A method for measuring semiconductor depletion layer recombination lifetime and inversion layer interface state recombination lifetime based on ac-SPV

Abstract

The application provides a method for measuring semiconductor depletion layer recombination lifetime and inversion layer interface state recombination lifetime based on ac-SPV, comprising the following steps: establishing an equivalent circuit model of a semiconductor in a strong inversion state, wherein the equivalent circuit model characterizes the surface response of the semiconductor as parallel depletion layer capacitance, depletion layer recombination conductance, inversion layer charge storage capacitance and inversion layer charge transfer conductance; fixing the light intensity of incident laser light, measuring at multiple modulation frequencies f, and obtaining ac-SPV signals at each frequency point; converting the measured signals into total conductance and total capacitance; separating the depletion layer recombination conductance and the inversion layer charge transfer conductance from the total conductance in combination with known and ; substituting multiple groups of ω and corresponding data into a formula to perform curve fitting, and obtaining the depletion layer recombination lifetime; substituting multiple groups of ω and corresponding data into a formula to perform curve fitting, and obtaining the inversion layer interface state recombination lifetime.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of semiconductor device manufacturing, and particularly relates to a method for measuring semiconductor depletion layer recombination lifetime and inversion layer interface state recombination lifetime based on ac-SPV. BACKGROUND

[0002] In the field of semiconductor device manufacturing and characterization, Surface Charge Analysis (SCP) technology is an important non-destructive testing method. Through alternating current surface photovoltage (ac-SPV) measurement, surface recombination lifetime parameters can be obtained to evaluate the surface quality and interface characteristics of semiconductor materials. In the prior art, the real part (Re(δVs)) and the imaginary part (Im(δVs)) of the ac-SPV signal are used to calculate the surface recombination lifetime τ, and the expression is as follows:

[0003]

[0004]

[0005]

[0006] Wherein, δVs is the ac-SPV signal value, q is the electronic charge, is the incident light flux, ω is the angular frequency, is the dielectric constant of the semiconductor, R is the surface reflectivity, is the depletion layer width.

[0007] However, τ in the existing SCP technology is the equivalent comprehensive lifetime of the surface area (including the depletion layer and the inversion layer interface) recombination process, rather than the independent depletion layer recombination lifetime or the inversion layer interface state recombination lifetime. This simplified model is due to the limitations of SCP test conditions and theoretical assumptions, which cannot distinguish the two different physical mechanism recombination processes. Since both of these two recombination processes occur in the “light-generated carrier generation region” (near the surface), and the carriers cannot diffuse to the bulk region, the SCP model will equate the two independent recombination processes as a “whole surface recombination process”, and the corresponding lifetime τ is the comprehensive equivalent lifetime of the two processes. As can be seen from the expressions of Re(δVs) and Im(δVs): only one τ term is used in the model to describe the loss of the recombination process (without distinguishing between depletion layer recombination lifetime or inversion layer interface state recombination lifetime), which is the embodiment of “equating multiple surface recombination processes to a single comprehensive lifetime”.

[0008] Mixing the depletion layer recombination lifetime and the inversion layer interface state recombination lifetime together brings the following adverse consequences:

[0009] The source of defects is unclear: it is impossible to distinguish whether the composite loss is caused by bulk defects in the depletion layer (such as uneven doping or lattice defects) or interface state defects between the inversion layer and the oxide layer (such as dangling bonds or impurity adsorption), making it impossible to trace the source of material or structural problems in a targeted manner.

[0010] Analysis of recombination mechanisms is distorted: depletion layer recombination is a direct recombination of charge carriers within the bulk phase, while inversion layer interface recombination is a capture-emission process of interface states. The dynamic laws (such as dependence on temperature and frequency) of the two differ significantly. Conflating them will cause physical models to deviate from reality and make it impossible to accurately derive the carrier loss path.

[0011] Process optimization lacks precise targeting: If process fluctuations lead to changes in lifetime, it is impossible to determine whether the problem lies in the oxide layer growth / surface cleaning process (which affects the recombination lifetime of the inversion layer interface state) or the semiconductor doping / wafer fabrication process (which affects the recombination lifetime of the depletion layer), resulting in low efficiency of process optimization.

[0012] Device performance-related failures: For Si / SiO2-based devices (such as MOSFETs), the recombination lifetime of the inversion layer interface states directly affects the threshold voltage stability, while the recombination lifetime of the depletion layer affects carrier transport efficiency. Treating these as separate issues makes it impossible to establish a correlation between lifetime parameters and device performance, hindering device design optimization.

[0013] Therefore, there is an urgent need in the field for an accurate measurement method that can distinguish between the recombination lifetime of depleted layers and the recombination lifetime of inversion layer interfaces, in order to address the shortcomings of existing technologies. Summary of the Invention

[0014] The purpose of this invention is to propose a method for measuring the recombination lifetime of the depletion layer and the recombination lifetime of the inversion layer interface states based on ac-SPV, which can distinguish between the recombination lifetime of the depletion layer and the recombination lifetime of the inversion layer interface states.

[0015] To achieve the above objectives, this invention provides a method for measuring the recombination lifetime of semiconductor depletion layers and the recombination lifetime of inversion layer interface states based on ac-SPV, comprising the following steps:

[0016] An equivalent circuit model of a semiconductor in a strong inversion state is established, wherein the surface response of the semiconductor is characterized as a parallel depletion layer capacitance. Depletion layer composite conductivity Inversion layer charge storage capacitor and inversion layer charge transfer conductance The total admittance of the equivalent circuit model Represented as: Among them, the inversion layer charge storage capacitor and depletion layer capacitance These are known quantities determined based on structural parameters;

[0017] Modulation frequency scanning experiment: With the incident laser intensity fixed, measurements were taken at multiple modulation frequencies f, corresponding to angular frequencies ω=2πf, to obtain the ac-SPV signal at each frequency point. ;

[0018] Based on the equivalent circuit model and formula , will be measured Signal converted to total conductance and total capacitance , Photocurrent density;

[0019] according to Combined with known depletion layer capacitance and inversion layer charge storage capacitor From total conductivity Depletion layer composite conductivity separated from the middle and inversion layer charge transfer conductance ;

[0020] Multiple sets of ω and their corresponding Data substitution Curve fitting was performed to obtain the depletion layer recombination lifetime. t w ;

[0021] Multiple sets of ω and their corresponding Data substitution Curve fitting was performed to obtain the recombination lifetime of the inversion layer interface states. t inv .

[0022] In the optional scheme, the total conductivity The calculation formula is:

[0023] ,

[0024] The total capacitance The calculation formula is:

[0025]

[0026] in, Photocurrent density, , q For electron charge, R The light reflectance of the semiconductor surface. For incident light flux, Re(δVs) ac-SPV signal δVs The real part, Im(δVs) ac-SPV signal δVs The imaginary part.

[0027] In an optional embodiment, the inversion layer charge storage capacitor Calculated using the following formula:

[0028]

[0029] in, The dielectric constant of the oxide layer is... The thickness of the oxide layer;

[0030] The depletion layer capacitance Calculated using the following formula:

[0031]

[0032] in, Where is the dielectric constant of the semiconductor. The maximum width of the depletion layer under strong inversion is calculated from the doping concentration of the semiconductor substrate.

[0033] Among the options, from the total conductance Separate the depletion layer conductivity and inversion layer conductivity The methods include:

[0034] Inversion layer conductance within a specific frequency range of the modulation frequency scan The contribution is negligible, approximately equal to ≈ ;

[0035] In already obtained or Negligible frequency range, utilizing = - The inversion layer conductivity was obtained. .

[0036] The beneficial effect of the present invention is that it can distinguish between the recombination lifetime of the depleted layer and the recombination lifetime of the inversion layer interface state. Attached Figure Description

[0037] The above and other objects, features and advantages of the present invention will become more apparent from the accompanying drawings, in which like reference numerals generally denote like parts.

[0038] Figure 1 This is a schematic diagram of the physical structure of the ac-SPV experiment in one embodiment of the present invention.

[0039] Figure 2 for Figure 1The corresponding equivalent circuit model diagram. Detailed Implementation

[0040] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The advantages and features of the present invention will become clearer from the following description and drawings. However, it should be noted that the concept of the technical solution of the present invention can be implemented in many different forms and is not limited to the specific embodiments described herein. The accompanying drawings are all in a very simplified form and use non-precise proportions, and are only used to facilitate and clarify the illustration of the embodiments of the present invention.

[0041] It should be understood that when an element or layer is referred to as "on," "adjacent to," "connected to," or "coupled to" other elements or layers, it may be directly on, adjacent to, connected to, or coupled to other elements or layers, or there may be intervening elements or layers. Conversely, when an element is referred to as "directly on," "directly adjacent to," "directly connected to," or "directly coupled to" other elements or layers, there are no intervening elements or layers. It should be understood that although the terms first, second, third, etc., may be used to describe various elements, components, areas, layers, and / or portions, these elements, components, areas, layers, and / or portions should not be limited by these terms. These terms are only used to distinguish one element, component, area, layer, or portion from another element, component, area, layer, or portion. Therefore, without departing from the teachings of this invention, the first element, component, area, layer, or portion discussed below may be referred to as the second element, component, area, layer, or portion.

[0042] Spatial relation terms such as “below,” “under,” “below,” “under,” “above,” “above,” etc., are used herein for convenience of description to describe the relationship between one element or feature shown in the figure and other elements or features. It should be understood that, in addition to the orientation shown in the figure, spatial relation terms are intended to also include different orientations of the device in use and operation. For example, if the device in the figure is flipped, then the element or feature described as “below” or “under” the other element or feature will be oriented “above” the other element or feature. Therefore, the exemplary terms “below” and “under” can include both upper and lower orientations. The device may be otherwise oriented (rotated 90 degrees or otherwise) and the spatial descriptive terms used herein will be interpreted accordingly.

[0043] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention. When used herein, the singular forms “a,” “an,” and “the” are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the terms “comprising” and / or “including,” when used in this specification, identify the presence of the stated features, integers, steps, operations, elements, and / or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups. When used herein, the term “and / or” includes any and all combinations of the associated listed items.

[0044] Example

[0045] Reference Figure 1 and Figure 2 This embodiment provides a method for measuring the recombination lifetime of semiconductor depletion layer and inversion layer interface states based on ac-SPV, including the following steps:

[0046] An equivalent circuit model of a semiconductor in a strong inversion state is established, wherein the surface response of the semiconductor is characterized as a parallel depletion layer capacitance. Depletion layer composite conductivity Inversion layer charge storage capacitor and inversion layer charge transfer conductance The total admittance of the equivalent circuit model Represented as: Among them, the inversion layer charge storage capacitor and depletion layer capacitance These are known quantities determined based on structural parameters;

[0047] Modulation frequency scanning experiment: With the incident laser intensity fixed, measurements were taken at multiple modulation frequencies f, corresponding to angular frequencies ω=2πf, to obtain the ac-SPV signal at each frequency point. ;

[0048] Based on the equivalent circuit model and formula , will be measured Signal converted to total conductance and total capacitance , Photocurrent density;

[0049] according to Combined with known depletion layer capacitance and inversion layer charge storage capacitor From total conductivity Depletion layer composite conductivity separated from the middle and inversion layer charge transfer conductance ;

[0050] Multiple sets of ω and their corresponding Data substitution Curve fitting was performed to obtain the depletion layer recombination lifetime. t w ;

[0051] Multiple sets of ω and their corresponding Data substitution Curve fitting was performed to obtain the recombination lifetime of the inversion layer interface states. t inv .

[0052] Specifically, Figure 2 for Figure 1 The equivalent circuit model characterizes the surface response (space charge region) of the semiconductor as parallel depletion layer capacitances. (corresponding to the maximum exhaustion layer width) Depletion layer composite conductivity (Corresponding to the depletion layer carrier recombination lifetime τw), inversion layer charge storage capacitance (Corresponding oxide layer capacitance) and inversion layer charge transfer conductance (Corresponding to the recombination lifetime τinv at the inversion layer interface). Photogenerated current density. Corresponding to laser-excited carrier generation rate, spatial coupling capacitance The gap between the laser and the device surface.

[0053] Depletion layer capacitance Strong inversion depletion layer width For a constant value, it is determined by the doping concentration N of the semiconductor substrate (e.g., P-type). A Decision, depletion of layer capacitance (Per unit area) is equivalent to a "parallel plate capacitor": ;

[0054] in, Let εs be the dielectric constant of the semiconductor, such as Si, where εs = 11.7ε0 and ε0 = 8.85 × 102. 14 F / cm; The maximum width of the depletion layer under strong inversion is calculated from the doping concentration of the semiconductor substrate.

[0055] Maximum width of depletion layer under strong inversion From P-type Fermi potential Doping concentration N A Decide,

[0056] .

[0057] Depletion layer composite conductivity This corresponds to the recombination loss of carriers within the depleted layer, and the recombination lifetime. t w (Determined by volume defects / impurities), and related to the optical modulation angular frequency ω=2πf.

[0058] .

[0059] Inversion layer charge storage capacitor In strong inversion, charge storage in the inversion layer is dominated by the oxide layer capacitance.

[0060] .

[0061] in, The dielectric constant of the oxide layer (SiO2) is given by [insert value here]. The thickness of the oxide layer (SiO2); the dielectric constant of SiO2 ( =3.9ε0).

[0062] Inversion layer charge transfer conductance The interface state trapping-emission loss corresponding to inversion layer electrons, and the interface state recombination lifetime. t inv Related,

[0063] .

[0064] Photocurrent density The carrier generation rate is determined by the laser-excited rate (assuming the laser penetration depth is ≤). (All the light is absorbed by the depletion layer).

[0065] ;

[0066] R is the light reflectivity of the semiconductor surface; The incident light flux is the number of photons per unit area per unit time.

[0067] Parallel connection yields total conductance :

[0068] ;

[0069] From Ohm's law for alternating currents, the strong inverse form is obtained. ;

[0070]

[0071] .

[0072] Depleted layer composite lifetime t w Composite lifetime of interface states with inversion layert inv These parameters can be obtained through experimental measurement and data fitting using ac-SPV. The core idea is to utilize "modulation frequency scanning". "Real / Imaginary response", combined with t w , t inv Fit the dependency relationship.

[0073] I. Measurement Prerequisites: Obtaining data at different modulation frequencies The signal needs to undergo a modulation frequency scanning experiment:

[0074] Fixed laser intensity (to ensure) (Unchanged), but the modulation frequency f (corresponding to the angular frequency ω=2πf);

[0075] Measure each ω using a lock-in amplifier (or dedicated ac-SPV equipment). The real part Re( ) and imaginary part Im( ), or amplitude |δVs| and phase angle θ.

[0076] II. Depletion Layer Composite Lifetime t w Calculation / fitting

[0077] t w With depletion layer conductance The relationship is:

[0078] ;

[0079] ;

[0080] It is a known quantity.

[0081] step:

[0082] 1. Extract the total conductivity from the experimental data and total capacitance Experimental data acquisition And θ, according to the complex function, the real part Re( )that is ×cosθ, imaginary part Im( )that is ×sinθ.

[0083] according to Rationalization yields:

[0084] .

[0085] Therefore, we can conclude that:

[0086] .

[0087] .

[0088] 2. Separation

[0089] ;

[0090] ;

[0091] It is a known quantity, determined by the oxide layer parameters.

[0092] If within a specific frequency range (such as high frequency) It can be ignored, or determined through preliminary experiments. The contribution interval can be approximated. .

[0093] 3. Fitting t w

[0094] Measure multiple sets of ω corresponding to Substitute the data By performing curve fitting, we can obtain... t w .

[0095] III. Recombination Lifetime of Inversion Layer Interface States t inv Calculation / fitting

[0096] t inv With inversion layer conductivity The relationship is:

[0097] ;

[0098] in It is a known quantity, determined by the oxide layer parameters.

[0099] step:

[0100] 1. Separation :

[0101] Depend on Having already obtained (or in) (Negligible frequency range), we can obtain .

[0102] 2. Fitting tinv

[0103] Measure multiple sets of ω corresponding to Substitute the data By performing curve fitting, we can obtain... t inv .

[0104] Derivation and The core concepts are the "frequency response of the carrier recombination process" and the "admittance analysis of the equivalent RC unit" under AC modulation. These two conductivities describe the AC conductance of the "carrier recombination process": the recombination process simultaneously includes "charge storage (corresponding to capacitance C)" and "energy loss (corresponding to conductance g)," which is equivalent to a parallel unit of "capacitor + resistor controlling recombination lifetime"; and under AC modulation, the carrier recombination response changes with the modulation frequency (i.e., "when the response cannot keep up with the frequency, the signal will exhibit phase delay").

[0105] I. Depletion Layer Composite Conductivity Derivation

[0106] Taking the carrier recombination process within the depletion layer as an example:

[0107] Step 1: Carrier rate equation for recombination process (small-signal approximation).

[0108] Let the concentration of photogenerated carriers in the depletion layer be... (Sinusoidal modulation, small signal), the recombination lifetime of the charge carrier is τw, then the rate equation for the charge carrier is:

[0109] ;

[0110] in It is the photogenerated carrier generation rate (proportional to the modulation light intensity).

[0111] Step 2: Solve for the frequency response of the carrier concentration.

[0112] Differentiating with respect to time yields Substituting into the rate equation:

[0113] ;

[0114] The complex amplitude solution of the carrier concentration (reflecting the frequency response) is obtained by rearranging:

[0115] .

[0116] Step 3: Equivalent admittance of the composite process.

[0117] The physical essence of the recombination process is "charge storage (corresponding to depletion layer capacitance)". ")" + "Combined loss (corresponding lifetime)" t w Therefore, the equivalent admittance is the capacitive admittance multiplied by the carrier frequency response factor:

[0118] Depletion layer capacitance The admittance is jω C dp ;

[0119] The frequency response factor of the charge carrier is 1 / (jω+1 / t w (Obtained from the concentration solution in step 2).

[0120] Therefore, the actual admittance of the recombination process is:

[0121] ;

[0122] Step 4: Rationalize admittance and extract the real part (conductance).

[0123] Rationalize the admittance (multiply both numerator and denominator by 1) jω t w ):

[0124] ;

[0125] The real part of the admittance is the alternating conductance (the imaginary part is the susceptance), therefore:

[0126] .

[0127] II. Inversion Layer Interface State Conductivity Derivation

[0128] The derivation logic for the conductance of the inversion layer is exactly the same as that for the depletion layer; only the "depletion layer capacitance / lifetime" needs to be replaced with the "capacitance / lifetime of the inversion layer interface states":

[0129] Step 1: Composite lifetime and frequency response of interface states.

[0130] The recombination lifetime of inversion layer interface states (such as dangling bonds at the Si / SiO2 interface) is t inv Its frequency response to charge changes also satisfies:

[0131] .

[0132] Step 2: Equivalent admittance of the interface state.

[0133] Charge storage in the inversion layer corresponds to the interface state capacitance Therefore, the equivalent admittance of the interface state is:

[0134] .

[0135] Step 3: Rationalize admittance and extract conductance.

[0136] Similarly, after rationalizing the admittance, take its real part:

[0137] ;

[0138] Therefore, the AC conductance of the inversion layer interface state is:

[0139] .

[0140] Derivation Summary:

[0141] The core of these two formulas lies in the coupling between the "frequency response of the composite process" and the "capacitive admittance":

[0142] The carrier response during recombination varies with the modulation frequency by a factor of 1 / (jω+1 / τ).

[0143] The capacitance C corresponding to charge storage has an admittance of jωC;

[0144] Combining the two yields the complex admittance, which, after rationalization, yields the AC conductance by taking its real part (reflecting the frequency dependence of the composite loss).

[0145] This embodiment calculates the recombination lifetime of the depleted layer and the recombination lifetime of the inversion layer interface states, respectively.

[0146] The above description is merely a description of preferred embodiments of the present invention and is not intended to limit the scope of the present invention in any way. Any changes or modifications made by those skilled in the art based on the above disclosure shall fall within the protection scope of the claims.

Claims

1. A method for measuring the recombination lifetime of a semiconductor depletion layer and the recombination lifetime of interface states in an inversion layer based on ac-SPV, characterized in that, Includes the following steps: An equivalent circuit model of a semiconductor in a strong inversion state is established, wherein the surface response of the semiconductor is characterized as a parallel depletion layer capacitance. Depletion layer composite conductivity Inversion layer charge storage capacitor and inversion layer charge transfer conductance ; Total admittance of the equivalent circuit model Represented as: Among them, the inversion layer charge storage capacitor and depletion layer capacitance These are known quantities determined based on structural parameters; Modulation frequency scanning experiment: With the incident laser intensity fixed, measurements were taken at multiple modulation frequencies f, corresponding to angular frequencies ω=2πf, to obtain the ac-SPV signal at each frequency point. ; Based on the equivalent circuit model and formula , will be measured Signal converted to total conductance and total capacitance , Photocurrent density; according to Combined with known depletion layer capacitance and inversion layer charge storage capacitor From total conductivity Depletion layer composite conductivity separated from the middle and inversion layer charge transfer conductance ; Multiple sets of ω and their corresponding Data substitution Curve fitting was performed to obtain the depletion layer recombination lifetime. τ w ; Multiple sets of ω and their corresponding Data substitution Curve fitting was performed to obtain the recombination lifetime of the inversion layer interface states. τ inv .

2. The method for measuring the recombination lifetime of the semiconductor depletion layer and the recombination lifetime of the inversion layer interface states based on ac-SPV as described in claim 1, characterized in that, The total conductivity The calculation formula is: ， The total capacitance The calculation formula is: in, Photocurrent density, , q For electron charge, R The light reflectance of the semiconductor surface. For incident light flux, Re(δVs) ac-SPV signal δVs The real part, Im(δVs) ac-SPV signal δVs The imaginary part.

3. The method for measuring the recombination lifetime of semiconductor depletion layer and inversion layer interface states based on ac-SPV as described in claim 1, characterized in that, The inversion layer charge storage capacitor Calculated using the following formula: in, The dielectric constant of the oxide layer is... The thickness of the oxide layer; The depletion layer capacitance Calculated using the following formula: in, Where is the dielectric constant of the semiconductor. The maximum width of the depletion layer under strong inversion is calculated from the doping concentration of the semiconductor substrate.

4. The method for measuring the recombination lifetime of semiconductor depletion layer and inversion layer interface states based on ac-SPV as described in claim 1, characterized in that, From total conductivity Separate the depletion layer conductivity and inversion layer conductivity The methods include: Inversion layer conductance within a specific frequency range of the modulation frequency scan The contribution is negligible, approximately equal to ≈ ; In already obtained or Negligible frequency range, utilizing = - The inversion layer conductivity was obtained. .

Images