Modeling method of GaN HEMT nonlinear model
By conducting PIV tests within the 25-175℃ range and improving the drain-source current model, the accuracy problem of high and low temperature models for GaNHEMT devices was solved, achieving accurate performance prediction and microwave simulation under high and low temperature environments.
Patent Information
- Application Number
- CN202410655079.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-05-24
- Publication Date
- 2025-11-25
AI Technical Summary
Existing GaNHEMT device high and low temperature models lack accuracy, making it impossible to accurately predict performance under high and low temperature environments, which affects microwave power circuit analysis and design.
PIV tests were conducted in the temperature range of 25-175℃. The initial model equation of the leakage source current was improved and embedded into ADS software for fitting. The parameters related to thermal effects were determined, and an accurate high and low temperature model was established.
It enables accurate prediction of GaNHEMT device performance under high and low temperature environments, improves the accuracy of microwave simulation models, and meets the design requirements of high-power communication.
Smart Images
Figure CN121009845A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of semiconductor technology, and more specifically, to a modeling method for a nonlinear model of GaNHEMT (GaN High Electron Mobility Transistor). Background Technology
[0002] High electron mobility transistors (HEMTs) have broad prospects in microwave power applications due to their advantages such as good high-frequency performance and low on-resistance. In order to establish the relationship between process parameters and device microwave characteristics, and thus conduct process stability and circuit yield analysis, an accurate HEMT device simulation model is essential.
[0003] GaNHEMT devices, with their high power density and high efficiency, demonstrate great potential in microwave and millimeter-wave communication, radar, and satellite navigation systems. They are particularly advantageous in complex electromagnetic environments and harsh temperature conditions. This presents a significant challenge to reliable circuit and system design, as the electron mobility and saturation velocity of GaNHEMT devices are more affected by channel temperature than those of GaAs devices. The channel temperature depends not only on the device's power consumption but also on changes in ambient temperature. Therefore, establishing a large-signal model that accurately predicts the performance of GaNHEMT devices under high and low temperature environments is crucial for power circuit analysis and high-performance design. Microwave GaNHEMT devices typically operate under complex environmental conditions such as high frequency, high power density, and extreme temperatures. High-power operation leads to increased device power consumption, causing the electron temperature in the channel to rise and be transferred outwards as heat. Simultaneously, the increased electron temperature in the channel reduces electron mobility, thereby decreasing electron concentration and affecting current magnitude. Therefore, establishing accurate high and low temperature thermoelectric models is also essential.
[0004] Traditional thermoelectric models mostly only consider self-heating, with only a few considering high and low temperature models, and the accuracy of these models is also questionable. Therefore, accurate high and low temperature models are of great significance. In the future, the application of high-power, large-gate-width GaNHEMTs in the field of communications will increase, and the requirements for the accuracy of power amplifier design will become increasingly higher, with shorter design cycles. These factors place higher demands on the accuracy of high and low temperature models for GaNHEMT devices. Summary of the Invention
[0005] In view of this, the present invention provides a modeling method for GaNHEMT nonlinear models, which effectively solves the technical problems existing in the prior art, establishes an accurate model of drain-source current under high and low temperatures, and ensures that the GaNHEMT nonlinear model is more accurate when performing microwave simulations.
[0006] To achieve the above objectives, the technical solution provided by the present invention is as follows:
[0007] A modeling method for GaNHEMT nonlinear models includes:
[0008] The GaNHEMT was subjected to PIV (pulse current-voltage) testing within a temperature range of 25-175℃ to obtain PIV test data;
[0009] The initial model equation for the drain-source current of the GaNHEMT based on ambient temperature is improved into the target model equation.
[0010] The target model equations are embedded into the ADS software using symbolic definition devices;
[0011] In the ADS software, the PIV test data is fitted with the output characteristic curve of the target model equation to determine the parameters related to the thermal effect.
[0012] Optionally, PIV tests are performed on GaNHEMT within a preset temperature range to obtain PIV test data, wherein the static bias point is required to be (0, 0).
[0013] Furthermore, it is required that the gate and drain of the GaNHEMT be fed in a pulsed manner.
[0014] Optionally, the GaNHEMT is subjected to PIV tests at temperatures of 25°C, 50°C, 75°C, 100°C, 125°C, 150°C and 175°C respectively.
[0015] The pulse mode has a pulse width of 200 ns, a period of 200 μm, and a duty cycle of 0.1%.
[0016] Optionally, the drain-source current I ds The initial model equations are:
[0017]
[0018] Among them, V gs1 =V gs -V t ;
[0019]
[0020] V t =V t0 +γV ds ;
[0021] Where β is the fitted value related to transconductance, V gs For gate voltage, Vds V is the drain voltage. t γ and V are fitted values related to leakage pressure. K and V ST V is the gate voltage control factor, λ and α are control factors related to the knee voltage, and V L V represents the threshold voltage, psat represents the gate voltage corresponding to entering the saturation region, plin represents the device threshold voltage control factor, and V t0 Δ represents the fitting parameters related to leakage pressure when no leakage pressure is applied, and Δ represents the gate voltage fitting parameters.
[0022] Optionally, the initial model equation for the drain-source current of the GaNHEMT based on ambient temperature is improved into the target model equation, including:
[0023] Based on the ambient temperature T amb λ th Replace λ in the initial model equation, where:
[0024]
[0025] Where, λ th0 , λ th1 , λ th2 and λ th3 These are leakage pressure control factors at different temperatures.
[0026] Optionally, the initial model equation for the drain-source current of the GaNHEMT based on ambient temperature is improved into the target model equation, including:
[0027] Based on the ambient temperature T amb α th Replace α in the initial model equation, where:
[0028]
[0029] Where, α th0 α th1 and α th2 These are the knee voltage regulation factors at different temperatures.
[0030] Optionally, the initial model equation for the drain-source current of the GaNHEMT based on ambient temperature is improved into the target model equation, including:
[0031] Based on the ambient temperature T amb V Lth Replace V in the initial model equation L ,in:
[0032] V Lth =V Lth0 +V Lth1T amb ;
[0033] Among them, V Lth0 and V Lth1 This represents the threshold voltage adjustment factor at different temperatures.
[0034] Optionally, the symbol definition device includes a first port, a second port, and a third port, wherein the first port is the input of the gate-source voltage of the GaNHEMT, the second port is the source-drain channel of the GaNHEMT, and the third port is the ambient temperature.
[0035] Optionally, the target model equation is represented in the second port.
[0036] Optionally, determine parameters related to thermal effects, including:
[0037] The parameters that are independent of the ambient temperature include V. t0 V ST ,β,V K Δ, plin, psat, and γ are used to determine parameters related to the ambient temperature, including λ. th0 , λ th1 , λ th2 , λ th3 α th0 α th1 α th2 V Lth0 and V Lth1 .
[0038] Compared with the prior art, the technical solution provided by the present invention has at least the following advantages:
[0039] This invention provides a modeling method for a GaNHEMT nonlinear model, comprising: performing a PIV test on the GaNHEMT within a temperature range of 25-175℃ to obtain PIV test data; improving the initial model equation of the drain-source current of the GaNHEMT based on the ambient temperature into a target model equation; embedding the target model equation into ADS software using symbolic device definition; and fitting the PIV test data with the output characteristic curve of the target model equation in the ADS software to determine thermal effect-related parameters.
[0040] As can be seen from the above, the technical solution provided by the present invention improves the initial model equation of the source and drain current as the target model equation, taking into account the different ambient temperatures of GaNHEMT operation. The improved model can accurately predict the output characteristic curves at different temperatures, establish an accurate model of the drain and source current at high and low temperatures, and ensure that the GaNHEMT nonlinear model is more accurate when performing microwave simulations. Attached Figure Description
[0041] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.
[0042] Figure 1 This is a schematic diagram of the topology of the GaNHEMT nonlinear model;
[0043] Figure 2 This is a schematic diagram of the GaNHEMT thermoelectric model;
[0044] Figure 3 A flowchart illustrating a modeling method for a GaNHEMT nonlinear model provided in an embodiment of the present invention;
[0045] Figure 4 A block diagram of a current source model provided in an embodiment of the present invention;
[0046] Figure 5 This is a schematic diagram comparing the test curve and the model simulation curve at 25℃.
[0047] Figure 6 This is a schematic diagram comparing the test curve and the model simulation curve at 75℃.
[0048] Figure 7 This is a schematic diagram comparing the test curve and the model simulation curve at 125℃.
[0049] Figure 8 This is a schematic diagram showing the comparison between the test curve and the model simulation curve at 175℃. Detailed Implementation
[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0051] As mentioned in the background section, most traditional thermoelectric models only consider self-heating, with only a few considering high and low temperature models, and the accuracy of these models is also questionable. Therefore, accurate high and low temperature models are of great significance. In the future, the application of high-power, large-gate-width GaNHEMTs in the field of communications will increase, leading to higher requirements for the accuracy of power amplifier design and shorter design cycles. These factors place even greater demands on the accuracy of high and low temperature models for GaNHEMT devices.
[0052] Based on this, the present invention provides a modeling method for GaNHEMT nonlinear models, which effectively solves the technical problems existing in the prior art, establishes an accurate model of drain-source current under high and low temperatures, and ensures that the GaNHEMT nonlinear model is more accurate when performing microwave simulations.
[0053] To achieve the above objectives, the technical solutions provided by the embodiments of the present invention are as follows, in detail... Figures 1 to 8 The technical solutions provided in the embodiments of the present invention will be described in detail.
[0054] The technical solution provided in this invention embodiment can utilize a 4×100μm GaNHEMT device. The nonlinear model is established based on the linear model, such as... Figure 1 The topology of the GaNHEMT nonlinear model shown, and Figure 2 The GaNHEMT thermoelectric model is shown.
[0055] The first step is the establishment of the linear model. The establishment of the small-signal model mainly includes the extraction of parasitic parameters and intrinsic parameters, such as... Figure 1 As shown, parasitic parameters include parasitic capacitance (Cpg, Cpd), parasitic resistance and inductance (Rg, Rd, Rs, Lg, Ld, Ls), and intrinsic parameters include Ri, Cds, τ, Gm, Gd, Cgs, Cgd and Rgd.
[0056] Then, the S-parameters were tested. The test conditions were frequency 0-20GHz, bias conditions (-1.6V, 28V), and scan range: Vg (-4, 2), step 0.5 (i.e., test in steps of 0.5) and Vd (0, 48), step 1 (i.e., test in steps of 1).
[0057] Then, the intrinsic and parasitic parameters in the small-signal model are extracted using IVCAD software. The establishment of the large-signal model mainly considers nonlinear I... ds The model, along with Cgs, Cgd, and grid leakage current models, were established. Finally, the relevant parameters were determined through measured data and simulation fitting, and the model was validated.
[0058] The capacitance parameters in Cgs and Cgd are extracted using the charge model provided in IVCAD.
[0059] The gate leakage current was fitted using the built-in gate leakage current model of IVCAD, and relevant parameters of the leakage current model were extracted.
[0060] Furthermore, embodiments of the present invention provide a modeling method for the GaNHEMT nonlinear model. For example... Figure 3 The diagram shows a flowchart of a modeling method for a GaNHEMT nonlinear model provided in an embodiment of the present invention. The method includes:
[0061] S1. The GaNHEMT is subjected to a PIV test within a temperature range of 25-175℃ to obtain PIV test data. This invention relates to the extraction of environmental temperature-related parameters; therefore, the PIV test is used to eliminate the influence of other nonlinear effects such as self-heating and trapping effects. By fitting the PIV test data, parameter values independent of environmental temperature can be obtained.
[0062] S2. The initial model equation for the drain-source current of the GaNHEMT based on ambient temperature is improved into the target model equation.
[0063] S3. Embed the target model equation into the ADS software using a symbol definition device.
[0064] S4. Fit the PIV test data with the output characteristic curve of the target model equation in the ADS software to determine the parameters related to the thermal effect.
[0065] It is understood that the technical solution provided in the embodiments of the present invention improves the initial model equation of the source and drain current as the target model equation, taking into account the different ambient temperatures at which GaNHEMT operates. The improved model can accurately predict the output characteristic curves at different temperatures, establish an accurate model of the drain and source current at high and low temperatures, and ensure that the GaNHEMT nonlinear model is more accurate when performing microwave simulations.
[0066] In one embodiment of the present invention, the present invention provides a method for obtaining PIV test data by performing PIV testing on GaNHEMT within a preset temperature range, wherein the static bias point is required to be (0, 0).
[0067] Furthermore, it is required that the gate and drain of the GaNHEMT be fed in a pulsed manner.
[0068] Optionally, in embodiments of the present invention, PIV testing can be performed under seven temperature conditions, such as PIV testing of the GaNHEMT at temperatures of 25°C, 50°C, 75°C, 100°C, 125°C, 150°C, and 175°C.
[0069] Furthermore, the pulse width of the pulse mode provided in this embodiment of the invention is 200 ns, the period is 200 μm, and the duty cycle is 0.1%. The short pulse and low duty cycle can ensure that the GaNHEMT device is only affected by the ambient temperature and can basically eliminate the influence of self-heating effect.
[0070] In one embodiment of the present invention, the invention can be improved based on the initial model equations proposed by Fager et al. Wherein, the drain-source current I... ds The initial model equations are:
[0071]
[0072] Among them, V gs1 =V gs -V t ;
[0073]
[0074] V t =V t0 +γV ds ;
[0075] Where β is the fitted value related to transconductance, V gs For gate voltage, V ds V is the drain voltage. t γ and V are fitted values related to leakage pressure. K and V ST V is the gate voltage control factor, λ and α are control factors related to the knee voltage, and V L V represents the threshold voltage, psat represents the gate voltage corresponding to entering the saturation region, plin represents the device threshold voltage control factor, and V t0 Δ represents the fitting parameters related to leakage pressure when no leakage pressure is applied, and Δ represents the gate voltage fitting parameters.
[0076] Considering the impact of ambient temperature on the device, some parameters in the initial model equations need to be replaced. Optionally, the initial model equations for the drain-source current of the GaNHEMT based on ambient temperature are improved into the target model equations, including:
[0077] Based on the ambient temperature T amb λ th Replace λ in the initial model equation, where:
[0078]
[0079] Where, λ th0 , λ th1 , λ th2 and λ th3 These are leakage pressure control factors at different temperatures.
[0080] Optionally, the initial model equation for the drain-source current of the GaNHEMT based on ambient temperature is improved into the target model equation, including:
[0081] Based on the ambient temperature T amb α th Replace α in the initial model equation, where:
[0082]
[0083] Where, α th0 α th1 and α th2 These are the knee voltage regulation factors at different temperatures.
[0084] Optionally, the initial model equation for the drain-source current of the GaNHEMT based on ambient temperature is improved into the target model equation, including:
[0085] Based on the ambient temperature T amb V Lth Replace V in the initial model equation L ,in:
[0086] V Lth =V Lth0 +V Lth1 T amb ;
[0087] Among them, V Lth0 and V Lth1 This represents the threshold voltage adjustment factor at different temperatures.
[0088] Therefore, considering the ambient temperature T amb The impact on the device, λ th α th and V Lth The target model equation is obtained by embedding it into the initial model equation.
[0089] In one embodiment of the present invention, the present invention provides a method for embedding the target model equations into ADS software using a symbol definition device, which can select a three-port symbol definition device. For example... Figure 3 The topology shown is the one built in ADS, where, Figure 4 This invention provides a current source model block diagram. The symbol-defined device provided in this embodiment includes a first port 1, a second port 2, and a third port 3. The first port 1 is the input of the gate-source voltage Vgs of the GaNHEMT, the second port 2 is the source-drain channel of the GaNHEMT, and the third port 3 is the input of the ambient temperature T. ambThe input. Optionally, the second port 2 represents the source-drain channel, which can be used to input the ambient temperature T. amb The target model equation for the effect on the drain current is expressed at the second port 2, i.e., the drain-source current I. ds The target model equation is represented in the second port 2.
[0090] In one embodiment of the present invention, the measured PIV test data is fitted with the output characteristic curve of the target model equation considering the improvement of ambient temperature in ADS software, and then the thermal effect-related parameters are determined by fitting, including:
[0091] The parameters that are independent of the ambient temperature include V. t0 V ST ,β,V K Δ, plin, psat, and γ are used to determine parameters related to the ambient temperature, including λ. th0 , λ th1 , λ th2 , λ th3 α th0 α th1 α th2 V Lth0 and V Lth1 .
[0092] The verification referenced the signal-striking model under ambient temperature, i.e., the target model equation was jointly simulated with the measured PIV test data, such as... Figure 5-8 The comparison charts shown below (where T represents temperature, measurement represents measured PIV test data, and simulation represents simulation of the target model equation) at 25℃, 75℃, 125℃, and 175℃ demonstrate that the large-signal model at the reference ambient temperature can predict the output characteristic curves of the device well at different temperatures.
[0093] Compared with the prior art, the technical solution provided by the embodiments of the present invention has at least the following advantages:
[0094] This invention provides a modeling method for a GaNHEMT nonlinear model, comprising: performing a PIV test on the GaNHEMT within a temperature range of 25-175℃ to obtain PIV test data; improving the initial model equation of the drain-source current of the GaNHEMT based on the ambient temperature into a target model equation; embedding the target model equation into ADS software using symbolic device definition; and fitting the PIV test data with the output characteristic curve of the target model equation in the ADS software to determine thermal effect-related parameters.
[0095] As can be seen from the above, the technical solution provided by the embodiments of the present invention improves the initial model equation of the source and drain current as the target model equation, taking into account the different ambient temperatures of GaNHEMT operation. The improved model can accurately predict the output characteristic curves at different temperatures, establish an accurate model of the drain and source current at high and low temperatures, and ensure that the GaNHEMT nonlinear model is more accurate when performing microwave simulation.
[0096] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.
[0097] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.
[0098] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection, an electrical connection, or a connection that allows communication between them; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.
[0099] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can mean that the first feature is in direct contact with the second feature, or that the first feature is in indirect contact with the second feature through an intermediate medium. Furthermore, "above," "over," and "on top" of the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.
[0100] In this invention, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to a specific feature, structure, material, or characteristic described in connection with that embodiment or example, which is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.
[0101] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.
Claims
1. A modeling method for a GaNHEMT nonlinear model, characterized in that, include: PIV test data were obtained by performing a PIV test on the GaNHEMT within a temperature range of 25-175℃. The initial model equation for the drain-source current of the GaNHEMT based on ambient temperature is improved into the target model equation. The target model equations are embedded into the ADS software using symbolic definition devices; In the ADS software, the PIV test data is fitted with the output characteristic curve of the target model equation to determine the parameters related to the thermal effect.
2. The modeling method for the GaNHEMT nonlinear model according to claim 1, characterized in that, PIV test data was obtained by performing PIV tests on GaNHEMT within a preset temperature range, where the static bias point is required to be (0, 0). Furthermore, it is required that the gate and drain of the GaNHEMT be fed in a pulsed manner.
3. The modeling method for the GaNHEMT nonlinear model according to claim 2, characterized in that, The GaNHEMT was subjected to PIV tests at temperatures of 25℃, 50℃, 75℃, 100℃, 125℃, 150℃ and 175℃ respectively. The pulse mode has a pulse width of 200 ns, a period of 200 μm, and a duty cycle of 0.1%.
4. The modeling method for the GaNHEMT nonlinear model according to claim 1, characterized in that, The drain source current I ds The initial model equations are: ； in, ; ； ； ； Where β is the fitted value related to transconductance, V gs For gate voltage, V ds V is the drain voltage. t γ and V are fitted values related to leakage pressure. K and V ST V is the gate voltage control factor, λ and α are control factors related to the knee voltage, and V L V represents the threshold voltage, psat represents the gate voltage corresponding to entering the saturation region, plin represents the device threshold voltage control factor, and V t0 represents the fitting parameters related to leakage pressure when no leakage pressure is applied, and Δ represents the gate voltage fitting parameters.
5. The modeling method for the GaNHEMT nonlinear model according to claim 4, characterized in that, The initial model equation for the drain-source current of the GaNHEMT based on ambient temperature is improved into the target model equation, including: Based on the ambient temperature T amb λ th Replace λ in the initial model equation, where: ； Where, λ th0 , λ th1 , λ th2 and λ th3 These are leakage pressure control factors at different temperatures.
6. The modeling method for the GaNHEMT nonlinear model according to claim 5, characterized in that, The initial model equation for the drain-source current of the GaNHEMT based on ambient temperature is improved into the target model equation, including: Based on the ambient temperature T amb α th Replace α in the initial model equation, where: ； Where, α th0 α th1 and α th2 These are the knee voltage regulation factors at different temperatures.
7. The modeling method for the GaNHEMT nonlinear model according to claim 6, characterized in that, The initial model equation for the drain-source current of the GaNHEMT based on ambient temperature is improved into the target model equation, including: Based on the ambient temperature T amb V Lth Replace V in the initial model equation L ,in: ； Among them, V Lth0 and V Lth1 This represents the threshold voltage adjustment factor at different temperatures.
8. The modeling method for the GaNHEMT nonlinear model according to claim 1, characterized in that, The symbol-defined device includes a first port, a second port, and a third port, wherein the first port is the input of the gate-source voltage of the GaNHEMT, the second port is the source-drain channel of the GaNHEMT, and the third port is the ambient temperature.
9. The modeling method for the GaNHEMT nonlinear model according to claim 8, characterized in that, The target model equation is represented in the second port.
10. The modeling method for the GaNHEMT nonlinear model according to claim 7, characterized in that, Determine the parameters related to the thermal effect, including: The parameters that are independent of the ambient temperature include V. t0 V ST ,β,V K Δ, plin, psat, and γ are used to determine parameters related to the ambient temperature, including λ. th0 , λ th1 , λ th2 , λ th3 α th0 α th1 α th2 V Lth0 and V Lth1 .