Effects of Heavy Impurity Doping on Electron Injection in p +-n GaAs Diodes

Measurements of electron injection currents in p+‐n diodes are presented for a range of p‐type dopant concentrations. A successive etch technique was used to characterize the electron injection current in terms of the product (noDn). Measurements are presented for Zn‐doped GaAs solar cells with p‐layer hole concentrations in the range 6.3×1017−1.3×1019 cm−3. The results demonstrate that so‐called band‐gap narrowing effects substantially increase the injected electron current in heavily doped p‐type GaAs. These heavy doping effects must be accounted for in the modeling and design of GaAs solar cells and heterostructure bipolar transistors.

Effects of heavy impurity doping on electron injection in p + -n GaAs diodes  (Received 11 February 1988; accepted for publication 25 Apri11988) Measurements of electron injection currents in p + -n diodes are presented for a range of p-type dopant concentrations.A successive etch technique was used to characterize the electron injection current in terms of the product (noD,,).Measurements are presented for Zn-doped GaAs solar cells withp-layer hole concentrations in the range 6.3 X 10 17 -1.3X ION cm -3, The results demonstrate that so-caned band-gap narrowing effects substantially increase the injected electron current in heavily doped p-type GaAs.These heavy doping effects must be accounted for in the modeling and design of GaAs solar celIs and heterostructure bipolar transistors.
The efficiency of silicon sotar cells and the gain of silicon bipolar transistors are profoundly influenced by changes in the energy-band structure associated with heavy impurity doping.' The measurements of Slotboom and DeGraaff showed that heavy doping effects greatly enhance electron injection currents in silicon p t--n junctions, 2 but corresponding measurements for p+ -n GaAs have not yet been reported.In this letter we characterize electron injection currents inpt--GaAs doped from 6.3X 10 17 to 1.3x 10 19 cm-'.The results show heavy doping effects in p + -GaAs that are analogous to those observed in p + -Si and comparable in magnitude.This work demonstrates that heavy doping effects must be treated in order to accurately model GaAs bipolar devices.
The current density versus applied voltage for a forward-biased p-n diode can be represented by J=J01[exp(qVAlkBT) -1) where J o ; and J02 are the saturation current densities associated with carrier recombination in the quasi-neutral and space-charge regions, respectively.An diodes studied in this work were found to be wen described by (1).For a diode with a thi.n, unpassivated p-layer.the saturation current component due to electron injection in the quasi-neutral pregion can be written (2) where no is the equilibrium minority-carrier concentration, Dn is the minority-carrier electron diffusion coefficient, Sis the recombination velocity at the surface ofthe p-type layer, and Wp is the width of the quasi-neutral p-type layer.An effective intrinsic carrier concentration, n7e. is often introduced to relate no to the ionized dopant density by (3) where Po is the hole concentration in the p-layer.Measurements have shown that n te in heavily doped silicon substantially exceeds "fl io ' the intrinsic carrier concentration in lightly doped silicon.For device modeling purposes, this effect is often described by relating n te to (lto with a nonphysical, apparent band-gap shrinkage. 1 In this letter we make use of a recently described successive etch technique to quantify the electron saturation current density, J 01e ' as a function of the p-layer hole concentration, Po.3The results are reported in terms ofthe parameter most directly obtained from the measurement, the (noDn) product.Translation of these results into the form of apparent band-gap shrinkage data for use in numerical simulations is briefly discussed.
A cross section of the GaAs solar cells used for these experiments is displayed in Fig. 1.AU cells were grown by metalorganic chemical vapor deposition (MOCVD) in a commercial, five-wafer reactor (Spire Corporation model .Four percent of each cell's top surface was covered by a metal grid pattern which formed an ohmic contact to the p + -GaAs cap layer.The layer of interest in this study is the Zn-doped, p-type GaAs layer which hes just below the passivating p-(A109 Gao 1 ) As heteroface layer.Five cells, nominally identical except for the p-layer doping density, were studied.Details of the film growth and cell processing have been described by Tobin et al. 4  The cells were first characterized by fitting the mea- sured dark current-voltage (1-V) characteristics to ( 1).The resulting J 01 values were independent of the emitter doping density, which suggests that the initial n = 1 dark current component was dominated by hole injection into the quasineutral n-regi.on.After removing the p-GaAs cap and the p-(Al o .9 Ga o . 1 )As heteroface layers by chemical etching, J m was observed to increase.The magnitude of the increase, from a factor on for cells with the most heavily doped emitters to a factor of 22 for cells with the most lightly doped emitters, demonstrates that the n = 1 dark current of un passivated cells was controlled by electron injection into the quasi-neutralp-layer.A successive etch technique was then used to characterize the electron injection current.3 In brief, the technique consists of successive 20 s etches ofthe p-layer in a solution of (2H2S04:1H]02:96H20) at 25°C, followed by measurement of the forward-biased, dark J-V characteristic and extraction of J O ].During the etching process, J 01 was observed to increase as the p-layer was thinned.The electron injection component, J Ole , was deduced as a function of emitter thickness, W p ' by subtracting J 01 of the passivated cell (which was thought to be dominated by hole injection into the n-region) from the value of J 01 measured after each etch.Because J 01 was so low in the passivated cells, this subtraction had a minor influence on the value of J 01e deduced.
The current associated with electron injection into the quasi-neutral p-Iayer is described by ( 2) if the minority-carrier diffusion length exceeds the width of the p-region, Wp (0.5 pm in all but sampie No.3, for which Wp = 1.0/tm).
From a detailed analysis of the internal quantum efficiency and dark current of similar cells grown in the same reactor with an emitter doping of 2 X lOlR cm -3, an electron diffusion length of z 3-5 11m was deduced. 4Because alI celis used for this study had comparable internal quantum efficiencies and dark currents, we conclude that (2) should accurately describe J Ole • Equation ( 2) may be rearranged to show how the electron injection current varies with etch time t during the experiment: _I (WPO 1) ( R ) where R is the etch rate.According to (4), a plot of J o-:,} versus etch time should be linear; the experimental results confirm this prediction.From the slope of the line, R Iq(noD n ), the product (noDn ) was deducedo The result is independent of the surface recombination velocity, S.
Because the objective of this study was to determine the product, (noD,,), as a function of doping density, it was im-portant to thoroughly characterize the doping of the p-type layer.First, carrier concentration (from Han effect measurements, assuming a HaH factor of unity) was plotted ver~ sus resistivity for a series of p-type GaAs films grown in the same MOCVD reactor.For each solar cell used in the present study, the resistivity of the p-layer was measured using an adjacent test resistor.The hole concentration Po was then deduced for each cell from the measured resistivity, using the previously constructed plot.The results are displayed in Table 1.Next, Schottky barrier capacitors were formed by depositing aluminum on the p-layer of each cell, and the quantity (N A -N D) was deduced from reverse-biased capacitance-voltage (C-V) profiling measurements.The results of the C-V measurements are displayed in Table I.Finany, secondary ion mass spectroscopy (SIMS) confirmed that the p-layer of each sample was uniformly doped.SIMS analysis measured the Zn concentration, N zn .(However, the absolute accuracy of SIMS analysis was deemed to be only a factor of 2. ) Results of the measurements for cells with five different p-Iayer dopings are summarized in Table 1.The quantity (noDn) was obtained from the slope of J 01e versus etch time according to (4).The temperature during the experiment is also listed in Tabie 1.Following del Alamo, we have scaled all (noD,,) products to 300 K by using the known tempera~ ture dependence of n io 0 5 The maximum error introduced by this temperature scaling should not exceed 4%. Figure 2 is a plot of (naDn) at 300 K versus dopant density.To highlight the effects of heavy impurity doping, we also indicate the (naD,,) product computed without considering heavy doping effects (except for degeneracy of the hole gas).The dashed line was evaluated from using the minority-carrier electron mobilities predicted by Walukiewicz et at. 6for uncompensated p-GaAs, with lI io = 2.25 X 10 6 cm -3.5 Since measured minority-carrier electron mobilities in MOCVD-grown GaAs 7 are less than those predicted by Walukiewlcz et at.for uncompensated material, the dashed line in Fig. 2 should be regarded as an upper limit for (naDn) in the absence of heavy doping effects.Comparison of the dashed line with the experimental results shows that a substantial increase in (noD,,) can be associated with heavy doping effects, The increase is a factor of 10 at Po z 10 19 cm '-3, and underscores the importance of correctly modeling these phenomena in order to accurately NA -N v (cm-3 ) N zn (em ')  (n"vn) at T surements.The dashed curve was obtained using the theoretical minority electron diffusion coefficient from Ref. 6 with Eq. ( 5), as~uming no compensation.
predict the behavior of GaAs devices that contain heavily doped regions.Note that the behavior of the product (noDn ) versus hole concentration is quite similar to that observed in heavily doped silicon (see Fig. 7 2) we find (7) where (noDn) is the measured product of the equilibrium electron concentration and the electron diffusion coefficient on the p-side.Use ofthis definition of t:.E ~pp ensures that the modeled electron injection saturation current density, J"(},~d, will be equal to the measured J Ole • Equation ( 7) is the definiti.on of apparent band-gap shrinkage implicitly assumed by Slotboom and DeGraaW in their pioneering studies of heavy doping effects in p + -81.We do not quote apparent band-gap shrinkage values, because they depend on DO' the assumed minority-carrier electron diffusion coefficient, which is not wen known at present.Measurements of electron current in P + -n GaAs diodes were presented and analyzed.The large magnitude of the measured currents in cells doped greater than 10 18 cm-3 on the p-side was attributed to heavy doping effects in the p"-GaAs.These effects are analogous to so-caned band-gap narrowing effects in silicon and were found to be comparable in magnitude to those observed in p + -Sf.To accurately model GaAs devices such as solar cells and bipolar transistors, heavy doping effects must be treated.Further work is needed to extend the measurements over a wider range of doping densities and dopant types, to separate out the effects of heavy doping on the minority-carrier diffusion coefficient, and to explore heavy doping effects i.n n-GaAs.
FIG.1.Cross section of the solar cells used in this study (before etching).

FIG. 2 .
FIG. 2. Measured (noD")  product plotted vs hole concentration Pu at T = 300 K.The values of Po used were those obtained from Hall-effect mea-

TABLE I .
Summary of the measurements.The product (no D n ) is listed both at the measurement temperature Tand at 300 K. C-V measurements could Hot be obtained for the highest doped sample, No, 5.
of Ref. 1).A nonphysical, apparent band-gap shrinkage parameter is often introduced for device modeling purposes.!The saturation current density for electrons injected across a GaAs pn junction is modeled by the expression Ole = PoWp S+ (DnIW,,) exp kBT'   (6)where n io is the intrinsic carrier concentration assumed in the device model, Do is the assumed electron diffusion coefficient in p-GaAs for a hole concentration Po' and aE ~pp is the nonphysical apparent band-gap shrinkage.Equating (6) to