CN102313835A - Method for measuring electric parameter of gallium arsenide pseudomorphic HEMT (high electron mobility transistor) material - Google Patents

Abstract

The invention discloses a method for measuring an electric parameter of a gallium arsenide pseudomorphic HEMT (high electron mobility transistor) material and relates to a method for measuring the electric parameter of a semiconductor material. The method is used for measuring a carrier concentration and a mobility in the gallium arsenide pseudomorphic HEMT material by a non-contact Hall measurement method and comprises the following steps of: measuring an incident power, a reflection power and a Hall effect microwave power of the measured gallium arsenide pseudomorphic HEMT material by a microwave Hall measurement device; calculating conductance tensors of a measured sample in different magnetic fields; and calculating the carrier concentration and the mobility of the gallium arsenide pseudomorphic HEMT material. The method disclosed by the invention is nondestructive, is convenient and rapid, has high efficiency and can be used for accurately measuring the carrier concentration and the mobility in the gallium arsenide-based biplane doped pseudomorphic HEMT material. The defects that the existing measurement method is fussy to operate, has low efficiency and a certain error and cannot really and completely reflect the electrical properties of the material are overcome.

Description

The electric parameter measurement method of gallium arsenide pseudomorphic high electron mobility transistor material

Technical field

Technical scheme of the present invention relates to the measuring method of semiconductor material electrical quantity, specifically the electric parameter measurement method of gallium arsenide pseudomorphic high electron mobility transistor material.

Background technology

Gallium arsenide (hereinafter to be referred as GaAs) basic biplane (hereinafter to be referred as two δ) doped with Al GaAs/InGaAs pseudomorphic high electron mobility transistors (hereinafter to be referred as PHEMT) because its high power, high-level efficiency, the good linearity and can be in bigger voltage range characteristics such as operate as normal, be widely used in technical fields such as phased-array radar, satellite communication, Wireless Local Loop and person communication system; The PHEMTT device makes it become the main flow device of millimeter wave high-end applications particularly in the high-end characteristic with good power and efficient of millimeter wave.The performance of PHEMT device depends on the quality of corresponding PHEMT basic material electric property, and wherein carrier concentration and hall mobility are the key electrical quantity indexs of estimating the PHEMT quality of materials.

See that from the situation of domestic and international prior art and literature search the existing measuring method of PHEMT material carrier concentration and mobility mainly comprises standard law and vanderburg method.Limitation and deficiency below these two kinds of measuring methods exist in concrete the application:

(1) from having the operating procedure of measuring method now: standard law and vanderburg method all belong to the contact hall measurement, need on testing sample, make Hall electrode, and the distribution patterns of electrode and the relative size size of electrode and sample are had specific (special) requirements; Wherein standard law also needs sample is processed the rules specific shape, is made for the rectangle sample of length breadth ratio＞3 usually.The preparation process complex operation of appearance to be measured, inefficiency, the introducing of electrode simultaneously and the destruction of sample also can be brought certain error to measurement.

(2) from having the applicable situation of measuring method now; Standard law and the vanderburg Hall effect under fixed magnetic field owned by France is measured; Usually the contribution of having only a kind of charge carrier that electricity is led in the supposition detected materials accounts for absolute leading position, therefore only is suitable for the better simply situation of charge carrier constituent ratio.At least comprise δ in actual two δ doping PHEMT material ₁, δ ₂Charge carrier that mixes and the conduction of the charge carrier fellowship in the heavy doping cap layer, adopting the fixed magnetic field method to measure the electrical parameter that obtains is the result of a comprehensive effect, can not be truly the electric property of reaction material fully.

Summary of the invention

Technical matters to be solved by this invention is: the electric parameter measurement method that gallium arsenide pseudomorphic high electron mobility transistor material is provided; Be a kind of non-destructive, convenient and efficient and the method for accurately measuring carrier concentration and mobility in the GaAs based biplane doping pseudomorphic high electron mobility transistor material; The preparation process operation that has overcome appearance to be measured in the existing measuring method is loaded down with trivial details; Inefficiency; The introducing of electrode simultaneously also can bring certain error to measurement with the destruction of sample, and the electrical quantity that adopts the fixed magnetic field method to measure acquisition is the result of a comprehensive effect, can not be truly the shortcoming of the electric property of reaction material fully.

The present invention solves this technical problem the technical scheme that is adopted: the electric parameter measurement method of gallium arsenide pseudomorphic high electron mobility transistor material; Be to measure carrier concentration and mobility in the gallium arsenide pseudomorphic high electron mobility transistor material through a kind of noncontact Hall measuring method, its step is following:

The first step, incident power, reflective power and the Hall effect microwave power of the gallium arsenide pseudomorphic high electron mobility transistor material that employing microwave hall measurement measurement device is measured

Measured PHEMT material sample is placed on the sample stage of microwave hall measurement device 10GHz and TE that the circular waveguide through balance modulation will be sent by controllable magnetic field ₁₁The microwave of pattern is incorporated into the surface of measured gallium arsenide pseudomorphic high electron mobility transistor material; The characteristic impedance of waveguide is 700 Ω, and first detecting device of the forward microwave power through detecting sample under the varying magnetic field condition, second detecting device and the 3rd detecting device that detects the Hall effect microwave power of sample that detect the microwave reflection power of sample are measured TE respectively ₁₁The incident power P of pattern _In, TE ₁₁The mode reflection power P _ReTE with the material surface reflection ₁₀Pattern Hall effect microwave power P _Hall

In second step, calculate the electricity of sample under different magnetic field and lead tensor

The incident power P of the gallium arsenide pseudomorphic high electron mobility transistor material that measures according to the first step _InWith reflective power P _ReBy following formula (1) calculating voltage reflection coefficient Γ, and the incident power P of the gallium arsenide pseudomorphic high electron mobility transistor material that measures according to the first step _InWith Hall effect microwave power P _HallCalculate the sample place microwave electric field electric field strength E on X and Y coordinate axis respectively by following formula (2) and formula (3) _xAnd E _y

$\mathrm{\Γ}={(P_{\mathrm{Re}}/P_{\mathrm{In}})}^{\frac{1}{2}}$ Formula (1)

$E_x=(1+\mathrm{\Γ}){(P_{\mathrm{In}}/A)}^{\frac{1}{2}}$ Formula (2)

$E_y={(P_{\mathrm{Hall}}/A)}^{\frac{1}{2}}$ Formula (3)

A is a constant in the following formula, and it is worth by the integration decision of waveguide mode on whole circular section,

And then calculate sample through following formula (4) and formula (5) and lead tensor at the electricity under the different magnetic field,

${\mathrm{\σ}}_{\mathrm{Xx}}=\frac{(1/Z)\{1-{\mathrm{\Γ}}^2-{(E_y/E_x)}^2\}}{{(1+\mathrm{\Γ})}^2+{(E_y/E_x)}^2}$ Formula (4)

${\mathrm{\σ}}_{\mathrm{Xy}}=\frac{\{(E_y/E_x)/2\mathrm{\Γ}(1+\mathrm{\Γ})\}\{(1+\mathrm{\Γ})(3-\mathrm{\Γ})-{(E_y/E_x)}^2\}}{{(1+\mathrm{\Γ})}^2+{(E_y/E_x)}^2}$ Formula (5);

The 3rd step, the carrier concentration of gallium arsenide pseudomorphic high electron mobility transistor material and the calculating of mobility

Under relaxation time approximation, lead the σ of tensor unit through finding the solution Boltzmann equation acquisition electricity _Xx(B) and σ _Xy(B) with sample in all kinds of carrier concentration n _jAnd mobility [mu] _jRelation, shown in following formula (6) and formula (7), S wherein _jBe carrier electric charge property, electronics is-1, and the hole is+1,

${\mathrm{\σ}}_{\mathrm{Xx}}\left(B\right)=\underset{j}{\mathrm{\Σ}}\frac{{\mathrm{En}}_j{\mathrm{\μ}}_j}{1+{\mathrm{\μ}}_j^2{B}^2}$ Formula (6)

${\mathrm{\σ}}_{\mathrm{Xy}}\left(B\right)=\underset{j}{\mathrm{\Σ}}{S}_j\frac{{\mathrm{En}}_j{\mathrm{\μ}}_j^{2}B}{1+{\mathrm{\μ}}_j^2{B}^2}$ Formula (7)

Suppose that the mobility of electronics and hole is a continuous distribution in the sample, write formula (6) and formula (7) as integrated form, shown in following formula (8) and formula (9), s wherein ⁿ(μ) and s ^pThe electricity that (μ) is respectively electronics and hole is led density function, the contribution of representing electronics and hole that electricity is led, and its value answers>=0,

${\mathrm{\σ}}_{\mathrm{Xx}}\left(B\right)=\underset{0}{\overset{\∞}{\∫}}\frac{s^p\left(\mathrm{\μ}\right)+s^n\left(\mathrm{\μ}\right)}{1+{\mathrm{\μ}}^2{B}^2}\mathrm{D\μ}$ Formula (8)

${\mathrm{\σ}}_{\mathrm{Xy}}\left(B\right)=\underset{0}{\overset{\∞}{\∫}}\frac{[s^p\left(\mathrm{\μ}\right)-s^n\left(\mathrm{\μ}\right)]\mathrm{\μ\; B}}{1+{\mathrm{\μ}}^2{B}^2}\mathrm{D\μ}$ Formula (9)

Solve s by formula (8) and formula (9) ⁿ(μ) and s ^pEnvelope function S (μ) (μ), shown in following formula (10), S (μ) value makes σ under a certain mobility _Xx(B), σ _Xy(B) has the s of clear and definite physical significance ⁿ(μ) and s ^p(μ) upper limit of value has the electricity unit of leading dimension, uses S (μ) value to calculate the carrier concentration n (μ) under the corresponding mobility by following formula (11),

$S\left(\mathrm{\μ}\right)=\frac{{\left|v_{u^{\′}}\right|}^2}{{\mathrm{\α}}_{u^{\′}}}{\left[\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\frac{{\left(\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{Q}_{\mathrm{Ij}}{\left(v_{u^{\′}}\right)}_j\right)}^2}{{\mathrm{\λ}}_i}\right]}^{-1}$ Formula (10)

$n\left(\mathrm{\μ}\right)=\frac{S\left(\mathrm{\μ}\right)}{\mathrm{E\μ}}$ Formula (11)

Thereby obtain conductivity and carrier concentration with mobility continually varying spectrogram, obtain the charge carrier kind quantity j in the sample, and the concentration n of various charge carriers by this spectrogram _jWith mobility [mu] _jApproximate value, with the kind quantity j of the charge carrier that from above-mentioned spectrogram, obtains, and the concentration n of all kinds of charge carriers _jWith mobility [mu] _jApproximate value as initial value, adopt generalized least square method by formula (6) with formula (7) to electric derivative according to carrying out match, acquisition is the unique carrier concentration and mobility electrical quantity that can reflect gallium arsenide pseudomorphic high electron mobility transistor material real information finally.

The electric parameter measurement method of above-mentioned gallium arsenide pseudomorphic high electron mobility transistor material, wherein said microwave hall measurement device mainly comprises: the 3rd detecting device, sample stage, controllable magnetic field, hall probes and four directional couplers of second detecting device of the microwave reflection power of microwave source, circular waveguide, rectangle change circular waveguide converter, first detecting device that detects the forward microwave power of sample, detection sample and the Hall effect microwave power of detection sample; On the direction perpendicular to sample plane, apply controllable magnetic field, except that using between hall probes and the directional coupler coaxial cable is connected, conventional rectangular waveguide is all adopted in the connection between other each device.All parts of this device and installation method all are that the technician in present technique field knows.

The electric parameter measurement method of above-mentioned gallium arsenide pseudomorphic high electron mobility transistor material; Wherein said " varying magnetic field condition ", " A is a constant; its value is by the integration decision of waveguide mode on whole circular section ", " electricity of finding the solution electronics and hole is led the envelope function of density function ", " obtain the charge carrier kind quantity in the sample by conductivity and carrier concentration with mobility continually varying spectrogram; and the approximate value of every kind of carrier mobility and concentration ", " with the kind quantity of the charge carrier that from above-mentioned spectrogram, obtains; and the approximate value of the concentration of all kinds of charge carriers and mobility is as initial value; the employing generalized least square method carries out match to electric derivative certificate; acquisition is the unique carrier concentration and mobility electrical quantity that can reflect gallium arsenide pseudomorphic high electron mobility transistor material real information finally ", these conditions and disposal route all are that those skilled in the art of the present technique know.

The invention has the beneficial effects as follows:

The principle of the electric parameter measurement method of gallium arsenide pseudomorphic high electron mobility transistor material of the present invention is: measure acquisition PHEMT material through the microwave Hall effect and lead tensor at the electricity under the different magnetic field; Lead the dependence of tensor through analyzing electricity to magnetic field intensity, obtain electricity lead with carrier concentration with mobility continually varying spectrogram, and then infer the kind of charge carrier in the material, and the approximate value of the concentration of all kinds of charge carriers and mobility; , electric derivative certificate is handled as initial value with The above results, obtained unique electrical parameter that can reflect gallium arsenide pseudomorphic high electron mobility transistor material real information through the multiple carrier match.

The marked improvement of the electric parameter measurement method of gallium arsenide pseudomorphic high electron mobility transistor material of the present invention is:

(1) the inventive method is a kind of noncontact, a kind of non-destructive, convenient and efficient and the method for accurately measuring carrier concentration and mobility in the GaAs based biplane doping pseudomorphic high electron mobility transistor material; Overcome in the existing measuring method that the preparation process operation of appearance to be measured is loaded down with trivial details, inefficiency, the introducing of electrode simultaneously and the destruction of sample also can bring certain error to measurement; And to adopt the fixed magnetic field method to measure the electrical quantity that obtains be the result of a comprehensive effect, can not be truly the shortcoming of the electric property of reaction material fully.

(2) the inventive method is measured based on the microwave Hall effect, need not introduce Hall electrode, and sample shape is not also had specific (special) requirements.

(3) the present invention is based on the varying magnetic field Hall effect and measure, can overcome disadvantageous measurement influence factor (like the charge carrier in the heavy doping cap layer), obtain the accurate information of kind quantity, all kinds of carrier concentration and the mobility of whole charge carriers in the detected materials.The present invention not only can realize the accurate evaluation to the two δ doping PHEMT material electrical properties of GaAs base, and can be used for instructing the growth technique of judging this material.

Description of drawings

Below in conjunction with accompanying drawing and embodiment the present invention is further specified.

Accompanying drawing is that the structure of the used microwave hall measurement device of the inventive method is formed synoptic diagram.

Among the figure, 1.10GHz microwave source, 2. directional coupler, 3. isolator; 4. detect first detecting device of the forward microwave power of sample, 5. detect second detecting device of the microwave reflection power of sample, 6. rectangle becomes circular waveguide converter, 7. circular waveguide; 8. hall probes, 9. sample stage, 10. controllable magnetic field; 11. attenuator, 12. phase shifters, 13. detect the 3rd detecting device of the Hall effect microwave power of sample.

Embodiment

Accompanying drawing shows, the 3rd detecting device 13 that the microwave hall measurement device that the electric parameter measurement method of gallium arsenide pseudomorphic high electron mobility transistor material of the present invention is adopted becomes circular waveguide converter 6, circular waveguide 7, hall probes 8, sample stage 9, controllable magnetic field 10, attenuator 11, phase shifter 12 by 10GHz microwave source 1, four directional couplers 2, isolators 3, first detecting device 4 that detects the forward microwave power of sample, second detecting device 5, the rectangle that detect the microwave reflection power of sample and detects the Hall effect microwave power of sample constitutes.On the direction perpendicular to sample plane, apply controllable magnetic field 10, except that using between hall probes 8 and the directional coupler 2 coaxial cable is connected, conventional rectangular waveguide is all adopted in the connection between other each device.

Embodiment 1

The preparation of the two δ doping PHEMT materials of GaAs base.

Adopt the molecular beam epitaxy technique technology of preparing, step is: GaAs (100) substrate is successively carrying out preparatory degasification in the Sample Room fast under 90 ℃ and 150 ℃ after the system of packing into; Import pretreatment chamber subsequently; Import the growth room after the completion degasification down at 400 ℃, at 630 ℃, As ₂Carry out surperficial deoxidation 10min under the atmosphere protection, treat to grow when temperature drops to 580 ℃

The GaAs cushion, begin other layers of material of continued growth subsequently, As/Ga line ratio is 17～20, growth rate is 1 μ m/hour; In the InGaAs channel layer growth course, underlayer temperature is controlled at about 480 ℃, to reduce the segregation phenomena of In.In source oven temperature degree is 760 ℃, and the growth time of channel layer is about 30 seconds; Control Al component is 0.22 in the AlGaAs separation layer growth course, and underlayer temperature remains on more than 670 ℃, and the Al source temperature is 1170 ℃, and the AlAs growth rate does

Al source beam current density is 2.0 * 10 ¹⁴/ cm ²S, separation layer growth time are 60 seconds～80 seconds; In the planar silicon δ doping process, the temperature in silicon source is 1105 ℃, opens the As source and presses to guarantee As, opens the atmosphere that pure silicon is made in the Si source, controls bilateral doping content and ratio through the opening time of adjustment silicon source shutter during doping; Heavily mix in the growth course of GaAs cap layer, underlayer temperature is controlled to be 560 ℃, and the arsenic source temperature is 230 ℃, and growth line equivalence pressure is 8.1 * 10 ^-7Torr, silicon source temperature are elevated to 1120 ℃, and growth time is 3 minutes.The basic structure of the two δ doping PHEMT materials of the GaAs of system base is as shown in table 1 thus.

The basic structure of the two δ doping PHEMT materials of table 1GaAs base

Embodiment 2

The preparation of gallium arsenide pseudomorphic high electron mobility transistor material sample

Adopt the technology of embodiment 1 to prepare three groups of gallium arsenide pseudomorphic high electron mobility transistor material samples, two every group altogether.

The A group: the 2# sample comprises two of E and F.The 2# sample adopts smooth heterojunction boundary growing technology preparation in the technology of embodiment 1, promptly in preparation, adopt temperature control and interface growth pause method to being optimized in the InGaAs channel layer growth course, obtains the leveling interface.The 2# sample is thin cap layer structure.

The B group: the 3# sample comprises two of G and H.The 3# sample adopts the preparation of common process technology in the technology of embodiment 1, promptly use common process in the InGaAs channel layer growth course.The 3# sample is the full structure positive of 50nm cap layer thickness.

The C group: the 4# sample comprises two of K and L.The 4# sample adopts smooth heterojunction boundary growing technology preparation in the technology of embodiment 1, promptly in preparation, adopt temperature control and interface growth pause method to being optimized in the InGaAs channel layer growth course, obtains the leveling interface.The 4# sample is the full structure positive of 50nm cap layer thickness.

The structure contrast of three groups of samples is as shown in table 2.

The structure contrast of three groups of samples of table 2

Embodiment 3

Adopt microwave hall measurement device shown in the drawings, measure above-mentioned carrier concentration and the hall mobility of respectively organizing 2 dimensional electron gas (2DEG) in the tested gallium arsenide pseudomorphic high electron mobility transistor material sample channel layer with the inventive method.

3-1.A the measurement of group 2#E sheet sample electrical quantity

The first step, incident power, reflective power and the Hall effect microwave power of the gallium arsenide pseudomorphic high electron mobility transistor material that employing microwave hall measurement measurement device is measured

To place on the sample stage 9 of microwave hall measurement device 10GHz and TE that the circular waveguide 7 through balance modulation will be sent by 10GHz microwave source 1 by the 2#E sheet sample that embodiment 2 makes ₁₁The microwave of pattern is incorporated into the surface of measured gallium arsenide pseudomorphic high electron mobility transistor material; The characteristic impedance of waveguide is 700 Ω; Be respectively 0 in the magnetic field intensity that produces by controllable magnetic field 10, ± 0.1, ± 0.2, ± 0.4, ± 0.6 with the varying magnetic field condition of ± 0.8T under, first detecting device 4 of the forward microwave power through detecting sample, second detecting device 5 and the 3rd detecting device 13 that detects the Hall effect microwave power of sample that detect the microwave reflection power of sample are measured TE respectively ₁₁The incident power P of pattern _In, TE ₁₁The mode reflection power P _ReTE with the material surface reflection ₁₀Pattern Hall effect microwave power P _Hall, measurement result is as shown in the table;

In second step, calculate the electricity of sample under different magnetic field and lead tensor

The incident power P of the gallium arsenide pseudomorphic high electron mobility transistor material that measures according to the first step _InWith reflective power P _ReBy following formula (1) calculating voltage reflection coefficient Γ, and the incident power P of the gallium arsenide pseudomorphic high electron mobility transistor material that measures according to the first step _InWith Hall effect microwave power P _HallCalculate the sample place microwave electric field electric field strength E on X and Y coordinate axis respectively by following formula (2) and formula (3) _xAnd E _y

$\mathrm{\Γ}={(P_{\mathrm{Re}}/P_{\mathrm{In}})}^{\frac{1}{2}}$ Formula (1)

$E_x=(1+\mathrm{\Γ}){(P_{\mathrm{In}}/A)}^{\frac{1}{2}}$ Formula (2)

$E_y={(P_{\mathrm{Hall}}/A)}^{\frac{1}{2}}$ Formula (3)

A is a constant in the following formula, and its value is by the integration decision of waveguide mode on whole circular section.

And then through following formula (4) and formula (5) calculate sample be respectively 0 in magnetic field intensity, ± 0.1, ± 0.2, ± 0.4, ± 0.6 with the magnetic field of ± 0.8T under electricity lead tensor,

${\mathrm{\σ}}_{\mathrm{Xx}}=\frac{(1/Z)\{1-{\mathrm{\Γ}}^2-{(E_y/E_x)}^2\}}{{(1+\mathrm{\Γ})}^2+{(E_y/E_x)}^2}$ Formula (4)

${\mathrm{\σ}}_{\mathrm{Xy}}=\frac{\{(E_y/E_x)/2\mathrm{\Γ}(1+\mathrm{\Γ})\}\{(1+\mathrm{\Γ})(3-\mathrm{\Γ})-{(E_y/E_x)}^2\}}{{(1+\mathrm{\Γ})}^2+{(E_y/E_x)}^2}$ Formula (5);

The 3rd step, the carrier concentration of gallium arsenide pseudomorphic high electron mobility transistor material and the calculating of mobility

Under relaxation time approximation, lead the σ of tensor unit through finding the solution Boltzmann equation acquisition electricity _Xx(B) and σ _Xy(B) with sample in all kinds of carrier concentration n _jAnd mobility [mu] _jRelation, shown in following formula (6) and formula (7), S wherein _jBe carrier electric charge property, electronics is-1, and the hole is+1,

${\mathrm{\σ}}_{\mathrm{Xx}}\left(B\right)=\underset{j}{\mathrm{\Σ}}\frac{{\mathrm{En}}_j{\mathrm{\μ}}_j}{1+{\mathrm{\μ}}_j^2{B}^2}$ Formula (6)

${\mathrm{\σ}}_{\mathrm{Xy}}\left(B\right)=\underset{j}{\mathrm{\Σ}}{S}_j\frac{{\mathrm{En}}_j{\mathrm{\μ}}_j^{2}B}{1+{\mathrm{\μ}}_j^2{B}^2}$ Formula (7)

Suppose that the mobility of electronics and hole is a continuous distribution in the sample, can be write formula (6) and formula (7) as integrated form, shown in following formula (8) and formula (9), s wherein ⁿ(μ) and s ^pThe electricity that (μ) is respectively electronics and hole is led density function, the contribution of representing electronics and hole that electricity is led, and its value answers>=0,

${\mathrm{\σ}}_{\mathrm{Xx}}\left(B\right)=\underset{0}{\overset{\∞}{\∫}}\frac{s^p\left(\mathrm{\μ}\right)+s^n\left(\mathrm{\μ}\right)}{1+{\mathrm{\μ}}^2{B}^2}\mathrm{D\μ}$ Formula (8)

${\mathrm{\σ}}_{\mathrm{Xy}}\left(B\right)=\underset{0}{\overset{\∞}{\∫}}\frac{[s^p\left(\mathrm{\μ}\right)-s^n\left(\mathrm{\μ}\right)]\mathrm{\μ\; B}}{1+{\mathrm{\μ}}^2{B}^2}\mathrm{D\μ}$ Formula (9)

Solve s by formula (8) and formula (9) ⁿ(μ) and s ^pEnvelope function S (μ) (μ), shown in following formula (10), S (μ) value makes σ under a certain mobility _Xx(B), σ _Xy(B) has the s of clear and definite physical significance ⁿ(μ) and s ^p(μ) upper limit of value has the electricity unit of leading dimension, uses S (μ) value to calculate the carrier concentration n (μ) under the corresponding mobility by following formula (11),

$S\left(\mathrm{\μ}\right)=\frac{{\left|v_{u^{\′}}\right|}^2}{{\mathrm{\α}}_{u^{\′}}}{\left[\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\frac{{\left(\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{Q}_{\mathrm{Ij}}{\left(v_{u^{\′}}\right)}_j\right)}^2}{{\mathrm{\λ}}_i}\right]}^{-1}$ Formula (10)

$n\left(\mathrm{\μ}\right)=\frac{S\left(\mathrm{\μ}\right)}{\mathrm{E\μ}}$ Formula (11)

10 ²～10 ⁶Cm ²V ^-1S ^-1The mobility span in, this scope has contained the electricity that is close to all charge carriers in the semiconductor material leads contribution, gets 400 uniform discrete data points, through type (10) calculates corresponding S (μ) value, through type (11) calculates corresponding n (μ) value again.Can obtain conductivity and carrier concentration with mobility continually varying spectrogram through drawing S (μ)-μ and n (μ)-μ relation curve; Can confirm that by the number at peak in the mobility spectrum charge carrier kind quantity j in the sample equals 1; And such carrier electric charge property is an electronics, its mobility [mu] _jWith concentration n _jApproximate value be respectively 7526cm ²V ^-1S ^-1With 3.38 * 10 ¹²Cm ^-2With j=1, S _j=-1 substitution formula (6) and formula (7), and use 7526cm ²V ^-1S ^-1With 3.38 * 10 ¹²Cm ^-2As carrier concentration n _jWith mobility [mu] _jInitial value, adopt generalized least square method by formula (6) with formula (7) to resulting electric derivative of second step according to carrying out match, acquisition is the unique carrier concentration and mobility electrical quantity that can reflect the sample real information finally, is respectively 3.11 * 10 ¹²Cm ^-2And 7284cm ²V ^-1S ^-1, list in the table 3.The match of the calculating of mobility spectrum and electric derivative certificate all adopts the formula translation programming to realize, calculates operation platform based on the Pentium of Intel processor and the windows of Microsoft operating system.

3-2.A the measurement of group 2#F sheet sample electrical quantity

Except that A group 2#E sheet sample was replaced with A group 2#F sheet sample, other measuring methods and process were with the measurement of A group 2#E sheet sample electrical quantity, and electric parameter measurement the results are shown in Table 3.

3-3.B the measurement of group 3#G sheet sample electrical quantity

Except that A group 2#E sheet sample was replaced with B group 3#G sheet sample, other measuring methods and process were with the measurement of A group 2#E sheet sample electrical quantity, and electric parameter measurement the results are shown in Table 3.

3-4.B the measurement of group 3#H sheet sample electrical quantity

Except that A group 2#E sheet sample was replaced with B group 3#H sheet sample, other measuring methods and process were with the measurement of A group 2#E sheet sample electrical quantity, and electric parameter measurement the results are shown in Table 3.

3-5.C the measurement of group 4#K sheet sample electrical quantity

Except that A group 2#E sheet sample was replaced with C group 4#K sheet sample, other measuring methods and process were with the measurement of A group 2#E sheet sample electrical quantity, and electric parameter measurement the results are shown in Table 3.

3-6.C the measurement of group 4#L sheet sample electrical quantity

Except that A group 2#E sheet sample was replaced with C group 4#L sheet sample, other measuring methods and process were with the measurement of A group 2#E sheet sample electrical quantity, and electric parameter measurement the results are shown in Table 3.

The comparative example 3

Adopt existing vanderburg method that the electrical quantity of above-mentioned A group 2# and four same samples of B group 3# is measured; Wherein B organizes the G sheet of 3# and the full structure positive that the H sheet is 50nm cap layer thickness; Measure after removing heavy doping cap layer through chemical corrosion during measurement; To avoid the charge carrier in the thick cap layer that measurement result is exerted an influence, the electric parameter measurement result sees table 3.

Table 3 is respectively organized the electric parameter measurement result of sample

A group 2# sample (E, F) adopts smooth heterojunction boundary growing technology, δ _UpWith δ _DownIt is close to be entrained in the 2DEG mobility that generates in the passage; The cap layer thickness is 5nm simultaneously; The AlGaAs barrier layer is very thin relatively; Charge carrier can obviously not influence the measurement of interior 2DEG concentration of passage and mobility in the cap layer; So obviously respectively, the two all can not access the electrical parameter of accurate reflection material real information to the measurement result of the inventive method and vanderburg method.C group 4# sample (K, L) is the full structure positive of 50nm cap layer thickness; Adopt smooth interface growth technology; The electric parameter measurement result of its 2DEG is intimate identical with A group 2# sample, shows that the inventive method can correctly provide measurement result for the material system that comprises multiple charge carrier fellowship conduction.

B group 3# sample (G, H) adopts the common process growth, the differing greatly of InGaAs channel layer both sides heterojunction boundary situation, because the interface flatness at reef knot place is lower, interface scattering and residual impurity scattering will obviously reduce lower plane (δ _Down) mobility of the 2DEG that generates that mixes.When measuring through the inventive method, the 2DEG concentration of B group 3# sample is starkly lower than A group 2# and C group 4# sample, and hall mobility respectively not quite, shows that the inventive method can accurately distinguish plane (δ _Up) and lower plane (δ _Down) be entrained in the difference of the 2DEG character that generates in the passage, and provide its accurately real measurement result.When adopting the vanderburg method to measure B group 3# sample; Its 2DEG concentration is identical with A group 2# and C group 4# sample; And hall mobility is obviously on the low side, shows that the vanderburg hall measurement can't distinguish two types of 2DEG, only reflects the resultant effect of both concentration and its mobility.

" varying magnetic field condition " described in the foregoing description, " A is a constant; its value is by the integration decision of waveguide mode on whole circular section ", " electricity of finding the solution electronics and hole is led the envelope function of density function ", " getting the uniform discrete data point ", " number at peak is confirmed the charge carrier kind quantity in the sample in by mobility spectrum; and obtain the approximate value of carrier electric charge property and mobility and concentration ", " with the approximate value of carrier concentration and mobility as initial value; the employing generalized least square method carries out match to electric derivative certificate; acquisition is the unique carrier concentration and mobility electrical quantity that can reflect the sample real information finally ", " match of the calculating of mobility spectrum and electric derivative certificate ", all be that the technician in present technique field knows.

" generalized least square method " described in the foregoing description, " formula translation programming ", calculate operation platform based on the Pentium of Intel processor and the windows of Microsoft operating system ", the technician who is technical field of general engineering knows and grasps.

Claims (1)

1. the electric parameter measurement method of gallium arsenide pseudomorphic high electron mobility transistor material; It is characterized in that: be to measure carrier concentration and mobility in the gallium arsenide pseudomorphic high electron mobility transistor material through a kind of noncontact Hall measuring method, its step is following:

The first step, incident power, reflective power and the Hall effect microwave power of the gallium arsenide pseudomorphic high electron mobility transistor material that employing microwave hall measurement measurement device is measured

Measured PHEMT material sample is placed on the sample stage of microwave hall measurement device 10GHz and TE that the circular waveguide through balance modulation will be sent by controllable magnetic field ₁₁The microwave of pattern is incorporated into the surface of measured gallium arsenide pseudomorphic high electron mobility transistor material; The characteristic impedance of waveguide is 700 Ω, and first detecting device of the forward microwave power through detecting sample under the varying magnetic field condition, second detecting device and the 3rd detecting device that detects the Hall effect microwave power of sample that detect the microwave reflection power of sample are measured TE respectively ₁₁The incident power P of pattern _In, TE ₁₁The mode reflection power P _ReTE with the material surface reflection ₁₀Pattern Hall effect microwave power P _Hall

In second step, calculate the electricity of sample under different magnetic field and lead tensor

The incident power P of the gallium arsenide pseudomorphic high electron mobility transistor material that measures according to the first step _InWith reflective power P _ReBy following formula (1) calculating voltage reflection coefficient Γ, and the incident power P of the gallium arsenide pseudomorphic high electron mobility transistor material that measures according to the first step _InWith Hall effect microwave power P _HallCalculate the sample place microwave electric field electric field strength E on X and Y coordinate axis respectively by following formula (2) and formula (3) _xAnd E _y

$\mathrm{\Γ}={(P_{\mathrm{Re}}/P_{\mathrm{In}})}^{\frac{1}{2}}$ Formula (1)

$E_x=(1+\mathrm{\Γ}){(P_{\mathrm{In}}/A)}^{\frac{1}{2}}$ Formula (2)

$E_y={(P_{\mathrm{Hall}}/A)}^{\frac{1}{2}}$ Formula (3)

A is a constant in the following formula, and its value is by the integration decision of waveguide mode on whole circular section.

And then calculate sample through following formula (4) and formula (5) and lead tensor at the electricity under the different magnetic field,

${\mathrm{\σ}}_{\mathrm{Xx}}=\frac{(1/Z)\{1-{\mathrm{\Γ}}^2-{(E_y/E_x)}^2\}}{{(1+\mathrm{\Γ})}^2+{(E_y/E_x)}^2}$ Formula (4)

${\mathrm{\σ}}_{\mathrm{Xy}}=\frac{\{(E_y/E_x)/2\mathrm{\Γ}(1+\mathrm{\Γ})\}\{(1+\mathrm{\Γ})(3-\mathrm{\Γ})-{(E_y/E_x)}^2\}}{{(1+\mathrm{\Γ})}^2+{(E_y/E_x)}^2}$ Formula (5);

The 3rd step, the carrier concentration of gallium arsenide pseudomorphic high electron mobility transistor material and the calculating of mobility

Under relaxation time approximation, lead the σ of tensor unit through finding the solution Boltzmann equation acquisition electricity _Xx(B) and σ _Xy(B) with sample in all kinds of carrier concentration n _jAnd mobility [mu] _jRelation, shown in following formula (6) and formula (7), S wherein _jBe carrier electric charge property, electronics is-1, and the hole is+1,

${\mathrm{\σ}}_{\mathrm{Xx}}\left(B\right)=\underset{j}{\mathrm{\Σ}}\frac{{\mathrm{En}}_j{\mathrm{\μ}}_j}{1+{\mathrm{\μ}}_j^2{B}^2}$ Formula (6)

${\mathrm{\σ}}_{\mathrm{Xy}}\left(B\right)=\underset{j}{\mathrm{\Σ}}{S}_j\frac{{\mathrm{En}}_j{\mathrm{\μ}}_j^{2}B}{1+{\mathrm{\μ}}_j^2{B}^2}$ Formula (7)

Suppose that the mobility of electronics and hole is a continuous distribution in the sample, can be write formula (6) and formula (7) as integrated form, shown in following formula (8) and formula (9), s wherein ⁿ(μ) and s ^pThe electricity that (μ) is respectively electronics and hole is led density function, the contribution of representing electronics and hole that electricity is led, and its value answers>=0,

${\mathrm{\σ}}_{\mathrm{Xx}}\left(B\right)=\underset{0}{\overset{\∞}{\∫}}\frac{s^p\left(\mathrm{\μ}\right)+s^n\left(\mathrm{\μ}\right)}{1+{\mathrm{\μ}}^2{B}^2}\mathrm{D\μ}$ Formula (8)

${\mathrm{\σ}}_{\mathrm{Xy}}\left(B\right)=\underset{0}{\overset{\∞}{\∫}}\frac{[s^p\left(\mathrm{\μ}\right)-s^n\left(\mathrm{\μ}\right)]\mathrm{\μ\; B}}{1+{\mathrm{\μ}}^2{B}^2}\mathrm{D\μ}$ Formula (9)

Solve s by formula (8) and formula (9) ⁿ(μ) and s ^pEnvelope function S (μ) (μ), shown in following formula (10), S (μ) value makes σ under a certain mobility _Xx(B), σ _Xy(B) has the s of clear and definite physical significance ⁿ(μ) and s ^p(μ) upper limit of value has the electricity unit of leading dimension, uses S (μ) value to calculate the carrier concentration n (μ) under the corresponding mobility by following formula (11),

$S\left(\mathrm{\μ}\right)=\frac{{\left|v_{u^{\′}}\right|}^2}{{\mathrm{\α}}_{u^{\′}}}{\left[\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\frac{{\left(\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{Q}_{\mathrm{Ij}}{\left(v_{u^{\′}}\right)}_j\right)}^2}{{\mathrm{\λ}}_i}\right]}^{-1}$ Formula (10)

$n\left(\mathrm{\μ}\right)=\frac{S\left(\mathrm{\μ}\right)}{\mathrm{E\μ}}$ Formula (11)

Thereby obtain conductivity and carrier concentration with mobility continually varying spectrogram.Obtain the charge carrier kind quantity j in the sample by this spectrogram, and the concentration n of various charge carriers _jWith mobility [mu] _jApproximate value, with the kind quantity j of the charge carrier that from above-mentioned spectrogram, obtains, and the concentration n of all kinds of charge carriers _jWith mobility [mu] _jApproximate value as initial value, adopt generalized least square method by formula (6) with formula (7) to electric derivative according to carrying out match, acquisition is the unique carrier concentration and mobility electrical quantity that can reflect gallium arsenide pseudomorphic high electron mobility transistor material real information finally.

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