ProblemsandSolutionsto PhysicsofSemiconductorDevices

1 Problems and Solutions toPhysics of Semiconductor Lavrov Contents1 Properties of Semiconductors .. Schottky Diode .. Idealp-nJunction .. Nonidealp-nJunction .. Solar Cells .. Bipolar Transistor .. MIS/MOS Capacitor and MOSFET .. Low-dimensional Structures .. LEDs and Lasers .. 82 Literature93 Tables104 Answers and Properties of Semiconductors .. Schottky Diode .. Idealp-nJunction .. Nonidealp-nJunction .. Solar Cells .. Bipolar Transistor .. MIS/MOS Capacitor and MOSFET.

2 Low-dimensional Structures .. LEDs and Lasers .. 23 IAP/HLP, Tel: 33637, Physikgeb aude C305, Properties of of the following semiconductors are transparent, partially transparent, non-transparent for visible light ( = m): Si, GaAs, GaP, and GaN? gap of Si depends on the temperature asEg= eV 10 4T2T+ a concentration of electrons in the conduction band of intrinsic(undoped) Si atT= 77 K if at 300 Kni= 1010cm mobility in Si is 1400 cm2V 1s 1. Calculate the mean free time in scat-tering (Relaxationszeit) of electrons.

3 Effective mass ism e/m0= thermal velocity of electrons and holes in GaAs at room masses arem e/m0= andm h/m0= mobility in Ge at room temperature is 1900 cm2V 1s 1. Find the dielectric relaxation time inp-type Ge at room temperature. Assume thatall acceptors are 1015cm 3, = 16, p= 1900 cm2V 1s dielectric relaxation time in intrinsic Si at 300 K. = 12, n= 1400cm2V 1s 1, n= Debye length inp-type Ge at 300 K ifNa= 1014cm 3. Assume that allacceptors are ionized, = the ambipolar diffusion coefficient of intrinsic (undoped) Ge at 300 K.

4 N/ p= , n= 3900 cm2V 1s are injected inton-type Ge so that at the sample surface p0= 1014cm pat the distance of 4 mm from the surface if p= 10 3s andDp= 49 cm2 Schottky a hight of the potential barrier for a Au-n-Ge Schottky contact at room tem-perature (T= 293 K) if = 1 cm, Au= eV, and Ge= eV. Electronmobility in Ge is 3900 cm2V 1s 1, density of the states in the conduction band isNc= 1015 T3/2cm the depletion width for a Pt-n-Si Schottky diode (T= 300 K) atV= 0,+ , and 2 V. Concentration of doping impurity in Si equals 4 1016cm 3.

5 Workfunction of Pt is eV, electron affinity of Si is eV, Si= , density of thestates in the conduction band isNc= 1015 T3/2cm a Schottky contact Au-GaAs calculate the maximum electric fieldwithin thespace charge region atV= 0, + , and 100 1016cm 3, GaAs= eV, GaAs= Work function of Au is eV,T= 300K, density of the states in theconduction band isNc= 1013 T3/2cm is the electric fieldEfor a Schottky diode Au-n-Si atV= 5 V at the distanceof m from the interface at room temperature if = 10 cm, n= 1400 cm2V 1s 1,Nc= 1015 T3/2cm current densitiesjat room temperature for a Schottky diode Pt-n-GaAs atV= + and 5 V if = 50 cm.

6 N= 8800 cm2V 1s 1,mn/m0= , workfunction of Pt is eV, GaAs= eV,Nc= 1013 T3/2cm 3. Applythermionic-emission capacitance of a Au-n-GaAs Schottky diode is given by the relation 1/C2= 1015 1015V, whereCis expressed in F andVis in Volts. Taking thediode area to be cm2, calculate the barrier height and the dopant comparison of the de Broglie wavelength of electron with the depletion widthof a contact metal-n-Si, estimate the electron concentration at which Schottky diodeloses its rectifying characteristics. For the estimate, assume that the height of thepotential barrier a the contact is half the value of the band gap at room temperature(Eg= eV),m e=m0,T= 300 K, and Si= the built-in potential for ap-nSi junction at room temperature if the bulkresistivity of Si is 1 cm.

7 Electron mobility in Si at RT is 1400 cm2V 1s 1; n/ p= ;ni= 1010cm thep-nSi junction from the previous problem calculate the width of the spacecharge region for the applied voltagesV= 10, 0, and + V. Si= the parameters given in the previous problem find the maximum electric fieldwithin the space charge region. Compare these values with the electric field within ashallow donor:E e/ Sia2B, whereaBis the Bohr radius of a shallow donor,aB= Si~2/m ee2andm e/m0= the capacity of thep-njunction from the problem 2 if the area of thejunction is of ap-nSi junction has a resistivity of 1 cm.

8 What should be the resistivityofp-Si so that 99 % of the total width of the space charge region wouldbe located inn-Si (p+-njunction)? For the parameters needed see problem room temperature under the forward bias of V the currentthrough ap-njunction is mA. What will be the current through the junction under reverse bias? ap+-nSi junction the reverse current at room temperature is the minority-carrier lifetime ifNd= 1015cm 3,ni= 1010cm 3, and p= 450 cm2V 1s does the reverse current of a Sip-njunction change if the temperature raisesfrom 20 to 50 C?

9 The same for a Gep-njunction. Band gaps of Si and Ge are eV, temperatures at whichp-njunctions made of Ge, Si, and GaN lose theirrectifying characteristics. In all casesNa=Nd= 1015cm 3. Assume thatEgareindependent of the temperature and are , , and eV forGe, Si, and GaN,respectively. Intrinsic carrier concentrations at room temperature arenGei= 2 1013,nSii= 1010, andnGaNi= 10 9cm withNd= 7 1015cm 3additionally containsNt= 1015cm 3generation-recombination centers located at the intrinsic Fermi level with n= p= 10 15cm2andvt= 107cm/s.

10 Calculate generation rate, low as compared to the equilibrium value2. onlypis below the equilibrium Si,ni= 1010cm ofn-type Si (Nd= 1016cm 3) generates 1021cm 3/s electron-holepairs. Si hasNt= 1015cm 3generation-recombination centers with n= p=10 16cm2. Calculate equilibrium concentration of electrons and holes ifEt=Ei, whereEiis the Fermi level of intrinsic Si, andvt= 107 +-nSi junction (ni= 1010cm 3, = ) is formed in ann-type substratewithNd= 1015cm 3. If the junction contains 1015cm 3generation-recombinationcenters located at the intrinsic Fermi level with n= p= 10 15cm2(vt= 107cm/s),calculate generation current density at a reverse bias of 10 ap-nSi junction with thep-side doped to 1017cm 3, then-side doped to1019cm 3(n+-pjunction), and a reverse bias of 2 V, calculate the generation currentdensity at room temperature, assuming that the effective lifetime is10 ap-nGaAs junction at room temperature find the donor/acceptor concentrationat which de Broglie wavelength ( = 2 ~/ 2m E)