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Electrical characterisation of a heterojunction field effect transistor photodetector (HFETPD)
Solid-State Electronics Vol. 36, No. 9, pp. 1295-1302, 1993 Printed in Great Britain. All rights reserved
0038-I IO]/93 $6.00 + 0.00 Copyright 0 1993 Pergamon Press Ltd
ELECTRICAL CHARACTERISATION OF A HETEROJUNCTION FIELD EFFECT TRANSISTOR PHOTODETECTOR (HFETPD) DAVID THOMPSON, A. MCCOWBN and P. MAWBY Department of Electrical and Electronic Engineering, University College of Swansea, Singleton Park, Swansea SA2 gPP, Wales (Received 6 October 1992; in revised form 17 February 1993) Abstract-An analytic model is developed to determine the gate-substrate potential profile in a heterojunction field-effect transistor photodetector HFETPD. The potential profiles and the associated depletion widths determined by the model are shown to be in excellent agreement with a device simulator which numerically solves the drift-diffusion equations. The behaviour of the active layer depletion width is also studied as a function of gate bias and doping levels in the delta plane, the active layer and barrier
layer.
NOTATION
hole and electron concentrations (cme3) reference intrinsic carrier concentration (cm-‘) density of states (~m-~) doping concentration (c.rr~-~) delta doping concentration (cmW2) debye length (cm) active laver deoletion width (cm) average -optic& distance in the active layer (cm) gate length (cm) average area of electron concentration at delta plane (cm2) saturation velocity (cm/s) electron mobility (cm2/Vs) 3db frequency (H,) electronic charge (C) Boltzmann’s constant (J/K) lattice temperature (K) band parameters (V) electrostatic potential (V) active layer barrier height (V) gate voltage (V) quasi-fermi potential (V) electron affinity (eV) band gap (eV) permittivity (F/cm) resistance (&I) capacitance (F)
1. INTRODUCTION
and Simmons[l] have proposed a new concept for a high speed photodetector called a heterojunction field effect photodetector (HFETPD) which promises very low noise with avalanche gain. The importance of the detector is that it has a similar structure to the heterojunction field effect transistor (HFET)[2] and a range of light emitting diodes and lasers[3-6] which are actively
being considered for optoelectronic integrated circuits. As with the HFET the structure of the HFETPD comprises a delta doped layer at the heterojunction interface between the narrow band active layer and the wideband barrier layer directly under the gate. The depletion region in the narrowband layer formed by the “delta” doping at the heterojunction interface is the active region for optical absorption. Optically generated electrons are confined in the active region by the large barriers formed by the substrate and barrier layers, the electrons are then collected by the application of a source-drain voltage. The average distance travelled by the electrons is thus determined by the depletion width in the active layer and the gate length which may be made small for high speed operation. The HFETPD has a gate terminal which can be used to operate the device in avalanche mode with the gate voltage controlling the volume of the high field avalanche region. This paper presents a characterisation of the gate-substrate potential profile of the HFETPD in equilibrium and under gate bias. The primary aim of this analysis is the determination of the depletion width in the active layer for an arbitrary doping profile and gate voltage. Quantifying the depletion width is necessary to estimate the drift transit time (important in the speed of the transient response) of the photodetector and the total illuminated current. The analysis is an extension of the work by Board and Darwish[7l who considered a delta doped layer in a single crystal material to form a one-dimensional bulk barrier device. In addition the gate-substrate potential profile is also modelled by a two-dimensional semiconductor device simulator which numerically solves the classical semiconductor equations.
1295
DAVID THOMPWN et
1296
2. THEORETICAL TREATMENT OF HETEROJUN~ION DELTA DOPED STRUCTURES
where xc is the electron affinity and Y,, is the reference potential. Substituting (1) and (2) into Poisson’s equation we obtain the following expression which is valid in either of the depletion regions which exist on both sides of the charge sheet:
A cross-section of the HFETPD as proposed in [l] is shown in Fig. l(a) and the corresponding schematic cross section of the gate-substrate impurity profile is as shown in Fig. l(b). The “delta” doped n + + region is a very thin layer, typically 3040 A and is sufficiently thin to ignore any potential changes across it.
Eqn (5) is solved for Y,, the potential height of the barrier at the heterojunction interface. At the delta doped plane, where a sheet charge of zero thickness has been assumed, Gauss’s theorem can be applied as follows:
2.1. Equilibrium The band diagram and the potential profile betweeh the gate and the substrate is shown in Fig. 2(a,b). At equilibrium the electron and hole concentrations can be expressed using Boltzmann statistics as:
p =
ni,
,ww,
al.
(1) Using the following notation: 4y @‘=qo, @‘=40, (2) u=j-$
-w
’
where ni, is the intrinsic carrier concentration in the reference material, Y is the electrostatic potential and O,,, 0, are the band parameters given by the expression[S]:
kT’
’
kT’
%r
a = N, ’ Eqns (5) and (6) are recast in normalised form to give:
CATHODE p In&As Active Layer Undoped InP S.1 InP
Wd W
(b)
Nt Delta Doped Laye
I
Nal J
Barrier Layer
!-
II
Na2
I
I
Active Layer
Fig. 1. (a) 2-d schematic of the HFETPD and (b) a typical cross section of gate-substrate impurity profile.
Electrical characterisation
of a HFETPD
1297
(a)
BarrierLayer
Active Layer Xd
(b) POTENTIAL
uo
u2
-
REGION 2
REGION 1
”
ul
Fig. 2. (a) Energy band diagram and (b) electrostatic potential distribution through the gate-substrate cross section.
that:
Noting
Gauss eqn (8) the following obtained:
(9) Equation yield:
(7) can be integrated
across region 1 to
[~~-~,+~,(e~ebI-~o)+e(~I+~~_e~~~I-~I~ - e@bI+U1))] + a[uo - u2 + az(e(%2-u0)
(I > &
I
(11)
x-o-
+e(~;l-~o)_ece;,l-ul)_e(e;,I+ul))],
(lOa)
where u, = O;, - In(N~, /ni) is the normalised potential in the neutral bulk region of the barrier layer. In a similar manner eqn (7) can be integrated across region 2 to yield: 2
du
(I > dx
in u, is
+e(e~2+4)_e162-~z~_e(e;2+~z))]_q~~~I,
2
du
equation
x=0+
where U=
This equation can be readily solved numerically for u,. When u,, has been calculated the width, A’,, of the active layer depletion region can be determined using the standard depletion approximation:
(12) where u, = O;, - ln(N,/n,) is the normalised potential in the neutral bulk region of the active layer. On substituting eqns (lOa) and (lob) into the normalised
where V,, is the de-normal&l potential of the delta doped layer given by eqn (11).
DAVID THOMPWN et al.
1298
GATE 1.5 Km
P
4
,
lpm
*
p InAlAs Barrier Region
Nal
n++ Charge SheetNt p InGaAs Active Region
I
Na2
CATHODE Fig. 3. l-d approximation 2.2. Under bias
Under bias the electron and hole concentrations given in (1) and (2) are modified as follows: n = ni, e(WW - d. + e.) p = ni, ,c~/k7X~, - YJ + ep1
of the HFETPD.
Using doping values given in [l] the simulator was used to obtain potential and charge profiles for the 1-D HFETPD structure at equilibrium and at a gate bias of 0.5 V. These results are displayed in
(13) (a)
(14)
where I$,, #Jo are the electron and hole quasi-fermi potentials respectively. If VP is the voltage applied to the barrier layer then in the neutral bulk regions far from the barrier we have:
Applying these boundary conditions and using a similar procedure to that used in Section 2.1 we obtain the following normalised expression in uO: [Ug_U;+a,(e(~;,I-uo+~~l)+e(8:,I+uo-6;I) ~~~~~
_e(B6,-UI+~~bl)_e(B;I+U,-~I))] +cr[uo-~*+a*(e(Bb2-uo)+e(e;z+uo)
_eleg?-uii_ele;2+.ir)]=~,
0
(15)
I
0
,
,
,
,
,\
0.1 0.2 0.3 0.4 0.5
10”
(b)
where
,
,
,o”J
0.6 0.7 0.8 0.9 1.0
I I I
This again can be solved numerically for u0 but this time allows for the application of a bias. 3. RESULTS AND DISCUSSlON
In order to validate the analytical model developed in Section 2, the 2-D structure of the HFETPD was simplified to the 1-D structure shown in Fig. 3 and then modelled by a simulator[9] which numerically solves the classical drift-diffusion equations. Modifications to the simulator to account for the change in the material and energy band parameters of the heterojunctions were made along the lines reported in [8]. Particular care was taken to heavily mesh the heterojunction interface whenever inversion took place in the active layer.
-0.7 -0.8
I
-0.9 -1.0
0
’ 0.5
1 1 1 1 1.0 1.5 2.0 2.5
1 1 1 1 1 3.0 3.5 4.0 4.5 5.0
10-l
Fig. 4. (a) Potential plot and (b) charge plot obtained from the numerical simulator at V, = 0 V and V, = 0.5 V with N,, = lel7 cm-3, Na2= 2e16cme3, N, = le12 e.n-3. It should be noted that X, was obtained from eqn (12).
Electrical characterisation of a HFETPD Fig. 4(a,b). The analytical model predicts active layer barrier heights (Vk) of 0.368 V (V, = 0 V) and 0.512 V (V, = 0.5 V) which when used in conjunction with eqn (12) give active layer depletion widths (X,) of 0.12pm (V,=OV) and 0.20pm (V,=O.5V), respectively. It is apparent from Fig. 4(a) that there is a very close correlation between the analytical model and the numerical simulation. In addition Fig. 4(b) shows that the depletion approximation determined from eqn (12) provides a good estimate of the depletion width in the active layer. The level of doping Nal, N,,, and N, in the three regions will affect both the barrier height and the depletion width in the active layer at equilibrium. In addition Ve affects both these parameters. Figures 5
1299
and 6 show the behaviour of the barrier potential and depletion width in the active layer as a function of gate bias and the doping in the delta doped layer for a range of active and barrier layer doping levels. At the lowest value of N,, as the gate bias is increased, charge neutrality is provided by a slight decrease in the depletion width of the barrier layer with a corresponding increase in the depletion width of the active layer. As N, is increased the band bending in the active layer is sufficient to cause inversion and charge neutrality is provided by a change in this inversion charge with a change in the space-charge width of the barrier layer. It is apparent from Fig. 5 that this manifests itself as a saturation of the active layer barrier potentials with the excess minority carriers
(a)
0.1-L-,
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
%J(v)
0.1
0.2
0.3
0.4
0.5
0.6
We Fig. S(a. b). Caption overleaf: SEE 36,9--F
0.7
+
Nt-la12
+-
Nt=l.SelZ
T!%-
Nt=ZelZ
+
Nt4sd2
DAVID THOMPWN et al.
1300
0.6
0.2
0.1 0.0
0.1
0.2
0.3
0.4
0.5
0.6
+
Nt=i5e12
-kr
Nt=ZelZ
+
Nt=2.5elZ
0.7
Vbar(V)
0.6
-&
Nt45a12
0.1
Fig. 5. Active layer barrier potentials (V,,) varying with bias (V,) and doping (N, is in cm-*). (a) N,, = le17 cm-‘, Na2= 2e16 cmW3; (b) N,, = le17 cmm3, Na2= 8e16 err?; (c) N,, = 8el6 cnm3, Na2= 2e16 cm-‘; (d) N,, = 416 cm-‘, Np2= 2el6 cne3.
shielding the active layer from any increase in gate potential, the situation is thus very similar to depletion and strong inversion in a MOS device. A figure of merit can be given for the f& of the device using the 1-D HFETPD approximation shown in Fig. 3, for this particular case the doping values used were N,, = le17 crne3, Na2= 2el6 cme3, N, = 2el2 cm-* and it was assumed that the device was 100pm thick. There are three main factors that limit the speed of the transient response: (i) Drif transit time-As mentioned earlier the active layer depletion width plays an important part in the optical characterisation of the HFETPD. If d,, is the average distance travelled by the optically
generated electrons as they drift to the potential well and across to the drain then da, is given approximately by: d
_xd+Ls
w-y--’
(16)
where L, is the length of the gate. Thus the drift transit time for the detector is given by: (17) where v, is the saturation velocity in the active layer. Note that the holes generated in the depletion layer of the active region on average travel only a distance X,/2 before they enter the neutral region of the active layer. Hence in this case electrons will
0.0
0.1
0.1
0.2
0.2
0.3
vm
@I
0.4
0.4
WV)
0.3
(a)
0.!5
015
0.6
016
0.7
0.17
0.0
0.05-
O.l-
O.l5-
0.0
0.05-j
Xd(cmA)
,
0.1
I
0.1
,
02
I
0.2
Na2=2e16en-‘;
(d) N,, =4e16cm-‘,
Nti =2e16cm-‘.
Fig. 6. Active layer depletion widths (A’,) varying with bias (V,) and doping (N, is in cm-‘). (a) N,, = le17 cme3, Na2= 2e16 en-‘;
0.05
I
Xd(cmd)
0.0
Xd(ct&) 0241
,
w?4
blw
,
,
,
I
0.6
I
0.5
0.6
I
0.5
0.4
0.4
,
0.7
7
0.7
(b) N,, = le17 eme3, N,, = gel6em-‘;
0.3
I
0.3
Cc)
Nt=2.5e12
(c) N.1 = gel6 em-‘,
+
g
DAVID THOMFWN ef al.
1302
tend to be the frequency limiting species. Using Le = 1.5 pm, X, = 0.22 pm [calculated using (11) and (12)] and u, = 1 x 1O’cm s-‘[lo] we obtain rdrifi= 8.6 ps. (ii) Diffusion transit time-This is the time taken for carriers generated in the neutral region to diffuse to the depletion region, however if the optical generation occurs inside the active layer depletion region slow tails from diffusing carriers will not be a problem. (iii) RC eficts-To analyse these effects a simple equivalent circuit has been used comprising the capacitance associated with the active layer in series with a resistance associated with the lateral flow of electrons along the delta plane. The capacitance C of the active region was found to be 0.08 pF which was determined using the standard one sided junction expression. The resistance R of the electron channel can be determined from: (18) where K is the low field electron mobility along the delta plane, n,, is the electron concentration at the delta plane and 6 is the average area of the electron concentration at the delta plane which can be derived using eqn (A9) from [n. Using p, = 10000cm2v-’ s-‘[IO] 6 = 6 x 10egcm2 and n,, = 1.3 x lo’* cm-’ [calculated from (l)] we obtain R = 11 R which yields an RC time constant of tat = 0.88 ps. For this oarticular case the drift transit time will determine the value off,,, which can be defined as:
18 GHz.
(19)
4. CONCLUSIONS
An analytic model of the equilibrium and nonequilibrium potentials in a heterojunction delta doped device has been developed. This model has been validated using a numerical device simulation package and a comparison of the results have shown excellent agreement. Using the potential barrier height calculated from the model the depletion width in the active layer can be estimated using the depletion approximation. The model has been used to investigate the effect of doping levels and gate bias on the depletion width in the active layer and the simplified transient response of the device noting that the transient response can be controlled by changing the doping and geometry of the device. Further work is in progress on the optical characterisation and transient response of the HFETPD to take into account any 2-D effects. REFERENCES
1. G. W. Taylor and J. G. Simmons, Appl. Phys. tiff. SO, 1754 (1987). 2. G. W. Taylor
and J. G. Simmons, Electron. Left. 22,784 (1986). 3. G. W. Taylor and J. G. Simmons, Appl. Phys. L&t. 48,
1368 (1986). 4. G. W. Taylor, J. G. Simmons, A. Y. Cho and R. S. Mand, J. appl. Phys. 59, 596 (1986). 5. J. G. Simmons and G. W. Taylor, IEEE Trans. Electron Devices ED-34 (1987).
6. G. W. Tavlor. R. S. Mand. J. G. Simmons and A. Y. Cho, A&. Pl;ys. Lat. 49, ‘1406 (1986). 7. K. Board and M. Darwish, Solid-Sr. Electron. 25, 529 (1982). 8. J. R. Hauser and J. E. Sutherland, IEEE Trans. Electron Devices ED-24, 363 (1977). 9. Swansea Universitv Device Simulator User Manual:
Device modelling group, University College of Swansea. 10. Private communication from A. J. Holden, Memorandum on 1-D simulator HETRO, Plessey Research Caswell Ltd, Caswell, Towcester, Northants, U.K.
0038-I IO]/93 $6.00 + 0.00 Copyright 0 1993 Pergamon Press Ltd
ELECTRICAL CHARACTERISATION OF A HETEROJUNCTION FIELD EFFECT TRANSISTOR PHOTODETECTOR (HFETPD) DAVID THOMPSON, A. MCCOWBN and P. MAWBY Department of Electrical and Electronic Engineering, University College of Swansea, Singleton Park, Swansea SA2 gPP, Wales (Received 6 October 1992; in revised form 17 February 1993) Abstract-An analytic model is developed to determine the gate-substrate potential profile in a heterojunction field-effect transistor photodetector HFETPD. The potential profiles and the associated depletion widths determined by the model are shown to be in excellent agreement with a device simulator which numerically solves the drift-diffusion equations. The behaviour of the active layer depletion width is also studied as a function of gate bias and doping levels in the delta plane, the active layer and barrier
layer.
NOTATION
hole and electron concentrations (cme3) reference intrinsic carrier concentration (cm-‘) density of states (~m-~) doping concentration (c.rr~-~) delta doping concentration (cmW2) debye length (cm) active laver deoletion width (cm) average -optic& distance in the active layer (cm) gate length (cm) average area of electron concentration at delta plane (cm2) saturation velocity (cm/s) electron mobility (cm2/Vs) 3db frequency (H,) electronic charge (C) Boltzmann’s constant (J/K) lattice temperature (K) band parameters (V) electrostatic potential (V) active layer barrier height (V) gate voltage (V) quasi-fermi potential (V) electron affinity (eV) band gap (eV) permittivity (F/cm) resistance (&I) capacitance (F)
1. INTRODUCTION
and Simmons[l] have proposed a new concept for a high speed photodetector called a heterojunction field effect photodetector (HFETPD) which promises very low noise with avalanche gain. The importance of the detector is that it has a similar structure to the heterojunction field effect transistor (HFET)[2] and a range of light emitting diodes and lasers[3-6] which are actively
being considered for optoelectronic integrated circuits. As with the HFET the structure of the HFETPD comprises a delta doped layer at the heterojunction interface between the narrow band active layer and the wideband barrier layer directly under the gate. The depletion region in the narrowband layer formed by the “delta” doping at the heterojunction interface is the active region for optical absorption. Optically generated electrons are confined in the active region by the large barriers formed by the substrate and barrier layers, the electrons are then collected by the application of a source-drain voltage. The average distance travelled by the electrons is thus determined by the depletion width in the active layer and the gate length which may be made small for high speed operation. The HFETPD has a gate terminal which can be used to operate the device in avalanche mode with the gate voltage controlling the volume of the high field avalanche region. This paper presents a characterisation of the gate-substrate potential profile of the HFETPD in equilibrium and under gate bias. The primary aim of this analysis is the determination of the depletion width in the active layer for an arbitrary doping profile and gate voltage. Quantifying the depletion width is necessary to estimate the drift transit time (important in the speed of the transient response) of the photodetector and the total illuminated current. The analysis is an extension of the work by Board and Darwish[7l who considered a delta doped layer in a single crystal material to form a one-dimensional bulk barrier device. In addition the gate-substrate potential profile is also modelled by a two-dimensional semiconductor device simulator which numerically solves the classical semiconductor equations.
1295
DAVID THOMPWN et
1296
2. THEORETICAL TREATMENT OF HETEROJUN~ION DELTA DOPED STRUCTURES
where xc is the electron affinity and Y,, is the reference potential. Substituting (1) and (2) into Poisson’s equation we obtain the following expression which is valid in either of the depletion regions which exist on both sides of the charge sheet:
A cross-section of the HFETPD as proposed in [l] is shown in Fig. l(a) and the corresponding schematic cross section of the gate-substrate impurity profile is as shown in Fig. l(b). The “delta” doped n + + region is a very thin layer, typically 3040 A and is sufficiently thin to ignore any potential changes across it.
Eqn (5) is solved for Y,, the potential height of the barrier at the heterojunction interface. At the delta doped plane, where a sheet charge of zero thickness has been assumed, Gauss’s theorem can be applied as follows:
2.1. Equilibrium The band diagram and the potential profile betweeh the gate and the substrate is shown in Fig. 2(a,b). At equilibrium the electron and hole concentrations can be expressed using Boltzmann statistics as:
p =
ni,
,ww,
al.
(1) Using the following notation: 4y @‘=qo, @‘=40, (2) u=j-$
-w
’
where ni, is the intrinsic carrier concentration in the reference material, Y is the electrostatic potential and O,,, 0, are the band parameters given by the expression[S]:
kT’
’
kT’
%r
a = N, ’ Eqns (5) and (6) are recast in normalised form to give:
CATHODE p In&As Active Layer Undoped InP S.1 InP
Wd W
(b)
Nt Delta Doped Laye
I
Nal J
Barrier Layer
!-
II
Na2
I
I
Active Layer
Fig. 1. (a) 2-d schematic of the HFETPD and (b) a typical cross section of gate-substrate impurity profile.
Electrical characterisation
of a HFETPD
1297
(a)
BarrierLayer
Active Layer Xd
(b) POTENTIAL
uo
u2
-
REGION 2
REGION 1
”
ul
Fig. 2. (a) Energy band diagram and (b) electrostatic potential distribution through the gate-substrate cross section.
that:
Noting
Gauss eqn (8) the following obtained:
(9) Equation yield:
(7) can be integrated
across region 1 to
[~~-~,+~,(e~ebI-~o)+e(~I+~~_e~~~I-~I~ - e@bI+U1))] + a[uo - u2 + az(e(%2-u0)
(I > &
I
(11)
x-o-
+e(~;l-~o)_ece;,l-ul)_e(e;,I+ul))],
(lOa)
where u, = O;, - In(N~, /ni) is the normalised potential in the neutral bulk region of the barrier layer. In a similar manner eqn (7) can be integrated across region 2 to yield: 2
du
(I > dx
in u, is
+e(e~2+4)_e162-~z~_e(e;2+~z))]_q~~~I,
2
du
equation
x=0+
where U=
This equation can be readily solved numerically for u,. When u,, has been calculated the width, A’,, of the active layer depletion region can be determined using the standard depletion approximation:
(12) where u, = O;, - ln(N,/n,) is the normalised potential in the neutral bulk region of the active layer. On substituting eqns (lOa) and (lob) into the normalised
where V,, is the de-normal&l potential of the delta doped layer given by eqn (11).
DAVID THOMPWN et al.
1298
GATE 1.5 Km
P
4
,
lpm
*
p InAlAs Barrier Region
Nal
n++ Charge SheetNt p InGaAs Active Region
I
Na2
CATHODE Fig. 3. l-d approximation 2.2. Under bias
Under bias the electron and hole concentrations given in (1) and (2) are modified as follows: n = ni, e(WW - d. + e.) p = ni, ,c~/k7X~, - YJ + ep1
of the HFETPD.
Using doping values given in [l] the simulator was used to obtain potential and charge profiles for the 1-D HFETPD structure at equilibrium and at a gate bias of 0.5 V. These results are displayed in
(13) (a)
(14)
where I$,, #Jo are the electron and hole quasi-fermi potentials respectively. If VP is the voltage applied to the barrier layer then in the neutral bulk regions far from the barrier we have:
Applying these boundary conditions and using a similar procedure to that used in Section 2.1 we obtain the following normalised expression in uO: [Ug_U;+a,(e(~;,I-uo+~~l)+e(8:,I+uo-6;I) ~~~~~
_e(B6,-UI+~~bl)_e(B;I+U,-~I))] +cr[uo-~*+a*(e(Bb2-uo)+e(e;z+uo)
_eleg?-uii_ele;2+.ir)]=~,
0
(15)
I
0
,
,
,
,
,\
0.1 0.2 0.3 0.4 0.5
10”
(b)
where
,
,
,o”J
0.6 0.7 0.8 0.9 1.0
I I I
This again can be solved numerically for u0 but this time allows for the application of a bias. 3. RESULTS AND DISCUSSlON
In order to validate the analytical model developed in Section 2, the 2-D structure of the HFETPD was simplified to the 1-D structure shown in Fig. 3 and then modelled by a simulator[9] which numerically solves the classical drift-diffusion equations. Modifications to the simulator to account for the change in the material and energy band parameters of the heterojunctions were made along the lines reported in [8]. Particular care was taken to heavily mesh the heterojunction interface whenever inversion took place in the active layer.
-0.7 -0.8
I
-0.9 -1.0
0
’ 0.5
1 1 1 1 1.0 1.5 2.0 2.5
1 1 1 1 1 3.0 3.5 4.0 4.5 5.0
10-l
Fig. 4. (a) Potential plot and (b) charge plot obtained from the numerical simulator at V, = 0 V and V, = 0.5 V with N,, = lel7 cm-3, Na2= 2e16cme3, N, = le12 e.n-3. It should be noted that X, was obtained from eqn (12).
Electrical characterisation of a HFETPD Fig. 4(a,b). The analytical model predicts active layer barrier heights (Vk) of 0.368 V (V, = 0 V) and 0.512 V (V, = 0.5 V) which when used in conjunction with eqn (12) give active layer depletion widths (X,) of 0.12pm (V,=OV) and 0.20pm (V,=O.5V), respectively. It is apparent from Fig. 4(a) that there is a very close correlation between the analytical model and the numerical simulation. In addition Fig. 4(b) shows that the depletion approximation determined from eqn (12) provides a good estimate of the depletion width in the active layer. The level of doping Nal, N,,, and N, in the three regions will affect both the barrier height and the depletion width in the active layer at equilibrium. In addition Ve affects both these parameters. Figures 5
1299
and 6 show the behaviour of the barrier potential and depletion width in the active layer as a function of gate bias and the doping in the delta doped layer for a range of active and barrier layer doping levels. At the lowest value of N,, as the gate bias is increased, charge neutrality is provided by a slight decrease in the depletion width of the barrier layer with a corresponding increase in the depletion width of the active layer. As N, is increased the band bending in the active layer is sufficient to cause inversion and charge neutrality is provided by a change in this inversion charge with a change in the space-charge width of the barrier layer. It is apparent from Fig. 5 that this manifests itself as a saturation of the active layer barrier potentials with the excess minority carriers
(a)
0.1-L-,
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
%J(v)
0.1
0.2
0.3
0.4
0.5
0.6
We Fig. S(a. b). Caption overleaf: SEE 36,9--F
0.7
+
Nt-la12
+-
Nt=l.SelZ
T!%-
Nt=ZelZ
+
Nt4sd2
DAVID THOMPWN et al.
1300
0.6
0.2
0.1 0.0
0.1
0.2
0.3
0.4
0.5
0.6
+
Nt=i5e12
-kr
Nt=ZelZ
+
Nt=2.5elZ
0.7
Vbar(V)
0.6
-&
Nt45a12
0.1
Fig. 5. Active layer barrier potentials (V,,) varying with bias (V,) and doping (N, is in cm-*). (a) N,, = le17 cm-‘, Na2= 2e16 cmW3; (b) N,, = le17 cmm3, Na2= 8e16 err?; (c) N,, = 8el6 cnm3, Na2= 2e16 cm-‘; (d) N,, = 416 cm-‘, Np2= 2el6 cne3.
shielding the active layer from any increase in gate potential, the situation is thus very similar to depletion and strong inversion in a MOS device. A figure of merit can be given for the f& of the device using the 1-D HFETPD approximation shown in Fig. 3, for this particular case the doping values used were N,, = le17 crne3, Na2= 2el6 cme3, N, = 2el2 cm-* and it was assumed that the device was 100pm thick. There are three main factors that limit the speed of the transient response: (i) Drif transit time-As mentioned earlier the active layer depletion width plays an important part in the optical characterisation of the HFETPD. If d,, is the average distance travelled by the optically
generated electrons as they drift to the potential well and across to the drain then da, is given approximately by: d
_xd+Ls
w-y--’
(16)
where L, is the length of the gate. Thus the drift transit time for the detector is given by: (17) where v, is the saturation velocity in the active layer. Note that the holes generated in the depletion layer of the active region on average travel only a distance X,/2 before they enter the neutral region of the active layer. Hence in this case electrons will
0.0
0.1
0.1
0.2
0.2
0.3
vm
@I
0.4
0.4
WV)
0.3
(a)
0.!5
015
0.6
016
0.7
0.17
0.0
0.05-
O.l-
O.l5-
0.0
0.05-j
Xd(cmA)
,
0.1
I
0.1
,
02
I
0.2
Na2=2e16en-‘;
(d) N,, =4e16cm-‘,
Nti =2e16cm-‘.
Fig. 6. Active layer depletion widths (A’,) varying with bias (V,) and doping (N, is in cm-‘). (a) N,, = le17 cme3, Na2= 2e16 en-‘;
0.05
I
Xd(cmd)
0.0
Xd(ct&) 0241
,
w?4
blw
,
,
,
I
0.6
I
0.5
0.6
I
0.5
0.4
0.4
,
0.7
7
0.7
(b) N,, = le17 eme3, N,, = gel6em-‘;
0.3
I
0.3
Cc)
Nt=2.5e12
(c) N.1 = gel6 em-‘,
+
g
DAVID THOMFWN ef al.
1302
tend to be the frequency limiting species. Using Le = 1.5 pm, X, = 0.22 pm [calculated using (11) and (12)] and u, = 1 x 1O’cm s-‘[lo] we obtain rdrifi= 8.6 ps. (ii) Diffusion transit time-This is the time taken for carriers generated in the neutral region to diffuse to the depletion region, however if the optical generation occurs inside the active layer depletion region slow tails from diffusing carriers will not be a problem. (iii) RC eficts-To analyse these effects a simple equivalent circuit has been used comprising the capacitance associated with the active layer in series with a resistance associated with the lateral flow of electrons along the delta plane. The capacitance C of the active region was found to be 0.08 pF which was determined using the standard one sided junction expression. The resistance R of the electron channel can be determined from: (18) where K is the low field electron mobility along the delta plane, n,, is the electron concentration at the delta plane and 6 is the average area of the electron concentration at the delta plane which can be derived using eqn (A9) from [n. Using p, = 10000cm2v-’ s-‘[IO] 6 = 6 x 10egcm2 and n,, = 1.3 x lo’* cm-’ [calculated from (l)] we obtain R = 11 R which yields an RC time constant of tat = 0.88 ps. For this oarticular case the drift transit time will determine the value off,,, which can be defined as:
18 GHz.
(19)
4. CONCLUSIONS
An analytic model of the equilibrium and nonequilibrium potentials in a heterojunction delta doped device has been developed. This model has been validated using a numerical device simulation package and a comparison of the results have shown excellent agreement. Using the potential barrier height calculated from the model the depletion width in the active layer can be estimated using the depletion approximation. The model has been used to investigate the effect of doping levels and gate bias on the depletion width in the active layer and the simplified transient response of the device noting that the transient response can be controlled by changing the doping and geometry of the device. Further work is in progress on the optical characterisation and transient response of the HFETPD to take into account any 2-D effects. REFERENCES
1. G. W. Taylor and J. G. Simmons, Appl. Phys. tiff. SO, 1754 (1987). 2. G. W. Taylor
and J. G. Simmons, Electron. Left. 22,784 (1986). 3. G. W. Taylor and J. G. Simmons, Appl. Phys. L&t. 48,
1368 (1986). 4. G. W. Taylor, J. G. Simmons, A. Y. Cho and R. S. Mand, J. appl. Phys. 59, 596 (1986). 5. J. G. Simmons and G. W. Taylor, IEEE Trans. Electron Devices ED-34 (1987).
6. G. W. Tavlor. R. S. Mand. J. G. Simmons and A. Y. Cho, A&. Pl;ys. Lat. 49, ‘1406 (1986). 7. K. Board and M. Darwish, Solid-Sr. Electron. 25, 529 (1982). 8. J. R. Hauser and J. E. Sutherland, IEEE Trans. Electron Devices ED-24, 363 (1977). 9. Swansea Universitv Device Simulator User Manual:
Device modelling group, University College of Swansea. 10. Private communication from A. J. Holden, Memorandum on 1-D simulator HETRO, Plessey Research Caswell Ltd, Caswell, Towcester, Northants, U.K.