1.
Introduction
Due to the good metallurgical properties, wide operating temperature range, and radiation tolerance, the MESFET resonant tunneling diode (RTD) has been widely used in the field of integrated circuits. Resulting from the lack of minority carrier storage, these transistors can reach 100 GHz speeds with the advantage of the speed of the Schottky diode response and a very weak noise factor[1–3].
In this article, an analytical model was proposed to describe the static electrical characteristics of the MESFET, regardless of the channel length (L) and pinch-off voltage. Based on the interface states of the metal–semiconductor junction, a differential equations system has been designed by formulizing the parameters (e.g. the gate voltage, drain current, transconductance, conductance, and the capacitance of gate–source and gate–drain) obtained from the charge distribution and the electric field analysis in the channel of the transistor and carrier transport mechanisms. Also, the effect of the parasitic resistances of the source and drain (Rs & Rd) was taken into consideration in the development of this model.
2.
Methods
2.1
Potential and electric field calculation
Due to the difficulties imposed by the edge effects, several simplifying assumptions were modeling for the active region of the channel of MESFET. Assuming that the channel length was much greater than its thickness in the space charge region, the variation of the electric field in the structure direction was much larger than in the longitudinal direction. Poisson’s equation reduces to[4]:
$frac{{{{ m d}^2}Vleft( {x,y} ight)}}{{{ m d}{y^2}}} = - frac{q}{varepsilon }{N_{ m{d}}}left( {x,y} ight),$  | (1) |
where V(x, y) was the total electrostatic potential variation across the space charge region, ε = ε0εGaN, ε0 was the vacuum permittivity, εGaN was the dielectric constant and Nd the donor density. For a uniform doping and a space charge region (SCR) empty from carriers, the electric field was deduced by
ight)$
${E_{{y}}}left( x ight) = frac{{q{N_{ m{d}}}}}{varepsilon }left[ {y - hleft( x ight)} ight],$  | (2) |
${E_{{x}}}left( x ight) = - frac{{q{N_{ m{d}}}}}{varepsilon }hleft( x ight)frac{{{ m d}hleft( x ight)}}{{{ m d}x}}.$  | (3) |
In the following, hypothesize the gradual channel and use the similar triangles properties to calculate the expression of the thickness of the space charge region at a point x of the channel h(x) based on its values on source side hs and drain side hd (Supplementary Section 1):
$hleft( x ight) = frac{{{h_{ m{s}}} - {h_{ m{d}}}}}{L}x + {h_{ m{s}}}.$  | (4) |
2.2
Drain current in the canal
To find the expression of the drain current versus the voltage, assume an abrupt junction Schottky barrier and a uniform channel doping Nd(x, y) = Nd = constant. The gradual channel approximation (L
The current density in the canal can be estimated by the Ohm law as below[5]:
${J_{{x}}} = left( {x,y,z} ight){E_{{x}}},$  | (5) |
where σ(x, y, z) was the canal conductivity. ρ(x, y) was the fixed charges density in the depopulated region, the mobile charges density in the conductive channel region at a point (x, y, z) for an n-channel transistor was given by ?ρ(x, y):
${J_{{x}}} = ho left( {x,y} ight)mu left( {{E_{{x}}}} ight),$  | (6) |
where μ(Ex) was the carrier mobility.
The drain current, counted positively in the sense drain-source, was obtained by integrating (?Jx) on all the conductive section of the channel, which have been deduced in detail shown in the section Supplementary Section 3:
$begin{split} {I_{text{d}}} &= - intlimits_s {{J_{{x}}}{ m d}s} = zmu left( {{E_{{x}}}} ight){E_{{x}}}left( x ight)intlimits_h^a { ho left( {x,y} ight){ m d}y} & = - zmu left( {{E_{{x}}}} ight){E_{{x}}}left[ {Qleft( a ight) - Qleft( h ight)} ight]. end{split} $  | (7) |
The final current expression by integrating on the entire surface
${I_{ m{d}}} = frac{{{{left( {q{N_{ m{d}}}} ight)}^2}z{mu _{ m{n}}}}}{{varepsilon L}}left[ {frac{a}{2}left( {{h_{ m{d}}}^2 - {h_{ m{s}}}^2} ight) - frac{1}{3}left( {{h_{ m{d}}}^3 - {h_{ m{s}}}^3} ight)} ight].$  | (8) |
In general, the performance of GaN FET can be improved by reducing the gate length Lg[6]. However, when the gate width was small in size of submicron dimensions, some effects appear, such as interface effects[7]. In an actual device, there was a periodic disturbed noise at the interface of the semiconductor, which gives rise to a large number of permitted states in the band-gap of the semiconductor near the interface. These states are called "interface states". As shown in Fig. 1, they have energy values ranging from Ev to Ec occupied by electrons if it was below the Fermi level. Thus, a simple model like the Shockley equation cannot describe the MESFET behavior in all conditions. Interface effects were happening at the interface of a semiconductor and thin oxide layer when exposed to air with a thickness of d. So, the metal and semiconductor remain separated. The interface effects give rise to another Schottky barrier and a further reduction device Gm[8]. This additional Schottky barrier reduced the value of Φb and consequently, increases the Ig gate outflow current.
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Figure1.
(Color?online) Energy bands in the presence of interface states (a) before contact with the metal and (b) after contact. EF shifts down relative to Ec at the interface and previously filled traps are emptied.
In the Schottky theory, the barrier height Φb should depend on the metal work function as[9]:
${varPhi _{ m{b}}} = {varPhi _{ m{m}}}-chi .$  | (9) |
Without the interface states, the negative charge Qm on the metal surface must be equal to the positive charge Qd in the semiconductor. However, in real conditions, with interface states, the neutrality condition as:
${Q_{ m{m}}} + {Q_{ m{d}}} + {Q_{{ m{ss}}}} = 0,$  | (10) |
where Qss is the interface states charge.
The occupation of the surface was determined by the Fermi level EF, which was constant throughout the region in the absence of the applied polarization, and was represented by EFN and EFM for semiconductor and metal respectively. The gate–source polarization plays an important role when operating the GaN MESFET in saturation mode, so the output conductance depends not only on Vds but also on Vgs. We note that the gate–source polarization effect was very important in the modeling of both the output conductance and the capacity of the MESFET. This effect was taken into consideration by some models and neglected by others.
Devices with interface states have the higher gate leakage. Therefore, controlling the thickness of the channel by the gate potential was weaker. Taking into account the interfacial states causes a non-ideality of the MESFET Schottky barrier. The interfacial states has consumed a finite quantity of Vgs. The potential amplitude which varies the channel height was different from the applied Vgs. In such circumstances, a simulation done by considering Vgs as a variable cannot predict the behavior of the device accurately.
$begin{split} {V_{{text{gs}}}} & left[ text{gate-source region} ight] = {V_{{text{gs}}}}left[ {{text{interface}};{text{region}}} ight] &qquad + {V_{{text{gs}}}}left[ {{text{depletion}};{text{region}}} ight].end{split}$  | (11) |
The above expression indicates that the applied voltage was consumed by the interfacial states. If the states density at a Schottky junction interface was high, the contribution of Vgs in the interface region was too high to be ignored; what was observed experimentally would not agree to the theory of GaN MESFET. To solve this problem and set the exponential nature of the density of states, the following expression was given to change Vgs[10]:
${V_{{ m{eff}}}} = frac{{{V_{{ m{gs}}}}}}{{1 + x{{ m e}^{{V_{{ m{gs}}}}}}}}.$  | (12) |
The parameter x was an adjustment variable that simulates the quality of the Schottky barrier, and the x ≥ 0. As x = 0, the Schottky barrier was supposed perfect and the interface states effects were negligible. Thus, modeling becomes more flexible, so each GaN device has a specific variable x which gives us an idea about the quality of the metal-SC junction (Supplementary Section 2).
To obtain the extrinsic performances of the device (Ids, Vds, Vgs), the effects of the source and the drain access parasitic resistances Rs and Rd respectively have to be taken into account. Also, the effect of the resistance Rp parallel to the channel, due essentially to the dispersive effects of the substrate, must be included. The currents were as follows (Supplementary Section 2):
$begin{split} & {I_{text{d}}}left( {{V_{text{d}}},{V_{text{g}}},{R_{text{s}}},{R_{text{d}}}} ight) = {I_{text{p}}}{B_1}left[ {frac{{{V_{text{d}}} - left( {{R_{text{s}}} + {R_{text{d}}}} ight){I_{text{d}}}}}{{{V_{text{p}}}}}} ight.& - left. {frac{2}{3}{{left( {frac{{{V_{{text{bi}}}} - {V_{{text{eff}}}} + {V_{text{d}}} - {R_{text{s}}}{I_{text{d}}}}}{{{V_{text{p}}}}}} ight)}^{3/2}} + frac{2}{3}{{left( {frac{{{V_{{text{bi}}}} - {V_{{text{eff}}}} + {R_{text{s}}}{I_{text{d}}}}}{{{V_{text{p}}}}}} ight)}^{3/2}}} ight]. end{split} $  | (13) |
For linear regime:
${I_{ m{d}}}left( {{V_{ m{d}}},{V_{ m{g}}},{R_{ m{s}}},{R_{ m{d}}}} ight) = {I_{ m p}}left[ {1 - {{left( {frac{{{V_{{ m{bi}}}} - {V_{{ m{eff}}}}}}{{{V_{ m{p}}}}}} ight)}^{1/2}}} ight].left[ {frac{{{V_{{ m{ds}}}} - left( {{R_{ m{s}}} + {R_{ m{d}}}} ight){I_{ m{d}}}}}{{{V_{ m{p}}}}}} ight].$  | (14) |
For saturated regime:
$begin{split}& {I_{{ m{dsat}}}} = {I_{ m{p}}}{B_2}left[ {frac{1}{3} - left( {frac{{{V_{{ m{bi}}}} - {V_{ m{g}}} + {R_{ m{s}}}{I_{ m{d}}}}}{{{V_{ m{p}}}}}} ight) + frac{2}{3}{{left( {frac{{{V_{{ m{bi}}}} - {V_{{ m{eff}}}} + {R_{ m{s}}}{I_{ m{d}}}}}{{{V_{ m{p}}}}}} ight)}^{3/2}}} ight],& {B_1} = {B_2} = frac{{left[ {1 + {{left{ {left( {{v_{ m{s}}}left( {{V_{{ m{ds}}}} - left( {{R_{ m{s}}} + {R_{ m{d}}}} ight){I_{ m{d}}}} ight)} ight)} ight}}^3}/{mu _{ m{n}}}{L_3}{E_{ m{c}}}^4} ight]}}{{left[ {1 + left( {{V_{{ m{ds}}}} - left( {{R_{ m{s}}} + {R_{ m{d}}}} ight){I_{ m{d}}}} ight)/L{E_{ m{c}}}} ight]}}.end{split}$  | (15) |
2.3
Application of the model
2.3.1
Calculation of the transconductance Gm
By integrating the drain current, according to the formula below, for the linear regime:
${g_{{ m{mL}}}} = frac{{zmu q{N_{ m{d}}}a{V_{ m{d}}}{V_{{ m{eff}}}}left( {1 + {V_{{ m{eff}}}} - {V_{{ m{gs}}}}} ight)}}{{2L{V_{{ m{gs}}}}{V_{ m{p}}}{{left( {left( {{V_{{ m{bi}}}} - {V_{{ m{eff}}}}} ight)/{V_{ m{p}}}} ight)}^{1/2}}}}.$  | (16) |
For the saturated regime, putting
m{eff}}}}}}{{{V_{{
m{gs}}}}}} = frac{1}{{1 + x{{
m e}^{{V_{{
m{gs}}}}}}}}$
${,g_{{ m{ms}}}} = frac{{{I_{{ m{ps}}}}C}}{{{V_{ m{p}}}}}left[ {left( {xC{V_{{ m{gs}}}}{{ m e}^{{V_{{ m{gs}}}}}} - 1} ight){{left( {frac{{{V_{{ m{bi}}}} - {V_{{ m{gs}}}}C}}{{{V_{ m{p}}}}}} ight)}^{1/2}} - x{V_{{ m{gs}}}}{{ m e}^{{V_{{ m{gs}}}}}}C - 1} ight].$  | (17) |
2.3.2
Calculation of the conductance Gd
By integrating the drain current, according to
m{d}}} = frac{{partial {I_{
m{d}}}}}{{partial {V_{
m{d}}}}}$
${g_{{ m{dL}}}} = frac{{zmu q{N_{ m{d}}}a}}{L}left( {1 - {{left( {left( {{V_{{ m{bi}}}} - {V_{{ m{eff}}}}} ight)/{V_{ m{p}}}} ight)}^{1/2}}} ight).$  | (18) |
But for the saturated regime, gds = 0.
2.3.3
Capacity calculations
Rely on the fact of the simplified distributions of charges stored in the space charge region. The capacity was obtained as follows:
$C = frac{{partial Q}}{{partial V}}.$  | (19) |
Thus, the capacity Cgs was given by:
${C_{{ m{gs}}}} = {left| {frac{{partial Q}}{{partial {V_{ m{g}}}}}} ight|_{{V_{ m{d}}} = {C_{{ m{st}}}}}}.$  | (20) |
On the other hand, the Cgd was given by:
${C_{{ m{gd}}}} = {left| {frac{{partial Q}}{{partial {V_{ m{d}}}}}} ight|_{{V_{ m{g}}} = {C_{{ m{st}}}}}}.$  | (21) |
The charge stored in the space charge region was given as follows:
$Q = q{N_{ m{d}}}ZS.$  | (22) |
where S was the area of the longitudinal section of the SCR.
Fig. 2 shows the distribution of the depletion region in the linear regime.
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Figure2.
(Color?online) Distribution of the depletion region in the linear regime.
${Q_{{ m{Lin}}}} = frac{{q{N_{ m{d}}}Z}}{2}left( {mathop sum limits_{n = 1}^3 {S_{{n}}}} ight) = frac{{q{N_{ m{d}}}Z}}{2}left( {Lleft( {{h_{ m{d}}} + {h_{ m{s}}}} ight) + frac{pi }{2}left( {h_{ m{s}}^2 + h_{ m{d}}^2} ight)} ight).$  | (23) |
The gate–source capacity Cgs/L was calculated as below:
${C_{{ m{gsL}}}} = {left| {frac{{partial {Q_{{ m{Lin}}}}}}{{partial {V_{ m{g}}}}}} ight|_{{V_{ m{d}}} = {C_{{ m{st}}}}}}.$  | (24) |
The Cgs/L becomes:
${C_{{ m{gsL}}}} = frac{{Zvarepsilon frac{{{V_{{ m{eff}}}}}}{{{V_{ m{g}}}}}left( {{V_{ m{g}}} - {V_{{ m{eff}}}} - 1} ight)}}{2}left[ {Lleft( {frac{1}{{{h_{ m{d}}}}} + frac{1}{{{h_{ m{s}}}}}} ight) + 2pi } ight].$  | (25) |
This expression includes the lateral capacity, calculated from the lateral charges stored in the two overflow regions of the depletion zone, S1 and S3 surfaces. The intrinsic capacity, calculated from the charge stored directly under the gate on the surface S2.
The gate–drain capacity Cgd/L was calculated as below:
${C_{{ m{gd}}}} = {left| {frac{{partial {Q_{{ m{Lin}}}}}}{{partial {V_{{ m{gd}}}}}}} ight|_{{V_{ m{g}}} = {C_{{ m{st}}}}}}.$  | (26) |
The Cgd/L becomes:
${C_{{ m{gdL}}}} = frac{{varepsilon Z}}{2}left[ {frac{L}{{{h_{ m{d}}}}} + pi } ight].$  | (27) |
For the saturated regime, as shown in Fig. 3, the distribution of the depletion layer was made in five regions, and therefore:
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Figure3.
(Color?online) Distribution of the depletion region in the saturation regime.
$begin{split}{Q_{{ m{sat}}}} & = frac{{q{N_{ m{d}}}Z}}{2}left( {sumlimits_{n = 1}^5 {{S_{{n}}}} } ight)= frac{{q{N_{ m{d}}}Z}}{2}left( {left( {L - {L_{ m{s}}}} ight)frac{{{h_{ m{s}}} + a}}{2} + a{L_{ m{s}}} + frac{pi }{4}h_{ m{s}}^2} ight. & left. { + frac{a}{2}{{left( {h_{ m{d}}^2 - {a^2}} ight)}^{1/2}} + frac{{h_{ m{d}}^2}}{2}{ m {arcsin}}left( {frac{a}{{{h_{ m{d}}}}}} ight)} ight).end{split}$  | (28) |
To calculate the gate–source capacity Cgs/Sat as:
${C_{{ m{gs}}}}/{S_{{ m{st}}}} = {left| {frac{{partial {Q_{{ m{sat}}}}}}{{partial {V_{ m{g}}}}}} ight|_{{V_{ m{d}}} = {C_{{ m{st}}}}}},$  | (29) |
the Cgs/Sat becomes:
$begin{split}begin{array}{l}{C_{{ m{gs}}}}/{S_{{ m{st}}}} = q{N_{ m{d}}}ZBigggl{{30} {frac{{{a^2}}}{{4{V_{ m{p}}}}}Bigggl[{30} {pi + 2frac{{{V_{{ m{eff}}}}}}{{{V_{ m{g}}}}}left( {{V_{ m{g}}} - {V_{{ m{eff}}}} - 1} ight)frac{{L - {L_{ m{s}}}}}{{{h_{ m{s}}}}} + } Bigggr.{23.5}} Bigggr.{23.5}{ m {arcsin}}frac{a}{{{h_{ m{d}}}}} + left( {frac{{{V_{{ m{eff}}}}}}{{a {V_{ m{g}}}}}left( {{V_{ m{g}}} - {V_{{ m{eff}}}} - 1} ight)left( {2left( {{h_{ m{d}}} - {a^2}} ight) + L + {L_{ m{s}}}} ight)} ight)end{array}{left. {left. {{{left( {1 + left( {frac{{{V_{ m{c}}}}}{{{V_{ m{g}}} - {V_{ m{p}}}}}} ight)} ight)}^2} + frac{{{K_{ m{d}}}left( {{h_{ m{s}}} - a} ight)}}{{2{E_{ m{s}}}sqrt {1 + {{left( {frac{{pi {K_{ m{d}}}left( {{V_{ m{d}}} - {V_{ m{c}}}} ight)}}{{2a{E_{ m{s}}}}}} ight)}^2}} }}} ight]} ight}.}end{split}$  | (30) |
The gate–drain capacity Cgd/Sat was calculated using the formula below:
${C_{{ m{gs}}}}/{S_{{ m{st}}}} = {left| {frac{{partial {Q_{{ m{sat}}}}}}{{partial {V_{ m{d}}}}}} ight|_{{V_{ m{g}}} = {C_{{ m{st}}}}}}.$  | (31) |
The Cgd/Sat was:
${C_{{ m{gs}}}}/{S_{{ m{st}}}} = frac{{{K_{ m{d}}}left( {{h_{ m{s}}} - a} ight)}}{{2{E_{ m{s}}}sqrt {1 + {{left( {frac{{pi {K_{ m{d}}}left( {{V_{ m{d}}} - {V_{ m{c}}}} ight)}}{{2a{E_{ m{s}}}}}} ight)}^2}} }} + frac{{{a^2}}}{{2{V_{ m{p}}}}}{ m {arcsin}}left( {frac{a}{{{h_{ m{d}}}}}} ight).$  | (32) |
2.3.4
Calculation of the cut-off frequency
The cut-off frequency was a very important performance parameter for the GaN MESFET. It is the maximum frequency of use of the transistor as a power amplifier. This frequency was defined by the relation below[11]:
${f_{ m{c}}} = frac{{{g_{ m{m}}}}}{{2pi left( {{C_{{ m{gs}}}} + {C_{{ m{gd}}}}} ight)}},$  | (33) |
where gm was the transconductance, Cg was the gate capacitance given by the following expression:
${C_{{ m{gs}}}}/{S_{{ m{st}}}} = left| {frac{{partial {Q_{{ m{dep}}}}}}{{partial {V_{ m{g}}}}}} ight|,;;{Q_{{ m{dep}}}} = - q{N_{ m{d}}}Z{S_{{ m{dep}}}},$  | (34) |
where Sdep was the area of the space charge region controlled by the gate.
The maximum operating frequency of the transistor was given as following:
${f_{max }} = frac{{{f_{ m{c}}}}}{{2sqrt {left[ {{R_{ m{g}}}left( {{g_{ m{d}}} + 2pi {f_{ m{c}}}{C_{{ m{gd}}}}} ight)} ight]} }},$  | (35) |
where Rg was the resistance associated with the gate metallization.
3.
Results and discussion
In the work, the parameters of MESFET have been used to prove the model, as shown in Table 1.
| L (μm) | A (μm) | Z (μm) | Nd (m?3) | μ0 (m2 /(V·s)) | Vbi (V) | Rs (?) | Rd (?) | Rp (?) |
| 0.25 | 0.090 | 100 | 1.17 × 1023 | 0.386 | 0.45 | 2.3 | 2.3 | 1000 |
Table1.
Geometrical and technological parameters of the transistors MESFET.
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| L (μm) | A (μm) | Z (μm) | Nd (m?3) | μ0 (m2 /(V·s)) | Vbi (V) | Rs (?) | Rd (?) | Rp (?) |
| 0.25 | 0.090 | 100 | 1.17 × 1023 | 0.386 | 0.45 | 2.3 | 2.3 | 1000 |
The carrier mobility has been calculate by the electric field based on the complex Monte Carlo methods[12]. Thus, several approximate analytical expressions have been proposed for this purpose. For low electric fields:
$mu left( E ight) = {mu _0}.$  | (36) |
As the electrons velocity was v(E), for high electric fields, the validity of the drain current was[13]:
${mu _2}left( E ight) = frac{{{mu _0} + {v_{ m{s}}}left( {displaystylefrac{{{E^3}}}{{{E_{ m{c}}}^4}}} ight)}}{{1 + {{left( {displaystylefrac{E}{{{E_{ m{c}}}}}} ight)}^4}}}.$  | (37) |
As Fig. 4 shows, the variation of drain current ΔIds can be calculated by the drain voltage under the different gate voltage Vgs. There were two operation regions of the field effect transistor as one Ohmic region and one saturation region. The variation of the drain current Ids as a function of the drain voltage Vds, which was almost linear in the Ohmic region, means the linear operating mode. In the second region, the current was almost constant, which was the saturated operating region, that means the drain current hardly depends on the drain voltage Vds. Afterwards, comparing the theoretical results with the experimental data as shown in Fig. 4, the experiments results and the theoretical simulation in the linear region were clearly coincident. Also, in the saturation region, for high values of Vds, it was clearly coincident. This is certainly due to the incorporation of Veff. Thereby, our modulation became more flexible. The adjustment parameter x could also provide information on the status of the metal-semiconductor interface junction.
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Figure4.
(Color?online) The experimental data and calculated results of I–V performances with our model and the Islam model. (Full line: proposed model. Dashed line: Islam’s model. Dot: experimental data).
Meanwhile, Fig. 4 shows the comparison of the measured and calculated I–V performances of the MESFET using two models, our method and Islam’s model[14]. For Vgs = ?3.3 V, we clearly observe that the two approaches are in good agreement with the experimental data. For Vgs = ?2.2 V, our approach gives the best modeling than Islam’s model in the Ohmic region (Supplementary Section 4). When Vgs was equal to ?1.1 V, the results obtained by Islam’s model are better. Finally, for zero Vgs, the new approach gives a better modulation than the other method. For a good and a complete comparison, we used the least squares method. The results are in Table 2. From here, we can conclude that the simulations are better when taking into consideration the interface effects. This shows the validity of the proposed method.
| Model | Calculated errors for different values of Vgs | ||||
| Vgs = ?3.3 V | Vgs = ?2.2 V | Vgs = ?1.1 V | Vgs = 0.0 V | Average gap | |
| Islam’s Model | 1.1033 | 0.1462 | 1.8865 | 1.0626 | 1.0497 |
| The new Approach | 1.0095 | 0.4424 | 0.8954 | 0.0465 | 0.5984 |
Table2.
Average gap of the two models.
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| Model | Calculated errors for different values of Vgs | ||||
| Vgs = ?3.3 V | Vgs = ?2.2 V | Vgs = ?1.1 V | Vgs = 0.0 V | Average gap | |
| Islam’s Model | 1.1033 | 0.1462 | 1.8865 | 1.0626 | 1.0497 |
| The new Approach | 1.0095 | 0.4424 | 0.8954 | 0.0465 | 0.5984 |
Fig. 5 shows the variations of the transconductance Gm versus Vgs and Vds respectively. Fig. 5(a) reveals that Gm increases when the absolute value of Vg decreases. Fig. 5(b) shows that the Gm increases at the opposite of the Vd changes, until the saturation regime where Gm is saturated. We also emphasize that Gm reaches its limit value when the gate voltage is zero and the drain voltage is equal or above the saturation voltage. Gm takes its minimum value when the gate voltage approaches the threshold voltage. Obviously, by increasing the gate voltage in absolute value, the width of the space charge region increases. Thus, the extension of this zone ends when it occupies the entire width of the channel. No current flow is then possible. The corresponding gate voltage in this state is called the threshold voltage. This explains the dependence of Gm versus Vg. In addition, the current changes are even lower when the voltage Vd is low, that is to say, in the linear region. So, the transconductance also depends on the drain voltage Vd.
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Figure5.
(Color?online) (a) Change in transconductance as a function of gate voltage for the MESFET. (b) Change in transconductance as a function of drain voltage for MESFET.
As shown in Fig. 6(a), we can see the variation of the cutoff frequency fc versus Vgs for the MESFET. We remark that the cut-off frequency in the saturation region was greater than that in the linear region. The cut-off frequency was invariant under linear conditions. Also, the effects of the transconductance, the gate-source capacity Cgs and gate-drain capacity Cgd on the cutoff frequency are shown in Figs. 6(b)–6(d). It is noted that fc is even greater with the increasing of transconductance. We made the same observation for Cgd and Cgs. This demonstrates that the modulation of the space charge region under the applied voltages variations affects capacity and the cut-off frequency, which is very sensitive to the conductance of the device.
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Figure6.
(Color?online) Cut-off frequency for the MESFET. (a) The cut-off frequency of the variation with Vgs. (b) The transconductance on the cut-off frequency. (c) The gate-source capacitance on the cut-off frequency. (d) The gate-drain capacitance on the cut-off frequency.
4.
Conclusions
This work develops an analytical model to describe the static electrical operation of the GaN MESFET based on the interface effect of the Schottky junction. The I–V performances of MESFET under different channel length and different operating system (pinch-off or not) have been achieved by our model, which was strictly depended on carrier velocity. In the experiment, the operating frequency of the field effect transistor has been demonstrated by calculating the electrical parameters of MESFET, such as the drain–gate capacity Cgd, the source–gate capacity Cgs, the transconductance and the conductance. By the model and the experiment, the minimum values of these parameters have been calculated to get the maximum frequency for the GaN MESFET.
