THEORETICAL ANALYSES OF a-Si : H DIODE CHARACTERISTICS

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THEORETICAL ANALYSES OF a-Si : H DIODE CHARACTERISTICS

I. Chen, S. Lee

To cite this version:

I. Chen, S. Lee. THEORETICAL ANALYSES OF a-Si : H DIODE CHARACTERISTICS. Journal de Physique Colloques, 1981, 42 (C4), pp.C4-499-C4-502. �10.1051/jphyscol:19814106�. �jpa-00220721�

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JOURNAL DE PHYSIQUE

CoZloque C4, suppl6ment au nOIO, Tome 42, octobre 1981 page C4-499

THEORETICAL ANALYSES OF a-Si:H DIODE CHARACTERISTICS

I. Chen and S. Lee

Xerox Webster Research Center, Webster, N . Y., U . S. A.

Abstract.- A mathematical modelling of a-Si:H Schottky barrier diode characteristics has revealed an interesting relation between the observed quality factor and the composition of the diode current. Each component, i.e. the driWdiffusion current JD or the recombination current JR has a characteristic value of the quality factor, j?

<

^{1.1 for}

JD and j?

>

1.8 for JR. The relative magnitudes of the two components vary with the device thickness, the density of localized states, the surface barrier potential and the recombination mechanism. Thus, the observed values of quality factor can be correlated with the material parameters and indicate the upper or lower limits of the, carrier recombination lifetime.

One of the most intriguing questions in the physics of a-Si:H is the nature of carrier recombination, and its impact on device characteristics. For example, the values of "minority carrier" (holes) lifetime reported by various workers differ by orders of magnitude [l-71. Most measurements were made on photo-excited carriers. Since undoped a-Si:H is a highly resistive and weakly n-type material [8], under a typical photo-excitation the density of excess carriers easily exceeds that of dark caniers. Then, the concept of majority or minority caniers ceases to exist in such experiments. Moreover in a Schottky diode, because of the weak n character and the upward band bending near the metal contact, there exists a region in which the hole concentration is not smaller than the electron concentration. Therefore, both electrons and holes must be considered in electronic processes of undoped a-Si:H.

In this paper, the current-voltage (J-V) characteristics of a-Si:H Schottky diodes are analyzed by mathematical modelling. The device considered consists of a thin film (- 1 pm) of undoped a-Si:H, bounded on the front by a high work function metal (e.g. Pd or Pt), and at the rear by a highly doped n+ layer of amorphous silicon.

Although it has been recognized that the electrical characteristics of such devices are strongly influenced by the existence of localized states in the energy gap, experimental data [g- 111 have been interpreted with the theory initially formulated for crystalline semiconductor devices. In non-crystalline semiconductors, the dominant contribution to the space charge density comes from the charge trapped in the localized states. Let us represent the distribution of localized states ( ~ m - ~ e v - l ) by N(E) = NAexp(E/a)

+

ND exp(-E/G). The first term is the density of acceptor-like states which are negatively charged if occupied. The second term is the density of donor-like state which are positively charged if empty. Then, using the Fermi-Dirac statistics, the space-charge density is evaluated as a function of the potential V and the quasi-Fermi energies,Sp and

S,,

for holes and electrons.

This derivation of space-charge density differs from that of Shur et al. [l21 in (1) the use of Fermi statistics, (2) an explicit specification of the relations between the occupation and charge states of the donor-like and the acceptor-like localized states, and (3) the consideration of non-equilibrium condition by the use of quasi-Fenni levels.

Using this space-charge density , Poisson's equation can be solved for the potential

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19814106

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JOURNAL DE PHYSIQUE

distribution V(x), provided the quasi-Fermi energies

Sp

and

c,

are known. The latter can be obtained by integrating the current continuity equation. However, since V (X), Sp(x) and {,(X) are inter-dependent, the solutions of Poisson's equation are obtained by an iterative relaxation method.

The total current density JT, can be represented by the sum of two components:

(1) the drift/diffusion current JD, and (2) the recombination current JR.The driftldiffusion current JD is solely determined by the potential profile, which in principle, is also a function of carrier recombination. However, in this case, since the space-charge is dominated by the charge in the localized states, the potential profile remains practically the same with or without recombination. Thus V(x) and JD are calculated independent of the recombination parameters.

The magnitude of JD varies inversely with the diode thickness while that of JR varies directly with the thickness. A property of a- Si:H Schottky diode whicti distinguishes it from its crystalline counterpart is the thin film

(I

lpm) nature of the device. Thus, while JD is a minor component in crystalline diode current, it can be a significant one in thin f h devices.

The relative magnitude of JD and JR

calculated at five values of applied forward V, (volts)

bias V, are shown in Fig. 1. The recombin-

ation rate in the mono-molecular mechanism is Fig. 1. The two components of diode given by the Shockley-Read-Hd formula, R cu"ents, JD line) and JR (dashed

= (np-ni2)/[rp(n+ni)+ ~ , ( p + ~ ~ ) ] were rp lines) at five values of applied bias voltage ( T ~ ) is the hole (electron) lifetime, and is V,, calculated with the parameters shown m related to the diffusion length Lp(Ln) by the figure. JR's are calculated with the Shockley-Read-Hall recombination model.

~ p ~ = p ~ ~ ~ k ~ / ~ . In an extrinsic semiconductor, e.g. n-type, where n>>ni>>p, R is

controlled by the minority carrier lifetime: R ZZ p / ~ ~ . Since undoped a-Si:H is weak n- type, the hole concentration in a Schottky diode is not small everywhere compared to the electron concentration. Therefore, the latter formula is not appropriate in this case. Numerical results obtained with it differ markedly from those obtained with the full expression.

The recombination currents are specified by three material parameters: the electron diffusion length Ln, the mobility ratio pp/pn, and the lifetime ratio T ~ / T ~ . The three combine to determine the hole diffusion length LP. Slnce it has been suggested that the PT products of electrons and holes in a-Si:H are nearly equal [l31 this relation (which leads to Lp=L,) has been used in calculating the curves in Fig. 1.

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Both JD and JR increase exponentially with V,, and can be represented by the expression, J

=

J,[exp (~V,/PKT)

-

l]. For JD (solid line), the "quality factor" is

P

= 1.05, while for JR (dashed lines),

P

is in the range 1.8 to 2.0.

The experimentally observed Schottky diode currents have been reported to have a quality factor very close to unity [9,11]. ?'his suggests that the current is dominated by the JD component. Then, a reference to the calculated values of JD and JR in Fig. 1 indicates that in these samples the canier diffusion length must be greater than 0.lpm.

For a given set of L, and LP values, looE , ^I the recombination current still varies with the

mobility ratio pp/pn. In Fig. 1 the mobility -

ratio is p p / p n = l ~ - 3 , a value suggested from 3 the time-of-flight measurements [l41 of drift

mobility. However, the applicability of these transient values of mobility in steady state phenomena is not certain. In the steady state

the mobility ratio can be as large as unity. -

When larger values of mobility ratios are used

-

to calculate the recombination currents, JR is f - -

found to increase somewhat less than linearly

with pp/pn. The quality factor remains the ; ^-

same large value

P

1.8

-

2.0. With a ^-

mobility ratio pp/pn = 1, the experimentally

observed quality factor

P <

1.1 at V, as low as ^Np.^{= 6}^X10'~crn-~e~-' -

Q = 4 k T -

0.1 volt indicates that the difhsion length is L 8 = 2 5 k ~

>

lpm. In samples with shorter diffusion ^v0⁼^0.6^VONS

lengths, the J-V curves would deviate from the p p / p n = o 001

exponential form at lower bias voltages, changing to a smaller slope. Such a feature

has been reported in the literature [g]. The l6;o 0'1 _{0 2}Î ₀₃Î _{0 4}Î 0 5

above conclusions are equally valid even if the

pr products for electrons and holes are not ^v, ^(volts)

equal. Fig. 2 Calculated values of JD (solid line)

Another element affecting the relative and ^JR(dashed lines) at five values 'a* as magtlitudes of JD and JR is the surface barrier in Fig. 1, except .that the surface barrier potential. In a Schottky diode with Pd potential V, 1s increased to ^{O e 6} electrode, the surface potential is V, Z 0.4 depicting a PIN diodes.

volts, which is used in Fig. 1. In a PIN diode,

V, can be increased to as high as 0.6 volts. Fig. 2 shows the J-V curves calculated with this value of V,. Even with pp/pn = 10-3, JR (dashed lines) is comparable to or even larger than JD (solid line) at low biases. Thus, the recombination current is a significant, if not the dominant component of the PIN diode current. This conclusion is consistent with the observation[lO] that the quality factor of PIN diode J-V characteristics is much larger than unity.

An alternative mechanism of recombination is the diffusion-controlled birnolecular model [15,16] with the recombination rate given by R = q (pn

+

pp) (np-ni2)/e. The recombination currents calculated with this model are shown in Fig. 3 together with the JD's (for V, = 0.4 and 0.6 volts) which have already been shown in previous figures. As in the previous model, JR is much smaller than JD in the case of V, = 0.4 and comparable to JD in the case of V, = 0.6 volts. However, in contrast to the Shockley-Read-Hall model, the quality factor

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C4-502 JOURNAL DE PHYSIQUE

associated with this JR is small,

p <

1.1. This stems from the bimolecular nature of the model. Since a larger /3

>

1.5 has been observed experimentally, [10], this bimolecular recombination model does not seem to represent the actual mechanism in a-Si:H.

The same conclusion regarding the recombination model has been amved from a different argument.

Acknowledgement: The authors wish to thank J. Mort for helpful discussions.

Fig. 3 The two components of diode current, .lD (solid lines) and .lR (dashed lines) versus applied bias V,, calculated for

two values of surface potential V, = 0.4 10-7t

and 0.6 volts. JR's are calculated with the

diffusion-controlled bimolecular r e a m - 16;o I I I I

bination model. ⁰¹ ^{0 2} ^{0 3} ^0.4 ^{0 5}

v, (volt81

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