Semiconductor Space Charge Region Research Articles

Space charge regions in semiconductors

Poisson's equation is solved for a homogeneous semiconductor in equilibrium and the results are presented in a form which is relatively independent of the impurity concentration. Some convenient analytic forms are given for the dependence of carrier concentration on field and the spatial variation of these quantities. The application of the results to surface field-effect experiments and to abrupt p- n junctions is discussed. In particular, it is shown that the field at an asymmetric junction depends on the impurity concentration on the more heavily doped side. A formula is also given for a critical transistor base width below which the entire base region becomes inverted in equilibrium.

The Distribution of Potential at the Germanium Aqueous Electrolyte Interface

Measurement of the interfacial capacity of germanium electrodes in aqueous solutions of pH 4.5–11.5 permits the determination of the potential difference (p.d.) across the semiconductor space charge region . Hence, under changing conditions, changes in the p.d. across the Helmholtz region may be deduced since where is the electrode potential on an arbitrary scale. The steady‐state value of depends on anodic current density. The values of corresponding to a fixed current density vary by about 59 mv per decade of hydrogen ion concentration. This supports a recent view that a “dissociation double layer” is formed by the pH dependent ionization of surface hydroxyl groups. For solutions more acid than pH 4.5 and more alkaline than pH 11.5 the data indicate that considerable densities of fast surface states occur.

The Interface between Germanium and a Purified Neutral Electrolyte

Measurement of the differential capacity of the interface between germanium (100) and , phosphate buffered to pH 7.4, yields data indicating that only the capacity of the semiconductor space charge region is observed. Analysis of the data yields the simple relationship for distribution of potential where is a constant for a given condition at the interface. Surface recombination velocity is found to be close to zero. This, coupled with the absence of capacity additional to the space charge region, indicates the absence of fast surface states under these conditions. Measurement of the surface conductivity of germanium as a function of surface potential does not agree with theory but is reproducible.

Optical Spectrum of the Semiconductor Surface States from Frustrated Total Internal Reflections

Through the use of multiple internal reflection and a modulation of the charge in the surface via the field effect, sufficient sensitivity is obtained to observe absorption of infrared radiation resulting from transitions involving the semiconductor surface states. This offers the possibility of obtaining the optical spectra and thus some rather direct information about the surface states. The principal other mechanism which contributes to the signal in this experiment is the free-carrier absorption arising from a modulation of the free-carrier density in the semiconductor space-charge region. The results of some observations on a silicon surface are discussed.

Fluctuation Noise in Semiconductor Space-Charge Regions

In addition to noise arising from the circuit, a semiconductor diodic junction must contain a basic noise source. This basic noise mechanism is due to fluctuations in the ionization state of the impurity atoms which occur at random relative to the probability of ionization, w=nD+/nD. In an n-type semiconductor, a neutral impurity that suddenly becomes ionized releases a mobile electron whose movement forms a noise current pulse; similarly for the elemental deionization event. The net result is a short-circuited noise current given approximately by the formula, 2 IIDA TV (1 -we) q(VB + Vc)]- TD+ w kT Using typical numbers, this formula indicates that the fundamental noise associated with a 0.3 ??fd depletion layer capacitance at 100 Mc is equivalent to the thermal noise of a 6-ohm series resistor at 40°K and a 0.1-ohm series resistor at 300°K. Experimental verification of this type of noise is not known. When it is observed experimentally, a new method for evaluating some of the basic properties of semiconductors will be available, and computations of minimum noise factor of parametric amplifiers will be possible.

Analog Solution of Space-Charge Regions in Semiconductors

Analytical solutions of space-charge regions in semiconductors can be carried out when a one-dimensional symmetry exists. Analog solutions can be used to solve Poisson's equation for more complex geometries. An analog method is described which has been used with some success. This method consists of a rubber membrane with surface mass loading being used to simulate the semiconductor space charge.