CN102830260B - Method for measuring carrier concentration in semiconductor quantum well - Google Patents

Abstract

The invention discloses a method for measuring carrier concentration in a semiconductor quantum well. The method includes steps of measuring local conductance distribution of the cross section of the semiconductor quantum well by the electric detection mode of a scanning probe microscope; setting up a numerical model capable of reflecting relation between a conducting probe-quantum well Schottky contact conductivity and carrier concentration in the quantum well; and determining parameters and carrier concentration of the quantum well of the numerical model according to the measured conductivity distribution. The method is high in spatial discrimination and has advantages in analysis of a narrow quantum well and in coupling of the quantum well, is applicable to wider carrier concentration range from non-degeneracy to degeneracy doping conditions, and has significance value for analysis of internal performances of a semiconductor photoelectric device taking a quantum well as a functional structure.

Description

The measuring method of carrier concentration in semiconductor quantum well

Technical field

The present invention relates to the detection of optical semiconductor sulfate ferroelectric functional material characteristic parameter, specifically refer to the acquisition methods of carrier concentration in a kind of semiconductor quantum well.

Background technology

Migration electronics in semiconductor or hole, i.e. charge carrier are the function carriers of modern (light) electron device.In the opto-electronic device, the transition of charge carrier between different energy state, the absorption of corresponding photon and transmitting, thus realize the conversion between luminous energy and electric energy.Given this, in semiconductor functional structure, the concentration of charge carrier and microscopic distribution thereof are the essential informations determining device performance, especially true in semiconductor quantum functional structure, no matter be to quantum well photoelectric detector or quantum cascade laser, the charge carrier population density in its core texture-quantum well has direct impact to the leakage current characteristic of device and photoelectricity (or electric light) conversion efficiency.

Below in semiconductor photoelectric device, the width of quantum well is everlasting ten nanometers, this makes the carrier concentration detection technique of more current routines no longer applicable for quantum well device structures, such as Hall (Hall) method.Other measuring method with spatial resolving power mainly comprises Electrochemical C-V method (ECV) and secondary ion mass spectrum method (SIMS), these two kinds of methods are all from specimen surface, successively corrode also analytical sample and directly or indirectly obtain the Carrier Profile information of depth direction, but this mode measures no longer valid for the carrier concentration in the quantum well indirectly adulterated or coupled quantum well structure; And ECV method and the lateral dimension of SIMS method to sample to be tested there are certain requirements, the device architecture detection difficulty for ten microns of even more small scales is higher.Corresponding is in recent years based on the exploitation of the profile survey technology of Scanning Probe Microscopy with it, these class methods extract carrier concentration by the electronics distribution of measuring ability material transversal section, but its concrete scheme or spatial discrimination can't resolve quantum well yardstick, as scanning capacitance microscopic method (SCM); Or artificial adjustable parameter is relied on to the deciphering of actual measurement electronics information, the unidirectional extraction of carrier concentration can't be realized thus, as scanning distributed resistance microscopic method etc.Also it may be noted that, to response wave length in quantum well functional structure that is infrared and even far infrared band, its subband energy gap is very narrow, the charge carrier binding energy determined in quantum well only has below hundred milli electron volts, close to the energy of thermal motion fluctuation of room temperature electron, above-mentioned most detection method all faces larger difficulty in feasibility and measuring accuracy.

For this reason, the present invention, in conjunction with the micro-electricity distribution measuring of scan-probe and the numerical modeling that detects experiment, proposes a kind of way obtaining carrier concentration profile in semiconductor quantum well structures.

Summary of the invention

The object of this invention is to provide a kind of method obtaining carrier concentration in semiconductor quantum well.Distributing according to the conductance being quantum well xsect of the method can by conducting probe scanning survey, and the distribution of this conductance is dull corresponding with the carrier concentration in quantum well, and can be described by the numerical model based on schottky junction Current mechanism.

According to above-mentioned principle, it is as follows that the present invention obtains the step of carrier concentration in quantum well:

1. first measure the local conductance distribution of semiconductor quantum well xsect.This step needs the electrical detection pattern utilizing scanning probe microscopy, can be scanning distributed resistance microscope modes also can be conductive atomic force microscope modes, wherein requires that detecting range ability covers 10 ⁵to 10 ¹¹the range of current of ohm or equivalence with it.For reaching necessary detection resolution and effect, sample should be treated to obtain enough smooth xsect, suitable section mean square roughness is 1 nanometer and following, and the method for this reason adopted comprises along the crystal orientation as-cleaved sample perpendicular to surface, or carries out meticulous polishing to sample section.Then look material and the doping characteristic of semiconductor to be measured, the public electrode of preparation electrical measurement, needs sample to throw angle if desired, and uses deposit electrode material and alloying electrode process.When measuring the conductance distribution of quantum well xsect, select hardness higher than the conducting probe of detected semiconductor material or its needle point coating material, to obtain high electricity spatial discrimination and stably measured effect.Measuring condition is: the relative semiconductor samples positively biased of conducting probe, and the setting principle of concrete bias voltage amplitude is: record the local conductance signal that quantum well relative quantum potential barrier is stronger, avoids bias voltage excessive generation highfield effect simultaneously and departs from Schottky behavior.Be generally conducting probe and quantum well forms Schottky contact barrier height less than 80%, the initial value of schottky barrier height can first be estimated by the work function of conducting probe and semiconductor material.Simultaneously conducting probe adjusts, to ensure the optimal spatial resolution that conductance distribute and relative signal intensity according to the width of quantum well, material behavior and institute's biasing the contact of sample.

2. set up the numerical model of conducting probe-quantum well Schottky contacts current density.

Conducting probe and quanta trap semiconductor material define Schottky contacts, and its current transfer mechanism is thermionic emission, and consider that the equivalent Schottky barrier that image force and heat assist tunneling effect to cause reduces, Schottky contacts current density is described by following formula simultaneously:

$J_{\mathrm{TE}}=A^{*}{T}^2\exp \left(\frac{q({\mathrm{\φ}}_{\mathrm{Bn}0}-{\mathrm{\Δ\Φ}}_{\mathrm{IMF}}-{\mathrm{\Δ\Φ}}_{\mathrm{TFE}})}{\mathrm{kT}}\right)(\exp \left(\frac{q{V}_F}{\mathrm{kT}}\right)-1)$

Wherein φ _bn0the schottky barrier height that needle point conductive material and semiconductor material are formed, ΔΦ _iMFthe equivalent Schottky barrier reducing amount that image force effect causes, ΔΦ _tFEbe the equivalent Schottky barrier reducing amount that the auxiliary tunneling effect of heat causes, T is measuring tempeature, and q is unit charge amount, and k is Boltzmann constant, V _fmeasure the forward bias applied, be effective Jason Richardson's constant, m* is electron effective mass, and h is Planck's constant.

The impact of quantum well carrier concentration on Schottky conductance (electric current) has two aspects: namely image force effect and heat assist tunneling effect.The equivalent reducing amount of probe-quantum well schottky barrier height that wherein image force effect causes is given by the following formula:

${\mathrm{\Δ\Φ}}_{\mathrm{IMF}}={\left[\frac{q^{3}N|{\mathrm{\φ}}_{\mathrm{Bn}0}-{\mathrm{\φ}}_n-V_F|}{{8\mathrm{\π}}^2{{\mathrm{\ϵ}}_s}^3}\right]}^{1/4}$

Wherein, ε _sbe the relative dielectric constant of semiconductor material, N is the carrier concentration of semiconductor quantum well, φ _nit is the energy level difference at the bottom of the conduction band of semiconductor and between Fermi level.

The equivalent reducing amount of probe-quantum well schottky barrier height that the auxiliary tunneling effect of heat causes is given by the following formula:

${\mathrm{\Δ\Φ}}_{\mathrm{TFE}}={\left(\frac{3}{2}\right)}^{2/3}{E_{00}}^{2/3}{|{\mathrm{\φ}}_{\mathrm{Bn}0}-{\mathrm{\φ}}_n-V_F|}^{1/3}$

Wherein E ₀₀for:

$E_{00}=\frac{\mathrm{qh}}{4\mathrm{\π}}\sqrt{\frac{N}{m^{*}{\mathrm{\ϵ}}_s}}$

The foundation of schottky current transportation model in C++ program platform and realization:

Utilize C++ program platform to set up schottky current transportation, i.e. thermionic emission Transport Model, the local conductance that the carrier concentration in semiconductor quantum well and experiment record is connected.C Plus Plus has the feature of Object-Oriented Design, namely can the demand concrete according to user carry out program module self-defined, combination and debugging.Utilize its characteristic, the present invention can process the detection data of batch simultaneously, and carries out real-time monitored and feedback debugging to result of calculation.Primary data needed for calculating leaves in textual form document and calls for master routine, utilizes the Structured Programming of C++ to carry out programming and revises, result of calculation being imported in text document.

If to record local conductance peaks be σ in experiment, current density is J, and maximum effective contact area of probe and quantum well is that the relation of S. quantum well carrier concentration and local conductance σ is described by following formula:

$\mathrm{\σ}=\frac{J\·S}{V_F}$

3. determine the parameter of conducting probe-quantum well local current values model, calculate Schottky contacts local

First, conducting probe and semiconductor effective electricity contact area when the half-peak breadth distributed according to the conductance of each quantum well recorded in step 1 extrapolates measurement.Conducting probe is when vertical inswept semiconductor quantum well, if the contact radius of probe and semiconductor is R, the trap of quantum well is wide is d, and the half-peak breadth of local conductance is 2k, and the analytic relationship of three is:

${2R}^2\arcsin \left(\frac{d}{2R}\right)+d\sqrt{R^2-\frac{d^2}{4}}={2R}^2\arccos \left(\frac{k-\frac{d}{2}}{R}\right)-(k-\frac{d}{2})\sqrt{R^2-{(k-\frac{d}{2})}^2}$

This is a transcendental equation, utilizes business mathematics software as matlab, can obtain R by the method for iteration, can determine maximum effective contact area S of probe and each quantum well.

Secondly, conducting probe-semiconductor quantum well schottky barrier height is determined.On the sample of known carrier concentration, recording electric current (conductance)-bias relation with conducting probe with quantum well same material, and the current values relation set up by step 2 simulates schottky barrier height.

By testing in the numerical model of the effective contact area of conducting probe-quantum well and schottky barrier height and other constant parameter substitution step 2 determined, calculate the relation curve of probe-quantum well local conductance and carrier concentration.

4. record the local conductance peaks of quantum well according to step 1, carrier concentration N in step 3 releases carrier concentration in quantum well along with anti-on the relation curve of local conductance σ.

The present invention is that the mensuration of carrier concentration in nano-width semiconductor quantum well provides a comparatively pervasive scheme, and indirectly adulterates in thin pillar semiconductor quantum well and involuntary doping, potential barrier, has advantage in the carrier concentration mensuration of coupling quantum well.

Xsect detection scheme of the present invention, by the impact of same other functional area of sample, is applicable to comprise the detection of specific quantum well layer carrier concentration in the photoelectric device of sophisticated functions structure.

In the quantum well carrier concentration of micrometering scheme of the present invention also in mensuration small size device unit, there is unique advantage.

The present invention or a kind of non-expendable measurement scheme, can implement duplicate detection to sample.

Accompanying drawing explanation

Fig. 1 is one group of N-shaped doped quantum well structures schematic diagram used in the embodiment of the present invention.

Fig. 2 utilizes scanning distributed resistance microscopy (Scanning Spreading Resistance Microscopy, SSRM) to carry out measuring the rear local conductance distribution obtained to doped quantum well in the embodiment of the present invention.

Fig. 3 is peak value in each quantum well of the local conductance that obtains after utilizing scanning distributed resistance microscopy to carry out measuring to doped quantum well in the embodiment of the present invention and half-peak breadth.

Fig. 4 is the geometirc illustration of quantum well local conductance half-peak breadth origin in the embodiment of the present invention.

Fig. 5 is the running signal of model on C++ platform in the embodiment of the present invention.

Fig. 6 utilizes Numerical modelling to go out the relation curve of quantum well carrier concentration and local conductance in the embodiment of the present invention.

Fig. 7 is carrier concentration in the quantum well drawn in the embodiment of the present invention.

Fig. 8 is the inventive method flow chart of steps.

Embodiment

Below with the acquisition of carrier concentration in the GaAs/AlGaAs quantum well of one group of N-shaped doping, elaborate to the specific embodiment of the present invention by reference to the accompanying drawings, but limit the present invention absolutely not, namely the present invention is in no way limited to this embodiment.

Fig. 1 is one group of GaAs/AlGaAs doped quantum well be grown on GaAs (001) substrate used in the present invention, wherein the N-shaped doping content consecutive variations within the specific limits of each quantum well, and quantum well width is all 6nm; It is 5 × 10 that sample also comprises known doping content ¹⁷cm ^-3n-shaped GaAs electrode layer is demarcated for the electrical measurement of schottky barrier height.The physics constant of GaAs quantum-well materials: conduction band electron effective mass is 0.063m ₀(m ₀for electron rest mass), relative dielectric constant is 12.9, and conduction band available state density is 4.3e ¹⁷cm ^-3.

The scanning distributed resistance microscope modes of application scanning probe microscope measures the xsect conductance distribution of quantum well.First preparation connects the public electrode of each quantum well layer, then along (110) crystal orientation cleavage quantum well sample wafer, can obtain the section that local atomic level is smooth.Sample is vertically placed on multiple mode scanning probe microscope sample stage, selects the conducting probe through heavy doping diamond coatings, stable electricity distribution signal can be obtained under the prerequisite guaranteeing high-space resolution.Exemplarily, the micro-SSRM pattern of scanning distributed resistance is used to measure the section conductance distribution of quantum well.By to the electrical measurement of known doping content N-shaped GaAs electrode layer and matching, determine that the Schottky barrier true altitude that in the present embodiment, conducting probe and GaAs are formed is φ _bn0=1.178eV.

Meanwhile, the high-resolution local conductance through each quantum well layer of GaAs/AlGaAs under the 0.9V bias voltage obtained by SSRM measurement distributes as shown in Figure 2.Wherein DC sample bias=-0.9V to represent by metal probe to the forward bias of quantum well is 0.9V.The local conductance peaks of each quantum well and the half-peak breadth of each quantum well electric conductivity value are shown in Fig. 3.

The actual contact radius of probe and semiconductor is made by the half-peak breadth of the local conductance recorded.The iterative computation of the European geometry of embody rule and matlab:

Geometric expression: as Fig. 4, the wherein circular contact area representing probe and semiconductor reality, if to be R, GaAs quantum well trap wide is d=6nm for the radius in this region.When left figure is experiment measuring, there is situation during peak value in local conductance, and now effective contact area of probe and trap is maximum:

$S1={2R}^2\arcsin \left(\frac{d}{2R}\right)+d\sqrt{R^2-\frac{d^2}{4}}$

When right figure is experiment measuring, when the distance of probe movement is k, local conductance is the situation of a half of peak value, and now effective contact area of probe and trap is the half of maximal value S1:

$S2=R^2\arccos \left(\frac{k-\frac{d}{2}}{R}\right)-(k-\frac{d}{2})\sqrt{R^2-{(k-\frac{d}{2})}^2}$

The iterative computation of matlab: by S1=2S2, d=6nm, 2k=half-peak breadth, the iterative calculation method of matlab is utilized to find, along with half-peak breadth is from minimum 10.036nm to maximum 11.029nm, the radius value R of effective contact area of probe and semiconductor changes not quite, substantially at 6.6nm.Then maximum effective contact area S of probe and quantum well is 8.22e ^-17m ², now correspond to the peak value of local conductance.C++ platform realizes the numerical model of the needle point-semiconductor Schottky pickup current density calculation described in invention step 2, as shown in Figure 5.Involved parameter and constant are substituted into model, comprising: schottky barrier height φ _bn0=1.178eV, GaAs relative dielectric constant ε _s=12.9, conduction band electron effective mass m ^*=0.063m ₀(m ₀for electron rest mass), unit charge amount q=1.602e ^-19c, experimental temperature T=300K, Boltzmann constant k=1.38e ^-23j/K, Planck's constant h=6.626e ^-34js, tests the forward bias V applied _f=0.9V, maximum effective contact area S=8.22e of probe and each quantum well ^-17m ².

By model calculate GaAs quantum well carrier concentration N change in the relative broad range of 1E15 to 2E18cm-3 time, the relation curve of needle point-quantum well local conductance σ, as Fig. 6. quantum well local conductance peaks (table 3) experimentally recorded instead releases carrier concentration in quantum well, as Fig. 7.

Claims (6)

1. the measuring method of carrier concentration in semiconductor quantum well, is characterized in that step is as follows:

1) use the electrical measurement pattern of scanning probe microscopy to measure the local conductance distribution of quantum well xsect, under this measurement pattern, conducting probe and quantum-well materials form Schottky contacts, and survey local conductance and distribute and can differentiate single quantum well layer;

2) the current density numerical model of Schottky contacts between conducting probe and quantum well is set up, this numerical model based on the thermoelectronic emission current transport mechanism of Schottky contacts, and comprises the equivalent potential barrier correction effect relevant to carrier concentration in quantum well;

3) parameter of conducting probe-quantum well Schottky contacts current density numerical model is determined, comprise the effective contact area between conducting probe and semiconductor quantum well and schottky barrier height, and calculate the relation curve of local conductance and quantum well carrier concentration between conducting probe-quantum well;

4) according to the quantum well local conductance peaks that step 1 records, carrier concentration in step 3 releases carrier concentration in quantum well along with anti-on the relation curve of local conductance.

2. the measuring method of carrier concentration in a kind of semiconductor quantum well as described in claim 1, it is characterized in that: the scanning probe microscopy electrical measurement pattern of use comprises conductive atomic force microscope modes or scanning distributed resistance microscope modes, and ensures spatial discrimination and the electrical signal stability of local conductance distribution measuring by meeting following manner simultaneously:

1) acquisition of quantum well xsect comprises and using along crystal orientation cleavage or meticulous finishing method to obtain nano level section flatness;

2), when measuring, select the hardness of the tip point material of conducting probe or needle point coating material should higher than detected semiconductor material;

3) amplitude applying forward bias between conducting probe and quantum well xsect is no more than 80% of schottky barrier height.

3. the measuring method of carrier concentration in a kind of semiconductor quantum well as claimed in claim 1, it is characterized in that: the calculating of Schottky contacts current density is based on thermoelectronic emission current transport mechanism, and count the equivalent Schottky barrier that image force and heat assists tunneling effect to cause and reduce, that is:

$J_{\mathrm{TE}}=A^{*}{T}^2\exp \left(\frac{q({\mathrm{\φ}}_{\mathrm{Bn}0}-{\mathrm{\Δ\Φ}}_{\mathrm{IMF}}-{\mathrm{\Δ\Φ}}_{\mathrm{TFE}})}{\mathrm{kT}}\right)(\exp \left(\frac{q{V}_F}{\mathrm{kT}}\right)-1),$

Wherein φ _bn0the schottky barrier height that conductive pinpoint and Spectrum of Semiconductor Quantum Wells are formed, ΔΦ _iMFthe equivalent Schottky barrier reducing amount that image force effect causes, ΔΦ _tFEbe the equivalent Schottky barrier reducing amount that the auxiliary tunneling effect of heat causes, A* is effective Jason Richardson's constant, and T is measuring tempeature, and q is unit charge amount, and k is Boltzmann constant, V _fmeasure the forward bias applied.

4. the measuring method of carrier concentration in a kind of semiconductor quantum well as described in claim 1, is characterized in that: step 3) in effective contact area between conducting probe and quantum well according to step 1) half-peak breadth of local conductance distribution that records calculates and obtains.

5. the measuring method of carrier concentration in a kind of semiconductor quantum well as claimed in claim 1, is characterized in that: step 3) in schottky barrier height between conducting probe-quantum well extracted by the electric current of probe on the semiconductor material of the same race of known carrier concentration-bias relation.

6. the measuring method of carrier concentration in a kind of semiconductor quantum well as described in claim 3, is characterized in that: in the calculating of equivalent Schottky barrier reducing amount, and the schottky barrier height equivalence reducing amount that image force effect causes is:

${\mathrm{\Δ\Φ}}_{\mathrm{IMF}}={\left[\frac{q^{3}N|{\mathrm{\φ}}_{\mathrm{Bn}0}-{\mathrm{\φ}}_n-V_F|}{{8\mathrm{\π}}^2{{\mathrm{\ϵ}}_s}^3}\right]}^{1/4},$

Wherein ε _sthe relative dielectric constant of quantum-well materials, N is the carrier concentration of quantum well, φ _nit is the energy level difference at the bottom of the conduction band of semiconductor quantum well and between Fermi level; The schottky barrier height equivalence reducing amount that the auxiliary tunneling effect of heat causes is: ${\mathrm{\Δ\Φ}}_{\mathrm{TFE}}={\left(\frac{3}{2}\right)}^{2/3}{E_{00}}^{2/3}{|{\mathrm{\φ}}_{\mathrm{Bn}0}-{\mathrm{\φ}}_n-V_F|}^{1/3},$ Wherein $E_{00}=\frac{\mathrm{qh}}{4\mathrm{\π}}\sqrt{\frac{N}{m^{*}{\mathrm{\ϵ}}_s},}$ M ^*be the conduction band electron effective mass of semiconductor material, h is Planck's constant.