WO2010116293A1 - Method and apparatus for determining dopant density in semiconductor materials - Google Patents

Method and apparatus for determining dopant density in semiconductor materials Download PDF

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Publication number
WO2010116293A1
WO2010116293A1 PCT/IB2010/051404 IB2010051404W WO2010116293A1 WO 2010116293 A1 WO2010116293 A1 WO 2010116293A1 IB 2010051404 W IB2010051404 W IB 2010051404W WO 2010116293 A1 WO2010116293 A1 WO 2010116293A1
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sample
semiconductor material
temperature
density
determining
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PCT/IB2010/051404
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French (fr)
Inventor
Johannes Reinhardt Botha
Magnus Carr Wagener
Viera Wagener
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Nelson Mandela Metropolitan University
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Publication of WO2010116293A1 publication Critical patent/WO2010116293A1/en
Priority to ZA2011/06897A priority Critical patent/ZA201106897B/en

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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01L—SEMICONDUCTOR DEVICES NOT COVERED BY CLASS H10
    • H01L22/00—Testing or measuring during manufacture or treatment; Reliability measurements, i.e. testing of parts without further processing to modify the parts as such; Structural arrangements therefor
    • H01L22/10—Measuring as part of the manufacturing process
    • H01L22/14—Measuring as part of the manufacturing process for electrical parameters, e.g. resistance, deep-levels, CV, diffusions by electrical means

Definitions

  • the method may typically comprise determining the dopant density in the sample of the semiconductor material by way of the following formula:
  • a sample temperature controller arranged to:
  • the processor may also be configured to determine or calculate the intrinsic carrier density, ni, of the sample of the semiconductor material at the determined average sample temperature
  • the processor may be configured to determine the dopant density by way of the following formula: , where:
  • Figure 1 shows a schematic block diagram of an apparatus in accordance with an example embodiment
  • Figure 5 shows a flow diagram of a method in accordance with an example embodiment.
  • the apparatus 10 also includes thermoelectric properties monitor in the form of a thermoelectric current monitor 18 arranged to monitor a thermoelectric current in the sample 14, particularly along a length thereof at respective end portions of the sample 14.
  • thermoelectric properties monitor may be arranged to monitor voltage characteristics in the sample 14.
  • the processor 20 is communicatively coupled to or arranged to access a corresponding look-up table in order to determine the dopant density of the sample of semiconductor material.
  • the look-up table comprises at least information indicative of dopant densities of a plurality of semiconductor materials and may be accessed by using one or more of the determined n,, T stg ⁇ .change > and the mobility ratio, ⁇ n / ⁇ p .
  • the look-up table may advantageously be provided in the apparatus 10.
  • the Seebeck coefficient is determined from the following formula:
  • the invention as hereinbefore described advantageously provides an easier, more desirable approach to determining semiconductor dopant densities/concentrations.
  • the invention as hereinbefore described is (ess computationally intensive as conventional approaches to determining dopant densities, for example Hall effect measurements, as the method does not require information indicative of the thickness of the sample of semiconductor material.
  • the method as hereinbefore described allows for determination of dopant densities of semiconductor materials irrespective of the layer quality of the material. In other words the method is relatively insensitive to the layer quality.

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  • Manufacturing & Machinery (AREA)
  • Computer Hardware Design (AREA)
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  • Investigating Or Analyzing Materials Using Thermal Means (AREA)

Abstract

This invention relates firstly to a method of determining dopant density in a semiconductor material, particularly a p-type semiconductor material. The method comprises the steps of generating a thermal gradient along a length of a sample of the semiconductor material; monitoring thermoelectric current of the sample of the semiconductor material; heating the sample of the semiconductor material whilst maintaining the thermal gradient along the length of the sample of the semiconductor material; determining an average sample temperature at which the monitored thermoelectric current changes sign; and determining a corresponding dopant density in the sample of the semiconductor material by using at least the determined average sample temperature. The invention extends also to an associated apparatus for determining or facilitating determining dopant densities in semiconductor materials.

Description

METHOD AND APPARATUS FOR DETERMINING DOPANT DENSITY IN SEMICONDUCTOR MATERIALS
BACKGROUND OF THE INVENTION
THiS invention relates to a method of and an apparatus for determining dopant density in a semiconductor material, particularly a p-type semiconductor material.
Hall effect measurements have typically been the preferred method for determining doping and conduction characteristics of semiconductor materials. However, this method is problematic for semiconductor materials having more complex conduction systems, such as for semiconductor materials having contributions from additional surface and/or interface conduction pathways.
These problems have resultantly necessitated more complex analysis to extract the basic doping and conduction properties of the semiconductor materials. Additional variables associated with degenerate conduction pathways usually require more detailed Hall measurements which take into account variables such as temperature dependence, layer thickness, magnetic field strength, or the like and their separate contributions to a measured Hall voltage. The success of the Hall effect measurements is further hampered for semiconductor materials with iow mobilities and high intrinsic carrier densities. This is apparent for semiconductor materials such as p-type InAs (Indium Arsenide/ Indium Monoarsenide) where a surface accumulation layer completely conceals bulk characteristics of the material. This limitation of Hall effect measurements results from its sensitivity to degenerate conduction pathways in these semiconductor materials. As a result, Hall effect measurements typically rely on results obtained for highly doped material in order to extrapolate the doping characteristics of lightly doped material.
It is an object of the present invention at least to address the abovementioned problems.
SUMMARY OF THE INVENTION
According to a first aspect of the invention, there is provided a method of determining dopant density in a semiconductor material, the method comprising:
generating a thermal gradient along a length of a sample of the semiconductor material;
monitoring thermoelectric current of the sample of the semiconductor material;
heating the sample of the semiconductor material whilst maintaining the thermal gradient along the length of the sample of the semiconductor material;
determining an average sample temperature, Tsigπ-chaπge, at which the monitored thermoelectric current changes sign; and determining a corresponding dopant density in the sample of the semiconductor material by using at least the determined average sample temperature TShgn-change.
It will be noted that the semiconductor material may typically be a p-type semiconductor material.
The method may comprise using one or more of the determined average sample temperature Tsιgn-Change, a mobility ratio, μjμp, and an intrinsic carrier density, n,, of the sample of the semiconductor material, at the determined average sample temperature
Figure imgf000004_0001
to determine the dopant density in the sample of the semiconductor material.
ft follows that the method may comprise determining or calculating the intrinsic carrier density, n,, of the sample of the semiconductor material at the determined average sample temperature Tsign^hange.
The method may typically comprise determining the dopant density in the sample of the semiconductor material by way of the following formula:
Figure imgf000004_0002
, where:
NA is the dopant density in the sample of the semiconductor material; n, is the intrinsic carrier density of the sample of the semiconductor material, at the determined average sample temperature Tsign-Change; and μn/μp is the mobility ratio.
Instead, or in addition, the method may comprise determining the dopant density by way of a look-up table, using one or more of the determined average sample temperature Tsιgn-Change, the mobility ratio, μπ/μp, and the intrinsic carrier density, n, of the sample of the semiconductor material at
I sign-change- In an example embodiment, the method may further comprise fabricating ohmic contacts onto the sample of the semiconductor material. The method may therefore comprise monitoring the thermoelectric current between the ohmic contacts.
Instead, or in addition, the method may comprise mounting the sample of the semiconductor material between at least two conductive members. The method may therefore comprise monitoring the thermoelectric current between the conductive members.
According to a second aspect of the present invention, there is provided an apparatus for determining, or facilitating determining, dopant density in a semiconductor material, the apparatus comprising:
a sample temperature controller arranged to:
generate a thermal gradient along a length of a sample of the semiconductor material; and
heat the sample of the semiconductor materia! whilst maintaining the thermal gradient along the length of the sample of the semiconductor material;
; and
a thermoelectric properties monitor configured to monitor thermoelectric properties of the sample of the semiconductor material.
The thermoelectric properties monitor may preferably comprise a thermoelectric current monitor configured to monitor thermoelectric current in the sample of the semiconductor material. In a preferred example embodiment, the apparatus may comprise a processor configured to:
determine an average sample temperature, TS!gn-change, at which the monitored thermoelectric current changes sign; and
determine a corresponding dopant density in the semiconductor material by using at least the average sample temperature Tsιgn_ change-
The processor may also be configured to use one or more of the determined average sample temperature Tsign-Change, a mobility ratio, μn/μp, and an intrinsic carrier density, n,, of the sample of semiconductor material, at the determined average sample temperature TSιgiH;h3ngΘI to determine the dopant density in the sample of the semiconductor material.
It will be appreciated that the processor may also be configured to determine or calculate the intrinsic carrier density, ni, of the sample of the semiconductor material at the determined average sample temperature
' sign-change-
The processor may be configured to determine the dopant density by way of the following formula:
Figure imgf000006_0001
, where:
NA is the dopant density in the sample of the semiconductor materia!; n, is the intrinsic carrier density of the sample of the semiconductor material, at the determined average sample temperature Tsιgrw;nange; and μn/μp is the mobility ratio.
Instead, or in addition, the processor may be configured to access a corresponding iook-up table, with at least one or more of the determined average sample temperature the mobility ratio, μn/μp, and the intrinsic carrier density, n,, of the sample of the semiconductor material, at Tεigπ-chaπge> in order to determine the dopant density of the sample of the semiconductor material.
The look-up table may typically comprise at least information indicative of dopant densities of a plurality of semiconductor materials.
The apparatus may comprise a temperature monitor arranged to monitor the temperature of the sample of the semiconductor material.
The apparatus may conveniently comprise at least two conductive members, such that the sample of the semiconductor material is mountable between the conductive members, in use. Each of the conductive members may be in communication with and may be independently heated by the sample temperature control module.
BRIEF DESCRtPTION OF THE DRAWINGS
Figure 1 shows a schematic block diagram of an apparatus in accordance with an example embodiment;
Figure 2 shows at least part of the apparatus of Figure 1 in accordance with an example embodiment, in use;
Figure 3 shows a schematic diagram of a setup for obtaining Hail effect measurements in order to determine dopant density of a semiconductor material;
Figure 4 shows a graph illustrating the temperature dependence of the Hall coefficient of cadmium doped InAs;
Figure 5 shows a flow diagram of a method in accordance with an example embodiment.
Figure 6 shows a graph illustrating the temperature dependence of the Seebeck coefficient of cadmium doped InAs; and
Figure 7 shows a graph illustrating the acceptor concentration of p- type InAs as a function of cadmium mole fraction.
DESCRIPTION OF PREFERRED EMBODIMENTS
In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of an embodiment of the present disclosure. It will be evident, however, to one skilled in the art that the present disclosure may be practiced without these specific details.
Referring to Figures 1 and 2 of the drawings where an apparatus for determining, or facilitating determining, dopant densities/concentrations in semiconductor materials is generally indicated by reference numeral 10. The apparatus 10 comprises a sample temperature controller 12 arranged to generate a thermal gradient along a length of a sample of a semiconductor material 14 {illustrated in Figure 2).
The sample temperature controller 12 is also arranged to heat the sample 14 whilst maintaining the thermal gradient along the length of the sample 14.
In an example embodiment, the apparatus 10 comprises or is in conductive or thermal communication with at least two conductive members 16.1 and 16.2. The conductive members 16.1 , 16.2 are typically copper blocks in communication with the sample temperature controller 12. In the illustrated example embodiment, the blocks 16.1 , 16.2 are arranged to be heated by the sample temperature controller 12 by way of resistive heating.
The sample 14 is preferably mountable between the blocks 16.1 and 16.2 such that it can be heated by the sample temperature controller 12 via the blocks 16.1 and 16.2.
The controller 12 may be arranged to heat each copper block 16.1 and 16.2 independently and to different temperatures thereby to generate the thermal gradient along the sample 14 as hereinbefore mentioned.
The temperature difference between the blocks 16.1 and 16.2 may be varied between 0 K and 10 K. The average temperature of the metal blocks 16.1 and 16.2 may be varied by the controller 12 from 100 K to 600 K using a combination of cooling {using Peltier cooling, liquid Nitrogen, Joule-Thomson cooling, or the like) and resistive heating.
It will be appreciated that the air around the copper blocks 16.1 , 16.2 is evacuated to prevent condensation, as weli as convection effects at the surface of the sample 14. it may be mentioned that the sample 14 is a cleaved rectangular 5mmχ2mmχO.5mm semiconductor material with a GaAs (Gallium Arsenide) substrate 14.1 and an InAs (Indium Arsenide) surface film or epilayer 14.2. The sample 14 is typically a doped p-type semiconductor material.
The apparatus 10 also includes thermoelectric properties monitor in the form of a thermoelectric current monitor 18 arranged to monitor a thermoelectric current in the sample 14, particularly along a length thereof at respective end portions of the sample 14. In another example embodiment (not shown), the thermoelectric properties monitor may be arranged to monitor voltage characteristics in the sample 14.
The sample 14 may preferably have ohmic contacts 24, fabricated at each end portion of the sample 14. In this particular example embodiment the current monitor 18 is arranged to monitor the thermoelectric current along the length of the sample 14 via the ohmic contacts 24. This may be done by way of electrical contacts connectable to the ohmic contacts 24.
Instead, or in addition, the current monitor 18 is arranged to monitor the thermoelectric current along the length of the sample 14 via the blocks 16.1 and 16.2. In this particular example embodiment, the ohmic contacts may be provided on the blocks 16.1, 16.2.
It will be appreciated that the thermoelectric current is advantageously monitored instead of the thermoelectric EMF in order to eliminate the possibility of additional voltage contributions from the circuitry of the apparatus 10.
in a preferred example embodiment, the apparatus 10 comprises a processor 20 arranged to determine an average sample temperature, Tsign- change, at which the monitored thermoefectric current changes sign. The processor 20 is further arranged to determine a corresponding dopant density using Tsιgi>change for the sample 14 semiconductor material. In this regard, the processor 20 is arranged to use TSιgn-change, the mobility ratio, μn/μp, and an intrinsic carrier density, n,, of the sample 14 at Tsign-Change, to determine the dopant density in the sample 14.
It will be appreciated that the processor 20 may be arranged to determine or calculate n, of the sample 14 at TSign-change.
In any event, the processor 20 is advantageously arranged to calculate the dopant density by way of the following formula:
NA = n, [(μπ/μp)1/2 - l] , where:
NA is the dopant density in the sample of the semiconductor materia!; n, is the intrinsic carrier density of the sample of the semiconductor material, at the determined average sample temperature Tsign^hange; and μn/μp is the mobility ratio.
Instead, or in addition, the processor 20 is communicatively coupled to or arranged to access a corresponding look-up table in order to determine the dopant density of the sample of semiconductor material. It follows that the look-up table comprises at least information indicative of dopant densities of a plurality of semiconductor materials and may be accessed by using one or more of the determined n,, Tstgπ.change> and the mobility ratio, μn/μp. The look-up table may advantageously be provided in the apparatus 10.
For a non-degenerate conductor, the Seebeck coefficient is determined from the following formula:
OW.
Figure imgf000011_0001
where n and p are the carrier concentrations, m* the effective masses, and r the scattering parameter for electrons and holes, respectively, and k and h are Boltzmann's and Planck's constants. Considering mixed conduction, the contributions of both carriers are weighted by the conductivities of the conduction and valence bands, such that the total Seebeck coefficient is given by:
abulk ~ W + Hnn
When considering small band gap p-type semiconductors, the Seebeck coefficient changes sign from positive to negative as the temperature is increased from the extrinsic (p » ή) to intrinsic (p ~ n) temperature range. It will be noted that this transition temperature, Tsigπ-Ctiange is directly related to the mobility ratio of the carriers and the net hole concentration. In the absence of any additional conduction paths, this transition occurs when the intrinsic carrier density, n^ = NA/ [(μn/μp) - lL
For degenerate layers, the Seebeck coefficient is analysed using Fermi- Dirac statistics, in which case
k \r + 2 Fr+1{η) l
and
Figure imgf000012_0001
where η is the reduced Fermi level (= EF//cT). The scattering parameter, r = 0 for lattice phonon scattering and r = 2 for scattering by impurity ions. For Seebeck measurements performed above 300K, phonon scattering is assumed to dominate.
Polar semiconductors, such as InAs (sample 14), are known to form a degenerate charge accumulation layer at the surface thereof. A sample with surface layer or film with, for example an electron density of 1018 cm"3 typically has a Seebeck coefficient of 0.1 mV/K at 600 K, decreasing to 0.05 mV/K at 300 K. Since these values are relatively low compared to that of the bulk, combined with the increased bulk conductivity at elevated temperatures, a degenerate electron conduction layer is expected to make a negligible contribution to the overall thermoelectric EMF, or thermoelectric current for that matter.
In the presence of a degenerate conduction layer the observed Seebeck coefficient is decreased to
^■apparent - °b , abulk
where <xs and σb are the sheet conductivities of the bulk and degenerate layer, respectively. The sign of the Seebeck coefficient is thus solely determined by the bulk conduction properties, leaving the transition temperature,
Figure imgf000013_0001
unaffected by the addition of a degenerate conduction layer.
The accuracy by which the dopant density is determined is limited by knowledge of the intrinsic carrier density and mobility ratio of the carriers within the bulk material at the transition temperature. Although the transition temperature typically exceeds the temperature range of Varshni equations for most semiconductor materials, it generally remains a valid extrapolation due to the linearity of the bandgap energy above room temperature.
It will be appreciated that the Seebeck coefficient is accurately described by the abovementioned non-degenerate approximation formula, since the transition temperature increases with increased dopant density, thereby assuring that the Boltzmann approximation remains valid throughout the doping range investigated. In any event, it will be noted that the apparatus further comprises a temperature monitor 22 arranged to monitor the temperature of the sample 14. This is useful to determine Tsign^hange. It follows that the processor 20 is communicatively coupled to the temperature monitor 22 to determine Tsi9n- chaπge.
The temperature monitor 22 may be arranged to determine the temperature at the ohmic contacts 24 at each respective end portion of the sample 14. Instead, or in addition, the temperature module 22 is coupled to a thermocouple mounted to each copper block 16.1 and 16.2.
Referring to Figures 3 and 4 of the drawings, a setup to determine dopant densities/concentrations of semiconductor materials using Hall effect measurements is generally indicated by reference numeral 30.
Hail effect measurements will be briefly discussed to better understand the advantages of the present invention in determining dopant densities in semiconductor materials.
The setup 30 uses a sample similar to the sample 14 where InAs layers were grown by metal-organic vapour phase epitaxy on semi-insulating GaAs substrate. The sample in the setup 30 is also Cadmium doped. The layers are all specular and are roughly 4 μm thick. The sample has van der Pauw contact geometry, with four indium ohmic contacts fabricated on each corner of the epilayer. The van der Pauw contact geometry is used to measure the Hall voltage and conductivity in the sample.
Hall effect measurements are typically performed in a 1 kG magnetic field, with the sample placed in a closed system helium cryostat for the low temperature measurements.
Figure 4 shows a graph 40 which illustrates the temperature dependence of the Hall coefficient measured for the cadmium doped p-type InAs epilayer {solid circles). The solid line represents the theoretical curve calculated for a two-layer structure composed of a bulk layer with an acceptor concentration of NA = 2.3x1016Cm"3 and a negative accumulation layer, with the dashed line representing the bulk component.
A comparison of the measured Hall coefficient and the calculated bulk contribution reveals that the HaIi effect measurements drastically underestimate the bulk values throughout most of the temperature range studied. The only reasonable correlation exists near 50 K, where the bulk mobility is sufficiently high to suppress the contribution by the surface accumulation layer. The degree to which the measured Hail coefficient represents the bulk value is therefore highly sensitive to the mobility, and hence the quality of the epilayer investigated.
It is important to note that undesirably the large temperature range used for the Hall measurements is essential for the extraction of the basic doping characteristics of the semiconductor material. The measurements obtained within the intrinsic temperature range are most sensitive to the dopant density, whereas the contribution from surface conduction dominates at low temperatures. The accurate analysis of material with larger dopant densities therefore requires a progressively larger temperature range for the Hall measurements.
Example embodiments will now be further described with reference to Figures 5 to 7. The example method shown in Figure 5 is described with reference to Figures 1 and 2 as well as Figures 6 and 7. It will be appreciated that the example method may also be applicable to other systems (not illustrated).
Referring in particular to Figure 5 of the drawings where a flow diagram of a method of determining dopant density of semiconductor materials is generally indicated by reference numeral 50. The method 50 comprises generating, at block 52, a thermal gradient along a length of the sample 14 as hereinbefore described by way of the sample temperature controller 12.
The method 50 comprises monitoring, at block 54 by way of the current monitor 18, at least the thermoelectric current of the sample 14.
The method 50 further comprises heating, at block 56, the sample whilst maintaining the thermal gradient along the length of the sample 14. Also as hereinbefore mentioned, this is done by way of the sample temperature controller 12.
The method 50 preferably comprises determining, at block 58 by way of the processor 20 and temperature monitor 22, the average sample temperature, Tsigri-Change, at which the monitored thermoelectric current changes sign. This sign change may be positive to negative or vice versa.
The method 50 further comprises determining, at block 60, also by way of the processor 20, a corresponding dopant density using Tsign-Change for the sample 14. In this regard, the method 50 typically includes using one or more of Tsign-Chaπge, the mobility ratio, μjμp, and the intrinsic carrier density, n,, of the sample 14, at the determined Tsign-Change to determine the dopant density of the sample 14.
It will be appreciated that the method 50 may also comprise determining (not illustrated) the intrinsic carrier density, n,, of the sample 14 at the determined Tsign<hange.
In one example embodiment the method 50 comprises calculating the dopant density by way of the following formula:
NA = H1 [(μn/μp)1/2 - l]. It follows that while the mobility ratio, μn/μP, and the determined intrinsic carrier density, n^, of the sample 14 are used in the above equation to determine the dopant density of the sample 14, the determined TSigπ-Chaπge is used to determine the corresponding intrinsic carrier density, n,, for the above equation.
In other example embodiments, the method 50 comprises determining the dopant density from Tsign-Change by way of a look-up table as hereinbefore described.
It will be noted that the method 50 may further comprise fabricating (not shown) ohmic contacts 24 onto the sample 14 at respective end portions thereof. The thermoelectric current is therefore monitored between the ohmic contacts 24.
The method 50 also comprises the step of mounting the sample 14 between the copper blocks 16.1 , 16.2. it follows that in other example embodiments, the method may include monitoring the thermoelectric current between the conductive blocks 16.1 and 16.2.
Reference will now be made to Figure 6 of the drawings where a graph of experimentally obtained Seebeck coefficients is generally indicated by reference numeral 70.
The graph 70 graphically illustrates the temperature dependence of the Seebeck coefficient measured for the the cadmium doped InAs sample 14 (solid circles). The solid line represents a theoretical curve calculated for a two-layer structure with a bulk acceptor concentration of NA = 3.5x1016Cm"3, with the dashed line representing the bulk contribution.
The sign reversal observed at 355 K (Tsign-Change) corresponds to an acceptor concentration of 3.6*1016 cm"3 using formulas described above. It is apparent that the Seebeck coefficient displays an anomalous temperature dependence compared to the expected bulk behavior (represented by the dashed curve). The incorporation of a surface conductivity term into the Seebeck model, however, provides a good representation of the measurements obtained.
It wiil be noted that contrary to Hall effect measurements, Seebeck measurements advantageously allow for the hole density to be easily determined by only noting the temperature at which the Seebeck coefficient reverses sign. It will be noted that the Seebeck coefficient dictates the sign of the thermoelectric current.
Referring now to Figure 7 where a graph of acceptor concentration of the sample 14 as a function of cadmium mole fraction introduced during thin film growth is generally indicated by reference numeral 80.
Using the method 50 as hereinbefore described for a series of samples 14 of p-type InAs layers grown with different cadmium dopant concentrations, the Seebeck transition temperature {Tεign-change) increases from 374 K to 535 K as the cadmium moie fraction in the metal-organic vapour phase epitaxial reactor is increased from 2X10"5 to 3*10"4. The corresponding acceptor concentrations (assuming negligible compensation) in graph 80 display a desirable one-to-one relation to the cadmium mole fraction. This approach advantageously gives direct information on the incorporation efficiency of lightly doped p-type InAs.
It follows that the invention as hereinbefore described advantageously provides an easier, more desirable approach to determining semiconductor dopant densities/concentrations. The invention as hereinbefore described is (ess computationally intensive as conventional approaches to determining dopant densities, for example Hall effect measurements, as the method does not require information indicative of the thickness of the sample of semiconductor material. Also, the method as hereinbefore described allows for determination of dopant densities of semiconductor materials irrespective of the layer quality of the material. In other words the method is relatively insensitive to the layer quality.

Claims

Claims
1. A method of determining dopant density in a semiconductor material, the method comprising:
generating a thermal gradient along a length of a sample of the semiconductor material;
monitoring thermoelectric current of the sample of the semiconductor material;
heating the sample of the semiconductor material whilst maintaining the thermal gradient along the length of the sample of the semiconductor material;
determining an average sample temperature, TSign-Change, at which the monitored thermoelectric current changes sign; and
determining a corresponding dopant density in the sample of the semiconductor material by using at least the determined average sample temperature Tsignκ;hange.
2. A method as claimed in claim 1, wherein the method comprises determining the dopant density in a p-type semiconductor material.
3. A method as claimed in either claim 1 or claim 2, wherein the method comprises using one or more of the determined average sample temperature TSjgn-change, a mobility ratio, μjμp, and an intrinsic carrier density, ni5 of the sample of the semiconductor material, at the determined average sample temperature
Figure imgf000019_0001
to determine the dopant density in the sample of the semiconductor material.
4. A method as claimed in claim 3, wherein the method comprises determining or calculating the intrinsic carrier density, n,, of the sample of the semiconductor material at the determined average sample temperature Tsign-Chaπge.
5. A method as claimed in claim 3, wherein the method comprises determining the dopant density in the sample of the semiconductor material by way of the following formula:
Figure imgf000020_0001
, where:
NA is the dopant density in the sample of the semiconductor material; ni is the intrinsic carrier density of the sample of the semiconductor material, at the determined average sample temperature Ts;gn-Change; and μn/μp is the mobility ratio.
6. A method as claimed in claim 3, wherein the method comprises determining the dopant density by way of a look-up table, using one or more of the determined average sample temperature Tsisn-Change, the mobility ratio, μπ/μp, and the intrinsic carrier density, rij of the sample of the semiconductor material at TΞign-change.
7. A method as claimed in any one of the preceding claims, wherein the method further comprises fabricating ohmic contacts onto the sample of the semiconductor material.
8. A method as claimed in claim 7, wherein the method further comprises monitoring the thermoelectric current between the ohmic contacts.
9. A method as claimed in any one of claims 1 to 6, wherein the method comprises mounting the sample of the semiconductor material between at least two conductive members.
10. A method as claimed in claim 9, wherein the method further comprises monitoring the thermoelectric current between the conductive members.
1 1. An apparatus for determining, or facilitating determining, dopant density in a semiconductor material, the apparatus comprising:
a sample temperature controller arranged to:
generate a thermal gradient along a length of a sample of the semiconductor material; and
heat the sampie of the semiconductor material whilst maintaining the thermal gradient along the length of the sample of the semiconductor material;
; and
a thermoelectric properties monitor configured to monitor thermoelectric properties of the sample of the semiconductor material.
12. An apparatus as claimed in claim 11, wherein the thermoelectric properties monitor comprises a thermoelectric current monitor configured to monitor thermoelectric current in the sample of the semiconductor material.
13. An apparatus as claimed in claim 12, wherein the apparatus comprises a processor configured to: determine an average sample temperature, Tsigπ<hange, at which the monitored thermoelectric current changes sign; and
determine a corresponding dopant density in the semiconductor material by using at least the average sample temperature Tsιgn-Change.
14. An apparatus as claimed in claim 13, wherein the processor is configured to use one or more of the determined average sample temperature Tsign-Change, a mobility ratio, μjμp, and an intrinsic carrier density, n,, of the sample of semiconductor material, at the determined average sample temperature Tsιgn-Change, to determine the dopant density in the sample of the semiconductor material.
15. An apparatus as claimed in claim 14, wherein the processor is configured to determine or calculate the intrinsic carrier density, ni, of the sample of the semiconductor material at the determined average sample temperature Tsigπxfiange.
16. An apparatus as claimed in .claim 14, wherein the processor is configured to determine the dopant density by way of the following formula:
^A = ni [(μn/μp)1/2 - l].
, where:
NA is the dopant density in the sample of the semiconductor material; ni is the intrinsic carrier density of the sample of the semiconductor material, at the determined average sample temperature Tsign-Chaπge; and μ^/μp is the mobility ratio.
17. An apparatus as ciaimed in claim 14, wherein the processor is configured to access a corresponding look-up table, with at least one or more of the determined average sample temperature T5J9n- change, the mobility ratio, μn/μP, and the intrinsic carrier density, ni, of the sample of the semiconductor material, at Tsign-Change, in order to determine the dopant density of the sample of the semiconductor material.
18. An apparatus as claimed in claim 17, wherein the look-up table comprises at least information indicative of dopant densities of a plurality of semiconductor materials.
19. An apparatus as claimed in any one of claims 11 to 18, wherein the apparatus comprises a temperature monitor arranged to monitor the temperature of the sample of the semiconductor material.
20. An apparatus as claimed in any one of claims 11 to 19, wherein the apparatus comprises at least two conductive members, such that the sample of the semiconductor material is mountable between the conductive members, in use.
21. An apparatus as claimed in any one of claims 11 to 19, wherein each of the conductive members is in communication with and is independently heated by the sample temperature control module.
22. A method substantially as herein described with reference to the accompanying drawings.
23. An apparatus substantially as herein described with reference to the accompanying drawings.
PCT/IB2010/051404 2009-04-07 2010-03-31 Method and apparatus for determining dopant density in semiconductor materials WO2010116293A1 (en)

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