An improved large signal model of InP HEMTs

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本站小编 Free考研考试/2022-01-01

1.
Introduction

InP high electron mobility transistors (HEMTs) have the characteristics of high electron mobility, low noise, low power consumption and high gain^{[1, 2]}. InP HEMTs are widely used in solid-state power microwave and millimeter-wave (MMW) electronics^{[3, 4]}. DC and microwave performances of InP HEMTs can be greatly improved by decreasing the gate length (L_g), thereby the devices have the capability of being used in higher frequency^[5–7]. The integration of devices into a circuit environment for circuit design and simulation requires compact modeling of the device operating under various bias conditions and different signal levels. This has led to the desire for compact models that accurately predict DC, AC (small- and large-signal), trans-conductance frequency dispersion and other characteristics of devices. Developing models of InP HEMTs has an important role for accurate application and re-manipulation of these characteristics.

Many commercial experience models, including the Curtice model^[8], the Statz model^[9], the Angelov–Chalmers model^[10] and the EEHEMT model implemented in Keysight Advanced Design Systems (ADS)^[11] have been reported. Special functions such as the hyperbolic function are used to develop most of these models. These compact model^[8–11] forms are based on GaAs MESFET/HFET or silicon devices, without considering the necessary physical mechanisms in InP technology. Compact models that are suitable for GaN HEMTs large-signal modeling have been proposed in Refs. [12, 13]. There are also several models proposed for use with GaN HEMTs, each with its own focus on a narrow range of applications^[14–17]. InP HEMTs have unique physical properties. InAlAs/ InGaAs interface in InP devices has greater conduction band discontinuity, high electron density of two electrons, high ternary electron concentration in conductive channel, and greatly improves the current processing capability of the device. InP HEMT has a higher operating frequency than GaN HEMT and GaAs HEMT and the models of GaN HEMT and GaAs HEMT can only be used for reference^{[18, 19]}. The study of large-signal modeling of InP HEMTs has been proposed in Refs. [20, 21]. Two models^{[22, 23]} proposed for use with InP HEMTs focus more on low-frequency noise. The result presented in Ref. [24] just described the current-voltage characteristics of InP HEMT. Research on large-signal modeling for short gate length InP HEMTs is less involved, and understanding of the physical characteristics of the InP HEMTs is helpful for the modeling of the devices.

HEMTs of high indium content channel usually suffer from low breakdown voltage and high output conductance, which is caused by the generation of electron–hole pair created by impact ionization^[25]. This phenomenon is even more remarkable for short gate length devices where much higher electric field exists under the gate area. To improve the frequency and gain of InP HEMT devices and circuits, and to reduce noise, the key is to reduce the gate length^[26]. This will lead to the drain-induced barrier lowering (DIBL) effect. The DIBL effect refers originally to a reduction of threshold voltage of the transistor at higher drain voltages and causes the output volt-ampere characteristic curve to be not saturated, that is to say, the output AC resistance is decreased and the voltage gain of the device is decreased^{[20, 27]}. To simulate the DIBL effect caused by gate length, higher challenge is put forward for modeling.

The purpose of this paper is to introduce nonlinear modeling of InP HEMTs. In order to accurately model the drain current with DIBL effect, a method of regional current fitting is introduced^{[10, 28, 29]}. Both the equations for channel current and gate charge models were all continuous and high-order drivable, and the proposed gate charge model satisfied the charge conservation. The channel current model could fit DC performance of devices, such as the positive, negative, cut-off and sub-threshold region. The model is implemented by using Verilog-A language, which has been complied and linked into Keysight ADS for simulation. The modeling technique have been verified through comparison with measured DC I–V, C–V, small-signal S-parameters up to 40 GHz for a 2 × 25 μm × 70 nm InP HEMT using self-aligned T-gate process, fabricated at a commercial foundry.

A description of the nonlinear large model is provided in Section 2. The method to overcome the problems caused by DIBL effect for InP HEMTs modeling is presented. In Section 3, the model verification results are provided. Section 4 summarizes and concludes this work.

2.
Model description

The nonlinear model of InP HEMTs is shown in Fig. 1. The intrinsic elements of the model consists of the bias-dependent capacitances C_gsi, C_gdi, C_dsi and the drain–source current I_ds. L_g, L_d, L_s, R_g, R_d and R_s are the parasitic inductors and resistors of gate (G), drain (D) and source (S), respectively. I_gd and I_gs are the gate–source and gate–drain diodes, respectively. C_gsx, C_gdx and C_dsx represent the external bias-independent parasitic capacitors. R_gsx, R_gdx represent the external bias-independent parasitic resistance. A simple AC current I_dp, combined with R_dp and C_dp, is introduced to characterize the transconductance frequency dispersion effect of HEMTs. The thermal sub-circuit, which describes the thermal impedance behavior is also identified in Fig. 1.

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Figure1.
(Color online) Large-signal model topology for compound semiconductor HEMTs.

A schematic cross section of typical InP HEMTs is shown in Fig. 2, in which L_g is gate length and L_c is gate cap length. The micrograph of InP HEMTs is shown in Fig. 3. The devices are fabricated by using process of self-aligned T-gate structure, dry etch and E-beam lithography. T-gate device has smaller parasitic parameters and can be used in high frequency and high gain applications. Coplanar waveguide (CPW) and common source structure are used in our device to reduce the effect of high order electromagnetic waves.

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Figure2.
(Color online) Schematic cross-section of InP HEMTs.

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Figure3.
(Color online) Micrograph of InP HEMTs.

2.1
Drain current model

For the drain-induced barrier lowering effect which appears when the drain–source voltage is relatively low, a method of regional drain current modeling is introduced. Fig. 3 shows the schematic of regional drain current fitting method. In order to model the I–V curve more accurately, drain current is separated into two regions, region A and region B with current I_dsa and I_dsb, respectively. The overall drain current is I_ds = I_dsa + I_dsb. We use Angelov drain current equations to model both I_dsa and I_dsb.

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Figure4.
(Color online) Schematic of regional drain current fitting method.

The equation for the drain current in the nonlinear model is

$${I_{
m {ds}}} = {I_{
m {dsa}}} + {I_{
m {dsb}}},$$

(1)

$${I_{
m {dsx}}} = 0.5left( {{I_{
m {dsp_x}}} - {I_{
m {dsn_x}}}}
ight),$$

(2)

$$begin{split}{I_{
m {dsp_x}}} =,,& {I_{
m {pk0x}}}tanh left( {{psi _{
m {px}}}}
ight)left[ {1 + tanh left( {{alpha _{
m {px}}}{V_{
m {ds}}}}
ight)}
ight] & times ,, left[ {1 + {lambda _{
m {px}}}{V_{
m {ds}}} + {lambda _{
m {p1x}}}exp left( {frac{{{V_{{
m{ds}}}}}}{{{V_{
m {knx}}}}} - 1}
ight)}
ight],end{split}$$

(3)

$$begin{split}{I_{
m {dsn_x}}} =,, & {I_{
m {pk0x}}}tanh left( {{psi _{
m {nx}}}}
ight)left[ {1 - tanh left( {{alpha _{
m {nx}}}{V_{
m {ds}}}}
ight)}
ight] & timesleft[ {1 - {lambda _{
m {nx}}}{V_{
m {ds}}} - {lambda _{
m {n1x}}}exp left( {frac{{{V_{{
m{ds}}}}}}{{{V_{
m {knx}}}}} - 1}
ight)}
ight],end{split}$$

(4)

$$begin{split}{psi _{
m {px}}}=,, & {P_{
m {1mx}}}left( {{V_{
m {gs}}} - {V_{
m {pkm_x}}}}
ight) + {P_{
m 2x}}{left( {{V_{
m {gs}}} - {V_{
m {pkm_x}}}}
ight)^2}& + {P_{
m {3x}}}{left( {{V_{
m {gs}}} - {V_{
m {pkm_x}}}}
ight)^3},end{split}$$

(5)

$$begin{split}{psi _{
m {nx}}} =,, & {P_{
m {1mx}}}left( {{V_{
m {gd}}} - {V_{
m {pkm_x}}}}
ight) + {P_{
m {2x}}}{left( {{V_{
m {gd}}} - {V_{
m {pkm_x}}}}
ight)^2} &+ {P_{
m {3x}}}{left( {{V_{
m {gd}}} - {V_{
m {pkm_x}}}}
ight)^3},end{split}$$

(6)

$${P_{1{
m{mx}}}} = {P_{
m {1x}}}left[ {1 + {B_{
m {1x}}}/{{cosh }^2}left( {{B_{
m {2x}}}{V_{
m {ds}}}}
ight)}
ight],$$

(7)

$$begin{split}{V_{
m {pkm_x}}} = ,, & {V_{
m {pks_x}}} - {D_{
m {vpks_x}}} &+ {D_{
m {vpks_x}}}tanh left( {{A_{
m {lphas_x}}}{V_{
m {ds}}}}
ight),end{split}$$

(8)

$${alpha _{
m {ux}}} = {A_{
m {lphar_x}}} + {A_{
m {lphas_x}}}left[ {1 + tanh left( {{psi _{
m {ux}}}}
ight)}
ight],$$

(9)

$${lambda _{
m {ux}}} = {L_{
m {ambda_x}}} + {L_{
m {vgx}}}left[ {1 + tanh left( {{psi _{
m {ux}}}}
ight)}
ight],$$

(10)

$${lambda _{
m {u1x}}} = {L_{
m {ambda_x}}} + {L_{
m {vgx}}}left[ {1 + tanh left( {{psi _{
m {ux}}}}
ight)}
ight],$$

(11)

where the B_1x, B_2x, P_1x, P_2x, P_3x, I_pk0x, V_{pks_x}, D_{vpks_x}, A_{lphar_x}, A_{lphas_x}, V_trx, L_{ambda_x}, L_{ambda1_x}, L_vgx, V_knx, λ_px, λ_nx, λ_p1x, λ_n1x are the model parameters for drain current I_dsa and I_dsb. The value of x can be taken as a or b. The value of u in Eqs. (9)–(11) can be taken as n or p. The Eqs. (2)–(11) describe how to model the drain current I_dsa and I_dsb. The I_pk0x is the drain current at which the maximum of the transconductance occurs. The V_{pkm_x} is the gate voltage at maximum transconductance. The L_{ambda_x} and L_{ambda1_x} are the channel length modulation parameters. The hyperbolic tangent function tanh(Ψ_x) and tanh(Ψ_nx) are mainly used to simulate the general contour of the I–V characteristic curve of the device. The V_trx, V_knx, λ_p1x and λ_n1x are parameters that control the breakdown effect. The tanh(α_xV_ds) and tanh(α_nxV_ds) are used to control the degree of bending of the I–V characteristic curve near the knee voltage.

2.2
Terminal charges model

The gate capacitance of the large signal model is connected in the form of a charge source or a non-linear capacitor at the corresponding node in the patch structure. In order to achieve the best convergence effect, charge-based models are used to model the gate charge. The model satisfies the law of charge conservation and can guarantee the continuity and self-consistency of large signal model and small signal model.

The charge-based models can be expressed as

$${L_{
m {c1}}} = ln left[ {cosh left( {{P_{10}} + {P_{11}}{V_{
m {gsc}}} + {P_{111}}{V_{
m {ds}}}}
ight)}
ight],$$

(12)

$${Q_{
m {gs0}}} = {P_{10}} + {P_{111}}{V_{
m {ds}}} + ln left[ {cosh left( {{P_{10}} + {P_{111}}{V_{
m {ds}}}}
ight)}
ight],$$

(13)

$${L_{
m c4}} = ln left[ {cosh left( {{P_{40}} + {P_{41}}{V_{
m {gdc}}} - {P_{111}}{V_{
m {ds}}}}
ight)}
ight],$$

(14)

$${Q_{
m {gd0}}} = {P_{40}} - {P_{111}}{V_{
m {ds}}} + ln left[ {cosh left( {{P_{40}} - {P_{111}}{V_{
m {ds}}}}
ight)}
ight],$$

(15)

$$begin{split}{Q_{{text{gs}}}} =& {C_{{text{gsp0}}}}{V_{{text{gsc}}}} + {C_{{text{gsi}}}},left( {{P_{{text{hi1}}}} + {L_{{text{c1}}}} - {Q_{{text{gs0}}}}}
ight), hfill & times left{ {left[ {1 - {P_{111}} + tanh left( {{P_{{text{hi2}}}}}
ight)}
ight]/{P_{11}} + ,,2{P_{111}}{V_{{text{gsc}}}}}
ight}, hfill end{split} $$

(16)

$$begin{split} {Q_{{text{gd}}}} =& {C_{{text{gdp0}}}}{V_{{text{gdc}}}} + {C_{{text{gdi}}}} left( {{P_{{text{hi4}}}} + {L_{{text{c4}}}} - {Q_{{text{gd0}}}}}
ight) hfill & times left{ {left[ {1 - {P_{111}} + tanh left( {{P_{{text{hi3}}}}}
ight)}
ight]/{P_{41}} + ,,2{P_{111}}{V_{{text{gdc}}}}}
ight},end{split}$$

(17)

where P_hi1 = P₁₀ + P₁₁V_gsc + P₁₁₁V_ds, P_hi2 = P₂₀ + P₂₁V_ds, P_hi3 = P₃₀ ? P₃₁V_ds, P_hi4 = P₄₀ + P₄₁V_gdc ? P₁₁₁V_ds. The main structure of the charge model equation is the ln (cosh ()) function, and the P_ij (i = 1, 2, 3, 4; j = 0, 1) parameters are used to control the main trend of the C–V curve. The Q_gs and Q_gd equations can be used to derive the equations for C_gs and C_gs. C_gsp0, C_gdp0 is the gate–source capacitance and gate leakage capacitance of the device cutoff state. C_gsp0 and C_gsi, P₁₁, P₁₀ parameters are used to control the trend of the linear and saturation regions of the C_gs–V_gs curve. The P₂₁ and P₂₀ parameters are used to describe the effect of V_ds on the C_gs capacitance. C_gdp0 and C_gdi, P₃₁ and P₃₀ are used to control the main trend of C_gd capacitance with V_ds. P₄₁ and P₄₀ parameters are used to improve the fitting accuracy of C_gd with V_gd. The parameter P₁₁₁ can be used to improve the fitting accuracy of C_gs and C_gd with V_ds curve.

3.
Model verification

For verification, an InP HEMT with 2 gate fingers, that has a 25 μm gate width for each finger, 70 nm gate length, was fabricated by a commercial technology. On-wafer measure is executed for parameter extraction. S-parameters were measured and de-embedded (open + short) for parasitics introduced by GSG PAD using an Agilent E8364A network analyzer and a CASCADE Summit probe station for model parameter extraction. The DC characteristics of the device were measured using an Agilent 4156C Semiconductor Parameter Analyzer. In this work, extrinsic parasitics are extracted by using pinched and cold S-parameters. Then I_ds model parameters can be determined from DC I_ds–V_ds, I_ds–V_gs measurements. Intrinsic charge model parameters are extracted using hot S-parameters. The model parameters for I_gs and I_gd are determined from the forward bias I–V measurements. C_th is set to 1 μF for thermal effect simulation. C_dp and R_dp are simply determined by optimizing the g_m and g_ds calculated from the hot S-parameters. The extracted results from the 2-finger HEMT are listed in Tables 1 and 2.

The model equation is described in Verilog-A language and is implanted in the Keysight ADS simulation tool for simulation. The model also implements the integration in the Keysight IC-CAP environment and extracts the model parameters.

In order to evaluate the accuracy of the model fitting, the relative error equation is introduced to evaluate the fitting ability of the model to the DC characteristics and AC characteristics of the device. The equation is as follows:

$${
m {RMS}}{_{
m {targ et}}} = sqrt {frac{1}{N}sumlimits_{i = 1}^N {{
m {Meas}}{{left( {i}
ight)}^2}} } ,$$

(18)

$${
m{RM}}{{
m{S}}_{{
m{error}}}} = sqrt {frac{1}{N}sumlimits_{i = 1}^N {frac{{{{left| {{
m{Meas}}left( i
ight){
m{ - Simu}}left( i
ight)}
ight|}^2}}}{{{{left| {{
m{RM}}{{
m{S}}_{{
m{t}}arg {
m{et}}}}}
ight|}^2}}}} } .$$

(19)

Meas(i) in Eqs. (18) and (19) represents the i-th measurement data, Simu(i) represents the i-th simulation data, and N represents the total number of data points.

Figs. 5 and 6 show the measured and simulated I_ds versus V_ds and g_ds versus V_ds at at T_nom = 25 °C for V_gs = ?0.5 to 0.1 V, 0.1 V steps and V_ds = 0 to 1.2 V, 0.05 V steps. Figs. 7 and 8 show the measured and simulated g_m versus V_gs and I_ds versus V_gs at T_nom = 25 °C for V_ds = 0 to 1.2 V, 0.2 V steps and V_gs = ?0.5 to 0.1 V, 0.025 V steps.

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Figure5.
(Color online) Measured and simulated I_ds versus V_ds at T_nom = 25 °C for V_gs = ?0.5 to 0.1 V, 0.1 V steps and V_ds = 0 to 1.2 V, 0.05 V steps.

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Figure6.
(Color online) Measured and simulated g_ds versus V_ds at T_nom = 25 °C for V_gs = ?0.5 to 0.1 V, 0.1 V steps and V_ds= 0 to 1.2 V, 0.05 V steps.

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Figure7.
(Color online) Measured and simulated g_m versus V_gs at T_nom = 25 °C for V_ds = 0 to 1.2 V, 0.2 V steps and V_gs = ?0.5 to 0.1 V, 0.025 V steps.

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Figure8.
(Color online) Measured and simulated I_ds versus V_gs at T_nom = 25 °C for V_ds = 0 to 1.2 V, 0.2 V steps and V_gs = ?0.5 to 0.1 V, 0.025 V steps.

It can be seen from the output characteristic curve that the fitting accuracy of the Angelov-GaN model in saturation region is low and the RMS_error is large. The relative error of I_ds versus V_ds of propesd model is 2.1% while the the traditional model is 66.6%. The relative error of g_ds versus V_ds of propesd model is 15.2% while the the traditional model is 90.3%. The leakage barrier reduction effect is not considered in the traditional model. From the I–V curve and the transconductance/leakage conductance curve, the fitting degree of the new proposed model can accurately fitting the DC characteristics of the InP HEMTs. The I–V curve is very smooth, and the overall fitting precision is high, which can accurately simulate the DC characteristics of the InP HEMT device.

Fig. 9 shows the comparison of the C–V characteristics of the devices extracted from the bias-dependent S-parameters obtained from the test and simulation. The gate charge model parameters are listed in Table 2. It can be seen that the measurement curve and simulation curve that the improved model has better fitting effect than the traditional model. The relative error of C_gs of proposed model is 8.2% while the the traditional model is 12.5%. The relative error of C_gd of proposed model is 9.3% while the the traditional model is 14.1%. From the comparison results, the proposed capacitance model the gate charge model can be proposed to achieve accurate fitting of the C–V characteristics of the InP HEMTs.

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Figure9.
(Color online) C_gs and C_gd extracted from measured and simulated S-parameters at Freq = 10 GHz, T_nom = 25 °C for V_gs = ?0.5 to 0.1 V, 0.05 V steps and V_ds= 0 to 0.9 V, 0.3 V steps.

To demonstrate the accuracy of the model for small-signal RF drive condition, small-signal S-parameters simulations of the InP HEMTs model for different biases have been performed over a frequency range of 1–40 GHz and show close agreement with measured data (see Fig. 10). Validation of the model for small-signal operation also suggests that the extraction and modeling of the parasitic extrinsic are correct.

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Figure10.
(Color online) Measured and modeled S-parameters for 1 to 40 GHz, 1 GHz steps at (a) V_ds = 0.8 V, V_gs = ?0.1 V and (b) V_ds = 0.8 V, V_gs = ?0.05 V.

The extracted results from the 2-finger HEMT are listed in Tables 1 and 2. The experimental results show that the InP HEMT model proposed in this paper can accurately characterize the DC I–V, C–V and bias related S parameters of InP HEMTs accurately.

Parameter	Value	Parameter	Value
P₁₀	1.761	P₄₀	0.9383
P₁₁	7.353	P₄₁	3.108
P₁₁₁	0.1626	C_gs0	1.720 fF
P₂₀	0.2277	C_gdi	9.869 fF
P₂₁	0.9625	C_gd0	6.456 fF
P₃₀	1.275	C_gdi	0.2882 fF
P₃₁	0.9696

Table2.
Extracted terminal charges model parameter values from a 2-finger InP HEMT.

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Parameter	Value	Parameter	Value
P₁₀	1.761	P₄₀	0.9383
P₁₁	7.353	P₄₁	3.108
P₁₁₁	0.1626	C_gs0	1.720 fF
P₂₀	0.2277	C_gdi	9.869 fF
P₂₁	0.9625	C_gd0	6.456 fF
P₃₀	1.275	C_gdi	0.2882 fF
P₃₁	0.9696

Parameter	Value	Parameter	Value
I_pk0a	3.264 mA	I_pk0b	0.010 81 mA
V_{pks_a}	?280.7 mV	V_{pks_b}	?378.8 mV
D_{vpks_a}	?183.5 mV	D_{vpks_b}	?1.152 V
P_1a	0.6875	P_1b	0.9929
P_2a	0.2338	P_2b	0.4749
P_3a	0.4857	P_3b	0.6076
A_{lphar_a}	13.58	A_{lphar_b}	2.111
A_{lphas_a}	0.045 07	A_{lphas_b}	2.194
V_kna	1.0 V	V_knb	1.0 V
V_tra	50.0 V	V_trb	50.0 V
L_{ambda_a}	2.467	L_{ambda_b}	0.4419
L_{ambda1_a}	0.004 526	L_{ambda1_b}	0.067 31
B_1a	1.852	B_1b	2.882
B_2a	0.1618	B_2b	0.072 43

Table1.
Extracted drain current model parameter values from a 2-finger InP HEMT.

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Parameter	Value	Parameter	Value
I_pk0a	3.264 mA	I_pk0b	0.010 81 mA
V_{pks_a}	?280.7 mV	V_{pks_b}	?378.8 mV
D_{vpks_a}	?183.5 mV	D_{vpks_b}	?1.152 V
P_1a	0.6875	P_1b	0.9929
P_2a	0.2338	P_2b	0.4749
P_3a	0.4857	P_3b	0.6076
A_{lphar_a}	13.58	A_{lphar_b}	2.111
A_{lphas_a}	0.045 07	A_{lphas_b}	2.194
V_kna	1.0 V	V_knb	1.0 V
V_tra	50.0 V	V_trb	50.0 V
L_{ambda_a}	2.467	L_{ambda_b}	0.4419
L_{ambda1_a}	0.004 526	L_{ambda1_b}	0.067 31
B_1a	1.852	B_1b	2.882
B_2a	0.1618	B_2b	0.072 43

4.
Conclusion

An improved large-signal model of InP HEMTs is presented in this paper. A method of regional drain current modeling is introduced for the drain-induced barrier lowering effect, and good fitting result is achieved. The characterization of the charge conservation, the high-order derivability and continuity of the model equations, which are key requirements for nonlinear simulation, is thus guaranteed in the proposed model. The quality of the model is verified and validated by direct comparison to DC measurements, small signal S-parameters of a 2 × 25 μm × 70 nm InP HEMT. The nonlinear large model can be used in the simulation and design of InP HEMTs-based circuits.