GaAs p-i-n diodes have been modeled using numerical simulation, and the theoretical results have been compared to those of experiment. The simulations predict that with a lifetime of the carriers of 10^(-7)s, devices that have good i-layer modulation may be built. This is in agreement with currently available commercial devices

Atwater, H.

Gopinath, A.

Caltech Authors - Main

414 IEEE TRANSACTIONS ON ELECTRON DEVICES. VOL 35. NO. 4, APRIL 1988 
Simulation of GaAs p-i-n Diodes 
A. GOPINATH, SENIOR MEMBER, IEEE, AND H. ATWATER, SENIOR MEMBER, IEEE 
Abstract-GaAs p-i-n diodes have been modeled using simulation, 
and the results have been compared to experiment. The simulations 
predict that with a lifetime of the carriers of lo-' s, devices that have 
good i-layer modulation may be built. This is in agreement with cur- 
rently available commercial devices. 
I. INTRODUCTION 
aAs p-i-n diodes have been used as photodetectors G for some considerable time, but their appearance as 
a microwave switch element is comparatively recent [ 13- 
[3]. The problem perceived as preventing their applica- 
tion in this context was the minority-carrier lifetime of 
about lo-' s and hence the ambipolar diffusion length of 
about 3 pm. Thus, a diode with an i-layer of 10 pm would 
not be easily modulated at reasonable current densities. 
However, lifetimes now are in the range of s, and 
thus commercial diodes with i-layers in the range of 3 to 
30 pm are available. 
While the silicon p-i-n diode has been examined in great 
detail [4]-[6], the GaAs device is only now being inves- 
tigated. The simple theory for silicon devices where the 
mobility ratio of electrons to holes is approximately 3, 
and the ratio of the i-layer thickness to diffusion length is 
less than unity, cannot be used for GaAs diodes, without 
substantial modification. The present paper reports on the 
results of an investigation on these devices, using numer- 
ical simulation and measurements. In these devices, the 
i-layer is low-doped p- or n-, and for this investigation, 
the layer was assumed to be low-doped n- type. The dop- 
ing level was chosen so that this i-layer is entirely de- 
pleted under zero-bias condition due to the built-in junc- 
tion potential. Thus, the diode equivalent circuit of the 
device at zero or negative bias takes the form of a capac- 
itor, with a shunt resistor to represent the leakage current 
and a resistance in series with this parallel circuit to ac- 
count for the contact resistance (see Fig. 1) .  The capaci- 
tance in this state may be calculated quite simply with a 
knowledge of the diode dimensions for a uniformly doped 
diode. The shunt and series resistors are dependent on the 
i-layer material and the fabrication technique used. The 
equivalent circuit under zero or reverse bias in this case 
is shown in Fig. 1. 
Manuscript received August, 24, 1987; revised November 17, 1987. 
This work was sponsored by the Department of the Army. 
A. Gopinath was with the MIT Lincoln Laboratory, Lexington, MA 
02173. He is now with the Department of Electrical Engineering, Univer- 
sity of Minnesota, Minneapolis, MN 55455. 
H. Atwater was with the MIT Lincoln Laboratory, Lexington, MA 
02173. He is now with the Naval Postgraduate School, Monterey, CA 
93940. 
IEEE Log Number 8718964. 
OTf$ 
0 
(b) 
Fig. 1. (a) Structure of p-i-n diode. (b) Equivalent circuit of p-i-n diode. 
The forward bias case is much more complex, and the 
investigation has examined the parameters contributing to 
the equivalent circuit components under this condition. 
The capacitance in this case is due to charge storage in 
the i-layer in Fig. 1 .  The shunt resistance is that of the i- 
layer modulated by the carrier injection from the p+ and 
nf regions. For microwave switch applications, this re- 
sistance should be as low as possible, since it is the major 
factor in the insertion loss to isolation ratio. Analysis of 
the diode under all forward bias conditions is difficult, 
and only the case with very high injection [7], [8] may be 
treated. Under this condition, the hole and electron dens- 
ities may be assumed to be equal almost everywhere in 
the diode, and thus the electron and hole density distri- 
bution through the diode may be estimated. From this, the 
voltage drop across the diode may be calculated, from 
which diode forward resistance may be obtained. We do 
not include this analysis, but interested readers may refer 
to Ghandhi [7]. However, the approximations in this anal- 
ysis, while providing a result for the high-injection con- 
dition, do not pertain to all the bias conditions in the de- 
vice. Thus, numerical analysis provides the answers for 
the whole range of injection levels. 
The results of this numerical investigation are for the 
cases where the lifetime of the carriers is fixed and device 
length varied, and also where the device length is fixed 
and the carrier lifetime is varied. They show that when 
the lifetime of the carriers falls, and thus, the ratio of 
diode length to diffusion length is much greater than about 
3,  the operation of the device with low forward resistance 
requires a large voltage drop across the i-region and may 
not be satisfactory. Comparison with experimental mea- 
surements on commercial diodes confirms the trends ob- 
tained here. 
11. NUMERICAL SIMULATIONS AND RESULTS 
As the whole range of bias conditions cannot be easily 
analyzed, numerical simulation of the diode has been car- 
0018-9383/88/0400-0414$01 .OO O 1988 IEEE 
7 1 -___ 7- 1 -  
GOPINATH AND ATWATER: SIMULATION OF GaAs p-i-n DIODES 415 
ried out. This simulation follows the usual solution of the 
Poisson and the continuity equations for electrons and 
holes simultaneously using the Scharfetter-Gummel ap- 
proximation, which is the ' 'up-stream" formulation for 
current. The finite-difference and finite-element methods 
in one dimension lead to identical equations for solution 
purposes. The low-injection case may be handled using 
the Gummel scheme of separation of the solutions of the 
Poisson and the continuity equations. However, New- 
ton's method was used here since both the low- and high- 
injection cases are to be solved. The choice of the param- 
eter to prevent overshoot in Newton's method followed 
that of Banks and Rose [9] (see also [lo]), with additional 
upper and lower limits placed on the method. Conver- 
gence was very rapid (less than 10 iterations) with proper 
choice of the overshoot parameter, but a more conserva- 
tive estimate of this parameter resulted in convergence, 
even with very high injection within 50 iterations at most. 
As in all simulations, the equations have been scaled in 
the manner discussed by Selberherr [ 1 13. 
The choice of the structure analyzed was governed by 
various considerations including time-dependent solu- 
tions (which will be reported elsewhere). The structure 
has p+ and n+ and regions, a central n- region, with ta- 
pered changes between the p+ and n- region and the n- 
and n+ region, both within 0.2 pm. The p+ and n+ doping 
densities were chosen to be 1017 per cm3 with complete 
ionization, which, in general, is low for these devices, but 
the results are not unduly affected by this choice. The i- 
layer (n- region) width was chosen as 10 pm for one set 
of computations, and other widths were used for a second 
set. The n- density for all of the diodes examined was 
lOI3  cm-3 with complete ionization, and this depleted due 
to the p+-n- junction barrier voltage. The recombination 
terms included single-level traps of the usual form of 
Shockley -Read-Hall 
Auger recombination was assumed to be of the form 
RA = r(n2p + p2n).  
Radiative recombination was assumed to be given by 
R, = Pnp. ( 3 )  
In ( l ) ,  7p was set to be equal to 7,, and this parameter 
was varied from to 3 x lo-'' s for the 10-pm i-layer 
diode. 
The Auger recombination term only becomes signifi- 
cant at levels of 10'' cm-3 and thus was not the control 
mechanism in these simulations. The radiative term is in 
general small unless densities reach the high 10l8 ~ m - ~ .  
The values of r and fl  chosen were and 7.2 X lo-'', 
respectively. 
The barrier heights were estimated using the usual for- 
mulas for N,, Nu, using the effective masses as m, = 
0.065mo for electrons and mh = 0.5% for holes, with Eg 
at room temperature of 1.42 eV (see Sze [12]). The ve- 
locity-field expression for electrons takes the form 
where Eo = 4 X lo3 V/cm and po = 5000 cm2/V s. 
The hole velocity was assumed to vary as 
( 5 )  
where Eo = 2 x lo4 V/cm and ph = 400 cm2/V * s. 
Einstein's relationship was assumed to hold, and thus 
the diffusion constant was estimated from these expres- 
sions. 
Fig. 2(a) and (b) shows a sequence of results from these 
calculations in which the carrier density distributions and 
potential are shown at different bias conditions for a diode 
with an n- layer of 10 pm, a total length of 10.8 pm, 7 
of lop9 s in the n- layer, and lo-'' s in the n+ and p+ 
regions. The current-voltage relationship in these devices 
provides a summary of all the computed cases; two sets 
of results are reported here, and we discuss each set in 
turn. In the first set, the doping density of the device 
structure was kept constant, and the i-layer (n- type) 
thickness was varied form 3 to 20 pm. In this computa- 
tion, the lifetime was set to s, and with a hole mo- 
bility of 400 cm2 / V - s; the diffusion length La is about 
3 pm. Fig. 3 shows the J-Y plots for this set of calcula- 
tions, and we note that the ideality factor at low current 
densities is close to unity; this factor becomes larger at 
higher bias values. Note that the current density in the 20- 
pm diode is much lower for the same bias, suggesting that 
i-layer modulation may be poor for this diode. In this case 
the ratio of d / L a  = 3 (note that 2d = 20 pm here), which 
suggests that, when the d / L ,  ratio exceeds about 2, i- 
layer modulation is poor. Note that the i-layer in the 20- 
pm device is not completely depleted. 
The second set of results in Fig. 4 is for a 10-pm i-layer 
for different values of lifetime; r varies from to 3 X 
lO-'Os. Thus, the diffusion length varies from a maxi- 
mum of 30 pm to about 0.5 pm, and the d / L a  ratio varies 
from about 0.16 to about 10. We note that the same trend 
is followed as in Fig. 3 ,  and again d / L ,  ratios of 2 up- 
ward ( and 3 X lo-'' s )  show that current densities 
do not rise far enough for reasonable i-layer modulation. 
Note that the two sets of curves, while showing similar 
trends, show differences in detail. The curves in Fig. 4 at 
the lower lifetimes and thus smaller d / L a  ratios, seem to 
coalesce, whereas there is still an increase in current den- 
sity at the smaller i-layer widths in Fig. 3. 
The slope of the J-V curves at any bias point is the 
incremental resistance seen by small signal RF voltage. 
111. MEASUREMENTS 
Comparison between experiment and theory is difficult 
because the doping profiIe of the devices is not known. 
The devices measured are expected to have p+ and n+ 
regions doped to about 10l8 acceptors or donors per cubic 
416 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 35, NO. 4, APRIL 1988 
I 
NORMALIZED DISTANCE 
(a) 
/ 
- 1.5 ol 10 
NORMALIZED DISTANCE 
(b) 
Fig. 2. Sequence of steady state (a) camer density and (b) potential dis- 
s and density is loi3 ~ r n - ~  tribution for a 10-am i-layer diode, T = 
in this region for different bias conditions. 
0.4 0.8 1.2 
BIAS VOLTAGE ( V I  
Fig. 3.  Current density versus bias voltage for GaAs p-i-n diode, i-layer 
density is lOI3 ~ r n - ~ ,  7 = lo-' s, for different i-layer widths. 
centimeter. The choice of the n- doping for the i-region 
is also not known, and this could vary from l O I 4  per cm3 
to lower values, depending on the i-layer thickness. Thus, 
the built-in potential, calculated at 1.23 V for the struc- 
tures considered may not be the correct value for the de- 
vices on which measurements were made. Furthermore, 
the mobility values chosen for the computations may not 
agree with device values, and this will in turn affect the 
'Ol---l 
BIAS VOLTAGE (V)  
Fig. 4 .  Current density versus bias voltage for GaAs p-i-n diode, i-layer 
density 10'' c U 3 ,  width is 10 pn, for different values of T. 
diffusion coefficients that are used in the calculations. 
Thus, comparison between experiment and theory would 
indicate trends, rather than agreement in detail. 
In Fig. 4, the J-V characteristic is plotted for the ex- 
perimental device, a 10-pm i-layer, 100-pm-diaemeter 
mesa structure. Note that the slope is almost the same as 
the computed results for 7 = lop7 s .  The shift of the curve 
with respect to the voltage axis arises from several rea- 
sons: the surface depletion effect permits no current to 
flow in this depleted area and thus decreases the effective 
area of the diode. The second reason for the shift in the 
voltage axis is due to the ohmic contact drops, modeled 
as a series resistance. The third reason is that the built-in 
potential in the calculations may be smaller by about 40 
mV. Thus, with these effects taken into account, the J-V 
curves show good agreement. 
Fig. 5 shows the incremental resistance of this device 
obtained from the measured I- V characteristics. The slope 
of the I-V curve has its ideality factor close to unity, and 
this indicates that the current flow is still not dominated 
by recombination effects. The modeled curve in Fig. 4 
with 7 of lop7 s is close to the measured curve, and there- 
fore not superposed on it, and shows good agreement with 
experiment. 
Microwave measurements were also performed in 
which the diode was connected to ground at the end of a 
50-Q line. Since the resistance values are small, the de- 
embedding of the measurements and the separation of the 
parasitics are difficult with high accuracy. A length of 50- 
Q microstrip line was measured with a short circuit, an 
open circuit, and a 50-Q chip resistor. The problem is that 
the short is not a true short, but a small inductance to 
ground, and the open is not a true open, but a small ca- 
pacitance to ground. In the process, however, the wire 
bond is modeled into the parameters for this microstrip 
line, but the other parasitics are neglected. With the line 
parameters known, the devices are bonded-in in turn, 
measured, and de-embedded. The resistance values are 
I 1 T 1 -  -- - 
GOPINATH AND ATWATER: SIMULATION OF GaAs p-i-n DIODES 417 
0.8 1.0 1.2 1.4 
B I A S  VOLTAGE ( V I  
Fig. 5 .  GaAs p-i-n diode measured forward resistance values for different 
bias from the slope of the I-V curve and also from microwave measure- 
ment at 10 GHz. 
plotted in Fig. 5 and show broad agreement with theory 
dc results. The difference between the dc and RF data may 
be attributed to the fall in resistance discussed by Caverly 
and Hiller [ 131. 
IV. SUMMARY 
Numerical simulations have also been carried out for 
the GaAs p-i-n diode. Experimental J- V characteristics 
and forward resistance show good agreement with theory. 
The measured diodes show that the minority-carrier life- 
time is about lo-’ s, allowing devices in the range of 3- 
to 30-pm i-layer thickness to be built. 
REFERENCES 
[ I ]  C .  Barratt, A. Christou, N. Jansen, R. E. Neidert, M. L. Ruess, 
Jr., C.  W. Young, “New GaAs PIN diodes with lower dissipation 
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Microwave Symp. Dig. (Boston, May 31-June 3, 1983), pp. 507- 
509. 
[2] “GaAs PIN diodes,” MA/COM Data Sheet for MA-4GPOO1, MA- 
[3] A. Gopinath, “Comparison of GaAs MESFET and GaAs p-i-n diodes 
as switch elements,” IEEE Electron Device Lett . ,  vol. EDL-6, pp. 
[4] D. Leenov, “The silicon PIN diode as microwave radar protector at 
megawatt levels,” IEEE Trans. Electron Devices, vol. ED-1 1, p. 53- 
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[5] J.  Lepoff, “A new PIN diode for UHF-VHF applications,” IEEE 
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[6] J. F. White, Microwave Semiconductor Engineering. New York: 
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18) R. J. Chaffin, Microwave Semiconductor Devices: Fundamentals and 
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191 R. E.  Banks and D. J. Rose, “Parameter selection for Newton-like 
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[13] R. H. Caverly and G. Hiller, “Microwave resistance of gallium ar- 
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* 
A. Gopinath, (S’64-M’65-SM’80) photograph and biography not avail- 
able at the time of publication. 
* 
H. Atwater, (S’46-SM’59) photograph and biography not available at the 
time of publication. 


Simulation of GaAs p-i-n diodes

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