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Comments on “theoretical analysis of current gain of normally-off junction type field-effect transistor”
Solid-Stare Ekcrronics Vol. 37, No. IO, pp. 1791-1792, 1994 Copyright 0 1994 Elsevier Science Ltd 0038-1101(94)EOO27-C Printed in Great Britain. All rights reserved 0038-I lOI/ s7.00 + 0.00
Pergamon
LETTER
TO THE EDITOR
COMMENTS ON “THEORETICAL ANALYSIS OF CURRENT GAIN OF NORMALLY-OFF JUNCTION TYPE FIELD-EFFECT TRANSISTOR” (Received
1993; in revisedform 24 January
7 October
In [l] is proposed an analytical model for the current gain of normally-off JFET devices. The approach used can be summarized as follows: (I) The potential distribution V(x, y) in the channel of the device is calculated, by using an approximate analytical approach to solve the Poisson equation in the depletion approximation. (2) From the obtained expression for V(X, y) the drain current is calculated as: Zo = A:: J,(O), where A$ is the effective channel area and J,(O) is the vertical component of the electron current density at the saddle point of the potential distribution. (3) The gate current Zo is computed by considering the contributions due to hole injection in the source and gate regions, hole recombination in the epilayer and also generation in the drain space-charge region. The current gain is then calculated as h, = I, /Zo. Analysis of JFET devices operating in both unipolar and bipolar mode have been already performed in the published literature (see, for instance [2--S] and the references therein), but the authors of [l] seem to be unaware of these contributions. The expression for J,(O) was previously given in [3-51 as a function of the abscissa x, of the saddle point and the potential barrier height r$* = ] V(X, ,O) ] In the same way, the expression for the effective
1994)
channel area was also previously obtained in [2,3]. The formulas (I 1) and (18))(20) given in [l] can be obtained from previously published results with the substitution do* = -(V,, + V,,)/m. From this point of view, it appears that the main contribution of 111 to the modelling of the unipolar region is limited to the above approximation for the potential barrier height. It is to be pointed out, moreover, that the theory proposed in [l] does not allow to calculate the value of m as a function of the physical and geometrical parameters of the device. As a matter of fact [see eqn (7a)], m is given as a function of x,. In turn (as recognised in the conclusion of [l]) the proposed theory does not give any equation for X, but instead assumes that X, is a given constant. More detailed theories can be found in ]3,6]. The model proposed in [ 1] can be applied for small drain currents, over a limited range of values. In particular, it is incorrect to use this theory in the range of drain current in which h, decreases with I, (see Section 5.2 and Fig. 4 in [l]). Normally-off operation of vertical JFET devices is obtained when the built-in voltage of the gate epilayer junction is able to pinch-off the channel and to create a potential barrier into it. This requires the utilization of lowly doped epitaxial region. As a consequences of the low epi doping, forward bias of the gate junction may result in a conductivity modulation of the channel region even for “medium” drain
1
0
2
4
6 Distance
6
10
12
14
[pm]
Fig. I. Carriers distribution along the channel axis of the device, for three values of drain current. Solid lines: electron. Dashed lines: holes. Inset: Current gain as a function of drain current from MEDIC1 simulation. 1791
1792
Letter
to the Editor
current. This phenomenon, similarly to standard bipolar transistor, produces a falloff of the current gain, as the one shown in Fig. 4 of [l]. In order to better investigate this effect, we have undertaken a two-dimensional numerical simulation of the device N-5 of [7]. This device was also used in [I] to check the theoretical results. The simulation has been performed by using MEDICI[8], including the most important physical effects, such as bandgap narrowing, SHR and Auger recombination, different minority and majority carriers mobility, etc. The current gain obtained with this simulation is reported in the inset of the Fig. 1. The overall behaviour is in agreement with the experimental results of [7]. The carriers distribution along the channel axis for three different values of In is also reported in Fig. I (note that in this device the epi doping N,,, = 2 x 1O”cm ‘). It can be noted that high-level injection condition. with n 2 p B N‘,>. exists even for a “small” drain current Ii, = 13 mA. The injection level and the extension of the plasma region increase with In, For Io = 75 mA an injection level p(O)/N,, = 75 is obtained. The results of Fig. I clearly demonstrate that the theory developed in [I], which does not include high injection condition and is instead based on the depletion approximation for the channel region, is completely inadequate to model the h, falloff (note that in Fig. 4 of [I] the theoretical results are reported for drain currents up I, = IA, note moreover that the curve reported in Fig. 3 for I, = 20 mA and T = 300 K also corresponds to a condition of high-level injection in the channel). The agreement exhibited in [I] between analytical and experimental results, even in a range of currents in which the
basic assumptions of the analytical model are not verified, is probably due to the somewhat arbitrary choice of X, and hence of m. As a consequence, the usefulness of the theory proposed in [I] to estimate the effects of the various design and processing parameters on the current gain, claimed in the conclusions of [l], seems questionable. Depurtment of Electronic Engineeritzg Uniwrsity of Naples via Chdio 80125 Naples Itc&
ANTONIOG.
M.STROLLO
21
REFERENCES I. B. W. Kang and W. Zhao.
Solid-St.
Electron.
36, 1385
( 1993). 2. T. Yamamoto, K. Matsumoto and A. Yusa, Solid-St. Electron. 30, 549 (1987). 3 P. Spirito, A. G. M. Strollo and A. Caruso, Solid-St. E/ectron. 33, 1401 (1990). 4. P. Plotka and B. Wilamowski, Solid-St. Electron. 23, 693 (1980). 5. B. J. Baliga, Modern Power Devices, Chap. 4. Wiley,
New York (1987). 6. C. Bulucea and A. Rusu,
Solid-St.
Electron.
30, 1227
(1987). 7. H. Iwasaki. 0. Ozawa and Y. Sasaki, Japan Pl~y.r. 17, Suppl. 17-1, 245 (1978). 8. MEDlCf User Guide. Technology Modelling
ates, Paolo
Alto, Calif. (1993).
J. appl.
Associ-
Pergamon
LETTER
TO THE EDITOR
COMMENTS ON “THEORETICAL ANALYSIS OF CURRENT GAIN OF NORMALLY-OFF JUNCTION TYPE FIELD-EFFECT TRANSISTOR” (Received
1993; in revisedform 24 January
7 October
In [l] is proposed an analytical model for the current gain of normally-off JFET devices. The approach used can be summarized as follows: (I) The potential distribution V(x, y) in the channel of the device is calculated, by using an approximate analytical approach to solve the Poisson equation in the depletion approximation. (2) From the obtained expression for V(X, y) the drain current is calculated as: Zo = A:: J,(O), where A$ is the effective channel area and J,(O) is the vertical component of the electron current density at the saddle point of the potential distribution. (3) The gate current Zo is computed by considering the contributions due to hole injection in the source and gate regions, hole recombination in the epilayer and also generation in the drain space-charge region. The current gain is then calculated as h, = I, /Zo. Analysis of JFET devices operating in both unipolar and bipolar mode have been already performed in the published literature (see, for instance [2--S] and the references therein), but the authors of [l] seem to be unaware of these contributions. The expression for J,(O) was previously given in [3-51 as a function of the abscissa x, of the saddle point and the potential barrier height r$* = ] V(X, ,O) ] In the same way, the expression for the effective
1994)
channel area was also previously obtained in [2,3]. The formulas (I 1) and (18))(20) given in [l] can be obtained from previously published results with the substitution do* = -(V,, + V,,)/m. From this point of view, it appears that the main contribution of 111 to the modelling of the unipolar region is limited to the above approximation for the potential barrier height. It is to be pointed out, moreover, that the theory proposed in [l] does not allow to calculate the value of m as a function of the physical and geometrical parameters of the device. As a matter of fact [see eqn (7a)], m is given as a function of x,. In turn (as recognised in the conclusion of [l]) the proposed theory does not give any equation for X, but instead assumes that X, is a given constant. More detailed theories can be found in ]3,6]. The model proposed in [ 1] can be applied for small drain currents, over a limited range of values. In particular, it is incorrect to use this theory in the range of drain current in which h, decreases with I, (see Section 5.2 and Fig. 4 in [l]). Normally-off operation of vertical JFET devices is obtained when the built-in voltage of the gate epilayer junction is able to pinch-off the channel and to create a potential barrier into it. This requires the utilization of lowly doped epitaxial region. As a consequences of the low epi doping, forward bias of the gate junction may result in a conductivity modulation of the channel region even for “medium” drain
1
0
2
4
6 Distance
6
10
12
14
[pm]
Fig. I. Carriers distribution along the channel axis of the device, for three values of drain current. Solid lines: electron. Dashed lines: holes. Inset: Current gain as a function of drain current from MEDIC1 simulation. 1791
1792
Letter
to the Editor
current. This phenomenon, similarly to standard bipolar transistor, produces a falloff of the current gain, as the one shown in Fig. 4 of [l]. In order to better investigate this effect, we have undertaken a two-dimensional numerical simulation of the device N-5 of [7]. This device was also used in [I] to check the theoretical results. The simulation has been performed by using MEDICI[8], including the most important physical effects, such as bandgap narrowing, SHR and Auger recombination, different minority and majority carriers mobility, etc. The current gain obtained with this simulation is reported in the inset of the Fig. 1. The overall behaviour is in agreement with the experimental results of [7]. The carriers distribution along the channel axis for three different values of In is also reported in Fig. I (note that in this device the epi doping N,,, = 2 x 1O”cm ‘). It can be noted that high-level injection condition. with n 2 p B N‘,>. exists even for a “small” drain current Ii, = 13 mA. The injection level and the extension of the plasma region increase with In, For Io = 75 mA an injection level p(O)/N,, = 75 is obtained. The results of Fig. I clearly demonstrate that the theory developed in [I], which does not include high injection condition and is instead based on the depletion approximation for the channel region, is completely inadequate to model the h, falloff (note that in Fig. 4 of [I] the theoretical results are reported for drain currents up I, = IA, note moreover that the curve reported in Fig. 3 for I, = 20 mA and T = 300 K also corresponds to a condition of high-level injection in the channel). The agreement exhibited in [I] between analytical and experimental results, even in a range of currents in which the
basic assumptions of the analytical model are not verified, is probably due to the somewhat arbitrary choice of X, and hence of m. As a consequence, the usefulness of the theory proposed in [I] to estimate the effects of the various design and processing parameters on the current gain, claimed in the conclusions of [l], seems questionable. Depurtment of Electronic Engineeritzg Uniwrsity of Naples via Chdio 80125 Naples Itc&
ANTONIOG.
M.STROLLO
21
REFERENCES I. B. W. Kang and W. Zhao.
Solid-St.
Electron.
36, 1385
( 1993). 2. T. Yamamoto, K. Matsumoto and A. Yusa, Solid-St. Electron. 30, 549 (1987). 3 P. Spirito, A. G. M. Strollo and A. Caruso, Solid-St. E/ectron. 33, 1401 (1990). 4. P. Plotka and B. Wilamowski, Solid-St. Electron. 23, 693 (1980). 5. B. J. Baliga, Modern Power Devices, Chap. 4. Wiley,
New York (1987). 6. C. Bulucea and A. Rusu,
Solid-St.
Electron.
30, 1227
(1987). 7. H. Iwasaki. 0. Ozawa and Y. Sasaki, Japan Pl~y.r. 17, Suppl. 17-1, 245 (1978). 8. MEDlCf User Guide. Technology Modelling
ates, Paolo
Alto, Calif. (1993).
J. appl.
Associ-