured value; If meet to find the solution and to check V parameter ₀Value whether seriously greater than the reference value of built-in potential, if greater than, then Schottky barrier is the desirable Schottky of substantial deviation.

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